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Procedia Manufacturing 32 (2019) 591–595 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
The The 12th 12th International International Conference Conference Interdisciplinarity Interdisciplinarity in in Engineering Engineering
Hilbert-Huang Hilbert-Huang Transform Transform in in Fault Fault Detection Detection
Manufacturing Engineering Society International 2017, 28-30 June a, , Conference 2017, MESIC a a, *, Horatiu Stefan Grifa Zoltan German-Sallo 2017, Vigo (Pontevedra), Spain Zoltan German-Sallo * Horatiu Stefan Grif 0F
0F
a a
University of Medicine, Pharmacy, Sciences and Technology of Tirgu Mures, 38 Gherghe Marinescu street, 540139 Targu Mures, Romania University of Medicine, Pharmacy, Sciences and Technology of Tirgu Mures, 38 Gherghe Marinescu street, 540139 Targu Mures, Romania
Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency Abstract Abstract
Failures of manufacturing systems representaa, significant costa,*in, both repairs band A bconsiderable percentage of the A. Santana P. Afonso A. Zanin , R.downtime. Wernke Failures of manufacturing systems represent a significant cost in both repairs and downtime. A considerable percentage of the maintenance cost is caused by unexpected drivetrain failures. This paper proposes a Hilbert-Huang transform (HHT)-based a maintenance cost is caused by unexpected drivetrain failures. ThisGuimarães, paper proposes a Hilbert-Huang transform (HHT)-based University of Minho, 4800-058 Portugal algorithm to effectively detect malfunctioning by revealing the instantaneous amplitude and frequency of nonlinear and b algorithm to effectively detect malfunctioning by revealing theChapecó, instantaneous amplitude and frequency of nonlinear and Unochapecó, 89809-000 SC, Brazil nonstationary signals. The proposed algorithm is tested on synthetic signals created for this purpose. This paper presents the nonstationary signals. The proposed algorithm is tested on synthetic signals created for this purpose. This paper presents the principles of this fault diagnosis method, results indicate that the proposed procedure can handle fault detection issues in principles of this fault diagnosis method, results indicate that the proposed procedure can handle fault detection issues in manufacturing systems. manufacturing systems. Abstract © 2018The Authors. Published by Elsevier Ltd. 2019 TheAuthors. Authors.Published Publishedby byElsevier ElsevierLtd. Ltd. © 2018The This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Under theopen concept of "Industry productionlicense processes will be pushed to be increasingly interconnected, This is an access article under the4.0", CC BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Selection and based peer-review undertime responsibility the 12th International Conference Interdisciplinarity in Engineering. information on a real basis and,ofnecessarily, much more efficient. In this context, capacity optimization
goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. Keywords:Fault diagnosis, signal analysis, Hilbert-Huamg transform, instantaneous frequency Keywords:Fault signal analysis, Hilbert-Huamgimprovement transform, instantaneous frequency Indeed, lean diagnosis, management and continuous approaches suggest capacity optimization instead of maximization. The study of capacity optimization and costing models is an important research topic that deserves contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical 1. Introduction 1. Introduction model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was capacityisand to design towards the maximization of organization’s Fault detection asused part to ofanalyze quality idle monitoring essential partstrategies in manufacturing systems management. Information Fault detection as part of quality monitoring is essential part in manufacturing systems management. Information about functional conditions operations to improve efficiency quality andis increase throughput. considered value. The trade-off capacityenables maximization vs operational highlighted and it is Fault shownis that capacitya about functional conditions enables operations to improve quality and increase throughput. Fault is considered a variation of at leasthide oneoperational characteristic parameter from an admissible condition. It is a state, which may lead to a optimization might inefficiency. variation of at least one characteristic parameter from an admissible condition. It is a state, which may lead to a malfunction or failure of thebysystem [1]. Detection of faults is based on symptoms that are changes of observable © 2017 The Authors. Published Elsevier B.V. malfunction or failure of the system [1]. Detection of faults is based on symptoms that are changes of observable Peer-review undertheir responsibility of the scientific committee of thesignals Manufacturing Engineering Society International Conference quantities from normal behaviour. These are usually provided by sensors. The HHT is a relatively new quantities from their normal behaviour. These are usually signals provided by sensors. The HHT is a relatively new 2017. method for time-frequency analysis that is able to calculate the instantaneous amplitude and frequency of nonlinear method for time-frequency analysis that is able to calculate the instantaneous amplitude and frequency of nonlinear and nonstationary signals [2]. Unlike other signal transforms, the HHT is based on an adaptive algorithm. and nonstationary signals [2]. Unlike other signal transforms, theOperational HHT is based on an adaptive algorithm. Keywords: Cost Models; ABC;knowledge TDABC; Capacity Management; Capacity; Therefore, no prior of the signal isIdle required to performEfficiency the HHT [3]. As a differentiation-based Therefore, no prior knowledge of the signal is required to perform the HHT [3]. As a differentiation-based 1. Introduction * Corresponding author. Tel.: +4-074-025-1344. * The Corresponding author. Tel.: +4-074-025-1344. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address:
[email protected] E-mail address:
[email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789© 2018Thetons Authors. Published by Elsevier Ltd. hours of manufacturing, etc. The management of the idle capacity in several ways: of production, available 2351-9789© 2018The Authors. Published by Elsevier Ltd. This is anAfonso. open access under the761; CC BY-NC-ND * Paulo Tel.:article +351 253 510 +351 253license(https://creativecommons.org/licenses/by-nc-nd/4.0/) 604 741 This is an open access article under the CC fax: BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. E-mail address:
[email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering.
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.257
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method, there is no uncertainty principle limitation in the result as that in the convolution-based wavelet and Fourier transforms [4]. The HHT integrates the Hilbert transform spectrum analysis with Empirical Model Decomposition (EMD) to produce an experience-based method for generating time-frequency spectra of a variety of nonlinear and nonstationary signals [5]. The HHT has been found powerful and successful in condition monitoring of electric machines using vibration data [6], and in detection of rotor bar failures of induction machines using stator current data [7]. 2. The Huang-Hilbert transform The Hilbert-Huang transform (HHT) is NASA's designated name for the combination of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). The key part of the HHT is the EMD method with which any complicated data set can be decomposed into a finite and often small number of components, called intrinsic mode functions (IMF). An IMF is defined as any function having the same (or differing at most by one) numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima, respectively. With the Hilbert transform, the IMF's yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The empirical mode decomposition (EMD) decompose any signal in intrinsic mode functions as follows: For a given discrete signal 𝑠𝑠(𝑡𝑡), 𝑚𝑚1 is the mean value of its upper and lower envelope curves of local maxima and minima. The first prototype component 𝑐𝑐1 is computed:
c1 = s(t ) − m1
(1)
In the second sifting process, 𝑐𝑐1 is treated as the data, and 𝑚𝑚11 is the mean of 𝑐𝑐1 ’s upper and lower envelopes:
c11 = c1 − m11
(2)
This sifting procedure is repeated 𝑘𝑘 times, until 𝑐𝑐1𝑘𝑘 is an IMF, that is:
c1 (k − 1) − m1k = c1k → c1
(3)
If this component satisfies the stop criteria for IMF sifting, 𝑐𝑐1 this will be the first IMF. The residual signal will be constructed as follows:
r (t ) = s(t ) − c1
(4)
If 𝑟𝑟(𝑡𝑡) satisfies the stop criterion for EMD then it will be the final residual signal and the EMD process will be finished. The IMF sifting method cancels the riding waves and make prototype IMFs more symmetric according to zero. The sifting process ends when a mathematical defined stoppage criterion is satisfied. This criterion serves to obtain a fair decomposition without any loss of information. The most common stoppage criterion was defined by Cauchy and acts when the standard deviation between two consecutive IMFs reaches a predefined value. The number of functions in the set depends on the original signal and on the threshold value used by the stoppage criterion. The instantaneous frequency can be computed through the Hilbert Transform, with which any real valued function x(t) of Lp class can be transformed into an analytic function by adding a complex part, y(t) , given by
y (t ) =
1
π
⋅P⋅
=∞
x(α )
∫ t − α ⋅ dα
−∞
(5)
Zoltan German-Sallo et al. / Procedia Manufacturing 32 (2019) 591–595 Zoltan German-Salloa and Horatiu Stefan Grif / Procedia Manufacturing00 (2018) 000–000
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in which the P indicates the principal value of the singular integral. With the Hilbert transform, the analytic function is then
z (t ) = x(t ) + j ⋅ y (t ) = a(t ) ⋅ e jϕ (t )
(6)
y a(t ) = x 2 + y 2 ; ϕ (t ) = arctg x
(7)
Here a is the instantaneous amplitude, and θ is the phase function; and the instantaneous frequency is simply
ϕ=−
dω dt
(8)
This represents the best local fit of an amplitude and phase varying trigonometric function to X(t) . But the Hilbert Transform can only produce physically meaningful results for a so called mono-component signals [8]. 3. Materials and method At first a test signal was created. This signal carries all the already mentioned characteristics which can lead to faulty functioning in machinery. In order to obtain noisy test signal, additive Gaussian white noise was added. These signals were synthesized in Matlab and are presented on figure2. Test signal
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Fig. 1. The proposed test signal.
This signal can be a sensor provided signal, it’s easy to observe the changes appeared as consequence of faulty function. The proposed procedure is presented below (figure2) Empirical Mode Decomposition (EMD)
Hilbert Transform Of IMFs Fig. 2. The proposed method.
Fault detection (Through instantaneous Frequency detection)
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4. The obtained results The EMD performed on the test signal yields the following IMFs. As it can be seen the IMFs have descending frequency in the evolution of sifting process 2 testsignal
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Fig. 3 The resulted IMFs after the EMD.
The instantaneous frequency of the analyzed signal is represented on figure 4. The result demonstrates that the procedure is able to reveal any changes in the signal which can drive to a malfunction Instantaneous frequency
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Fig. 4 The instantaneous frequency of the signal.
If the type of fault can be identified, the instantaneous frequency as fault detector can be computed just for a few (or maybe just one) characteristic IMFs, is not necessary for the whole signal. In this case the stoppage criterion for the sifting process can be simpler, yielding a smaller number of iterations and IMFs. Figure 5 presents the same way determined instantaneous frequency for the first IMF.
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Instantaneous frequency for IMF1
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Instantaneous Frequency faulty gear IMF1 8
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Fig. 5. The instantaneous frequency for the first IMF.
4. Concluding remarks In this paper an adaptive mode decomposition algorithm (EMD) and instantaneous frequency estimation approach through Hilbert transform (HHT) were introduced. The relative simplicity and visual evidence of this method, as well as, an opportunity of its hardware or software realization in real time are important for fault detection in manufacturing systems. The EMD is effective for most signals but the lack of a rigorous mathematical formulation could be a serious disadvantage. The instantaneous frequency determination is useful because fault signature is usually carried or manifested by specific frequencies. References [1] M. Grasso and B. M. Colosimo, ``An automated approach to enhance multiscale signal monitoring of manufacturing processes,'' J. Manuf. Sci.Eng., vol. 138, no. 5, p. 051003, Nov. 201. [2] R. Y. Zhong, Q. Dai, T. Qu, G. Hu, G. Q. Huang, RFID-enabled real-time manufacturing execution system for mass-customization production, Robotics and Computer-Integrated Manufacturing, 29 (2013) 283-292. [3] I. P. Tsoumas, G. Georgoulas, E. D. Mitronikas, and A. N. Safacas, “Asynchronous machine rotor fault diagnosis technique using complex wavelets,” IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 444–459, Jun. 2008. [4] Huang, et al. 1998: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Roy. Soc. Lond., 454, 903-993. [5] Q. Du and S. Yang, “Improvement of the EMD method and applications in defect diagnosis of ball bearings,” Measurement Science and Technology, 17, pp. 2355-2361, 2006. [6] R. Yan and R. X. Gao, “Hilbert-Huang Transform-Based Vibration Signal Analysis for Machine Health Monitoring”, IEEE Transaction on Instrumentation and Measurement, 55, No. 6, pp. 2320-2329, 2006. [7] D. Yu, J. Cheng, and Y. Yang, ``Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings,'' Mech. Syst. Signal Process., vol. 19, no. 2, pp. 259-270, Mar. 2005. [8] Z. Feng, F. Chu, and M. J. Zuo, ``Timefrequency analysis of time-varying modulated signals based on improved energy separation by iterative generalized demodulation,'' J. Sound Vib., vol. 330, no. 6, pp. 12251243, Mar. 2011. [9] X. Xu, From cloud computing to cloud manufacturing, Robotics and computer-integrated manufacturing, 28 (2012) 75-86. [10] Z. K. Peng, P. W. Tse, and F. L. Chu, ``A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing,'' Mech. Syst. Signal Process., vol. 19, no. 5, pp. 974-988, Sep. 2005. [11] Z. K. Peng, P. W. Tse, and F. L. Chu, ``An improved HilbertHuang transform and its application in vibration signal analysis,'' J. Sound Vib., vol. 286, no. 1, pp. 187-205, Aug. 2005. [12] S. J. Loutridis, ``Damage detection in gear systems using empirical mode decomposition,'' Eng. Struct., vol. 26, no. 12, pp. 1833-1841, Oct. 2004.