使用隐马尔可夫模型的流体机械故障检测外文文献

Fault detection on fl uid machinery using Hidden Markov Models P Arpaia a U Cesaroa b M Chadlib H Coppierb L De Vitoc A Espositoe f F Gargiulo a M Pezzettid aDepartment of Electrical Engineering and Information Technology DIETI Universita degli Studi di Napoli Federico II Italy bLaboratory of Modeling Information and Systems University of Picardie Jules Verne France cDepartment of Engineering University of Sannio Italy dDepartment of Technology CERN Switzerland eDepartment of Electronics and Telecommunications DET Polytechnic of Turin Italy fCRdC Tecnologie Scarl Naples Italy a r t i c l ei n f o Article history Received 11 June 2019 Received in revised form 3 September 2019 Accepted 1 October 2019 Available online 9 October 2019 Keywords Fluid machinery Fault diagnostics Fault detection Hidden Markov Models a b s t r a c t A fault detection method exploiting Hidden Markov Models HMMs is proposed for fl uid machinery without adequate a priori information about faulty conditions The method is trained only on data acquired during normal machine operation For anomaly detection typical quantities measured in mon itoring fl uid machines namely 3 axis acceleration electric power consumption temperature inlet and outlet pressure are monitored Principal Component Analysis is exploited for features extraction Then data is clustered and an HMM is trained Finally the trained model is employed together with a goodness of fi t test to detect faulty states by processing online data The method was tested and vali dated at CERN on screw compressors for cryogenic cooling 2019 Elsevier Ltd All rights reserved 1 Introduction Fluid machines are devices exploiting the energy stored in fl u ids by transforming it in mechanical energy or vice versa These machines are widely employed in several industrial plants Although these are highly reliable machines a fault occurrence is a deleterious event in terms of correct operation time and costs Fault detection mechanisms are in charge of identifying whether the monitored component or process is properly working or not 1 In literature a wide variety of fault detection mechanisms have been proposed In particular in 2 a review on fault detection methods for pipelines highlights that usually a single quantity is measured Among the analyzed techniques and approaches it is shown that procedures are usually complex when good fault detec tion performance is required In 3 a review about wind turbines derives that vibration analysis has been widely used in fault diag nosis and feature extraction However gathering data about faulty conditions in actual working conditions turns out diffi cult espe cially for complex machines like energy turbines or high power compressors Several specifi c signals and often custom invasive monitoring based on multiple specifi c sensors have to be installed directly on fi eld Potential faulty conditions of whatever type have to be forecast modeled and experimented Finally in 4 6 fault detection methods are proposed for the monitoring of compressors operation The methods usually rely on the analysis of vibration signals and it is shown that the training of the fault detection mod els exploit both measures related to normal and faulty conditions This is also confi rmed in 7 where faults are classifi ed with a Sup port Vector Machine by taking into account a big amount of data 300 TB to identify and validate the model A promising trend research in fault detection with exceptional ability in modeling 1D sensor signals is related to Hidden Markov Models HMMs A simple Markov Model is a Markov Chain i e a fi nite state machine governed by a stochastic process This process is described with a probability matrix in which each element aijis the probability of the transition from the state i to the state j aiiis the probability to remain in the same state A Markov chain allows to compute the probability for a sequence of states to be observed In many cases however the states of interest may not be directly observable and thus the state sequence is hidden In such a case it is possible to calculate the probability of the sequence according to the Markov model as well as the state sequence that most likely produced the observations Such a model is an HMM Firstly introduced in 1989 8 to solve speech recognition prob lems recently these models have been extended to pattern identi fi cation 9 10 health monitoring human action recognition biological sequence analysis economics 11 and fault detection https doi org 10 1016 j measurement 2019 107126 0263 2241 2019 Elsevier Ltd All rights reserved Corresponding author E mail address pasquale arpaia unina it P Arpaia Measurement 151 2020 107126 Contents lists available at ScienceDirect Measurement journal homepage In particular HMM based approaches were used to monitor fault detection in mechanical devices such as bearings 12 15 or in industrial processes 16 18 The wide use of this methodology may be attributed to the following reasons applicability to embedded stochastic processes whose states are not directly observable but they can be deduced through another process training easiness due to the easiness in estimating the model parameters even when training samples are abundant independence of multiple models i e the possibility to use a number of independent HMM to describe different conditions of a process By relying on the peculiar features of the HMM a novel fault detection method is here proposed The above mentioned works exemplify that most researches considered acoustic vibrations or employed accelerometers to measure the state of the monitored process Moreover measures were often obtained with a dense sampling Instead in actual applications measures are sparse and asynchronous Then in general one single physical quantity may not be suffi cient to detect an incipient failure condition For instance in case of an operating anomaly the machine could not have abnormal vibrations but it may overheat Finally in fl uid machinery with constraining requirements of reliability the dynamics of the fault detection model is such that it will remain in a fault free state for long stretches of time In this paper a fault detection method for fl uid machinery with out adequate a priori information about faulty conditions is pro posed by exploiting HMM The procedure takes into account multiple physical quantities and it deals with the sparsity and non synchronization of these measures The core of the proposed method is the ability to train a Hidden Markov Model by merely exploiting data related to normal machine operation This extends its employability to reliable machines where the fault is a rare though deleterious event The proposed method by taking into account multiple factors can be generalized and extended to com plex systems where various physical quantities can be monitored According to 1 and with the researches mentioned above fault detection is a preliminary and essential step for fault diagnostics Moreover many applications simply require the detection of a fault such as in the case study of the present work Therefore the aim of this work is to build a fault detection model while fur ther extension to diagnostics or prognostics will be addressed in future works The remainder of this paper is organized as follows Section 2 presents the proposed method for fault detection in fl uid machin ery Section 3 introduces a case study at CERN where screw com pressors are employed for cryogenic cooling and the inherent results regarding the HMM training and fault detection are reported 2 Proposal A fault detection method based on Hidden Markov Models tak ing sparse measures of multiple physical quantities is proposed The method is sketched in Fig 1 The problem of sparsity and non synchronization of data is faced fi rst by fi lling the input data on a coherent time base and then by applying a decimation Next a Principal Component Analysis PCA is employed to project the data in a new space and to select the principal components Finally data are clustered After this data processing the HMM is trained by means of the Baum Welch algorithm The trained model is then employed for fault detection by means of a goodness of fi t test as shown in Fig 1b In the following subsections the blocks in Fig 1a and b are detailed Then test and validation of the model are reported in the next sections by referring to a case study at CERN 2 1 Data processing The fi rst step in data processing is the fi lling In general sensors installed on the monitored fl uid machine can return non uniformly acquired data with data acquisition not synchronous Indeed the sampling rate depends on the expected variation of each physical measurand However for the next steps of training and fault detec tion structured data are necessary To this aim a time base is con sidered with equally spaced time instants so that every measure can be referred to a reference instant Then the value of each quan tity is replicated for each time instant up to the next measured value It is assumed that a data is obtained in a stationary operating condition namely that measures are not acquired during transi tions of the machine to a regime After that data are decimated in order to diminish the computa tional burden and allow further processing The optimal decima tionfactorisfoundbalancingthetrade offbetweenthe computational burden and the fi nal accuracy of the model This factor does depend on the available data and a determination example is reported in the following section within the discussion of the case study As mentioned above the Principal Component Analysis PCA fol lows The purpose in using PCA is to represent the variation of measured quantities with a smaller number of factors or main components The samples are represented in a new space by redefi ning the axes through the main components instead of the original variables PCA captures the variance of data and accounts for correlations among variables The resulting lower dimensional representations of data can improve the profi ciency of detecting and diagnosing faults using multivariate statistics The number of principal components to take into account depends again on the available data The proposed criterion is that the fi rst discarded component would add an amount of data variance lower than 1 This step can be executed with the MATLAB function pca by deriving the scores associated to each component Data processing is concluded with a cluster analysis Its purpose is to group data according to some criteria of similarity As an example the clusters are determined in such a way that the obser vations are as homogeneous as possible within the same cluster and as uneven as possible between the different clusters The clus tering technique employed in the proposed method exploits the Euclidean metric According to that the data are clustered so that the Euclidean intra cluster distance is minimized and the extra cluster Euclidean distance is maximized For instance this can be done with the kmeans function available in MATLAB by exploiting the default distance measure sqeuclidean The success of this mod eling depends on the choice of the number of clusters Too many clusters would lead to ambiguities while choosing few clusters means fl attening observations and merging observations that are actually associated to different states The number of clusters is chosen with an iterative procedure aiming to fi nd the combination of clusters and states of the Markov model that maximized the accuracy of the trained model This is better described below in discussing the training algorithm 2 2 Training An HMM is usually characterized by fi ve elements 1 N the number of states 2 M the number of distinct observation symbols per state 3 A the state transition probability distribution 2P Arpaia et al Measurement 151 2020 107126 4 B the observation symbol probability distribution 5 pan initial state distribution Training refers to the process of obtaining the HMM parameter set In particular the matrices A and B are to fi nd Each element aij of the matrix A represents the probability of transition from the state i to the state j Instead each element bijof the matrix B rep resents the probability to observe the symbol i given a state j The training of an HMM consists in fi nding these two matrices from measured data The dimension of the matrix A as well as one dimension of matrix B is related to the number of hidden states N which is not known a priori Thus an iterative procedure is employed in order to fi nd the number of states that maximizes a likelihood function The iterative algorithm that constitutes the core of training in the proposed method is the Baum Welch algorithm Let h A B p be the model to train The algorithm is made of three steps i a forward procedure ii a backward procedure and iii an update procedure The forward procedure calculates the probability of a partial sequence of statesai fi nishing in state i given a model h To this aim an iterative procedure is imple mented The probability of observing a symbol y t 1 in state i is multiplied by the probability of entering the state i The iterative procedure is initialized withai 1 equal to the product between the probability of observing the symbol y1in state i and the probability that the initial state is i namelypi Eq 1 resumes this fi rst step where Y is the random variable representing the observed mea sure and S is the random variable representing the state ai t P Y1 y1 Yt yt St ijh ai 1 pibi y1 ai t 1 bi yt 1 X n j 1 aj t aij 1 On the contrary the backward procedure corresponds to fi nd the probability of generating the sub sequence from t 1 to T after entering the state i The iteration now considers the sum of all probabilities of entering the states after i and observe the symbol y t 1 multiplied by the probability of having the sub sequence bj Eq 2 resumes this second step The iteration is initialized con sidering that this probability is 1 in the last observation T i e bi T 1 Hence the initialization here considers the fi nal observa tion while the rest is obtained going backward bi t P Yt 1 yt 1 YT yT St ijh bi T 1bi t X N j 1 bj t 1 aijbj yt 1 2 Finally it is possible to calculate the probabilitycof being in state i at time t given the observed sequence Y and the parameters of model h and the probability n of being in state j at time t and t 1 given the observations Y and the parameters of h This allows to update the model parameters becausepiequalsc 1 namely the probability of being in state i equals the initial state probability the matrix A is updated with the ratio between the expected number of transitions from state i to state j and the number of transitions from state i to any other state while the matrix B is updated with the ration between the number of times that the output is k when the state is i divided by the total number of times that the state is i This update procedure is resumed in Eq 3 ci t ai t bi t PN j 1aj t bj t nij t ai t aijbj t 1 bj yt 1 PN j 1 PN j 1ai t aijbj t 1 bj yt 1 p i ci 1 a ij PT 1 t 1 nij t XT 1 t 1ci t b i vk PT t 11yt vkci t PT t 1ci t 3 where 1yt vkequals 1 when yt vkand 0 otherwise 2 3 Fault detection Once the model is trained it can be employed for the fault detection The data processing steps necessary in this phase and reported in Fig 1b comply with the corresponding ones of the training phase already detailed in the previous section Then the clusters are compared to the model and the likelihood function is returned The maximum likelihood is found with an Expectation Maximization EM algorithm which estimates the parameters of the statistical model 19 Finally a goodness of fi t test is executed between the likelihood sample obtained in the training phase and that obtained by the application of the test sequence A fault is detected when a different distribution is found for the two sam ples An example of goodness of fi t test is the Wilcoxon one 20 It is a non parametric test employed in case of non Gaussian distri bution of data Alternative statistical tests can also be used As an example the likelihood distribution could be analyzed with a preliminary statistical test and if a compliance is found with a Fig 1 Block diagram of the proposed method for a the Hidden Markov Model training and b the fault detection PCA Principal Component Analysis P Arpaia et al Measurement 151 2020 1071263 Gaussian distribution specifi c tests can be used such as the chi square test In the following the training and validation steps described above are resumed in an algorithmic form in order to clarify the method implementation Algorithm 1 Fault Detection with Hidden Markov Models Training 1 Collection of sequences Siin the data set S 2 procedurePRE PROCESSINGS 8Si2 S 3 Filtering discard all sequences out of ON period 4 Filling replication of the last available measurement 5 Decimation selecting 1 over N observations with N the decimation factor 6 PCA Extraction of the principal components 7 return Pre processed Sequences S1 8 end procedure 9 procedure Training of model80 of S1 multiple training needed 10 for all Si2 S1do 11 Clustering S1 ci EuclideanClusterization S 1 12 Training Mi Li BaumWelch S1 ci A A states number 13 end for 14 return Mi whose Li is Maximum 15 end procedur 16 procedureTESTING OF MODELMi 20 of S1 17 Check Li ExpectationMaximization Mi S1 ci 18 return number of sequences rejected 19 end procedure Algorithm2 Fault Detection with Hidden Markov Models Validation 1 procedureVALIDATIONMi 20 of S1 2 Anomaly injection Alteration of few values in the nominal observations Sa Alteration S1 3 Sa1 Pre Processing Sa 4 La ExpectationMaximization Mi Sa1 i 8Sa1 i 2 Sa1 5 Validation Pw Wilcoxon La i L a j with L a i L a j 2 Laand i j 6 return Pw 7 end procedure 3 Experimental case study 3 1 Description and test strategy At CERN liquid helium is used to cool superconducting magnets that accelerate the particle beam i