Development of a softsensor for particle size monitoring

Minerals Engineering, Vol. 9, No. 1, pp. 55-72, 1996

Pergamon 0892-6875(95)00131-X

Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0892-6875/96 $15.00+0.00

D E V E L O P M E N T O F A S O F T S E N S O R F O R P A R T I C L E SIZE M O N I T O R I N G

R. G. DEL VILLAR§*, J. THIBAULTt

and R. DEL VILLAR§

Depart. of Mining & Metallurgy, Laval University, Quebec (QC), Canada, G1K 7P4 Depart. of Chemical Engineering, Laval University, Quebec (QC), Canada, G1K 7P4 * Presently at Barrick Gold Co., Bousquet Division, 2 chemin Bousquet, Route 395, Preissac (QC), Canada JOY 2E0 (Received 26 July 1995; accepted 3 September 1995)

ABSTRACT Some key control variables of industrial processes, associated with product quality, often cannot be measured directly or frequently enough to establish adequate control. In such cases, it is possible to use available measurements to provide a prediction for these process variables and use them in a control strategy, thereby giving rise to what is now commonly called a softsensor. In some industrial grinding circuits, the on-line particle size analyzer is shared between various sampling points. Therefore, for a given location, the actual measurement is only available every 10 to 20 minutes, a delay which is unacceptable for automatic control purposes. To alleviate this problem, a soflsensor based on an artificial neural network has been investigated. First, the structure of the neural network and different schemes for the training process are analyzed. Then, the performance of the neural network softsensor is compared with other inferential methods such as ARMA models and Kalman filters.

Keywords Neural networks; particle size; process control; on-line analysis; process instrumentation

INTRODUCTION GRAIIM, French acronym of the Research Group on Computer Applications in the Mineral Industry at Laval University, began in 1990 a research project on Knowledge Based Automatic Control (KBAC). This project, sponsored by a consortium of eight mining companies and the federal and provincial governments, seeked to screen advanced (knowledge-based) methods for data processing (filtering, mass balancing, etc) and automatic control (model-based) for their use in the mineral processing operations and the transfer of the project results to the sponsor companies. In parallel to more academic research work, a number of case-studies have been undertaken with the cooperation of partner companies. Among such works, a very successful one has been the design and installation of a new control strategy for one of the Kidd Creek (Falconbridge Ltd.) grinding circuits. This project was related to the evaluation of a number of control strategies and the implementation of one of them, as selected by the plant management, in the concentrator.

Presented at Minerals Engineering '95, St. Ives, Cornwall,England,June 1995

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A total of sixteen control schemes were evaluated on one of the dynamic phenomenological simulators developed at GRAIIM, a trademark of this research group [1]. The calibration of the simulator models was done based on industrial data gathered by GRAIIM and Kidd Creek personnel. Then, the simulator was used to test the performance of various PID-based control schemes, designed to achieve the control objectives set by the Kidd Creek personnel. The best scheme proposed called for controlling the cyclone overflow particle size by manipulating the water addition rate to the cyclone feed box and the circulating load by manipulating the circuit ore feed. The particle size analyzer (PSI-200) available for monitoring the product size, was unfortunately shared (multiplexed) among various streams of the plant, which meant a 14 min delay between two consecutive readings for any particular stream. This induced the plant personnel to choose an alternative control strategy, one which controlled the cyclone feed density instead of the cyclone overflow particle size. This situation motivated us to evaluate the possibility of using a different approach to ensure a greater availability of particle size values for control purposes. One alternative are the so called softsensors or model-based sensors. A softsensor is an algorithm or a model that makes use of existing information to infer the value of a variable which cannot be obtained by a physical sensor. Inferred values obtained through a softsensor can be used reliably for control purposes and can provide a level of insight into process operations that was not previously available. As such, these softsensors have attracted considerable interest over the last decade. For instance, due to stringent regulation of emissions by the U.S. Environmental Protection Agency, a large number of companies are opting for predictive emission monitoring software in which future values of NO x ,SO x and particulate emissions are foreseen from present operating conditions using a predictive model that has been previously calibrated on site [2]. Other examples include the estimation of the digester quality control in a batch sulphite pulping process [3] and the estimation of the volatility of bottom atmosphere gas oil [4]. In the mineral processing industry, achieving an optimal particle size and therefore an optimal liberation of valuable minerals is an extremely important goal. As such, work has been conducted by some researchers to develop on-line particle size estimators capable of producing measurements that are both accurate and frequent enough to establish automatic control strategies. One of the earliest attempts to provide modelbased estimates of cyclone overflow size distributions for control purposes was performed in Australia [5] where a variant of Rao's equation [6], i.e. a simple linear relationship, was used. Wills [7] reports another use of the same type of model-based estimator of grinding product size distribution at the Vihanti concentrator in Finland. More recently, Chilean researchers [8,9,10] have developed particle size estimators for one of Codelco's concentrators in Chile, using both static (with dynamic compensation) and dynamic models. These models were based on measurement such as the fresh ore rate, pumpbox level, total water addition rate and percent solids at the cyclone feed, and were validated within existing control strategies. Among the many uses of a softsensor some of the most important are: a) the generation of more frequent values in the case of infrequent measurements resulting from sensor sharing (the case which originated this work) or simply from a lengthy measurement time, b)the replacement of an existing sensor (by reconstructing the values of the measured variable from other available readings or historical information) when the sensor fails or is under maintenance, c) the replacement of a physical sensor for economic or others reasons, in which case the physical sensor is still necessary at least during the process modelling period and for the validation of the softsensor, d) the estimation of a given process variable for which no on-line sensor exists. To produce such a model-based sensor, various types of mathematical tools can be used. In the present case we have chosen three well known methods: a neural network algorithm, an auto-regressive moving-average model (ARMA), and a Kalman filter. The soflsensor was designed to estimate the cyclone overflow particle size (percent passing 45 pm) based on available information (present and past values of pulp flow rates and densities of cyclone feed and overflow and past values of cyclone overflow particle size). The obtained softsensor is presently being implemented in the dynamic grinding circuit simulator for its use within the control strategy. Based on the simulation results that will be produced, the implementation of such an algorithm in the Kidd Creek control system will be considered.

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In the first section of this paper, the industrial grinding circuit and the control problems which originated the idea of using a softsensor for particle size estimation will be presented. Then, the dynamic simulator used in this study (unit models and main features) and its calibration with industrial data will be detailed. In the second section, the various mathematical tools used for developing the softsensor will be presented: neural networks, ARMA models, and Kalman filters. In each case, the model structure, the calibration procedure and the possibility for adaptation will be discussed. The third section is devoted to the presentation and analysis of the simulation results. Finally some conclusions are drawn.

BACKGROUND

Grinding circuit description The grinding circuit being considered in this study corresponds to that of the Kidd Creek concentrator (Falconbridge Ltd.) located near Timmins, Ontario. It processes 3.5 MM t/y of a Cu-Zn ore. The present work is related to one of their grinding circuits (line B), a classical rod mill (Allis Chalmers 3.2 m x 4.9 m) - ball mill (Allis Chalmers 3.7 m x 5.5 m) operating in closed-loop with a cluster of eight 380 m m Krebs hydrocylones. Both mill discharges are mixed in a 12 m 3 non-linear pump-box and the resulting pulp is fed to the hydrocyclones using a 12"x10" Linatex fixed-speed-drive centrifugal pump (Figure 1).

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When the process control study was undertaken by GRAIIM, the available instrumentation consisted of a Milltronics Compuscale A weightometer on the rod mill feed belt, three Rosemont magnetic flowmeters to measure the water flow rate to the rod mill (ratio-controlled), the ball mill and the cyclone pump-box. Cyclone overflow pulp density is measured by a Texas-Nuclear ~/-ray gauge, whereas ball mill discharge pulp density is measured several times during a shift using a Marcy scale. Product particle size is obtained from an Outokumpu PSI-200 particle size analyzer located on the cyclone overflow line. This device, whose response time is 2 minutes, was shared between seven points in the concentrator implying that each stream

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is sequently analyzed every 14 rain. Since the implementation of the new control strategy, instruments for monitoring the cyclone feed flow rate and pulp density were installed and their readings were considered for the design of the softsensor. Before the GRAIIM control project was initiated, Kidd Creek grinding line B was operated using the following control strategy (Figure 1): The rod mill feed tonnage was kept constant by manipulating the speed of the feeder conveyor, to achieve a daily average tonnage. The cyclone overflow pulp density was kept constant by manipulating the water flow rate to the pump box, to avoid an increase in pulp density which might cause pipe blockage. The rod mill pulp density was regulated by maintaining a constant water/ore ratio to achieve good milling efficiency. The ball mill discharge pulp density was kept constant by manipulating the water flow rate at the mill feed box, to ensure a good milling efficiency. Since the ore feed rate was not measured, only the mill percent solids was available, this control was done manually. To respond to abnormal operating conditions (e.g. stoppage for rod addition, extreme pump-box pulp level, plugged cyclones), operators normally manipulate the circuit tonnage set-point, the number of cyclones in operation or the cyclone overfow density set-point. The grinding dynamic simulator

Data used to develop the softsensor was generated using a grinding circuit dynamic simulator (Dynafrag) [11,12], whose flowsheet configuration corresponds to the Kidd Creek grinding circuit. The simulator includes the following process unit models: rod mill, ball mill, hydrocyclone, pump box, centrifugal pump, piping and conveyor belt. The ball mill is modelled using a population mass balance model [13], which requires the evaluation of the breakage function (characteristic of the ore), the selection function and the residence time distribution (both dependent on the mill environment). Since rod mill operation also implies some form of classification (some particle size classes disappear), the standard population mass balance model is not sufficient, a situation which has been successfully overcome in Dynafrag by modelling the rod mill as two ball mills in series. The hydrocyclone performance is reproduced by a variant of Plitt's model [14]. The whole process dynamic model then consists of a set of mass-balance equations (a hundred differential equations) for pulp, water and particles of differing hardness. A certain number of sensors and actuators are also reproduced in the simulator since they contribute to the system dynamic response (Figure 2). Five different actuators are implemented: the belt conveyor drive to control the fresh ore feed rate (Ul), the valve of the water addition to the rod mill feed (u2), the pump box water valve (u4), and the ball mill water valve (Us). The actuator u 3 , the variable speed drive to control the pump speed, was transformed in the present study into a fixed speed drive to reproduce the Kidd Creek circuit. In addition, seven sensors, with optional corresponding noise patterns, are simulated to measure: the rod mill ore feed rate (ml), the pump box pulp level (m2), the cyclone feed pulp flow rate (m3), the cyclone feed pulp density (m4), the cyclone overflow pulp flow rate (ms), the cyclone overflow pulp density (m6), and the cyclone overflow percent passing 45 pin (mT). Typical grinding process disturbances can be simulated through the following internal variables: the ore hardness (Pl), the rod mill feed size distribution (P2), the ore specific gravity (P3), the cyclone pump performance (P4), and the cyclone operation feature (P5) which can accommodate various types of cyclone problems (apex blockage, apex changes, addition/removal of units). In this study only Pl, P2 and P5 were used. Actuators and sensors can be simulated using additive noises: ai to the manipulated variables (u i ) and n i to the simulated measurement values (m i ). Various types of noise pattern are implemented in Dynafrag: white noise, step, ramp, AR, MA, ARMA model, PRBS and PRTS.

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Fig.2 Dynafrag, grinding circuit dynamic simulator The processed ore is characterized in Dynafrag in terms of three properties: size distribution, hardness and specific gravity. An adequate mixture (flow rate) of two key components, each having its own size distribution, hardness and specific gravity, allows the reproduction of any type of ore. By changing the proportion of both key-components, the effect of disturbances in hardness, size distribution and specific gravity on the final product quality or the process behaviour can be easily studied. The ore hardness is implemented in the grinding model through the mill selection function whereas the circuit feed size distribution is directly used in the calculations. Ore hardness is categorized in three levels, hard, medium and soft, whereas size distribution can be depicted as coarse, medium and fine. Desired disturbances can be pre-programmed (type and magnitude) and then used at anytime during the simulation. Before using Dynafrag for simulation purposes, a calibration on the stated circuit was performed. Both the steady-state and dynamic behaviour of the industrial grinding circuit were identified and accommodated into the mathematical models implemented in the simulator. The steady-state part of Dynafrag was calibrated through grinding and residence-time data obtained from carefully planned and completed sampling campaigns [12]. A total of nine steady state grinding tests were completed at different operating conditions. Samples were collected at the rod mill feed and discharge, at the ball mill feed and discharge, and at the cyclone overflow. Tracer tests were performed at both rod and ball mills to determine the residence time distribution. In the case of the rod mill, only tracer concentration data at the mill discharge were necessary since it operates in open loop. In the case of the ball mill, tracer data at both mill ends, feed and discharge, were required to deconvolute the open-loop RTD model (in this case the mill is continuously submitted to new tracer impulses as it recirculates to the mill via cyclone underflow). The gathered data was reconciliated using BILMAT, a material balance program [ 15]. Residence time distribution data (Li + concentration) were processed using the SPOC software [16]. Then the methodology proposed by the SPOC project was followed to determine the steady state model of both mills [17] and that of the hydrocyclones [18].

SOFTSENSORS FOR PARTICLE SIZE MONITORING Since the PSI-200 measurements were not sufficiently frequent for control purposes, the concentrator management decided not to retain the control scheme based on product size distribution envisaged by the GRAIIM in its study. Instead, a strategy based on the cyclone feed density was chosen. This situation motivated GRAIIM to explore some model-based methods which would allow a greater availability of particle size values for control.

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To predict the cumulative percent passing 45 lam (325 mesh) of the cyclone overflow, three different approaches were used. In this section, they will be described in turn. The process variables used in each model as input variables in view of predicting the percent passing 45 ~tm are variables that are measured on-line at each sampling instant. Neural Network Models Feedforward neural networks have attracted considerable interest in the past decade for their ability to capture with relative ease underlying phenomena between input and output variables of a process. A feedforward neural network can be viewed as a general nonlinear model. It is made of a series of processing units called n e u r o n s , organized in layers. Typically, a neural network comprises three types of layers: an input layer, one or more intermediate or hidden layers and an output layer. The neurons of the input layer are simply used to scale each of the input variables and to distribute the scaled inputs to each neuron of the first intermediate layer. Each neuron of this first intermediate layer performs a weighted sum of the outputs from all the neurons of the previous layer, processes this sum through a nonlinear transfer function to produce the output of that neuron, which in turn is transmitted to each of the neurons of the next layer. A constant-value neuron, called the bias, is included in the input layer and in all hidden layers, its role being similar to that of the constant term in a standard linear regression model. A neural network is thus characterized by the number of neurons and layers, the weights of the interconnections between neurons of adjacent layers and the nonlinear transfer function. Before using the neural network for predicting values of a given process variable, it must be trained, that is the internodal weighting factors (parameters of the model) must be determined. Network training is performed on a set of data by comparing the predicted output values to known target values and calculating the corresponding error for each of the output neurons. The errors are then used to adjust the weights of the connections, thus improving the quality of the output variable prediction. At the same time, the ideal number of intermediate layers and neurons (best network architecture) must be determined. Great care must be exercised in the choice of target values to be used in the training process to ensure the quality of the network predictions. Values should be chosen proportionally to the likelihood of their occurrence in the process. Preprocessing of the samples using domain knowledge is a mandatory step if the performance of the network is to be improved by reducing the number of neurons and therefore reducing the time necessary for the training. It is then clear that the use of this procedure is conditioned to the feasibility of the neural network training. For a more detailed description of neural networks, the reader is referred to the numerous and excellent textbooks on the subject [19,20]. In this investigation, a typical neural network is presented in Figure 3a where the cyclone feed flow rate (CFF), the cyclone overflow flow rate (COFF), the cyclone feed density (CFD) and the cyclone overflow feed density (COFD) are used as inputs to the network to predict the percent passing 325 mesh (M325). Numerous neural network architectures were investigated in view of selecting the architecture that will predict with adequate robustness and accuracy the percent passing 325 mesh. The architecture that was selected, as will be discussed in the results section, is presented in Figure 3b. In this architecture, the current and immediate past values of the four input variables along with the past percent passing 325 mesh were used to predict the current percent passing 325 mesh. At first glance, this structure may be surprising since the dynamics of the hydrocyclone is essentially instantaneous compared to the dynamics of the grinding circuit. It is reasonable to argue that past values should not have a direct incidence on the current particle size distribution at the hydrocyclone. However, the use of past values of the percent passing 325 mesh and of the flow rate and density of the inlet flow and the overflow of the hydrocyclone in addition to their current values allows capture of some of the dynamics of the overall grinding circuit. It is possible that the dynamics of the grinding circuit varies from the time when the data for training the network was gathered, leading to a deterioration of the particle size estimation. To remedy this problem, continuous adaptation is possible whereby, at each sampling instant, the most current input/output information is used to modify the weights of the network in order to produce a better fit. Doing a few backpropagation iterations using the most current information or to use a moving window comprised of a number of past measurements are two ways to achieve this objective [21].

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ARMA Models The linear counterpart of the neural network model is the auto-regressive moving average (ARMA) model. An ARMA model can be viewed as a neural network with an input layer, no hidden layers and an output layer, using a linear transfer function, as depicted in Figure 4. Among the advantages of an ARMA model are its simplicity and the ease of model calibration. The model parameters can be calculated using wellknown linear regression techniques to minimize the sum of squares of the errors. The main disadvantage is the usually narrow range of applicability for nonlinear processes. To circumvent this disadvantage and to compensate for process changes, the parameters of the ARMA model can be updated on-line at each sampling interval using the recursive least squares algorithm. This algorithm uses the most current information to calculate the estimation error and to change each of the parameters of the model to lead to a better process output estimation [22].

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Kalman Filter

The Kalman filter is used to estimate, using noisy measurements, the values of the state variables of a process subject to stochastic input disturbances [23]. To perform an estimation, a reasonably good model is required in order to relate measurements with state variables. A popular model commonly used with Kalman filters is the state-space model which is a representation of the dynamic behaviour of the process using a set of simultaneous first order differential equations and an auxiliary state vector. A schematic representation of the Kalman filter is provided in Figure 5.

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In other words, the state vector x is modified in order to reduce the model prediction error. K is the gain matrix that weighs this error vector. It is calculated at each sampling instant and depends on the covariance matrix of the state estimate error and the variances of the two noise matrices w and v. For a more detailed description, the reader is to referred to Ljung's book [24]. A phenomenological model of the hydrocyclone could have also been used instead of a state-space model for the estimation of the percent passing 325 mesh similarly to what has been done in the case of a bioreaction [25] and an exothermic chemical reaction [23].

RESULTS AND DISCUSSION The evaluation of the performance of each of the three different types of particle size softsensors developed, neural network (NN), ARMA model (AM), and Kalman filter (KF), was performed on data obtained from Dynafrag by introducing step changes to the set-points of some of the manipulated process variables and by modifying the state of some of the disturbance variables. To quantify the influence of the different operating variables, various individual step changes were made in Dynafrag while in steady-state operation: ___30% step changes in circulating load set-point (768 t/h); up to _+20% step changes in cyclone feed percent solids set-point (75%); step changes in ore composition, various feed mixtures were used ranging from 100% of one type of ore (hardness) to 100% of a different type of ore; sudden blockage and/or closure of one cyclone (out of a total of eight); preprogrammed changes of the feed size distribution; The simulation results showed that a continuous series of step changes of random but restricted duration and amplitude in ore hardness and particle size provided a data set rich enough for the development of the softsensor. The length of the data file thus obtained corresponds to 4V2 hours of process time (almost 200 data points). For comparison purposes two sets were generated, where applicable the first set was used for model calibration (learning data set) while the second was used as a baseline validation set, data that was not used during the model calibration. Each of the obtained data sets were then corrupted with different levels of noise to produce three data sets called noise-free, noise level 1 and noise level 2. The noise level selected to produce the first noisy data set is equivalent to that detected in Kidd Creek data records, whereas the one used for the second set is twice the previous value. These three data sets permitted the evaluation of the softsensor performance in noise-free and industrial-like environments. Neural Network As a first step, tests were conducted to establish the network structure that would result in both a simple and accurate particle size sensor. To that effect, simulations were made for a varying number of input nodes (each corresponding to the value of a particular operating variable at present and past sampling intervals), hidden layers (1 and 2) and nodes (1 to 10, 15 and 20 neurones per layer), transfer functions (hyperbolic tangent, sigmoidal and linear) and learning methods (quasi-Newton and standard back-propagation). Given the results it was concluded that a network of the structure presented in Figure 3b produced accurate results while at the same time limiting the complexity of the network. The retained structure included an input layer made of 10 nodes (including the bias), fed respectively with present and past (one sampling interval back) values of the flow rate and density of both cyclone feed and overflow and the inmediate past

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value of the cyclone overflow particle size, a three-node hidden layer and using a standard back-propagation method for training. Figures 6 present a comparison between the softsensor predictions (solid line) and the data sets generated by Dynafrag for: (a) the training data set without any noise, (b) the validation data set (not used in the learning process) without any noise, (c) the validation data set corrupted with noise level 1, and (d) corrupted with noise level 2. It can be seen that in all cases the neural network predictions are in good agreement with the actual size distribution "measurements" (percent passing 325 mesh values provided by Dynafrag).

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time (h) Fig.6 (cont.) (c) validation data set (noise level 1); (d) validation data set (noise level 2) A series of simulations were then performed to study the influence of the sampling horizon, o r in other words to evaluate the problem of an instrument with a long measurement rate. The sampling horizon refers to the number of sampling intervals without actual instrument readings, as a result of a long measuring time and/or the sharing of the instrument (increased number of sampling points). For longer sampling horizons, less information is available to calibrate the neural network model and, as a result, the cumulative percent passing 325 mesh is estimated with a reduced accuracy. In addition, in those cases where the neural network model requires past values of the particle size, past estimations must be used with their corresponding level of error. In the case of recursive modelling methods, a longer sampling horizon also means that less information is available for the adaptation of the model. This means that both initial adaptation and adaptation related to changing process conditions can only be performed at longer intervals, thereby deteriorating the overall performance of the model. Also in the case of an error in adaptation, less frequent measurements mean that

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the eventual corrections will take longer and therefore any single error in adaptation will have a greater impact on estimation. Obviously this behaviour is common to all three modelling methods, and an example will be discussed in the following section of this paper. To simulate the effect of a changing sampling horizon, only certain points from the data set were provided to the network for training (e.g. for a sampling horizon of 2, every second point was provided). Sampling horizons of lenght 1, 2, 4, 10 and 20 were simulated and the results are summarized in Figure 7. It can be seen that for the training data set (Figure 7a, squares), the network is able to come up with a reasonable model that does not deteriorate significantly with the sampling horizon. However, if the network is provided with less information (longer sampling horizon) it is increasingly difficult to produce a generalised model for the prediction of the particle size, as evidenced by the results obtained with the validation data set (Figure 7b, squares). When the network is adapted at each sampling instant, better estimation performance is achieved (Figures 7, triangles). Contrary to the standard neural network learning procedure (limited to the information contained in the training data set), the adaptive neural network is continuously trained (the interconnection weights are calculated) as new information is available. To this effect the network was first trained with a third data set and then it was adapted using both the training and the validation data sets. 20 LI~

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ARMA models Both the model structure and the simulation data described in the neural network section were used for the ARMA model to allow a meaningful comparison between these two methods. Initial tests of an ARMA model focused on simple static models, using a similar structure as that developed for the neural network (Figure 4). Those simulations resulted in extremely accurate predictions for noise free data but performance deteriorated for the noisy data. To improve these results a recursive calibration of the model was attempted, resulting in accurate predictions of the particle size in the case of noise free data. Results for the training and validation data sets are given in Figure 8 (first and third bars for an horizon of 1). While the introduction of noise deteriorates the performance of the ARMA predictions (second and fourth bars), it nonetheless gives better results than the static models previously used.

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R.G. Del Villar et

al.

values to calibrate the weighting matrix, very good estimates are obtained. If on the other hand, a more reasonable initial gain matrix is provided, the Kalman filter is able to give accurate estimates in a relatively low number of sampling periods as can be visualized in Figure 10b. In this case, the initial gain matrix corresponds to the final weight matrix obtained in a secondary simulation.

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70

R.G. De| Villar et al.

Figure 11 presents a comparison between the three different approaches for the estimation of the percent passing 325 mesh as a function of the noise level and for two distinct sampling horizons. Estimation algorithms based on a properly initialized Kalman filter or a neural network model are very efficient with a slight edge to a properly initialized Kalman filter with respect to estimation accuracy and robustness. However, the estimation algorithm based on a neural network is more straightforward to develop and to use because it requires significantly less expertise.

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CONCLUSIONS In this work three approaches have been considered for the development of a softsensor capable of estimating the particle size (cumulative percent passing 45 ~tm) of the final product (cyclone overflow) of a grinding circuit in view of its use within an automatic control strategy. The first approach is based on neural network models, the second uses an ARMA model with recursive identification and the third is a Kalman filter. The three methods exhibit good performance when the sampling horizon is relatively short and/or the input variables are free of noise. In the presence of noisy data the ARMA model deteriorates considerably and a recursive model must be used to maintain adequate predictive capabilities. Nontheless, it lacks robustness for increased sampling horizons. The neural network, even in its simplest form (without adaptation), provides excellent estimates of the cyclone overflow particle size. Moreover, it is reasonably robust in terms of increasing sampling horizon and with respect to the level of noise of the input variables. The adaptive version of the neural network increases dramatically the robustness of the approach in what concerns the problem of sampling horizon. Also, this approach requires less expertise from the user and is able to capture the underlying characteristics of the process over a wide range of operation. Finally, the Kalman filter has shown excellent performance when it is properly initialised, otherwise it requires a certain time before being able to produce adequate estimates of the output variable. It must be pointed out that this model was used only for a case where all physical measurements used were available at each control instant. A study is being pursued to use the Kalman filter with long sampling horizons by including the particle size measurements. The neural network soflsensor will be implemented in a grinding circuit control strategy and its performance will be evaluated in process control.

A softsensorfor particlesize monitoring

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ACKNOWLEDGMENTS

The authors wish to thank GRAIIM (Universit6 Laval) for its support in the execution of this project. Funding has been provided through the KBAC project, in turn supported by a consortium of eight mining companies (Cominco, Noranda, Falconbridge, Les Mines Selbaie, Mining Metall Co, Cie. Mini~re QurbecCartier, Brunswick Mining & Smelting, QIT-Fer et Titane), the Mining Technology Council of Canada (MITEC), the Association Mini~re du Qurbec, CANMET, the Centre de Recherches minrrales and NSERC. We would also like to acknowledge the support of Frrdrric Flament, research assistant at GRAIIM.

REFERENCES

.

.

3.

.

.

6. 7. 8.

.

10. 11. 12.

13. 14. 15.

16.

17.

18. ME 9:l-F

Flament, F., Desbiens, A., del Villar, R., Jakelski, D.M. & Pinard, S. Design of a control strategy for Kidd Creek grinding circuit line B. 26th Annual Meeting of the Canadian Mineral Processors. Ottawa, (Jan. 18th, 1994). Samdani, G.S., Software Takes on Air Monitoring. Chemical Engng., 30-33 (Dec. 1994). Rao, M. & J. Corbin., Intelligent Operation Support System for Batch Chemical Pulping Process. Proceedings of lFAC Symposium on Process Dynamics and Control. College Park (MD). 405--410 (1992). Kim, H.C., Shen, X. & Rao, M., Artificial Neural Network Approach to Inferential Control of Volatility in Refinery Plants. Proceedings of 2nd IFAC Workshop on Algorithms and Architectures for Real-Time Control. Seoul (Korea), 90-93 (1992). Lynch, A.J., Mineral crushing and grinding circuits. Elsevier Scientific Publications Company. Amsterdam, 342 (1992). Rao, T.C., The characteristics of hydrocylones and their application as control units in comminution circuits. Ph.D. Thesis, University of Queensland, Australia (1966). Wills, B.A., Mineral Processing Technology. 5th Edition. Pergamon Press. Oxford, 855 (1992). Gonzalez, G., Cipriano, A., Feddersen, A., Zamora, C. & Valenzuela, J., On-line dynamic particle size estimator for grinding plant control. Proceedings of IFAC Symposium on Identification and System Parameter Estimation. Beijing (PRC). (1988). Gonzalez, G., Mendez, H. & de Mayo, F., A Dynamic Compensation for Static Particle Size Distribution Estimators. ISA Transactions., 25(1), 47-51 (1986). Gonzalez, G., Gonzalez, M.A. & Cartes, J.C. Control problems due to the replacement of sensors by softsensors. ISA paper #92-0396 (1992). Dubr, Y., Lanthier, R. & Hodouin, D., Computer aided dynamic analysis and control design for grinding circuits. CIM Bulletin. 80(905), 65-70 (1987). Flarnent, F., del Villar, R. & Lanthier, R., Computer aided design of a control strategy for an industrial grinding circuit. Computer Applications in the Mineral Industry. Second Canadian Conference, Ed. A.L. Mular. Vancouver. (Sept. 1991). Austin, L.G., Klimpel, R.R. & Luckie, P.T., Process Engineering of Size Reduction: Ball Milling. ISBN 0-89520-421-5. SME/AIME. New York, 561 (1976). Plitt, L.R., The mathematical modelling of the hydrocyclone classifier, CIM Bulletin, 69(766), 114-123 (1976). Hodouin, D. & Flament, F., The SPOC manual, chapter 3.1, BILMAT computer program. CANMETkEMR SP85-1/3.1E. Ed.D.Laguitton. Canadian Government Publishing Services. Ottawa (1985) Flament, F., Hodouin, D. & Spring, R., The SPOC manual, chapter 7.3, RTD and MIXERS computer programs. CANMETkEMR SP85-1/7.3E. Ed.D.Laguitton. Canadian Government Publishing Services. Ottawa, (1985). Gupta, V.K., Hodouin, D. & Spring, R. The SPOC manual, chapter 7.2, FINBS computer program. CANMETkEMR SP85-1/7.2E. Ed.D.Laguitton, Canadian Government Publishing Services. Ottawa, (1985). Laguitton, D., The SPOC manual, chapter 5B, Unit models (Group B). CANMETkEMR SP85-1/1E. Ed.D.Laguitton. Canadian Government Publishing Services. Ottawa, (1985).

72 19.

20. 21. 22. 23. 24. 25.

R.G. Del Villaret al. Haykin, S., Neural Networks - - A Comprehensive Foundation. Maxwell Macmillan Canada. Toronto, 696 (1994). Caudill, M. & Butler, C., Naturally Intelligent Systems. The MIT Press. Cambridge, 304 (1990). Van Breusegem, V., Thibault, J. & Ch6ruy, A., Adaptive Neural Models for On-line Prediction in Fermentation. Can. J. Chem. Eng., 69, 481--487 (April 1991). Young, P., Recursive Estimation and Time-Series Analysis - - An Introduction. Springer-Verlag. New York, 300 (1984). Roffel, B. & Chin, P., Computer Control in the Process Industries. Lewis Publishers Inc. 257 (1987). Ljung, L., System Identification: Theory for the User. Prentice-Hall Inc., Englewood Cliffs 519 (1987). Thibault, J., Van Breusegem, V. & Ch6ruy, A., On-line Prediction of Fermentation Variables Using Neural Networks. Biotechnol. Bioeng., 36, 1041-1048 (1990).