DPLS-MSOM Modeling for Visual Industrial Fault Diagnosis and

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DPLS–MSOM modeling for visual industrial fault diagnosis and monitoring based on variation data from normal to anomalous Jiawei Tang, and Xuefeng Yan Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02590 • Publication Date (Web): 17 Nov 2017 Downloaded from http://pubs.acs.org on November 20, 2017

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Industrial & Engineering Chemistry Research

DPLS–MSOM modeling for visual industrial fault diagnosis and monitoring based on variation data from normal to anomalous Jiawei Tang Xuefeng Yan* Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai 200237, P. R. China Corresponding Author: Xuefeng Yan Email: [email protected] Address: P.O. BOX 293, MeiLong Road NO. 130, Shanghai 200237, P. R. China Tell: 0086-21-64251036

Abstract Process variables obtain significant dynamic variation characteristics from the moment faults are introduced through a continuous period of time. Therefore, these data possess not only strong corresponding fault information but also robust dynamic characteristics that can be effectively used for fault diagnosis. Accordingly, the dynamic partial least squares (DPLS) and selforganizing map (SOM) combination methodology is utilized for visual fault diagnosis and monitoring. Different types of fault data (from normal to anomalous) are collected and trained by DPLS in the form of a dynamic data matrix to reveal the most discriminated orientations for the

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different statuses. A multilayer SOM is then trained to model the relationship with different status data under such orientations to the regular positions on a two-dimensional map. The trained map can be used for deciding the real operating state of the online observations. Excellent experimental results on the Tennessee Eastman chemical process have demonstrated that DPLSMSOM is quite qualified for nonlinear and random faults. This method provides a new innovation in fault diagnosis on the basis of the dynamic analysis of normal to anomalous data. Keywords: self-organizing map, dynamic partial least squares, dynamic feature analysis, visual fault diagnosis and monitoring

1 Introduction Visual fault diagnosis methods are employed to analyze the principal cause of faults. The analysis can be simply interpreted as pattern recognition problem based on the historical fault database. Furthermore, visual fault diagnosis methods solve the classification issue by data projection, which indicates two main tasks: data visualization and clustering. The realization of visual fault diagnosis can be rather challenging, especially when numerous variables with high correlations exist. In general, fault diagnosis and detection techniques are merely devoted to detecting current faults that occurred in a system. However, instead of generating a detected fault alarm, providing the risk of the current fault alarm can be much more reasonable in practical applications because it is inadequate to neglect the potential impact of the current fault on the environment and system. Thus, risk-based fault detection and diagnosis has been proposed in recent years. Compared to the traditional methods, these risk-based methods are also concerned about the process structure. The risk of a process is defined as a combination of the probability of fault and severity of the


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fault. This process was proposed earlier by Bao et al.1, who finished the task with a simple univariate method. Later, Zadakbar et al.2 extended this method to multivariate approaches. A self-organizing map (SOM)3 is a special neural network capable of multiclass classification and data visualization. This neural network is qualified for visual fault diagnosis and has been adopted by many scholars in early research investigations. For example, Vandeventer et al.4 developed an online computer system based on textural analysis through an SOM to visually observe condition changes in froth flotation. These authors corroborated that the system can completely track changes in operating conditions. Garcia and Gonzalez5 established the relation among variables based on an SOM and a K-means algorithm. Their supervision techniques successfully estimate, monitor, and visualize the state of wastewater treatment plants. Hongyang Yu el al.6 utilized a dissimilarity index integrated with an SOM to classify the operating condition of the system. However, a basic SOM can be invalid in high-dimensional and correlated processes. Subsequently, some scholars focus on a statistical analysis integrated with an SOM. Chen and Yan7,8 extended the SOM capability of visual fault monitoring and diagnosis and then integrated SOM with a Fisher discriminant analysis (FDA) and a correlative component analysis (CCA). The results verify that their approaches have a low misclassification rate. Song and Yan9 further advanced the diagnosis property in a multiSOM with canonical variate analysis (CVA). Nevertheless, these statistical approaches, including principle component analysis (PCA), FDA, CCA, and CVA, are only appropriate for linear plants10. When faced with nonlinear and random plants, they are useless. Some scholars employed the kernel versions of statistical approaches, such as kernel PCA11, kernel FDA12, and kernel partial least squares (PLS)13, to solve the aforementioned problem. Yu14 proposed a nonlinear kernel Gaussian mixture model (NKGMM) associated with inferential


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monitoring for fault detection and diagnosis. After tests on a wastewater treatment process, the NKGMM outperformed traditional independent component analysis and the Gaussian mixture model in the early determination of process faults and detection of faulty variables. Recently, some scholars have adopted PCA with a Bayesian network for fault diagnosis. Li and Yang15 solved the problem of a single kernel function parameter by incorporating an ensemble learning approach with Bayesian inference. Sunday A. Adedigba et al.16 used PCA and BN to detect faults and estimate system failure risk. H. Gharahbagheri et al.17 combined KPCA and BN to diagnose the root cause of process faults. A new quality relevant and independent monitoring structure based on KPCA and mutual information has been proposed by Huang and Yan18. Jiao et al.19 proposed a novel nonlinear quality-related method based on KPLS for fault detection. Their approach has proved to be stable and effective when compared to relevant nonlinear methods. Nonetheless, the search of kernel parameters can be a time-consuming task20, and the results are restricted to a particular database. The same problem can be solved from different perspectives. A major issue involved in nonlinear plant classification is that the original data are highly blended. No valid direction exists upon which each data type can be well separated. When a fault is introduced, only a small deviation occurs in most of the variables, and no apparent change exists in all the variables. This deviation could be insignificantly evident under the tune of the control loop. This scenario definitely results in considerable difficulty for fault diagnosis. Consequently, a new view is proposed that emphasis should be placed on the data variation from normal to anomalous instead of the final anomalous state21,22. These dynamic variation data are abundant in characteristics of different operating statuses and can improve the visual fault diagnosis and monitoring.


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Partial least squares, also known as CCA, is a powerful dimension reduction algorithm for feature extraction. Barker and Rayens proved that PLS is superior to PCA when the goal is discrimination with a rigorous statistical derivation23. However, a common PLS classifier only guarantees good prediction accuracy when the data number of classes is small. Qu, Li, and Xu proposed an asymmetric PLS classifier to improve such deficiencies and demonstrated this method with an empirical simulation24. Zeng et al. utilized PLS and t-statistic feature selection scores for high-dimension reduction in a gene expression analysis25. The experimental results indicate that their classifier has reliable and effective behaviors. Therefore, PLS is an effective feature-extraction tool for feature extraction. A certain number of lagged variables are included in the algorithm called dynamic PLS (DPLS) to determine the discriminant elements among different classes by dynamic analysis. The variation data from normal to anomalous of different statuses are accordingly collected to construct matrices in lagged time. A self-organizing map is widely adopted for data visualization and clustering, and DPLS is an efficient dynamic feature analysis method. Therefore, a valid projection upon which those dynamic variation data are well separated can be extracted according to DPLS. When different types of fault dynamic data are projected onto feature space, an SOM is adopted to capture the topological structure of pairwise data and retained on a twodimensional visualization map. This approach can benefit engineers considerably for determining the real operating state of a plant. A single-layer SOM is commonly unsuitable for a large-number fault diagnosis. Therefore, a multilayer SOM integrated with DPLS, defined as DPLS–MSOM, is utilized for visual fault diagnosis and monitoring. The rest of this paper is arranged as follows. Section 2 presents a precise review of the SOM and DPLS methods. Section 3 explains the practical realization of DPLS–MSOM in visual fault diagnosis. Section 4


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introduces the methodology applied to the visual fault diagnosis and monitoring in the Tennessee Eastman (TE) process. Section 5 provides a concise summary of the results. Note that all the formula symbols described in this article are consistent.

2 Related works 2.1 SOM Self-organizing maps, first proposed by Kohonen26, are a useful tool for high-dimensional data reduction and clustering. The conventional structure of an SOM is composed of an array of neurons in a hexagonal grid orderly arranged on an output map. Each neuron on the map, called prototype vector, is connected to an input vector via a group of weights. Fig. 1 depicts the typical structure of an SOM.

L

i1

i2

in

Fig. 1. Topological structure of an SOM The training procedure of an SOM is mainly composed of three basic phases: (1) the competing phase, (2) the collaboration phase, and (3) the modification phase. In the competing phase, linear initialization along with the two largest eigenvectors attempt to initialize the weights of the prototypes. If the approach fails, then a random initialization is employed instead. The prototype then carries the weights closest to a data vector, called the best matching unit


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(BMU), which represents the data point on the map. The BMU of m - th input data im is found by the closest Euclidean distance between im and prototype weights wk :

wm,bmu = arg min(|| im − wk ||), ∀k

.

(1)

The BMU prototype holds the least dissimilar property to im in comparison with the other prototypes. The surrounding prototypes of the BMU are determined in the collaboration phase. In the last modification phase, the weights of the surrounding prototypes are gradually updated under the direction of im . The updated formula is represented by the following:

wk (t + 1) = wk (t ) + α (t )θ k ,bmu ( m ) (im (t ) − wk (t )) ,

(2)

where t is the discrete mapping step, α represents the learning rate that is monotonically decreasing and θ k ,bmu ( m ) is a neighborhood Gaussian function centered at the BMU of im .

θ k ,bmu ( m ) can be expressed as follows: θ k ,bmu ( m ) = e ( −||w

2 2 m ,bmu − w k || /2σ )

.

(3)

where σ , the kernel width, is controlled by monotonically decreasing its size to promote a smooth result of SOM training. After a series of tuning steps, the prototypes that are close to the BMU will become significantly similar to the latter, whereas the prototypes that are far away from the BMU will differ from the latter because of the kernel function θ k ,bmu ( m ) . Consequently, the BMUs can be considered the discrete data compression of the input data. 2.2 DPLS The partial least squares method aims to find a new linear combination of original variables that have high similarity with the target variables. When PLS is utilized for discriminant


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analysis, the outputs are considerably different from the normal regression. If a given historical dataset H ∈ R a × n is supposed, where a denotes the samples and n denotes the variables; then these data are separated into c different classes. The output of each class is marked by a cdimensional unit vector yk , yk = (0,L 0,1, 0, L , 0) 123 123 , k −1

c−k

(4)

where only the k − th element is 1 and the rest are 0. The output matrix Y belongs to a × c . Lagged inputs are a common tool for analyzing the dynamic system. The k - th variable of the historical data set, hk = (h1k , h2 k ,L hak )T , is taken as an example. hkτ delayed by time τ can be expressed as follows:  hak  h( a-1) k τ hk =   M   hτk

h( a-1) k h( a- 2) k M h( τ -1) k

L h( a-τ+1) k   L h( a-τ ) k  O M .  L h1k 

(5)

Subsequently, H delayed by time τ can be described as follows: H τ = ( h1τ , h2τ , L , hnτ ) .

(6)

The major problem of PLS is how to construct latent variables from inputs and outputs. A traditional strategy of PLS is to maximize the covariance between the latent variables and outputs ( Y ). Some scholars have addressed the issue with diverse approaches. In the present study, the most adopted training algorithm, called a nonlinear iterative PLS (NIPALS), is utilized.


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The input variables ( Hτ ) and targets ( Y ) are normalized to zero means with a unit variance. The first latent variable, t1 = Hτ p1 , is calculated by maximizing the covariance between y1 and t1 in concordance with || p1 ||= 1 . y1 is defined as the direction of largest variance of Y . The objective function is as follows:

p1 = arg max(Cov( Hτ p1 , y1 )), p1T p1 = 1 .

(7)

With the introduction of a Lagrange function

L( p1 , λ ) = p1T Hτ T y1 − λ (1 − p1T p1 ) ,

(8)

where λ is a Lagrange multiplier. When taking derivatives of function L , we can transform Equation (8) into the following:

Hτ T y1 = 2λ p1 .

(9)

Therefore, the solution of vector p1 is calculated as follows:

p1 =

Hτ T y1 || Hτ T y1 || .

(10)

The impact of t1 on the input space Hτ has to be subtracted to calculate the next latent variables. E1 is defined as the residual space after subtracting t1 from Hτ and is expressed as follows:

E1 = Hτ - t1t1T Hτ ( t1T t1 ) .

(11)

The principal part of the algorithm is illustrated above. Nonlinear iterative PLS is an iterative algorithm with low computational effort. This algorithm may be repeated for k steps, and k is the number of latent variables. A complete layout of NIPALS is listed below:


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1: E0 = Hτ , F0 = y1 , p = [], t = [], u = [], u0 = y1 , v = [], q = [] ; 2: for i = 1 to k do 3: pi = EiT−1ui −1 (uiT−1ui −1 )

pi = pi || pi ||;

4: ti = Ei −1 pi ; 5: bi = FiT−1ti ( tiT ti )

bi = bi || bi ||;

6: ui = Fi −1bi ; 7: vi = uiT ti (tiT ti ); 8: qi = FiT−1ui (uiT ui ); 9: Ei = Ei −1 − ti tiT Ei −1 (tiT ti )

Fi = Fi −1 − vi ti qiT ;

10: p = [ p, pi ], t = [t , ti ], u = [u, ui ], v = [v , vi ], q = [q, qi ]; 11: end for

3 Visual fault diagnosis and monitoring method This section discusses the principal framework of DPLS–MSOM. The main structure can be separated into an offline model and an online implementation. Fig. 2 depicts a general layout of the discussed method. A key point of the visual fault diagnosis and monitoring is the seeking of direction, under which the interested categories are apparently divided into independent groups. Nevertheless, this task can be difficult for nonlinear and random faults. These faults commonly


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result from one or two variable deviations with low magnitudes. The source variable of the fault could cause such minor changes to the other variables and increase noise. The process variables could vibrate back and forth to a certain fixed expectation under the effect of the controller and become increasingly similar to the normal variables. Compared with step change faults, none of the process variables shift dramatically after the faults occurred in the plant. In view of pattern recognition, those fault data points are deeply overlapped in the original space. This scenario can be difficult for the traditional statistical methods. Although direct data classification could be infeasible, analyzing the transitional process from normal to anomalous could be reasonable27,28. Original data points of the fault are substituted by the corresponding dynamic features. Dynamic PLS is utilized for feature extraction. The mean and standard deviation of the normal data are determined to normalize the fault data, and this determination is involved in the pretreatment procedure to render the fault data profoundly distinctive in the original space. These data are then integrated into the NIPALS training algorithm. The latent components ( t i ) are regarded as features, and the relevant directions ( pi ) are saved. t i is not calculated along the decreasing sequence of the variance in the NIPALS algorithm, and pi , qi , and bi are reused to determine the new t i along the descending sort of vi . t i is subsequently sent to the SOM with visualization and clustering. In the SOM, each data point is calibrated by a BMU, and each BMU on the map is labeled with most mapping data points. Therefore, the BMU label can be considered a standard to judge the identification of an unknown observation. This standard is employed to compute the classification accuracy of the map. A harmonic mean metric that comprises the fault diagnosis and misclassification rates, known as F-score29, is selected to completely assess the behavior of DPLS–MSOM, and the formula is set as follows:


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Fβ = (1 + β 2 )

recall × precision ( β × recall ) + precision , 2

recall =

TP TP + FN ,

precision =

TP TP + FP ,

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(12)

(13)

(14)

where TP is the number of true positive points, FP is the number of false positive points and FN is the number of false negative points. In this study, precision is as important as recall; thus, β = 1.

If the total accuracy is very low, then the map classification is significantly inferior. However, not all the F-scores of each category are equal. To Map1, if the F-score of fault1 is over the threshold, then fault1 is well classified. If the F-score of fault2 is below the threshold, then fault2 is placed in the unclassified group. After all the unclassified faults are determined, they are retrained with DPLS in the second SOM map2. The same instructions are conducted on Map3. A multi-SOM classifier is developed for visual fault diagnosis and monitoring. The corresponding parameters of DPLS and SOM are recorded on a computer and applied to the observed points during online implementation. A specific application of the offline and online operations is illustrated afterward. 3.1 Offline model 3.1.1 Step 1: Historical data collection and pretreatment Data collection involves taking the entire producing data from the historical database. No manual mistakes should occur during the data sampling procedure. The a×n historical data matrix ( H with c−1 types of fault data H1, H2 ,K, Hc-1 and normal data H 0 ) is constructed. The


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corresponding a × 1 matrix L , which represents the ideal label of H is also constructed to evaluate the classification rate. Each column in H represents a variable, and each row represents a data point. During the pretreatment phase, the normal data ( H 0 ) are scaled to a zero mean and unit variance with scaling vectors vmx and vstds . H1, H2 ,K, Hc-1 are also scaled with vmx and vstds . 3.1.2 Step 2: DPLS feature iteration Section 2 elucidates that the output of PLS Y is designed. Various types of normalized and time-lagged fault data ( Hτ ) are determined as the input of PLS. An iteration calculation is served in compliance with the NIPALS algorithm. Some intermediate variables ( pi , qi , and bi ) are derived to arrange the latent components ( t i ) along with the decreasing trend in vi . The lagged time τ can be an important parameter. Nevertheless, k , denoted as the number of t i , must be fully considered. If k is insufficient, then the offline model will have a low generalization capability. Similarly, the offline model will probably be overfitted given the significantly large k . In this degree, simple empirical methods are adopted to capture the optimum k and τ . 3.1.3 Step 3: SOM visualization and clustering Similar to k , the size of the SOM is also a crucial parameter of the model. The settlement of the map size and its ratio are elaborated as follows. A heuristic formula of 5 × a is used to determine the total number of map prototypes. The two largest eigenvalues of H are calculated, and the ratio of the map grid is set to the square root of these eigenvalues. The actual side lengths are then modified to make their product as close to the heuristic map size as possible. A unified distance matrix (U-matrix) and hit diagrams are applied to the bare map grid to produce


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straightforward mapping results. The U-matrix, proposed by Ultsch30 as one of the most widely applied distance matrices on an SOM, is a visual and effective tool for revealing the potential boundaries of various categories. In this phase, the latent components t i and label L are set as the inputs to the SOM. Label L is utilized to determine the label of each BMU on the map grid to serve as a classification of online observations. After the predefined updating steps, a map grid covered with the U-matrix and hit diagrams is presented. The corresponding SOM structure ( sMap ) involving the essential information of the model is saved for online implementation. 3.1.4 Step 4: Fault partition by accuracy and retreatment When the number of categories is significantly large, the final mapping result will be inaccurate. Some fault types will co-mingle, thereby leading to a low classification rate. Nonetheless, such fault categories would be easy for categorization when selected out of the previous map and treated on the second-layer SOM. Consequentially, the partition approach described in Section 2 is deemed as a criterion for this multilayer SOM. If the F-score of a certain fault Fi is over the threshold, then such a fault can be regarded as well classified. In contrast, a fault with a low Fi is regarded as insufficient and needs to be further retreated with DPLS in the second-layer SOM. Subsequently, the full power of DPLS–SOM is discovered. The multiple layers of the SOM structure are saved for evaluating the online observations. 3.2 Online implementation 3.2.1 Step 1: Online data sampling and normalization


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Online data sampling involves taking every data point Sonline directly from the sensors on site with certain intervals and storing the total data in the computer for accounting. Sonline is scaled by vectors vmx and vstds . 3.2.2 Step 2: Fault diagnosis After the normalization phase, Sonline is projected under the direction of pi for feature extraction. Sonline is then sent to the multi-SOM structure sMap ( s ) to generate the map grid. These parameters will be mapped to the same area as the historical data H , thereby forming different groups of clustering. In other words, various faults will apparently be distinguished. Different states of data have their own mapping areas on the map grid. When an online observation is captured by sensors, it is sent to the computer. Engineers can decide the current state of the process according to its mapping region on the map grid, which has already been calibrated during the offline model phase. With the guidance of current type of fault by DPLSSOM, corresponding actions would be taken by engineers based on the fault description database. This visualization is useful in realizing the real condition of the operating process. However, there may be some problems when implemented during a real industrial process. The DPLS-SOM is based on two procedures: an offline model and an online implementation. The offline model has to be constructed on the availability of the historical fault database and it cannot manage the case of unknown faults that are not included in the training set, which is quite common in real processes. In the case of an unknown fault, the diagnosis result of the DPLSSOM can be misleading.


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Online implementation

Offline model

S online

Normal data normalization Normal samples

START

Applied Preprocess & Feature

Normalization

Fault Data Preparation (selection)

Map1 clustering

Mean;Stds

Pre-treatment

F-s< threshold

Lagged inputs

N

No

ite>T

NIPALS

Dire:p

Visual fault diagnosis

Multi SOM Database Map2 clustering

t,p,q,b,v

…

Projection

Visual fault monitoring

Y

Processed Data

Yes

Yes

SOM train Mapn clustering

F-s< threshold N

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Map1

Map2

…

Mapn

END

Fig. 2. DPLS–MSOM structure

4 Experimental results and analysis 4.1 TE process All the relevant information concerning the TE process is included in the supporting information.


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4.2 Small-category fault case study 4.2.1 Case study on norm and faults 8, 10 Faults 1–7 are largely caused by step changes in several process variables, and the focus is on the nonlinear and random faults. Faults 8, 10 that resulted from random variations, which are difficult with traditional methods, are collected to testify the capability of the DPLS–MSOM. During the offline model, 480 points of the norm and faults 8, 10 are selected as H , and H belongs to 1440 × 52 . The 480 normal data ( H 0 ) are normalized to a zero means and unit variance with vectors vmx and vstds . The same operation is applied to H . The lagged time τ is set to 10, and the number of latent variables ( k ) is set to 4. After feature extraction by DPLS, the latent components ( t i ) are transported to the SOM. For the three-fault case study, the number of map units is fixed to1.25 × a and only a single layer of the SOM is utilized. Fig. 3 is the offline development result of H . Three data types are divided into individual groups. The left half of Fig. 3(a) is the U-matrix with hit diagrams, and the right part is the label of each prototype on the map. The fdr in the title of Fig. 3(a) represents the total classification accuracy of H . The horizontal axis of Fig. 3(b) serves as the points in each category, and the vertical axis is the fault label. The black dashed line in Fig. 3(b) symbolizes the ideal status of each point, and the red marker symbol is the judgment label of each point. Once sMap is adequately trained, this map can be utilized for online observations. When a fault has occurred in TE, Sonline is captured during the TE simulation in sequence with 3-min intervals. The previous section discussed that observations after the occurrence of a fault are considered the most representative observations. Consequently, only 200 samples shortly


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after the occurrence of the fault are captured, and the later samples are unnecessary because of two aspects. On one hand, the gradual impact of controllers, such a part of the samples, would be difficult to diagnose. On the other hand, the early part of the samples would be sufficient for engineers to discover the fault type and take immediate repairs. Sonline is turned to t i′ under the direction of pi and arranged in the descending sort of vi . t i′ is then mapped onto the wellestablished offline model ( sMap ). The specific type of each Sonline is determined according to the BMUs of sMap . Fig. 4 exhibits the online implementation result. Norm and faults 8, 10 are separated into different regions of sMap , and the F-scores of norm and faults 8, 10 are over 90%. Therefore, the employed approach is useful for nonlinear and random faults.

Fig. 3(a). Map grid of the offline result


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Fig. 3(b). F-score of the offline result

Fig. 4(a). Map grid of the online result


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Fig. 4(b). F-score of the online result 4.2.2 Case study on the norm and faults 11, 12 In this simulation, 480 points of the norm and faults 11, 12 are selected to construct the offline model. The same procedure is conducted as previously discussed (Section 3). The lagged time τ is set to 10, and the number of latent variables ( k ) is set to 3. The number of map units is fixed to 1.25 × a . Only 200 samples are captured during the online implementation. Figs. 5 and 6 are the offline development and online implementation results, respectively. Similarly, the final visual mapping is clearly divided into three blocks, and the classification accuracy of each fault is rather satisfactory.


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Fig. 6(b). F-score of the online result 4.2.3 Case study on the norm and faults 13, 14, 17 For this scenario, 480 points of the norm and faults 13, 14, 17 are selected to train the offline model. The lagged time τ is set to 20, and the number of latent variables ( k ) is set to 5. The number of map units is fixed to 1.25 × a . Eight-hundred observations are collected during the


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online implementation. The offline development and online implementation results are displayed in Figs. 7 and 8, respectively. To demonstrate the superiority of DPLS-SOM, the case of the norm and faults 13, 14, 17 is also studied with other conventional methods. Fig. 9 is the result studied by basic SOM [3] and Fig. 10 is the result by FDA-SOM [6]. It can be inferred that DPLS-SOM is far better than the conventional methods when dealing with non-step change faults during a TE process. Here, the SOM can be interpreted as a type of classifier. Thus, the comparison between conventional classification methods such as support vector machines (SVM) and back-propagation (BP) neural network is also studied with the case of 4.2.3. Figs. 11 and 12 are the respective results. The results also indicate that the classification accuracy by DPLS-SOM is much higher than those of SVM and BP neural network.



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Fig. 8(b). F-score of the online result

Fig. 9(a). Map grid of the online result (basic SOM)


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Fig. 9(b). F-score of the online result (the basic SOM)

Fig. 10(a). Map grid of the online result (FDA-SOM)


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Fig. 10(b). F-score of the online result (FDA-SOM)

Fig. 11. F-score of the online result (Bp neural network)


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Fig. 12. F-score of the online result (SVM classifier) 4.3 Large-category fault case study 4.3.1 Case study on norm and faults 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 17, 18, 20 A large-class experiment is conducted on faults 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 17, 18, 20, including norm data (a total of 15 data types), which are caused by various reasons, to illustrate the effectiveness of the proposed opinion. As argued in Section 3, the key characteristic of the proposed opinion is that emphasis should be placed on the analysis of how a fault varies from the normal state to the abnormal state. H is composed of 480 points of the norm and 14 types of the fault data. The number of latent

variables ( k ) is set to 30, and the lagged time is 10. The number of map units is fixed to

20 × a , and only 100 samples are captured online. The offline development and online implementation results are displayed in Figs. 13 and 14, respectively. The F-scores of faults 1, 2, 4, 5, 6, 7, and 14 are good, and the threshold is set as 85%. Accordingly, they are well classified during the first layer of the SOM, and the remaining data are retrained with DPLS and performed


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on the second layer of the SOM in Figs. 15 and 16. The relevant parameters are set as follows: the lagged time is 20; the latent variables are 49; the map units are 5 × a ; and 200 samples are captured online. The F-scores of the faults 10, 12, and 18 are lower than the threshold. These data are selected and performed on the third layer of the SOM in Figs. 17 and 18. The lagged time is 16, the latent variables are 45, the map units are 5 × a , and 200 samples are captured online. When the three-layer SOM is implemented online, the captured observations must meet a quantity of 10. Subsequent observations integrated with the previous ones are performed with DPLS and mapped onto the first layer of the SOM. If their F-scores are over 85%, then they are well classified. Step-change faults can be classified during the first layer because of the high Fscore. The remaining non-step change faults are projected with DPLS in a lagged time of 20 and mapped onto the second layer of the SOM for further classification. Only when the norm and faults 10, 12, 18 are lower than 85% will they be selected and retrained with the third-layer of the SOM with a lagged time of 16. Once the type of captured observation is determined by the DPLS-SOM, corresponding actions will be taken to ensure the safety of the system. Here, to create a comparison with other traditional methods, the online implementation results by SOM, FDA-SOM, BP neural network SVM ICA-SOM and PCA-SOM are collected together. Table 1 is the final contrast analysis result. Table 1 –F-score comparison of DPLS-SOM, SOM, FDA-SOM, and other methods Type

DPLSMSOM

SOM

FDASOM

BP neural network

SVM

ICA-SOM

PCA-SOM

Normal

0.836

0.157

0.139

0.653

0.300

0.369

0.171

Fault 1

0.878

0.869

0.704

0.979

0.965

0.926

0.849

Fault 2

0.853

0.983

0.804

0.923

0.956

0.808

0.968

Fault 4

0.923

0.123

/

0.830

0.576

0.438

0.141


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Fault 5

0.9

0.066

0.362

0.971

0.695

0.875

0.025

Fault 6

1

0.968

0.997

0.344

0.301

0.828

0.985

Fault 7

0.912

0.027

0.998

1

0.521

0.856

0.071

Fault 8 Fault 10 Fault 11 Fault 12 Fault 14 Fault 17 Fault 18 Fault 20 Averag e

0.864

0.321

0.599

0.682

0.404

0.254

0.323

0.807

0.146

0.137

0.828

0.287

0.704

0.126

0.918

0.124

0.189

0.620

0.273

0.190

0.134

0.875

0.301

0.338

0.798

0.626

0.441

0.296

0.977

0.180

/

0.954

0.813

0.566

0.186

0.966

0.475

0.171

0.908

0.690

0.653

0.493

0.880

0.785

0.453

0.785

0.122

0.724

0.804

0.844

0.168

0.220

0.820

0.480

0.737

0.105

0.895

0.379

0.470

0.806

0.534

0.625

0.378


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Fig. 13(a). Map grid of the offline result (first layer)

Fig. 13(b). F-score of the offline result (first layer)

Fig. 14(a). Map grid of the online result (first layer)


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Fig. 14(b). F-score of the online result (first layer)

Fig. 15(a). Map grid of the offline result (second layer)


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Fig. 15(b). F-score of the offline result (second layer)

Fig. 16(a). Map grid of the online result (second layer)


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Fig. 16(b). F-score of the online result (second layer)

Fig. 17(a). Map grid of the offline result (third layer)


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Fig. 17(b). F-score of the offline result (third layer)

Fig. 18(a). Map grid of the online result (third layer)


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Fig. 18(b). F-score of the online result (third layer)

5 Conclusions Two important perspectives are proposed in this study. First, not all data points from the beginning of the fault state to the end of the process are useful for fault diagnosis. The process variables become indistinctive and unfavorable for diagnostics with a significant impact of plant controllers. During a realistic industrial operation, engineers generally take direct measures when the fault type is determined. Therefore, the start points of a fault are sufficient for diagnosing the fault type. Second, instead of the traditional kernel tools in classifications, interest should be placed on the analysis of how a fault varies from a normal state to an abnormal state. The successful application of DPLS–MSOM on nonlinear and random faults indicates that leading with these two perspectives, even the traditional statistic approaches such as PLS, can handle the faults that can barely be solved previously. However, this finding is only a basic realization of


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proposed opinions, and considerable work has to be conducted regarding further research in abstract and intrinsic dynamic analyses.

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KPCA and Bayesian network. Ind. Eng. Chem. Res. 2017, 56, 2054-2070. (18) Huang, J.; Yan, X. Quality relevant and independent two block monitoring based on mutual information and KPCA. IEEE Trans. Ind. Electron. 2017. (19) Jiao, J.; Zhao, N.; Wang, G.; Yin, S. A nonlinear quality-related fault detection approach based on modified kernel partial least squares. ISA Trans. 2017, 66, 275-83. (20) Huang, C.; Wang C. A GA-based feature selection and parameters optimization for support vector machines. Expert Syst. Appl. 2006, 31, 231-240. (21) D’Angelo, M. F.; Palhares R. M.; Takahashi R. H. C.; et al. Incipient fault detection in induction machine stator-winding using a fuzzy-Bayesian change point detection approach. Appl. Soft. Comput. 2011, 11, 179-192. (22) D'Angelo, M. F.; Palhares R. M.; Takahashi R. H. C.; et al. Fuzzy/Bayesian change point detection approach to incipient fault detection. IET Contr. Theory Appl. 2011, 5, 539-551. (23) Barker, M.; Rayens, W. Partial least squares for discrimination. J. Chemometr. 2003, 17, 166-173. (24) Qu, H. N.; Li, G. Z.; Xu, W. S. An asymmetric classifier based on partial least squares. Pattern Recognit. 2010, 43, 3448-3457. (25) Zeng, X. Q.; Li, G. Z.; Wu, G. F.; et al. Irrelevant gene elimination for partial least squares based dimension reduction by using feature probes. Int. J. Data Min. Bioinform. 2009, 3, 85-103. (26) Kohonen, T. The self-organizing map. Neurocomputing 1998, 21, 1-6. (27) D’Angelo, M. F.; Palhares, R. M.; Camargos, Filho, M. C.; et al. A new fault classification approach applied to Tennessee Eastman benchmark process. Appl. Soft. Comput. 2016, 49, 676-686. (28) de Bessa, I. V.; Palhares, R. M.; D'Angelo, M. F.; et al. Data-driven fault detection and isolation scheme for a wind turbine benchmark. Renew. Energy 2016, 87, 634-645. (29) Powers, D. M. Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation 2011. (30) De, Backer, S.; Naud, A.; Scheunders, P. Non-linear dimensionality reduction techniques for unsupervised feature extraction. Pattern Recognit. Lett. 1998, 19, 711-720..


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TOC graphic

Offline Development

Online Implementation

Data Collection

Online observation

Normalization

Well-established map

DPLS feature extraction 1.SOM grid map 2.Classification result


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DPLS-MSOM Modeling for Visual Industrial Fault Diagnosis and

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