Graph Neural Networks with Trainable Adjacency Matrices for Fault Diagnosis on Multivariate Sensor Data

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Graph Neural Networks with Trainable Adjacency

Matrices for Fault Diagnosis on Multivariate Sensor

Data

Alexander Kovalenkoa, Vitaliy Pozdnyakovb,a, Ilya Makarovb,c

aHSE University, Moscow, Russia

bAIRI, Moscow, Russia

cNITU MISIS, Moscow, Russia

Abstract

Timely detected anomalies in the chemical technological processes, as well

as the earliest detection of the cause of the fault, signiﬁcantly reduce the

production cost in the industrial factories. Data on the state of the tech-

nological process and the operation of production equipment are received

by a large number of diﬀerent sensors. To better predict the behavior of

the process and equipment, it is necessary not only to consider the behavior

of the signals in each sensor separately, but also to take into account their

correlation and hidden relationships with each other. Graph-based data rep-

resentation helps with this. The graph nodes can be represented as data

from the diﬀerent sensors, and the edges can display the inﬂuence of these

data on each other. In this work, the possibility of applying graph neural

networks to the problem of fault diagnosis in a chemical process is studied.

It was proposed to construct a graph during the training of graph neural

network. This allows to train models on data where the dependencies be-

tween the sensors are not known in advance. In this work, several methods

for obtaining adjacency matrices were considered, as well as their quality was

studied. It has also been proposed to use multiple adjacency matrices in one

model. We showed state-of-the-art performance on the fault diagnosis task

with the Tennessee Eastman Process dataset. The proposed graph neural

networks outperformed the results of recurrent neural networks.

Keywords: Tennessee Eastman Process, Chemical Processes, Graph neural

networks, Fault diagnosis, Sensor data

arXiv:2210.11164v1 [cs.AI] 20 Oct 2022

1. Introduction

During the production, equipment often stops due to the various faults.

The process of ﬁnding the root case of the fault can take signiﬁcant amount

of time. The deviations of equipment parameters can lead to a defective

product. It is also mean the lost of time and lost of raw materials. All this

leads to ﬁnancial losses for companies. To reduce the cost of production, the

equipment must be in good condition and the deviations of the parameters

must be corrected as soon as possible. Sometimes the causes of faults are

completely non-obvious and have hidden dependencies. It creates additional

diagnostic diﬃculties even for highly qualiﬁed experts. For decades, scientists

and specialists have been developing methods to detect faulty equipment

conditions and determine the types of the faults. In the literature, such

problems are usually called fault detection and diagnosis (FDD).

The latest scientiﬁc discoveries and developments in the ﬁelds of elec-

tronics and computer science provide us with new opportunities in various

areas of our life, including industry. New types of automation sensors have

been available and computing capacity has increased. It is enabling the ap-

plication of machine learning models in practice. The concept of Industry

4.0 focuses on interconnectivity, automation, machine learning, and real-time

data in manufacturing [1]. Modern and modernized production equipment

consists of hundreds of sensors, data from which can be used to increase the

quality and productivity of production lines.

The multivariate sensor data gives information about the status of var-

ious equipment components aﬀecting the production process. These data

are usually presented in the form of time series. Modern machine learning

approaches and classical statistical FDD methods work only with numerical

values of time series and do not take into account the information about

possible correlations between them. Production equipment consists of many

devices that work together and deviations in the operation of one of them

can aﬀect the operation of the others. All these changes are also displayed

in the signals from the sensors of these devices. The received signals can

have hidden dependencies and can correlate with each other. To indicate

this correlation, such data can be represented as a graph. As nodes of the

graph, there can be values of time series from the sensors, and as edges, their

inﬂuence on each other.

The main goal of this work was to investigate the possibility of applying

graph neural networks (GNN) to industrial equipment data. These types

of neural networks show good results when working with graph-structured

data. The relationship between the nodes of the graph are usually described

by adjacency matrices. These data are very important but not always known

and can be of diﬀerent quality. Over the past year, very few papers have

been published on the use of GNN in fault diagnosis problems [2, 3]. In these

papers, the adjacency matrices are known in advance or obtained by various

methods before the start of the GNN training process. In this work, options

to obtain an adjacency matrix during the training process were proposed.

The adjacency matrix can be created in various ways by using trainable

parameters.

One adjacency matrix can not always describe all possible relationships

between sensors. Production equipment can have complex dynamic depen-

dencies between its devices. Diﬀerent modes of operation can be described

by diﬀerent adjacency matrices. A novel idea was proposed to learn in par-

allel and use several adjacency matrices during the training and evaluation

processes.

All GNN models were trained on the popular FDD benchmark to de-

termine the type of fault. The results were compared with baselines such

as multilayer perceptron (MLP), 1d convolutional neural network (1DCNN)

and Gated Recurrent Units (GRU).

There are three core contributions of this work:

•For the FDD problem, the architecture of the GNN model with various

ways to obtain a weighted adjacency matrix was investigated. It was

also proposed to train and use an adjacency matrix having both positive

and negative weights.

•The quality of the adjacency matrices obtained during model training

was studied.

•A novel idea of using multiple adjacency matrices was proposed and

explored.

The structure of this work is organized as follows. In Related Works,

FDD methods and GNN-based models are brieﬂy described. The architec-

ture of the GNN model with trainable adjacency matrix is proposed in the

Model Description section. Dataset Description contains information about

the benchmark used. The Experiment section consists of three parts that

describe the contributions listed above. In Conclusion, the results of this

work are summarized.

2. Related Works

Fault detection and diagnosis (FDD) methods provide great beneﬁts in

reducing production costs and improving quality and productivity. The data

structures used by these methods can be represented as graph structures. In

the same time, great development of graph neural networks in recent years

may allow them to be used as approaches for fault detection and diagnosis

problems. Recent papers in the ﬁelds of FDD and GNN are reviewed below.

2.1. Fault Detection and Diagnosis

Fault detection is the process of identifying that an equipment or process

is not in a normal state, and fault diagnosis is the process of determining

the root cause of the fault (Fig. 1). Many diﬀerent FDD techniques and ap-

proaches have been developed over the past decades [4]. These methods can

be classiﬁed into data-driven [5, 6, 7], model-based [8, 9, 10] and knowledge-

based groups [11, 12, 13]. The latter two require expert knowledge and

understanding of the technological process, which does not allow to create

unique FDD tools applicable to various industries. At the same time, data-

driven approaches depend on the analytical models used and on the quality of

historical data and could be scaled to diﬀerent production/processing equip-

ment.

Figure 1: Fault diagnosis task can directly classify the fault or ﬁrst detect abnormal state

as a subtask.

Many statistical and machine learning methods have been proposed for

data-driven FDD. Dimensional reduction methods, such as principal compo-

nent analysis (PCA), t-SNE, canonical variate analysis (CVA), partial least

squares (PLS), represent high-dimensional sensor data in low-dimensional

feature space making FDD tractable in cases of a large number of sensors

[14, 15, 16]. Hotelling’s T2, squared prediction error (SPE), Kullback-Leibler

divergence, and other statistics are calculated in feature space in order to de-

tect faults in a process. Cheng Ji and Wei Sun reviewed statistical methods

of root cause diagnosis [17], that are divided into three groups: contribution

plot-based methods [18], probability reasoning-based methods [19] and causal

reasoning-based methods [20]. Clustering methods, e.g. K-means and DB-

SCAN, are used as unsupervised FDD to separate sensor data into distinct

groups, each of them represents some state of a process [21]. Such clusters

can be manually labeled by experts for conﬁguring a process monitoring sys-

tem based on a clustering algorithm. On the other hand, supervised FDD

methods, such as random forest [22], support vector machine (SVM) [23],

k-nearest neighbors (k-NN) [24], are trained to detect faults using labeled

sensor data. Usually supervised methods are more accurate than unsuper-

vised methods, but require manual labeling of each data point, which can be

diﬃcult and expensive in real industrial cases [25].

The great advances in deep learning over the past decade have aﬀected

many areas, including the ﬁeld of fault detection and diagnosis. Convolu-

tional neural networks (CNN) have become widely used in FDD tasks [26, 27].

Ildar Lomov et al. [28] investigated the application of various architectures of

recurrent and convolutional neural networks for fault diagnosis in a chemical

process. Deep learning approaches show high eﬃciency but require a large

amount of training data.

2.2. Graph Neural Networks

Multivariate sensor data can be represented in the form of graph, where

the nodes are sensors. Two nodes are connected by the edge if the data from

these two sensors are depending on each other. The most commonly used

mathematical notation of the graph is G= (V, E), where Vis a set of nodes

and Eis a set of edges. The number of nodes is denoted by N=|V|. The

neighborhood of a node υ∈Vis deﬁned as N={u∈V|(υ, u)∈E}, where

(υ, u) is denoted as an edge between υand u. The structure of a graph can be

represented by adjacency matrix A∈RN×Nwith Aij =c > 0 if (υi, uj)∈E

and Aij = 0 if (υi, uj)/∈E(Fig. 2).

For a long time, signed directed graphs (SDG) have been widely used

for failure path analysis, however, they require expert knowledge of equip-

ment and processes [29]. On the other hand, data-driven methods are based

on only historical data. An example is representing relationships between

sensors by clustering sensors into the groups and ﬁnding the correlation be-

tween them [30]. Another way to represent relationships between sensors is

an adjacency matrix. Graph neural networks model the dependencies be-

tween nodes on historical data using predeﬁned adjacency matrix. The ﬁrst

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GraphNeuralNetworkswithTrainableAdjacencyMatricesforFaultDiagnosisonMultivariateSensorDataAlexanderKovalenkoa,VitaliyPozdnyakovb,a,IlyaMakarovb,caHSEUniversity,Moscow,RussiabAIRI,Moscow,RussiacNITUMISIS,Moscow,RussiaAbstractTimelydetectedanomaliesinthechemicaltechnologicalprocesses,aswellastheearlie...

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Graph Neural Networks with Trainable Adjacency Matrices for Fault Diagnosis on Multivariate Sensor Data

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