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Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Proceedings, IFAC Workshop on Mining, Mineral and Metal Processing 5th Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Processing Proceedings, 5th Workshop on Mineral Metal Available onlineand at www.sciencedirect.com Proceedings, 5th IFAC IFAC Workshop on Mining, Mining, Mineral and Metal Shanghai, China, August 23-25, 2018 Processing Shanghai, August 23-25, 2018 ProcessingChina, Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Processing Shanghai, China, August 23-25, 2018 Shanghai, Processing Shanghai, China, China, August August 23-25, 23-25, 2018 2018 Shanghai, China, August 23-25, 2018
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IFAC PapersOnLine 51-21 (2018) 88–93
A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delayGang analysis method for the variables of grinding process Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao*** process A time-delayGang analysis method for the variables of grinding Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao***
Gang Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao*** Gang Gang Yu*, Yu*, Junwu Junwu Zhou**, Zhou**, Qingkai Qingkai Wang***, Wang***, Jianjun Jianjun Zhao*** Zhao*** *Department of ITZhou**, & Automation, BGRIMM Technology Group, Gang Yu*, Junwu Qingkai Wang***, Jianjun Zhao*** *Department of IT & Automation, BGRIMM Technology Group, *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China [email protected]). **State Key Laboratory of(e-mail: Process Automation in Mining & *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 102600, China (e-mail: [email protected]) Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 102600, China (e-mail: [email protected]) **State Key Key Laboratory of Process Automation Mining & Metallurgy, Beijing 102600, China (e-mail: *** Beijing Laboratory Automation [email protected]) Miningin Metallurgy **State Key Key Laboratory of Process Automation inand Mining & Metallurgy, Beijing 102600,of China (e-mail: [email protected]) *** Beijing Laboratory of Automation of Mining and Metallurgy Metallurgy, Beijing 102600, China (e-mail: [email protected]) *** Beijing Key Laboratory of Automation of Mining and Metallurgy [email protected] ) Process, Beijing 102600, China (e-mail: [email protected], Metallurgy, Beijing 102600, China (e-mail: [email protected]) *** Beijing Beijing KeyChina Laboratory of [email protected], Automation of of Mining Mining and and Metallurgy [email protected] ) Process, Beijing Beijing 102600, (e-mail: *** Key Laboratory of Automation Metallurgy Process, 102600, China (e-mail: [email protected], [email protected] *** Beijing Key Laboratory of Automation of Mining and Metallurgy [email protected] ))) Process, Beijing Beijing 102600, 102600, China China (e-mail: (e-mail: [email protected], [email protected], [email protected] Process, Process, Beijing 102600, China (e-mail: [email protected], [email protected] ) Abstract: Data based expert knowledge mining is very important for intelligent and optimal grinding Abstract: Data based based expert expert knowledge knowledge mining mining is is very very important important for for intelligent intelligent and and optimal optimal grinding grinding Abstract: Data process control. However, theknowledge original process includes noise,forand there is and a certain time delay Abstract: Data based based expert mining data is very very important intelligent optimal grinding process control. However, the original process data includes noise, and there is a certain time delay Abstract: Data expert knowledge mining is important for intelligent and optimal grinding process control. However, the original process data includes noise, and there is aatocertain time delay between the variables of grinding process. These factors bring some difficulties the extraction of knowledge mining is very important for intelligent and optimal grinding Abstract: Data based expert process control. However, the original process data includes noise, and there is certain time delay between the variables of grinding process. These factors bring some difficulties to the extraction of process control. However, the original process data includes noise, and there is a certain time delay between the variables of grinding process. These factors bring some difficulties to the extraction of expert knowledge based on data analysis. To solve this problem, a method of combining wavelet deprocess control. However, the original process datafactors includes noise, and there is ato certain time delay between the variables of grinding process. These bring some difficulties the extraction of expert knowledge based on data analysis. To solve this problem, a method of combining wavelet debetween the variables of grinding process. These factors bring some difficulties to the extraction of expert knowledge based on data analysis. To solve this problem, aa method of combining wavelet denoising with cross-correlation is proposed for the time-delay analysis ofdifficulties variables in grinding process. between the variables of grinding process. These factors bring some to the extraction of expert knowledge based on data analysis. To solve this problem, method of combining wavelet deis proposed for the time-delay analysis of variables in grinding process. noising with cross-correlation expert knowledge based on data analysis. To solve this problem, a method of combining wavelet deof variables in grinding process. noising with is proposed forthe theeffectiveness time-delay analysis theaproposed method. The case studycross-correlation on the grinding process shows of expert knowledge based on data analysis. To solve this problem, method of combining wavelet deis for the time-delay analysis of in process. noising with cross-correlation The case study on the grinding process shows of the proposed method. is proposed proposed forthe theeffectiveness time-delay analysis of variables variables in grinding grinding process. noising with cross-correlation The case study on the grinding process shows the effectiveness of the proposed method. process. noising with cross-correlation is proposed for the time-delay analysis of variables in grinding The case study on the grinding process shows the effectiveness of the proposed method. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The case study on the grinding shows the effectiveness of the proposed Keywords: Time-delay analysis,process Wavelet de-noising, Cross-correlation analysis,method. Grinding process. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding The case study on the grinding process shows the effectiveness of the proposed method. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding process. process. Keywords: Keywords: Time-delay Time-delay analysis, analysis, Wavelet Wavelet de-noising, de-noising, Cross-correlation Cross-correlation analysis, analysis, Grinding Grinding process. process. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding signals and estimated the delay ofprocess. each variable by 95% of signals and estimated the delay of each variable by 95% of 1. INTRODUCTION signals and estimated the delay of each by 95% of the steady-state output (Bai (2017)). Thevariable delay relationship 1. INTRODUCTION signals and estimated the delay of each variable by 95% of 1. INTRODUCTION the steady-state output (Bai (2017)). The delay relationship signals and estimated the delay of each variable by 95% of 1. INTRODUCTION the steady-state output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. 1. INTRODUCTION Grinding is an important link in production of mineral the signals and estimated the delay of each variable by 95% of steady-state output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. the steady-state output (Bai (2017)). The delay relationship Grinding is an important link in production of mineral 1. INTRODUCTION between current and force was not mentioned. Huang et al. builtsteady-state an accurate mathematical model for the time-delay from Grinding is an important link in production of mineral processing, the quality of grinding products, especially the the output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. built an accurate mathematical model for the time-delay from Grinding is is the an quality important link in in products, productionespecially of mineral mineral between currenttoand wasmodel not mentioned. Huangsystem et al. processing, of grinding the Grinding an important link production of built an accurate mathematical for the time-delay from the controller theforce actuator of network control processing, quality of grinding especially the between currenttoand wasmodel not mentioned. Huangsystem et al. particle the efficiency of the subsequent built an accurate mathematical for the time-delay from Grinding size, is the aninfluence important link in products, production of mineral the controller controller theforce actuator of network network control processing, the quality of grinding products, especially the built an accurate mathematical model for the time-delay from particle size, influence the efficiency of the subsequent processing, the quality of grinding products, especially the the to the actuator of control system (Huang (2009)). The authors used the data in the buffer to particle size, influence the efficiency of the subsequent built an accurate mathematical model for the time-delay from flotation circuit. The over-coarse granularity of grinding the controller to The the authors actuatorused of network network control system processing, theinfluence quality ofthe grinding products, especially the the (Huang (2009)).to the data data in in the buffer buffer to particle size, efficiency of subsequent controller the actuator of control system flotation circuit. The over-coarse granularity of grinding particle size, influence the efficiency ofof the the subsequent (Huang (2009)). The authors used the the to build the estimated model by a threshold auto-regressive flotation circuit. The over-coarse granularity of grinding the controller to the actuator of network control system products is not up to the requirements the degree of (Huang (2009)). The authors used the data in the buffer to particle size, influence the efficiency of the subsequent build the estimated model by a threshold auto-regressive flotation circuit. The over-coarse granularity of grinding (Huang (2009)). The authors used the data in the buffer to products not up to the requirements of the of flotation is circuit. The over-coarse granularity ofdegree grinding build the estimated model by aa threshold auto-regressive modeling method. These researches on timeproducts not up to the requirements of dissociation, or the over-fined one may leadof tothe waste energy. (Huang (2009)). The authors used thefocused data in the the buffer to build the estimated model by auto-regressive flotation is circuit. The over-coarse granularity ofdegree grinding modeling method. These researches focused on the timeproducts is not up to the requirements of the degree of build the estimated model bythese a threshold threshold auto-regressive dissociation, or the over-fined one may lead to waste energy. products is not up to the requirements of the degree of modeling method. These researches focused on the timemodelling of single variables due to delay analysis dissociation, or the over-fined one may lead to waste energy. Therefore, it is very important to regulate the grinding circuit build the estimated model by a threshold auto-regressive modeling method. These researches focused on the timeproducts isit not upover-fined to the requirements ofto the degree of modeling delay analysis analysis modelling of these single variables due to dissociation, or the one may lead waste energy. method. These researches focused on the timeTherefore, is very important to regulate the grinding circuit dissociation, or the over-fined one may lead to waste energy. modelling of these single variables due to delay network transmission or mechanical structure, rather than the Therefore, it is very important to regulate the grinding circuit reasonably. modeling method. These researches focused on the timemodelling of single variables due to delay analysis dissociation, the over-fined may lead waste energy. transmission or mechanical mechanical structure, rather than the Therefore, it is important to the circuit modelling of these these single variables due to delay analysis reasonably. Therefore, it or is very very important one to regulate regulate thetogrinding grinding circuit network network transmission or structure, rather than the time-delay response between multiple variables. Bo et al. reasonably. modelling of these single variables due to delay analysis network transmission or mechanical structure, rather than the Therefore, it is very important to regulate the grinding circuit time-delay response between multiple variables. Bo et al. reasonably. network transmission or mechanical structure, rather than the reasonably. In the traditional mineral processing enterprises, the grinding proposed time-delay response between variables. Bo et al. a dynamic time delaymultiple analysis based rather on time series network transmission or mechanical structure, than the time-delay response between multiple variables. Bo et al. processing enterprises, the grinding In the traditional mineral reasonably. proposed a dynamic time delay analysis based on time series time-delay response time between multiple Bo et al. processing the In the mineral process is still dependent on manual enterprises, control to some extent, data proposed dynamic delay analysis based on time series in aaa simulation experiment on a variables. distillation column, time-delay response time between multiple Bo et al. processing enterprises, the grinding grinding In the traditional traditional mineral processing proposed dynamic delay analysis based on time series process is still dependent on manual control to some extent, data in aaa simulation simulation experiment on aa variables. distillation column, enterprises, the grinding In the traditional mineral proposed dynamic time delay analysis based on time series process is still dependent on manual control to some extent, although the basic automation and monitoring systems have data in experiment on distillation column, which is designed to estimate the transfer delay between the processing enterprises, the grinding In the traditional mineral proposed a dynamic time delay analysis based on time series process is still dependent on manual control to some extent, data inis aadesigned simulation experiment on aa distillation distillation column, although automation and monitoring systems have whichin to estimate estimate the transfer transfer delay between between the processestablished isthe stillbasic dependent manual control some extent, data simulation experiment on column, although the basic automation and systems have been in the on plant. Inmonitoring order toto stabilize the related which is designed to the delay the variables of the process. The dynamic delay is process is still dependent on manual control to some extent, data in a simulation experiment on a distillation column, although the basic automation and monitoring systems have which is isvariables designed of to estimate estimate the transfer transfer delay between between the been established in the plant. In order to stabilize the related the process. The dynamic delay is although the basic automation and monitoring systems have which designed to the delay the been established in the plant. In order to stabilize production process and ensure the product quality, have the related variables of the process. The dynamic delay is estimated off-line by calculating the similarity between the although the basic automation and monitoring systems which is designed to estimate the transfer delay between the been established in the plant. In order to stabilize the related variables of the process. The dynamic delay is production process and ensure the product quality, estimated off-line by calculating the similarity between the been established in the plant. In order to stabilize the related variables of the process. The dynamic delay is production process ensure the product quality, operators regulate the setting of the feeding ore and waterthe in related estimated off-line by calculating the similarity between the variables (Yang (2017)). However, thedelay above been established in and the plant. In order to stabilize related variables of the process. dynamic is production process and ensure the product quality, the estimated off-line by calculating the similarity between the operators regulate the setting of the feeding ore and water in related variables (Yang (2017)). However, the above production process and ensure the product quality, the estimated off-line by calculating theThe similarity between the operators regulate the setting of the feeding ore and water in the grinding process by experience, according to the variables (Yang (2017)). However, the above related literatures are mainly based on experimental data which are production process and ensure the product quality, the estimated off-line by calculating the similarity between the operators regulate the setting of the feeding ore and water in variables (Yang (2017)). However, the above related the grinding process by experience, according to the are mainly mainly based(2017)). on experimental experimental datathe which are literatures operators regulate the setting ofvariation the feeding oreofand water in related variables (Yang above the grinding process by experience, according to the measured process data and the trend these data. literatures are on data which are relatively smooth, sobased they(2017)). do notHowever, discuss data noise operators regulate the setting ofvariation the feeding oreofand water in related variables (Yang However, the above the grinding process by experience, according to the literatures are mainly based on experimental data which are measured process data and the trend these data. relatively smooth, so they do not discuss data noise the grinding process by experience, according to the literatures are mainly based on experimental data which are measured process data and the variation trend of these data. important to excavate Therefore, it process is data especially relatively smooth, they do not discuss noise the grinding by the experience, according to these the processing. literatures are mainlyso experimental datadata which are measured process and the variation trend trend of these these data. relatively smooth, so they not data noise important to excavate these Therefore, it is especially processing. measured process data and variation of data. relatively smooth, sobased theyondo do not discuss discuss data noise important to excavate these Therefore, it is especially operating experience and expert knowledge to realize processing. measured process data and the variation trend of these data. relatively smooth, so they do not discuss data noise important to excavate excavate these processing. Therefore, it is is especially especially operating experience and expert knowledge to realize important to these Therefore, it processing. Because of the complex mechanism of grinding process, it is operating experience and expert knowledge to realize automatic control grinding process. However, the original important to excavate these processing. Therefore, it is of especially Because of of the complex complex mechanism mechanism of of grinding grinding process, process, it it is is operating experience and expert knowledge to realize automatic control of grinding process. However, the operating experience and noise, expert knowledge to original realize Because difficult to the establish an mechanism accurate mathematical model under automatic control of grinding process. However, the original process data usually includes and there is a certain time Because of the complex of grinding process, it is operating experience and expert knowledge to realize difficult to establish an accurate mathematical model under automatic control of grinding process. However, the original Because of the complex mechanism of grinding process, it is process data usually includes noise, and there is aa certain time automatic control grindingwhich process. However, the original difficult to establish an accurate model under andthe uncertain Few works are found process data usually includes noise, and there is certain time Because of complex mechanism of grinding process, it to is delay between the of variables, brings some to dynamic difficult to establish an conditions. accurate mathematical mathematical model under automatic control of grindingwhich process. However, the original dynamic andestablish uncertain conditions. Few works are are found to process data usually includes noise, and there is aadifficulties certain time difficult to an accurate mathematical model under delay between the variables, brings some difficulties to process data usually includes noise, and there is certain time dynamic and uncertain conditions. Few works found to study the time-delay in the mineral process. It is very delay between the variables, which brings some difficulties to the extraction of expert knowledge based on data analysis. difficult to establish an accurate mathematical model under dynamic and uncertain conditions. Few works are found to process data usually includes noise, brings and there is data adifficulties certain time study the theand time-delay in the mineral mineral process. It found is very very delay between the variables, which some to uncertainain conditions. Few works areIt to the extraction of expert knowledge based on analysis. delay between the variables, which brings some difficulties to dynamic study the process. is necessary totime-delay develop time-delay analysis method forvery the the extraction of expert based on Hence, the de-noising andknowledge time-delay analysis ofdata the analysis. raw data dynamic and uncertainain conditions. Few works areIt found to study the time-delay the mineral process. is delay between the variables, which brings some difficulties to necessary to develop time-delay analysis method for the the extraction of expert knowledge based on data analysis. study the time-delay in the mineral process. It is very Hence, the de-noising and time-delay analysis of the raw data the the extraction of process expert knowledge based on data analysis. necessary to develop aaintime-delay analysis method for the grinding process. Hence, the de-noising and time-delay analysis of the raw data in grinding is an important prerequisite for study the time-delay the mineral process. It is very necessary to develop time-delay analysis method for the the extraction of expert knowledge based on data analysis. grinding process. Hence, the de-noising and analysis of necessaryprocess. to develop a time-delay analysis method for the in the grinding process is an important prerequisite for Hence, the de-noising and time-delay time-delay analysisprocess of the the raw raw data data grinding in the grinding process is an important prerequisite for necessaryprocess. to develop a time-delay analysis method for the grinding mining expert knowledge Hence, the de-noising and time-delay analysisprocess of the control. raw data in the the grinding process is of anthe important prerequisite for grinding grinding process. of the grinding control. mining the expert knowledge in the grinding process is an important prerequisite for 2. PROBLEM DESCRIPTION of the grinding process control. mining the expert knowledge grinding process. in the grinding process is an important prerequisite for 2. PROBLEM DESCRIPTION of the the grinding grinding process control. mining theaexpert expert knowledge analysis of process mining the knowledge There are lot of time-delay applications in control. industry. 2. PROBLEM DESCRIPTION 2. PROBLEM DESCRIPTION There are a lot of time-delay analysis applications in industry. of the grinding process control. mining the expert knowledge 2. PROBLEM DESCRIPTION In this paper, the Semi-autogenous Grinding (SAG) process There are lot of time-delay applications industry. Musleh etaa al. observed the analysis impact of time delayin in power In Grinding (SAG) process this paper, the Semi-autogenous 2. PROBLEM DESCRIPTION There are lot of time-delay analysis applications in industry. Musleh et al. observed the impact of time delay in power There are a lot of time-delay analysis applications in industry. In this paper, the Semi-autogenous Grinding (SAG) process of a copper mine in China is studied, as shown in Figure 1. Musleh et al. observed the impact of time delay in power system and developed an industry standard experimental In this paper, the Semi-autogenous Grinding (SAG) process There are a lot of time-delay analysis applications in industry. of a copper mine in China is studied, as shown in Figure 1. Musleh et al. observed the impact of time delay in power this paper, the Semi-autogenous Grinding (SAG) process system an industry experimental Muslehtoand et investigate al.developed observedthethe impact ofstandard time delay in power In of a copper mine in China is studied, as shown in Figure 1. The feed ore is transported from the ore bin through the belt system and developed an industry standard experimental setup time-delay effect of wide-area In this paper, the Semi-autogenous Grinding (SAG) process of aa feed copper mine in China China is is studied, as bin shown in Figure Figure 1. Muslehtoand et investigate al.developed observedthethe impact ofstandard time delay in power The ore is transported from the ore through the belt system an industry experimental of copper mine in studied, as shown in 1. setup time-delay effect of wide-area system and developed an industry standard experimental The feed ore is transported from the ore bin through the belt conveyors tomine thetransported SAG machine for ore crushing and grinding. setup to investigate time-delay effect of wide-area monitoring and control the systems in smart power grids (Musleh of a feed copper in China is studied, as bin shown in Figure 1. The feed ore is from the bin through the belt system and developed an industry standard experimental conveyors to the SAG machine for crushing and grinding. setup to investigate the time-delay effect of wide-area The ore is transported from the ore through the belt monitoring and control systems in smart power grids (Musleh setup to. Bai investigate the time-delay effect ofoutput wide-area conveyors to the SAG machine for crushing and grinding. SAG milling discharge passing through the screen is monitoring and control systems in smart power grids (Musleh (2018)) et al. analyzed the response time of force The feed ore is transported from the ore bin through the belt conveyors to the SAG machine for crushing and grinding. setup to. Bai investigate the time-delay effect ofoutput wide-area SAG milling discharge passing the screen is monitoring and control systems in smart power grids (Musleh conveyors to the SAG machine forthrough crushing and grinding. (2018)) et al. analyzed the response time of force monitoring and control systems in smart power grids (Musleh SAG milling discharge passing through the screen is classified into coarse and fine fraction. The fine fraction, i.e. (2018)) .. Bai et al. analyzed the response time of output force of magnetorheological elastomer actuator theoretically. conveyors to the SAG machine forthrough crushing and grinding. SAG milling discharge passing the screen is monitoring and control systems in smart power grids (Musleh classified into coarse and fine fraction. The fine fraction, i.e. (2018)) Bai et al. analyzed the response time of output force SAG milling discharge passing through the screen is of magnetorheological elastomer actuator theoretically. (2018)) . Bai et al. analyzed the response time of output force classified into coarse and fine fraction. The fine fraction, i.e. the qualified SAG grinding product, is discharged to the of magnetorheological elastomer actuator theoretically. method, the authors input step Through the experimental SAG milling discharge passing through the screen is classified into coarse and fine fraction. The fine fraction, i.e. (2018)) . Bai et al. analyzed the response time of output force the qualified SAG grinding product, is discharged to the of magnetorheological magnetorheological elastomer actuator theoretically. classified into coarse and fine fraction. The fine fraction, i.e. method, the authors input step Through the experimental of elastomer actuator theoretically. the qualified SAG grinding product, is discharged to the method, the authors input step Through the experimental classified into coarse and fine fraction. The fine fraction, i.e. the qualified SAG grinding product, is discharged to the of magnetorheological elastomer actuator theoretically. method, the the authors authors input input step step the qualified SAG grinding product, is discharged to the Through the the experimental experimental method, Through the qualified SAG Copyright ©the 2018 IFAC 2405-8963 2018, IFAC (International Federation of Automatic by Elsevier Ltd.grinding All rights product, reserved. is discharged to the method, the authors input Control) step 88 Hosting Through © experimental Copyright 2018 responsibility IFAC 88 Control. Peer review© of International Federation of Automatic Copyright ©under 2018 IFAC 88 Copyright © 2018 2018 IFAC IFAC 88 10.1016/j.ifacol.2018.09.397 Copyright © 88 Copyright © 2018 IFAC 88
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pump pool for the follow-up process. The Coarse fraction, i.e. the hard lock, is returned to the buffer bin of the crusher through the belt conveyor. The hard lock after crushing is fed with the fresh feeding ore to SAG mill for reprocessing. The process variables (denoted as PV) and the set points (denoted as SP) of the SAG milling circuit are listed as follows.
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of SAG mill, it is not suitable to apply these original process values directly for the regulation of milling process control. The focus of this work is the de-noising and time-delay analysis of the original data of various variables in the grinding process, to provide basis cleaned data for mining the expert knowledge of grinding process control. 3. DATA PROCESSING AND TIME-DELAY ANALYSIS 3.1 Data Preprocessing In the grinding process, a large number of historical data are obtained by the on-line instrument detection and recorded by the DCS system. For example, the material parameters consists of fresh feeding ore x1, total feeding ore x2 to SAG mill, hard lock x3, fresh water x6 feeding to SAG mill, etc. SAG mill parameters include mill power x7, axial pressure x8, etc. Due to interference and measurement errors, a part of the abnormal data may appear in these original historical data set. To make the mining rules accurate, the historical data are pre-processed by removing the abnormal data according to the feasible data range of the signal.
Fig. 1. SAG milling circuit. x1 - Fresh feeding ore (PV, measured by belt scale)
In this work, the original data set of production process in a SAG process of a mineral processing plant in China in May 2017 is studied. The initial sample set is composed of these data in which the abnormal data are excluded. For example, the pre-processed data set of the feeding ore is shown in Figure 2. The length of the time series is 523601, and the sampling period is 5 seconds.
x2 - Total tonnage of Ore feeding to SAG mill (PV, measured by belt scale) x3 - Hard lock (PV, measured by belt scale) x4 - SP of fresh feeding ore x5 - SP of fresh water feeding to SAG x6 - PV of fresh water feeding to SAG x7 - PV of SAG mill power x8 - PV of axial pressure of SAG mill In order to produce a qualified product and keep the SAG process stable, operators usually adjust the SP of feeding ore (x4) and the feeding water (x5) according to their experience. However, it is easy to cause fluctuations to the SAG process, due to lack of on-line measurement for the variation of the raw ore properties such as the hardness, particle size and the state change of SAG and crusher in the production process. It is difficult for the operator to track the fluctuation of the process manually, therefore, the operation adjustment is usually not in time and not in place. To reduce the labor intensity of the operator and make the production process more stable, it is an effective mean to develop and apply intelligent optimization control system for grinding process (Wang (2016)). In this sort of SAG control system applied in the engineering, the expert control rules are either designed by experts’ prior experience or discovered through data mining. In that way, the process data is the basis for rules mining. Because of the fluctuation of the above SAG process and the interference of instrument measurement under the environment of large noise and multiple disturbance, and the time-delay of belt transportation and the internal state change
Fig. 2. The pre-processed data set of the feeding ore. 3.2 Wavelet De-noising Let function φ (t)ϵL2(R) satisfies the (1) (Chui (1992), Meyer (1992, 1993)), then φ (t) is a mother wavelet or wavelet kernel , where ψ(t) is the Fourier transform of φ(t).
-
89
2
1
(t ) d
(1)
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A wavelet basis function is defined in the time and frequency domains by scaling and shifting φ(t) with parameter (a, b) as follows(Chui (1992), Meyer (1992, 1993)).
a ,b (t )
1 t b ( ), a 0, b R a a
The two parameters in Daubechies type wavelet basis function, i.e., the Daubechies wave base and the transform coefficient, are essential to the quality of signal de-noising. In This paper, the wavelet basis is adopted in the light of the following principles.
(2)
(1) Smooth wavelet with large regularity coefficient is chosen to present smooth signal, and singular one is chosen to present nonsmooth signal (Zhou (2003)). Relating to the grinding process, the data sequence of the feeding ore x1 and the feeding water x2 changes according to the operation setting, which belongs to the step type signal. Then the singular wavelet such as db1, i.e., Haar wavelet, is adopted. For the data sequence of x2, x3, x7, x8 which is more smooth than the step type signal, a smooth wavelet with large regularity coefficient such as db2~db5 is selected.
Providing signal x(t)ϵL2(R), the continuous time wavelet transform is as follows(Chui (1992), Meyer (1992, 1993)).
Wx (a, b) x (t ), a ,b (t ) x (t ) a ,b (t )dt
1 a
x(t ) (
t b )dt a
(3)
In the process of wavelet de-noising, the signal is decomposed first by wavelet, then the threshold value is used to process the wavelet decomposition coefficient, and the signal is reconstructed at last. In this paper, the data sequence are processed with the Daubechies type wavelet basis function and soft threshold where the details can be referred to Ali, et al. (2010); Donoho et al. (1995).
(2) On the one hand, low decomposition level leads to weak de-noising performance. On the other hand, too many decomposed layers may leads to the decrease of the similarity between the signal and the denoised signal, and even cause distortion. In this work, the number of decomposed layers is 3~6 by test. 3.3 Time-Delay Identification with Cross-Correlation Analysis The state of the SAG mill changes in a certain time delay after adjusting the SP of the feeding ore and water. The factors of the time delay include the belt transportation time and the gradual variation time of the internal state such as the mill load, etc. If the parameter values of the above variables in the SAG process sampled by DCS are analyzed directly, problems such as mismatch or omission of information in the data serials will appear. Therefore, time-delay identification is required for these associated variables. This process is also consistent with the regulation habits of the operator. The operator usually observe the variation of the state of the mill for a period of time, not just the value of variables at one moment, and then adjust the SP of the feeding ore and water. This process will repeated until the new relative stability of process is achieved.
Fig. 3. The original and denoised signal of x1.
Fig. 5. Time-delay identification with cross-correlation analysis. In this paper, the cross-correlation analysis method is presented to identify the time-delay between variables in SAG mill circuit. Two measurement signals of the SAG process, the fresh feeding amount x1(t) and the total feeding
Fig. 4. The original and denoised signal of x2. 90
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amount x2(t) , are taken as examples. Let x1(t) and x2(t) are already denoised signals, the total sample length is N, the method of time delay identification is as follows.
the feeding ore SP is reduced (or increased) by the operators, so as to stabilize the grinding process, mostly about 17 minutes later after the hard lock increase (or decrease) to some level. When τ(x7,x1) is 3300s, r(x7,x1) reaches minimum value -0.469. This shows that when the SAG power is increased (or reduced), the feeding ore SP is reduced (or increased) about 41 minutes later with the maximum probability. When τ(x8,x1) is 2460s, the minimal r(x8,x1) is 0.4849. This denotes that when the axial compression is increased (or reduced) to some level, the feeding ore SP will reduced (or increased) about 55 minutes later with the maximum probability.
Step 1. We determine the sequence length N0, i.e., the length of the data sequence windows that participates in the correlation analysis, where N0
Table 1. Correlation coefficient of the variables
N0
r1, 2 ( )
( x (t ) x )( x (t ) x ) t 1
1
1
N0
2
r(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8 1 x1 1 x2 0.5267 1 x3 -0.3413 1 x4 0.8191 1 x5 0.9929 1 x6 1 x7 -0.469 -0.4087 0.4892 -0.4983 0.4244 0.4215 x8 -0.4849 -0.4869 0.697 -0.424 0.2391 0.2373 0.7771 1
2
(4)
N0
（x (t ) x ） （x (t ) x ） t 1
1
1
2
2
t 1
2
2
where
1 x1 N0
N0
1 x1 (t ) , x2 N0 t 1
N0
x (t ) t 1
2
(5)
Table 2. Time-delay between the variables
Step 3. Set τ←τ+1, i.e., the time-delay interval increase 1. If τ≤N-N0, then return to step 2, if not, go to step 4. In practice, the magnitude of the time-delay can be determined in the light of the priori knowledge. For example, the magnitude of the time-delay between x1(t) and x2(t) is at the minute level. Thus the value N-N0 should reach the hour-period level which covers its real time-delay limit.
τ(xi,xj) x1 x2 0 x1 80s 0 x2 x3 1020s 10s x4 x5 x6 x7 3300s 1860s x8 2460s 840s
Step 4. The corresponding time-delay τ1,2 is obtained as follows.
1，2 arg max {| r1, 2 ( ) |} 0 ,1, N N 0
91
(6)
x3
x4
0 -
0
-
-
990s 380s
x5
x6
0 85s
0
2930s 2715s 2775s 2835s 2390s 2430s
4. CASE STUDY With the method presented above, the cross-correlation coefficients among signals x1(t),x2(t),...x8(t) are listed in Table 1, the obtained time-delay value are shown in Table 2. A part of corresponding curve are displayed in Figure 6. As shown in Figure 6 (a), (b), Table 1-2. When τ(x4,x1) is 10 seconds, r(x4,x1) reaches its maximum value 0.8191. It is to determine that the time-delay between x4 and x1 is 10s. This shows that the PV value of the feeding ore x4 is detected about 10s later after the SP value is set to x1. Similarly, when τ(x1,x2) is 80s, r(x1,x2) reaches maximum value 0.5267, this shows that it takes about 80s for feeding the fresh ore from bin to the entrance of SAG mill by belt conveyors which is consistent with the required belt transportation time. Here, the correlation coefficient r(x1,x2)=0.5267 indicates that the correlation is not very strong because x2 is not only determined by x1, but also influenced by x3. As shown in Figure 6 (c), (d), (e), Table 1-2. When τ(x3,x1) is 1020s, r(x3,x1) gets minimum value -0.3413, it denotes that 91
(a)
(b)
(c)
(d)
x7
x8
0 325s
0
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difficult to identify the time-delay by the correlation coefficient with the original data. The cross-correlation coefficient obtained by the filtered data is better to determine the time-delay.
(e)
When a step change input is made to a SAG milling process without any time delay. the correlation coefficient will not have a maximum at zero delay because of the dynamics. Taking the comminution kinetics model of SAG mill as an example, the mass balance model is formulated as belows (Salazar (2009)).
(f)
i 1 dw i f i * pi* K i wi ( K i K i 1 ) wl dt l 1 W 0 .1 M p k p D 2.5 L(1 A J )( ) c 1 910c V 2
(g)
(h)
(i)
(j)
(7) (8)
where, in (7), wi is the weight of size i particles in the SAG mill, fi* is the feed flow rate, pi* is the product flow rate from the SAG mill, Ki denotes the effective parameter. In (8), Mp is the power consumed by the mill, W is the total ore weight in and J the filling level of the mill, φc. Kp, A and V are parameters. In this model, ∑fi*, Mp are corresponding to x2, x7 respectively. It can be seen that transient response exists in this first order model, thus time-delay response appears between x2 and x7. Hence, the correlation coefficient |r2,7(0)| will not have a maximum with zero-delay assumption. Timedelay analysis by data mining will contribute to fit the parameters of the above mass balance model. Table 3. Correlation coefficient of the variables r(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8 1 x1 1 x2 0.2822 1 x3 -0.4685 1 x4 0.1538 1 x5 0.9776 1 x6 1 x7 -0.4419 -0.4320 0.7093 -0.4699 0.4041 0.4064 x8 -0.4946 -0.4881 0.5153 -0.4061 0.3056 0.2917 0.9566 1
Fig. 6. Correlation coefficient and time-delay curve. As shown in Figure 6 (i), Table 1-2. When τ(x5,x6)=85s, the maximal r(x5,x6) is 0.9929. It denotes that the time-delay between the feeding water SP and PV is about 85s. As displayed in Figure 6 (g), (h), Table 1-2. When τ(x7,x3)=990s, the maximal r(x7,x3) is 0.4892, it denotes that the mill power PV changes about 16.5 minutes later, the hard lock PV changes obviously. When τ(x8,x3)=380s, the maximal r(x8,x3) is 0.697, it denotes that the mill power PV changes about 6.33 minutes later, the hard lock PV changes obviously.
Table 4. Time-delay between the variables by DSW-Y τ(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8
As shown in Figure 6 (j), Table 1-2. When τ(x7,x8)=325s, the maximal r(x7,x8) is 0.7771. It denotes that the time-delay between the mill power PV and the axial pressure PV is about 5.42 minutes. The time delay relationship between the other variables in the SAG mill process is similar to the above, and it is not mentioned one by one here. In addition, it can be seen from the graph that the correlation between the filtered variables is stronger and the time-delay value is easier to be identified than the original ones, and the former correlation curve are more smooth than the latter. For example, as shown in Figure 6 (d), the r(x8,x1) with the filtered data is great different from the results with the original data. If the correlation threshold is set to -0.35, it may be considered uncorrelated between the variables when the correlation coefficient is larger than -0.35. Thus, it is
x1
x2
0 395s
x3
x4
0
600s 20s
-
0 -
0
-
-
-
-
x5
x6
0 70s
0
3180s 1860s 1365s 2855s 2685s 2745s 2460s 690s 1895s 2710s 1465s 1310s
x7
x8
0 275s
0
In addition, we test the time-delay of grinding process with the dynamic sliding window (denoted as DSW-Y) presented in (Bo (2017)). According to the recommended empirical 92
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data, the sliding width λk here is set to 5 times of the estimated time delay. The width of the dynamic window nk is set to 15 times of λk. It is noted that the estimated time delay is prerequisite by this mean. The results in Table 2 are taken as the estimated time delay. The results by DSW-Y are listed in Table 3-4.
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Huang, Z. and Zhang, Y. (2009). Network time delay analysis for networked control systems. International Conference on Test and Measurement, 2, 291-294. Yang, B., Li, Y., Wen, B. (2017). A dynamic time delay analysis approach for correlated process variables. Chemical Engineering Research & Design, 12, 141-150. Wang, Q., Yang, J., Zou, G., and Yu, G. (2016). Research on Optimization Control Technology for SAG Mill. Nonferrous Metals Engineering & Research, 37(3),1-6. Chui, C. K. (1992). An Introduction to Wavelets. Academic Press, San Diego. Meyer, Y. (1993). Wavelets: Algorithms and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 13-31. Meyer, Y. (1992). Wavelets and operators, Cambridge studies in advanced mathematics, 1-20. Ali, N. A., Wouter, A. S., and Ivan, W. S. (2010). Emerging applications of wavelets: A review. Physical Communication, 3, 1-18. Donoho, D.L. (1995). De-noising by soft-thresholding. IEEE Trans. On Inf. Theroy, 41(3), 613-627. Zhou, X., Ye, Y. (2003). Method of Choosing a wavelet for fault detection. Control Engineering of China, 10(4), 308-311. Salazar, J. L., Magne, L., Acuna, G., and Cubillos, F. (2009). Dynamic modelling and simulation of semi-autogenous mills. Mineral Engineering, 22, 70-77.
Comparing the Table 1 to the Table 3, the value of |r(x3,x1)|, |r(x7,x3)|, |r(x7,x8)| in the Table 3 are lager than the ones in the Table 1. The value of |r(x1,x2)|, |r(x4,x1)|, |r(x6,x5)| in the Table 3 are less than the ones in the Table 1. The other correlation coefficient are near to each other between the two tables. The value of τ(x2,x1), τ(x8,x5), τ(x8,x6) are different between the Table 2 and the Table 4 and the other delay responses are close to each other. τ(x8,x5) and τ(x8,x6) are more dynamic by DSW-Y and more stable by this work. However, τ(x2,x1) in the Table 4 is not consistent with the belt transportation time that is due to the smaller width of the dynamic window by DSW-Y than the one by this work. So it can be seen from the above results that the estimated time-delay is required and the unsuitable width of the dynamic window should be avoided by DSW-Y. 5. CONCLUSIONS There are a lot of noises in the grinding process variables, and these variables are coupled with multiple time delays. Therefore, it is difficult to extract expert control knowledge directly from the raw data. A time-delay identification method based on the combination of wavelet de-noising and cross-correlation analysis is proposed in this work. The timedelay relationship between the grinding process variables is analyzed by case study, and the results are basically keeping with the actual situation. It shows that the proposed method is effective and of certain anti-interruption ability. The proposed method can be extended to the total mineral process and other industrial processes, and it provides an idea of data processing for the realization of knowledge mining based on process data. It should be noted that we aim to provide valid data and response relation among multiple variables in this work, so we focus on the data de-nosing and time-delay analysis of grinding process, not to recreate what the operator is doing. We will extract expert knowledge and optimal control method for automation of the process by introducing the indicators of grinding products in our next work. REFERENCES Musleh A., Muyeen, S. (2018). Time-Delay Analysis of Wide-Area Voltage Control Considering Smart Grid Contingences in a Real-Time Environment. IEEE Transactions on Industrial Informatics , 14(3), 12421252. Bai, J., Fu, J., Lai, J., Liao, G., and Yu, M. (2017). Timedelay analysis of a magnetorheological elastomer actuator for semi-active control. Control And Decision Conference (CCDC), 29th Chinese, 366-370.
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A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delay analysis method for the variables of grinding process A time-delayGang analysis method for the variables of grinding process Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao*** process A time-delayGang analysis method for the variables of grinding Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao***
Gang Yu*, Junwu Zhou**, Qingkai Wang***, Jianjun Zhao*** Gang Gang Yu*, Yu*, Junwu Junwu Zhou**, Zhou**, Qingkai Qingkai Wang***, Wang***, Jianjun Jianjun Zhao*** Zhao*** *Department of ITZhou**, & Automation, BGRIMM Technology Group, Gang Yu*, Junwu Qingkai Wang***, Jianjun Zhao*** *Department of IT & Automation, BGRIMM Technology Group, *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China [email protected]). **State Key Laboratory of(e-mail: Process Automation in Mining & *Department of IT & Automation, BGRIMM Technology Group, Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 102600, China (e-mail: [email protected]) Beijing 102600, China (e-mail: [email protected]). **State Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 102600, China (e-mail: [email protected]) **State Key Key Laboratory of Process Automation Mining & Metallurgy, Beijing 102600, China (e-mail: *** Beijing Laboratory Automation [email protected]) Miningin Metallurgy **State Key Key Laboratory of Process Automation inand Mining & Metallurgy, Beijing 102600,of China (e-mail: [email protected]) *** Beijing Laboratory of Automation of Mining and Metallurgy Metallurgy, Beijing 102600, China (e-mail: [email protected]) *** Beijing Key Laboratory of Automation of Mining and Metallurgy [email protected] ) Process, Beijing 102600, China (e-mail: [email protected], Metallurgy, Beijing 102600, China (e-mail: [email protected]) *** Beijing Beijing KeyChina Laboratory of [email protected], Automation of of Mining Mining and and Metallurgy [email protected] ) Process, Beijing Beijing 102600, (e-mail: *** Key Laboratory of Automation Metallurgy Process, 102600, China (e-mail: [email protected], [email protected] *** Beijing Key Laboratory of Automation of Mining and Metallurgy [email protected] ))) Process, Beijing Beijing 102600, 102600, China China (e-mail: (e-mail: [email protected], [email protected], [email protected] Process, Process, Beijing 102600, China (e-mail: [email protected], [email protected] ) Abstract: Data based expert knowledge mining is very important for intelligent and optimal grinding Abstract: Data based based expert expert knowledge knowledge mining mining is is very very important important for for intelligent intelligent and and optimal optimal grinding grinding Abstract: Data process control. However, theknowledge original process includes noise,forand there is and a certain time delay Abstract: Data based based expert mining data is very very important intelligent optimal grinding process control. However, the original process data includes noise, and there is a certain time delay Abstract: Data expert knowledge mining is important for intelligent and optimal grinding process control. However, the original process data includes noise, and there is aatocertain time delay between the variables of grinding process. These factors bring some difficulties the extraction of knowledge mining is very important for intelligent and optimal grinding Abstract: Data based expert process control. However, the original process data includes noise, and there is certain time delay between the variables of grinding process. These factors bring some difficulties to the extraction of process control. However, the original process data includes noise, and there is a certain time delay between the variables of grinding process. These factors bring some difficulties to the extraction of expert knowledge based on data analysis. To solve this problem, a method of combining wavelet deprocess control. However, the original process datafactors includes noise, and there is ato certain time delay between the variables of grinding process. These bring some difficulties the extraction of expert knowledge based on data analysis. To solve this problem, a method of combining wavelet debetween the variables of grinding process. These factors bring some difficulties to the extraction of expert knowledge based on data analysis. To solve this problem, aa method of combining wavelet denoising with cross-correlation is proposed for the time-delay analysis ofdifficulties variables in grinding process. between the variables of grinding process. These factors bring some to the extraction of expert knowledge based on data analysis. To solve this problem, method of combining wavelet deis proposed for the time-delay analysis of variables in grinding process. noising with cross-correlation expert knowledge based on data analysis. To solve this problem, a method of combining wavelet deof variables in grinding process. noising with is proposed forthe theeffectiveness time-delay analysis theaproposed method. The case studycross-correlation on the grinding process shows of expert knowledge based on data analysis. To solve this problem, method of combining wavelet deis for the time-delay analysis of in process. noising with cross-correlation The case study on the grinding process shows of the proposed method. is proposed proposed forthe theeffectiveness time-delay analysis of variables variables in grinding grinding process. noising with cross-correlation The case study on the grinding process shows the effectiveness of the proposed method. process. noising with cross-correlation is proposed for the time-delay analysis of variables in grinding The case study on the grinding process shows the effectiveness of the proposed method. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The case study on the grinding shows the effectiveness of the proposed Keywords: Time-delay analysis,process Wavelet de-noising, Cross-correlation analysis,method. Grinding process. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding The case study on the grinding process shows the effectiveness of the proposed method. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding process. process. Keywords: Keywords: Time-delay Time-delay analysis, analysis, Wavelet Wavelet de-noising, de-noising, Cross-correlation Cross-correlation analysis, analysis, Grinding Grinding process. process. Keywords: Time-delay analysis, Wavelet de-noising, Cross-correlation analysis, Grinding signals and estimated the delay ofprocess. each variable by 95% of signals and estimated the delay of each variable by 95% of 1. INTRODUCTION signals and estimated the delay of each by 95% of the steady-state output (Bai (2017)). Thevariable delay relationship 1. INTRODUCTION signals and estimated the delay of each variable by 95% of 1. INTRODUCTION the steady-state output (Bai (2017)). The delay relationship signals and estimated the delay of each variable by 95% of 1. INTRODUCTION the steady-state output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. 1. INTRODUCTION Grinding is an important link in production of mineral the signals and estimated the delay of each variable by 95% of steady-state output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. the steady-state output (Bai (2017)). The delay relationship Grinding is an important link in production of mineral 1. INTRODUCTION between current and force was not mentioned. Huang et al. builtsteady-state an accurate mathematical model for the time-delay from Grinding is an important link in production of mineral processing, the quality of grinding products, especially the the output (Bai (2017)). The delay relationship between current and force was not mentioned. Huang et al. built an accurate mathematical model for the time-delay from Grinding is is the an quality important link in in products, productionespecially of mineral mineral between currenttoand wasmodel not mentioned. Huangsystem et al. processing, of grinding the Grinding an important link production of built an accurate mathematical for the time-delay from the controller theforce actuator of network control processing, quality of grinding especially the between currenttoand wasmodel not mentioned. Huangsystem et al. particle the efficiency of the subsequent built an accurate mathematical for the time-delay from Grinding size, is the aninfluence important link in products, production of mineral the controller controller theforce actuator of network network control processing, the quality of grinding products, especially the built an accurate mathematical model for the time-delay from particle size, influence the efficiency of the subsequent processing, the quality of grinding products, especially the the to the actuator of control system (Huang (2009)). The authors used the data in the buffer to particle size, influence the efficiency of the subsequent built an accurate mathematical model for the time-delay from flotation circuit. The over-coarse granularity of grinding the controller to The the authors actuatorused of network network control system processing, theinfluence quality ofthe grinding products, especially the the (Huang (2009)).to the data data in in the buffer buffer to particle size, efficiency of subsequent controller the actuator of control system flotation circuit. The over-coarse granularity of grinding particle size, influence the efficiency ofof the the subsequent (Huang (2009)). The authors used the the to build the estimated model by a threshold auto-regressive flotation circuit. The over-coarse granularity of grinding the controller to the actuator of network control system products is not up to the requirements the degree of (Huang (2009)). The authors used the data in the buffer to particle size, influence the efficiency of the subsequent build the estimated model by a threshold auto-regressive flotation circuit. The over-coarse granularity of grinding (Huang (2009)). The authors used the data in the buffer to products not up to the requirements of the of flotation is circuit. The over-coarse granularity ofdegree grinding build the estimated model by aa threshold auto-regressive modeling method. These researches on timeproducts not up to the requirements of dissociation, or the over-fined one may leadof tothe waste energy. (Huang (2009)). The authors used thefocused data in the the buffer to build the estimated model by auto-regressive flotation is circuit. The over-coarse granularity ofdegree grinding modeling method. These researches focused on the timeproducts is not up to the requirements of the degree of build the estimated model bythese a threshold threshold auto-regressive dissociation, or the over-fined one may lead to waste energy. products is not up to the requirements of the degree of modeling method. These researches focused on the timemodelling of single variables due to delay analysis dissociation, or the over-fined one may lead to waste energy. Therefore, it is very important to regulate the grinding circuit build the estimated model by a threshold auto-regressive modeling method. These researches focused on the timeproducts isit not upover-fined to the requirements ofto the degree of modeling delay analysis analysis modelling of these single variables due to dissociation, or the one may lead waste energy. method. These researches focused on the timeTherefore, is very important to regulate the grinding circuit dissociation, or the over-fined one may lead to waste energy. modelling of these single variables due to delay network transmission or mechanical structure, rather than the Therefore, it is very important to regulate the grinding circuit reasonably. modeling method. These researches focused on the timemodelling of single variables due to delay analysis dissociation, the over-fined may lead waste energy. transmission or mechanical mechanical structure, rather than the Therefore, it is important to the circuit modelling of these these single variables due to delay analysis reasonably. Therefore, it or is very very important one to regulate regulate thetogrinding grinding circuit network network transmission or structure, rather than the time-delay response between multiple variables. Bo et al. reasonably. modelling of these single variables due to delay analysis network transmission or mechanical structure, rather than the Therefore, it is very important to regulate the grinding circuit time-delay response between multiple variables. Bo et al. reasonably. network transmission or mechanical structure, rather than the reasonably. In the traditional mineral processing enterprises, the grinding proposed time-delay response between variables. Bo et al. a dynamic time delaymultiple analysis based rather on time series network transmission or mechanical structure, than the time-delay response between multiple variables. Bo et al. processing enterprises, the grinding In the traditional mineral reasonably. proposed a dynamic time delay analysis based on time series time-delay response time between multiple Bo et al. processing the In the mineral process is still dependent on manual enterprises, control to some extent, data proposed dynamic delay analysis based on time series in aaa simulation experiment on a variables. distillation column, time-delay response time between multiple Bo et al. processing enterprises, the grinding grinding In the traditional traditional mineral processing proposed dynamic delay analysis based on time series process is still dependent on manual control to some extent, data in aaa simulation simulation experiment on aa variables. distillation column, enterprises, the grinding In the traditional mineral proposed dynamic time delay analysis based on time series process is still dependent on manual control to some extent, although the basic automation and monitoring systems have data in experiment on distillation column, which is designed to estimate the transfer delay between the processing enterprises, the grinding In the traditional mineral proposed a dynamic time delay analysis based on time series process is still dependent on manual control to some extent, data inis aadesigned simulation experiment on aa distillation distillation column, although automation and monitoring systems have whichin to estimate estimate the transfer transfer delay between between the processestablished isthe stillbasic dependent manual control some extent, data simulation experiment on column, although the basic automation and systems have been in the on plant. Inmonitoring order toto stabilize the related which is designed to the delay the variables of the process. The dynamic delay is process is still dependent on manual control to some extent, data in a simulation experiment on a distillation column, although the basic automation and monitoring systems have which is isvariables designed of to estimate estimate the transfer transfer delay between between the been established in the plant. In order to stabilize the related the process. The dynamic delay is although the basic automation and monitoring systems have which designed to the delay the been established in the plant. In order to stabilize production process and ensure the product quality, have the related variables of the process. The dynamic delay is estimated off-line by calculating the similarity between the although the basic automation and monitoring systems which is designed to estimate the transfer delay between the been established in the plant. In order to stabilize the related variables of the process. The dynamic delay is production process and ensure the product quality, estimated off-line by calculating the similarity between the been established in the plant. In order to stabilize the related variables of the process. The dynamic delay is production process ensure the product quality, operators regulate the setting of the feeding ore and waterthe in related estimated off-line by calculating the similarity between the variables (Yang (2017)). However, thedelay above been established in and the plant. In order to stabilize related variables of the process. dynamic is production process and ensure the product quality, the estimated off-line by calculating the similarity between the operators regulate the setting of the feeding ore and water in related variables (Yang (2017)). However, the above production process and ensure the product quality, the estimated off-line by calculating theThe similarity between the operators regulate the setting of the feeding ore and water in the grinding process by experience, according to the variables (Yang (2017)). However, the above related literatures are mainly based on experimental data which are production process and ensure the product quality, the estimated off-line by calculating the similarity between the operators regulate the setting of the feeding ore and water in variables (Yang (2017)). However, the above related the grinding process by experience, according to the are mainly mainly based(2017)). on experimental experimental datathe which are literatures operators regulate the setting ofvariation the feeding oreofand water in related variables (Yang above the grinding process by experience, according to the measured process data and the trend these data. literatures are on data which are relatively smooth, sobased they(2017)). do notHowever, discuss data noise operators regulate the setting ofvariation the feeding oreofand water in related variables (Yang However, the above the grinding process by experience, according to the literatures are mainly based on experimental data which are measured process data and the trend these data. relatively smooth, so they do not discuss data noise the grinding process by experience, according to the literatures are mainly based on experimental data which are measured process data and the variation trend of these data. important to excavate Therefore, it process is data especially relatively smooth, they do not discuss noise the grinding by the experience, according to these the processing. literatures are mainlyso experimental datadata which are measured process and the variation trend trend of these these data. relatively smooth, so they not data noise important to excavate these Therefore, it is especially processing. measured process data and variation of data. relatively smooth, sobased theyondo do not discuss discuss data noise important to excavate these Therefore, it is especially operating experience and expert knowledge to realize processing. measured process data and the variation trend of these data. relatively smooth, so they do not discuss data noise important to excavate excavate these processing. Therefore, it is is especially especially operating experience and expert knowledge to realize important to these Therefore, it processing. Because of the complex mechanism of grinding process, it is operating experience and expert knowledge to realize automatic control grinding process. However, the original important to excavate these processing. Therefore, it is of especially Because of of the complex complex mechanism mechanism of of grinding grinding process, process, it it is is operating experience and expert knowledge to realize automatic control of grinding process. However, the operating experience and noise, expert knowledge to original realize Because difficult to the establish an mechanism accurate mathematical model under automatic control of grinding process. However, the original process data usually includes and there is a certain time Because of the complex of grinding process, it is operating experience and expert knowledge to realize difficult to establish an accurate mathematical model under automatic control of grinding process. However, the original Because of the complex mechanism of grinding process, it is process data usually includes noise, and there is aa certain time automatic control grindingwhich process. However, the original difficult to establish an accurate model under andthe uncertain Few works are found process data usually includes noise, and there is certain time Because of complex mechanism of grinding process, it to is delay between the of variables, brings some to dynamic difficult to establish an conditions. accurate mathematical mathematical model under automatic control of grindingwhich process. However, the original dynamic andestablish uncertain conditions. Few works are are found to process data usually includes noise, and there is aadifficulties certain time difficult to an accurate mathematical model under delay between the variables, brings some difficulties to process data usually includes noise, and there is certain time dynamic and uncertain conditions. Few works found to study the time-delay in the mineral process. It is very delay between the variables, which brings some difficulties to the extraction of expert knowledge based on data analysis. difficult to establish an accurate mathematical model under dynamic and uncertain conditions. Few works are found to process data usually includes noise, brings and there is data adifficulties certain time study the theand time-delay in the mineral mineral process. It found is very very delay between the variables, which some to uncertainain conditions. Few works areIt to the extraction of expert knowledge based on analysis. delay between the variables, which brings some difficulties to dynamic study the process. is necessary totime-delay develop time-delay analysis method forvery the the extraction of expert based on Hence, the de-noising andknowledge time-delay analysis ofdata the analysis. raw data dynamic and uncertainain conditions. Few works areIt found to study the time-delay the mineral process. is delay between the variables, which brings some difficulties to necessary to develop time-delay analysis method for the the extraction of expert knowledge based on data analysis. study the time-delay in the mineral process. It is very Hence, the de-noising and time-delay analysis of the raw data the the extraction of process expert knowledge based on data analysis. necessary to develop aaintime-delay analysis method for the grinding process. Hence, the de-noising and time-delay analysis of the raw data in grinding is an important prerequisite for study the time-delay the mineral process. It is very necessary to develop time-delay analysis method for the the extraction of expert knowledge based on data analysis. grinding process. Hence, the de-noising and analysis of necessaryprocess. to develop a time-delay analysis method for the in the grinding process is an important prerequisite for Hence, the de-noising and time-delay time-delay analysisprocess of the the raw raw data data grinding in the grinding process is an important prerequisite for necessaryprocess. to develop a time-delay analysis method for the grinding mining expert knowledge Hence, the de-noising and time-delay analysisprocess of the control. raw data in the the grinding process is of anthe important prerequisite for grinding grinding process. of the grinding control. mining the expert knowledge in the grinding process is an important prerequisite for 2. PROBLEM DESCRIPTION of the grinding process control. mining the expert knowledge grinding process. in the grinding process is an important prerequisite for 2. PROBLEM DESCRIPTION of the the grinding grinding process control. mining theaexpert expert knowledge analysis of process mining the knowledge There are lot of time-delay applications in control. industry. 2. PROBLEM DESCRIPTION 2. PROBLEM DESCRIPTION There are a lot of time-delay analysis applications in industry. of the grinding process control. mining the expert knowledge 2. PROBLEM DESCRIPTION In this paper, the Semi-autogenous Grinding (SAG) process There are lot of time-delay applications industry. Musleh etaa al. observed the analysis impact of time delayin in power In Grinding (SAG) process this paper, the Semi-autogenous 2. PROBLEM DESCRIPTION There are lot of time-delay analysis applications in industry. Musleh et al. observed the impact of time delay in power There are a lot of time-delay analysis applications in industry. In this paper, the Semi-autogenous Grinding (SAG) process of a copper mine in China is studied, as shown in Figure 1. Musleh et al. observed the impact of time delay in power system and developed an industry standard experimental In this paper, the Semi-autogenous Grinding (SAG) process There are a lot of time-delay analysis applications in industry. of a copper mine in China is studied, as shown in Figure 1. Musleh et al. observed the impact of time delay in power this paper, the Semi-autogenous Grinding (SAG) process system an industry experimental Muslehtoand et investigate al.developed observedthethe impact ofstandard time delay in power In of a copper mine in China is studied, as shown in Figure 1. The feed ore is transported from the ore bin through the belt system and developed an industry standard experimental setup time-delay effect of wide-area In this paper, the Semi-autogenous Grinding (SAG) process of aa feed copper mine in China China is is studied, as bin shown in Figure Figure 1. Muslehtoand et investigate al.developed observedthethe impact ofstandard time delay in power The ore is transported from the ore through the belt system an industry experimental of copper mine in studied, as shown in 1. setup time-delay effect of wide-area system and developed an industry standard experimental The feed ore is transported from the ore bin through the belt conveyors tomine thetransported SAG machine for ore crushing and grinding. setup to investigate time-delay effect of wide-area monitoring and control the systems in smart power grids (Musleh of a feed copper in China is studied, as bin shown in Figure 1. The feed ore is from the bin through the belt system and developed an industry standard experimental conveyors to the SAG machine for crushing and grinding. setup to investigate the time-delay effect of wide-area The ore is transported from the ore through the belt monitoring and control systems in smart power grids (Musleh setup to. Bai investigate the time-delay effect ofoutput wide-area conveyors to the SAG machine for crushing and grinding. SAG milling discharge passing through the screen is monitoring and control systems in smart power grids (Musleh (2018)) et al. analyzed the response time of force The feed ore is transported from the ore bin through the belt conveyors to the SAG machine for crushing and grinding. setup to. Bai investigate the time-delay effect ofoutput wide-area SAG milling discharge passing the screen is monitoring and control systems in smart power grids (Musleh conveyors to the SAG machine forthrough crushing and grinding. (2018)) et al. analyzed the response time of force monitoring and control systems in smart power grids (Musleh SAG milling discharge passing through the screen is classified into coarse and fine fraction. The fine fraction, i.e. (2018)) .. Bai et al. analyzed the response time of output force of magnetorheological elastomer actuator theoretically. conveyors to the SAG machine forthrough crushing and grinding. SAG milling discharge passing the screen is monitoring and control systems in smart power grids (Musleh classified into coarse and fine fraction. The fine fraction, i.e. (2018)) Bai et al. analyzed the response time of output force SAG milling discharge passing through the screen is of magnetorheological elastomer actuator theoretically. (2018)) . Bai et al. analyzed the response time of output force classified into coarse and fine fraction. The fine fraction, i.e. the qualified SAG grinding product, is discharged to the of magnetorheological elastomer actuator theoretically. method, the authors input step Through the experimental SAG milling discharge passing through the screen is classified into coarse and fine fraction. The fine fraction, i.e. (2018)) . Bai et al. analyzed the response time of output force the qualified SAG grinding product, is discharged to the of magnetorheological magnetorheological elastomer actuator theoretically. classified into coarse and fine fraction. The fine fraction, i.e. method, the authors input step Through the experimental of elastomer actuator theoretically. the qualified SAG grinding product, is discharged to the method, the authors input step Through the experimental classified into coarse and fine fraction. The fine fraction, i.e. the qualified SAG grinding product, is discharged to the of magnetorheological elastomer actuator theoretically. method, the the authors authors input input step step the qualified SAG grinding product, is discharged to the Through the the experimental experimental method, Through the qualified SAG Copyright ©the 2018 IFAC 2405-8963 2018, IFAC (International Federation of Automatic by Elsevier Ltd.grinding All rights product, reserved. is discharged to the method, the authors input Control) step 88 Hosting Through © experimental Copyright 2018 responsibility IFAC 88 Control. Peer review© of International Federation of Automatic Copyright ©under 2018 IFAC 88 Copyright © 2018 2018 IFAC IFAC 88 10.1016/j.ifacol.2018.09.397 Copyright © 88 Copyright © 2018 IFAC 88
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pump pool for the follow-up process. The Coarse fraction, i.e. the hard lock, is returned to the buffer bin of the crusher through the belt conveyor. The hard lock after crushing is fed with the fresh feeding ore to SAG mill for reprocessing. The process variables (denoted as PV) and the set points (denoted as SP) of the SAG milling circuit are listed as follows.
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of SAG mill, it is not suitable to apply these original process values directly for the regulation of milling process control. The focus of this work is the de-noising and time-delay analysis of the original data of various variables in the grinding process, to provide basis cleaned data for mining the expert knowledge of grinding process control. 3. DATA PROCESSING AND TIME-DELAY ANALYSIS 3.1 Data Preprocessing In the grinding process, a large number of historical data are obtained by the on-line instrument detection and recorded by the DCS system. For example, the material parameters consists of fresh feeding ore x1, total feeding ore x2 to SAG mill, hard lock x3, fresh water x6 feeding to SAG mill, etc. SAG mill parameters include mill power x7, axial pressure x8, etc. Due to interference and measurement errors, a part of the abnormal data may appear in these original historical data set. To make the mining rules accurate, the historical data are pre-processed by removing the abnormal data according to the feasible data range of the signal.
Fig. 1. SAG milling circuit. x1 - Fresh feeding ore (PV, measured by belt scale)
In this work, the original data set of production process in a SAG process of a mineral processing plant in China in May 2017 is studied. The initial sample set is composed of these data in which the abnormal data are excluded. For example, the pre-processed data set of the feeding ore is shown in Figure 2. The length of the time series is 523601, and the sampling period is 5 seconds.
x2 - Total tonnage of Ore feeding to SAG mill (PV, measured by belt scale) x3 - Hard lock (PV, measured by belt scale) x4 - SP of fresh feeding ore x5 - SP of fresh water feeding to SAG x6 - PV of fresh water feeding to SAG x7 - PV of SAG mill power x8 - PV of axial pressure of SAG mill In order to produce a qualified product and keep the SAG process stable, operators usually adjust the SP of feeding ore (x4) and the feeding water (x5) according to their experience. However, it is easy to cause fluctuations to the SAG process, due to lack of on-line measurement for the variation of the raw ore properties such as the hardness, particle size and the state change of SAG and crusher in the production process. It is difficult for the operator to track the fluctuation of the process manually, therefore, the operation adjustment is usually not in time and not in place. To reduce the labor intensity of the operator and make the production process more stable, it is an effective mean to develop and apply intelligent optimization control system for grinding process (Wang (2016)). In this sort of SAG control system applied in the engineering, the expert control rules are either designed by experts’ prior experience or discovered through data mining. In that way, the process data is the basis for rules mining. Because of the fluctuation of the above SAG process and the interference of instrument measurement under the environment of large noise and multiple disturbance, and the time-delay of belt transportation and the internal state change
Fig. 2. The pre-processed data set of the feeding ore. 3.2 Wavelet De-noising Let function φ (t)ϵL2(R) satisfies the (1) (Chui (1992), Meyer (1992, 1993)), then φ (t) is a mother wavelet or wavelet kernel , where ψ(t) is the Fourier transform of φ(t).
-
89
2
1
(t ) d
(1)
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A wavelet basis function is defined in the time and frequency domains by scaling and shifting φ(t) with parameter (a, b) as follows(Chui (1992), Meyer (1992, 1993)).
a ,b (t )
1 t b ( ), a 0, b R a a
The two parameters in Daubechies type wavelet basis function, i.e., the Daubechies wave base and the transform coefficient, are essential to the quality of signal de-noising. In This paper, the wavelet basis is adopted in the light of the following principles.
(2)
(1) Smooth wavelet with large regularity coefficient is chosen to present smooth signal, and singular one is chosen to present nonsmooth signal (Zhou (2003)). Relating to the grinding process, the data sequence of the feeding ore x1 and the feeding water x2 changes according to the operation setting, which belongs to the step type signal. Then the singular wavelet such as db1, i.e., Haar wavelet, is adopted. For the data sequence of x2, x3, x7, x8 which is more smooth than the step type signal, a smooth wavelet with large regularity coefficient such as db2~db5 is selected.
Providing signal x(t)ϵL2(R), the continuous time wavelet transform is as follows(Chui (1992), Meyer (1992, 1993)).
Wx (a, b) x (t ), a ,b (t ) x (t ) a ,b (t )dt
1 a
x(t ) (
t b )dt a
(3)
In the process of wavelet de-noising, the signal is decomposed first by wavelet, then the threshold value is used to process the wavelet decomposition coefficient, and the signal is reconstructed at last. In this paper, the data sequence are processed with the Daubechies type wavelet basis function and soft threshold where the details can be referred to Ali, et al. (2010); Donoho et al. (1995).
(2) On the one hand, low decomposition level leads to weak de-noising performance. On the other hand, too many decomposed layers may leads to the decrease of the similarity between the signal and the denoised signal, and even cause distortion. In this work, the number of decomposed layers is 3~6 by test. 3.3 Time-Delay Identification with Cross-Correlation Analysis The state of the SAG mill changes in a certain time delay after adjusting the SP of the feeding ore and water. The factors of the time delay include the belt transportation time and the gradual variation time of the internal state such as the mill load, etc. If the parameter values of the above variables in the SAG process sampled by DCS are analyzed directly, problems such as mismatch or omission of information in the data serials will appear. Therefore, time-delay identification is required for these associated variables. This process is also consistent with the regulation habits of the operator. The operator usually observe the variation of the state of the mill for a period of time, not just the value of variables at one moment, and then adjust the SP of the feeding ore and water. This process will repeated until the new relative stability of process is achieved.
Fig. 3. The original and denoised signal of x1.
Fig. 5. Time-delay identification with cross-correlation analysis. In this paper, the cross-correlation analysis method is presented to identify the time-delay between variables in SAG mill circuit. Two measurement signals of the SAG process, the fresh feeding amount x1(t) and the total feeding
Fig. 4. The original and denoised signal of x2. 90
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amount x2(t) , are taken as examples. Let x1(t) and x2(t) are already denoised signals, the total sample length is N, the method of time delay identification is as follows.
the feeding ore SP is reduced (or increased) by the operators, so as to stabilize the grinding process, mostly about 17 minutes later after the hard lock increase (or decrease) to some level. When τ(x7,x1) is 3300s, r(x7,x1) reaches minimum value -0.469. This shows that when the SAG power is increased (or reduced), the feeding ore SP is reduced (or increased) about 41 minutes later with the maximum probability. When τ(x8,x1) is 2460s, the minimal r(x8,x1) is 0.4849. This denotes that when the axial compression is increased (or reduced) to some level, the feeding ore SP will reduced (or increased) about 55 minutes later with the maximum probability.
Step 1. We determine the sequence length N0, i.e., the length of the data sequence windows that participates in the correlation analysis, where N0
Table 1. Correlation coefficient of the variables
N0
r1, 2 ( )
( x (t ) x )( x (t ) x ) t 1
1
1
N0
2
r(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8 1 x1 1 x2 0.5267 1 x3 -0.3413 1 x4 0.8191 1 x5 0.9929 1 x6 1 x7 -0.469 -0.4087 0.4892 -0.4983 0.4244 0.4215 x8 -0.4849 -0.4869 0.697 -0.424 0.2391 0.2373 0.7771 1
2
(4)
N0
（x (t ) x ） （x (t ) x ） t 1
1
1
2
2
t 1
2
2
where
1 x1 N0
N0
1 x1 (t ) , x2 N0 t 1
N0
x (t ) t 1
2
(5)
Table 2. Time-delay between the variables
Step 3. Set τ←τ+1, i.e., the time-delay interval increase 1. If τ≤N-N0, then return to step 2, if not, go to step 4. In practice, the magnitude of the time-delay can be determined in the light of the priori knowledge. For example, the magnitude of the time-delay between x1(t) and x2(t) is at the minute level. Thus the value N-N0 should reach the hour-period level which covers its real time-delay limit.
τ(xi,xj) x1 x2 0 x1 80s 0 x2 x3 1020s 10s x4 x5 x6 x7 3300s 1860s x8 2460s 840s
Step 4. The corresponding time-delay τ1,2 is obtained as follows.
1，2 arg max {| r1, 2 ( ) |} 0 ,1, N N 0
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(6)
x3
x4
0 -
0
-
-
990s 380s
x5
x6
0 85s
0
2930s 2715s 2775s 2835s 2390s 2430s
4. CASE STUDY With the method presented above, the cross-correlation coefficients among signals x1(t),x2(t),...x8(t) are listed in Table 1, the obtained time-delay value are shown in Table 2. A part of corresponding curve are displayed in Figure 6. As shown in Figure 6 (a), (b), Table 1-2. When τ(x4,x1) is 10 seconds, r(x4,x1) reaches its maximum value 0.8191. It is to determine that the time-delay between x4 and x1 is 10s. This shows that the PV value of the feeding ore x4 is detected about 10s later after the SP value is set to x1. Similarly, when τ(x1,x2) is 80s, r(x1,x2) reaches maximum value 0.5267, this shows that it takes about 80s for feeding the fresh ore from bin to the entrance of SAG mill by belt conveyors which is consistent with the required belt transportation time. Here, the correlation coefficient r(x1,x2)=0.5267 indicates that the correlation is not very strong because x2 is not only determined by x1, but also influenced by x3. As shown in Figure 6 (c), (d), (e), Table 1-2. When τ(x3,x1) is 1020s, r(x3,x1) gets minimum value -0.3413, it denotes that 91
(a)
(b)
(c)
(d)
x7
x8
0 325s
0
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difficult to identify the time-delay by the correlation coefficient with the original data. The cross-correlation coefficient obtained by the filtered data is better to determine the time-delay.
(e)
When a step change input is made to a SAG milling process without any time delay. the correlation coefficient will not have a maximum at zero delay because of the dynamics. Taking the comminution kinetics model of SAG mill as an example, the mass balance model is formulated as belows (Salazar (2009)).
(f)
i 1 dw i f i * pi* K i wi ( K i K i 1 ) wl dt l 1 W 0 .1 M p k p D 2.5 L(1 A J )( ) c 1 910c V 2
(g)
(h)
(i)
(j)
(7) (8)
where, in (7), wi is the weight of size i particles in the SAG mill, fi* is the feed flow rate, pi* is the product flow rate from the SAG mill, Ki denotes the effective parameter. In (8), Mp is the power consumed by the mill, W is the total ore weight in and J the filling level of the mill, φc. Kp, A and V are parameters. In this model, ∑fi*, Mp are corresponding to x2, x7 respectively. It can be seen that transient response exists in this first order model, thus time-delay response appears between x2 and x7. Hence, the correlation coefficient |r2,7(0)| will not have a maximum with zero-delay assumption. Timedelay analysis by data mining will contribute to fit the parameters of the above mass balance model. Table 3. Correlation coefficient of the variables r(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8 1 x1 1 x2 0.2822 1 x3 -0.4685 1 x4 0.1538 1 x5 0.9776 1 x6 1 x7 -0.4419 -0.4320 0.7093 -0.4699 0.4041 0.4064 x8 -0.4946 -0.4881 0.5153 -0.4061 0.3056 0.2917 0.9566 1
Fig. 6. Correlation coefficient and time-delay curve. As shown in Figure 6 (i), Table 1-2. When τ(x5,x6)=85s, the maximal r(x5,x6) is 0.9929. It denotes that the time-delay between the feeding water SP and PV is about 85s. As displayed in Figure 6 (g), (h), Table 1-2. When τ(x7,x3)=990s, the maximal r(x7,x3) is 0.4892, it denotes that the mill power PV changes about 16.5 minutes later, the hard lock PV changes obviously. When τ(x8,x3)=380s, the maximal r(x8,x3) is 0.697, it denotes that the mill power PV changes about 6.33 minutes later, the hard lock PV changes obviously.
Table 4. Time-delay between the variables by DSW-Y τ(xi,xj) x1 x2 x3 x4 x5 x6 x7 x8
As shown in Figure 6 (j), Table 1-2. When τ(x7,x8)=325s, the maximal r(x7,x8) is 0.7771. It denotes that the time-delay between the mill power PV and the axial pressure PV is about 5.42 minutes. The time delay relationship between the other variables in the SAG mill process is similar to the above, and it is not mentioned one by one here. In addition, it can be seen from the graph that the correlation between the filtered variables is stronger and the time-delay value is easier to be identified than the original ones, and the former correlation curve are more smooth than the latter. For example, as shown in Figure 6 (d), the r(x8,x1) with the filtered data is great different from the results with the original data. If the correlation threshold is set to -0.35, it may be considered uncorrelated between the variables when the correlation coefficient is larger than -0.35. Thus, it is
x1
x2
0 395s
x3
x4
0
600s 20s
-
0 -
0
-
-
-
-
x5
x6
0 70s
0
3180s 1860s 1365s 2855s 2685s 2745s 2460s 690s 1895s 2710s 1465s 1310s
x7
x8
0 275s
0
In addition, we test the time-delay of grinding process with the dynamic sliding window (denoted as DSW-Y) presented in (Bo (2017)). According to the recommended empirical 92
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data, the sliding width λk here is set to 5 times of the estimated time delay. The width of the dynamic window nk is set to 15 times of λk. It is noted that the estimated time delay is prerequisite by this mean. The results in Table 2 are taken as the estimated time delay. The results by DSW-Y are listed in Table 3-4.
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Huang, Z. and Zhang, Y. (2009). Network time delay analysis for networked control systems. International Conference on Test and Measurement, 2, 291-294. Yang, B., Li, Y., Wen, B. (2017). A dynamic time delay analysis approach for correlated process variables. Chemical Engineering Research & Design, 12, 141-150. Wang, Q., Yang, J., Zou, G., and Yu, G. (2016). Research on Optimization Control Technology for SAG Mill. Nonferrous Metals Engineering & Research, 37(3),1-6. Chui, C. K. (1992). An Introduction to Wavelets. Academic Press, San Diego. Meyer, Y. (1993). Wavelets: Algorithms and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 13-31. Meyer, Y. (1992). Wavelets and operators, Cambridge studies in advanced mathematics, 1-20. Ali, N. A., Wouter, A. S., and Ivan, W. S. (2010). Emerging applications of wavelets: A review. Physical Communication, 3, 1-18. Donoho, D.L. (1995). De-noising by soft-thresholding. IEEE Trans. On Inf. Theroy, 41(3), 613-627. Zhou, X., Ye, Y. (2003). Method of Choosing a wavelet for fault detection. Control Engineering of China, 10(4), 308-311. Salazar, J. L., Magne, L., Acuna, G., and Cubillos, F. (2009). Dynamic modelling and simulation of semi-autogenous mills. Mineral Engineering, 22, 70-77.
Comparing the Table 1 to the Table 3, the value of |r(x3,x1)|, |r(x7,x3)|, |r(x7,x8)| in the Table 3 are lager than the ones in the Table 1. The value of |r(x1,x2)|, |r(x4,x1)|, |r(x6,x5)| in the Table 3 are less than the ones in the Table 1. The other correlation coefficient are near to each other between the two tables. The value of τ(x2,x1), τ(x8,x5), τ(x8,x6) are different between the Table 2 and the Table 4 and the other delay responses are close to each other. τ(x8,x5) and τ(x8,x6) are more dynamic by DSW-Y and more stable by this work. However, τ(x2,x1) in the Table 4 is not consistent with the belt transportation time that is due to the smaller width of the dynamic window by DSW-Y than the one by this work. So it can be seen from the above results that the estimated time-delay is required and the unsuitable width of the dynamic window should be avoided by DSW-Y. 5. CONCLUSIONS There are a lot of noises in the grinding process variables, and these variables are coupled with multiple time delays. Therefore, it is difficult to extract expert control knowledge directly from the raw data. A time-delay identification method based on the combination of wavelet de-noising and cross-correlation analysis is proposed in this work. The timedelay relationship between the grinding process variables is analyzed by case study, and the results are basically keeping with the actual situation. It shows that the proposed method is effective and of certain anti-interruption ability. The proposed method can be extended to the total mineral process and other industrial processes, and it provides an idea of data processing for the realization of knowledge mining based on process data. It should be noted that we aim to provide valid data and response relation among multiple variables in this work, so we focus on the data de-nosing and time-delay analysis of grinding process, not to recreate what the operator is doing. We will extract expert knowledge and optimal control method for automation of the process by introducing the indicators of grinding products in our next work. REFERENCES Musleh A., Muyeen, S. (2018). Time-Delay Analysis of Wide-Area Voltage Control Considering Smart Grid Contingences in a Real-Time Environment. IEEE Transactions on Industrial Informatics , 14(3), 12421252. Bai, J., Fu, J., Lai, J., Liao, G., and Yu, M. (2017). Timedelay analysis of a magnetorheological elastomer actuator for semi-active control. Control And Decision Conference (CCDC), 29th Chinese, 366-370.
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