1. Introduction
Data acquisition systems play a vital role in the data collection of industry [
1]. Among them, the board tunnel, which is usually classified as analog input (AI), analog output (AO), digital input (DI), and digital output (DO) modules, is a bridge between the processor and sensors, which ensures the data conversion at the physical level [
2]. The tunnel board is made up of enclosed circuit boards that are convenient to be replaced immediately once they are found to have any faults occur due to security reasons. In order to detect the inertial faults of these circuit boards in time, most famous products, such as Siemens, Honeywell, etc., have provided error codes to help operators [
3,
4,
5]. However, these codes are limited to meeting the requirements of board channel diagnosis in a practical complex application.
Different kinds of methods for fault detection and diagnosis (FDD) have been developed, which are classified as model-based approaches, signal-based approaches, and data-driven approaches [
6,
7]. In model-based approaches, the fault diagnosis algorithms are developed to monitor the consistency between the measured outputs of the practical systems and the model-predicted outputs, which are based on an appropriate model, whether a physical model or equivalent model. Reference [
8] proposed a new method by combining the model-based FDD method and the support vector machine (SVM) method. In reference [
9], the spindle modes are determined through a three-step procedure in order to overcome these issues of the low number of sensors and the presence of many harmonics in the measured signals and to extract the characteristics of the system. In reference [
10], based on the information of fault-free data series, fault detection was promptly implemented by comparison with the model forecast and real-time process. Signal-based approaches include time-domain analysis, frequency-domain analysis, and both together. Reference [
11] proposed a novel “frequency-domain damping design” using a high-pass filter for acceleration-based bilateral control (ABC) based on modal space analysis. In reference [
12], a unified measurement model was utilized to simultaneously characterize both the phenomena of multiple communication delays and data missing, and a novel residual matching (RM) approach was developed to isolate and estimate the fault once it is detected. Reference [
13] proposed a least squares support vector machine (LS-SVM) model optimized by cross validation to implement FDD on a 90-ton centrifugal chiller. Reference [
14] investigated the achievable rates of frequency-division-duplex massive MIMO systems with spatially correlated channels. In fact, it is difficult for the board tunnel to build an appropriate model since different boards have different circuit structures. It is also a challenge to obtain the features of integer signals, especially for the fault cases, because the flawed board tunnel will be quickly replaced for safety reasons.
Board tunnels always work on a standard enclosed module, which prevents the circuit from being affected by external factors. This enclosed module is also suitable for quick disassembly or replacement. However, as a double-edged sword, this method introduces issues for fault detection and diagnosis because it loses the ability to directly observe internal states. The data-driven approach [
15,
16,
17,
18,
19,
20] provides a feasible way to solve this problem by external observation data. Reference [
15] aimed to provide a state-of-the-art overview on the existing fault diagnosis, prognosis, and resilient control methods and techniques for wind turbine systems, with which great success has been achieved in fault detection and diagnosis. Reference [
16] focused on data-driven techniques in the digital era and data analytics in all areas, including process industries. Reference [
17] proposed a new data-driven FDD method, which was named probability-relevant PCA (PRPCA), for electrical drives in high-speed trains. In reference [
18], a fault diagnosis method based on a deep convolutional neural network model consisting of convolutional layers, pooling layers, dropout, and fully connected layers was proposed for chemical process fault diagnosis. In reference [
19], an extended deep belief network (EDBN) was proposed to fully exploit useful information in the raw data. Reference [
20] presented a Special Issue on “data-driven approaches for complex industrial systems”. Using a data-driven approach to the board tunnel detection, two obstacles should be overcome: (1) A healthy board shows certain differences in response to the process conditions, working environment, and internal parameters. This dispersivity is difficult to be covered by limited sample data. (2) Generally, the stability of a data acquisition system is generally high, and there are few failures; even if a failure occurs, it will be replaced quickly in order to achieve safety. Therefore, there are almost no historical faulty data.
From the view of board performance, the healthy data will obey the law of health probability distribution, though the healthy data are dispersive in different working environments. Some excellent methods based on probability analysis, such as the conditional probability distributions, Bayesian network, etc., have been reported in chemical processes [
20,
21,
22,
23]. Motivated by the probability idea based on the concept that the acquired data signal is regarded as a realization of the distribution of the board, a probabilistic neural network (PNN) is proposed based on critical faulty data being artificially constructed to distinguish between healthy states and faulty states. Firstly, multiple data sources are applied to activate conditions on the board tunnel, and the internal register values are obtained by OPC technology. Then, the error time series are constructed to analyze the healthy state of the enclosed board channel. The critical faulty data are constructed based on the healthy data by using a null matrix with maximum projection. Finally, the healthy state of the enclosed board channel is judged by a probabilistic neural network. The advantages of the proposed approach are summarized as follows:
- (1)
Multiple input signals are proposed to activate the working state of the board tunnel, which extends the scope of exploration for the dispersivity of a healthy board concerning the working environment and internal parameters.
- (2)
The critical faulty data are successfully constructed by using the null matrix based on the health data, which overcomes the difficulty of lacking faulty data.
- (3)
The PNN is used to adapt to the law of probability hidden in the time series, and case studies verify the effectiveness.
The remainder of this article is organized as follows. In
Section 2, the acquisition of error time series and the relationship between multiple input signals and overall performance of the board tunnel are given.
Section 3 describes the proposed approach, including the probability neural network, the construction of critical faulty data, the structure, and the workflow. The case studies are illustrated in
Section 4, followed by conclusions in
Section 5.
2. The Error Time Series of Board Tunnel
The error between input signal and output (memory) mainly affected by internal factors of the board is regarded as a comprehensive index reflecting the performance of the board tunnel. A single sample is meaningless for evaluating the board performance because it is an instance and not enough to observe the law of probability. Thus, an error time series is taken as an analysis object of the enclosed board tunnel, and the error time series is obtained, as shown in
Figure 1.
Let the input signal of the board tunnel be
and the value of the corresponding memory be
; thus, the error time series is
where is the sampling time. Formula (1) is abbreviated as Formula (2) by using
x, y, z instead of
,
,
.
Notice that is the converted data of input signal
x according to the physical meaning of the board channel, and
z is regarded as a probability model of noisy influences that follows a normal distribution with a form of Formula (3):
where
and
are an expectation and a variance for the board, respectively.
It is worth noting that if the board input is enough to cover all the work conditions and influences of the environment, the expectation is equal to the mean, which ideally satisfies . Thus, thereafter, we use the mean instead of the expectation.
In fact, different input signals will cause some changes due to the influence of the environment and internal parameters.
Figure 2 releases the error time series of a healthy board channel under three kinds of different input signals.
Each input signal that is long enough will produce its own probability distribution laws with a form of
where
μi and
σi are the mean and the variance under the
i-th input signal. It is inevitable for some deviations to occur between
and
. From the view of fault detection and diagnosis, the board tunnel is considered to be in a healthy state as long as
is within the allowable range. However, these deviations between
and
will disturb the judgment of healthy states due to the limitation of the sampling data number. In order to establish the relation between sampling data and board performance, it is assumed that the mean
is equal to the mean of different input signals, that is,
Lemma 1. The mean μboard and varianceof the sampling data seriessatisfying normal distribution can be replaced bysub-sampling data whose mean isand whose variance is. That is,
Proof. For the data series
that follows normal distribution with a mean
and variance
, suppose the data series z has enough data of
samples to reflect the statistical characteristics of a whole. The unbiased estimate of
is
, and the unbiased estimate of
is obtained according to
□
Consider the relation of the mean between the whole and sub-sampling data. Let the
samples be divided into
groups with the mean and the length of the
k-th group being
and
:
Thus, the mean of a whole is
Formula (10) shows the unbiased estimate of . Therefore, can be estimated by the above formula.
For a variance, it is well known that the sample mean of normal distribution also obeys normal distribution according to the mathematical statistical theory. Thus, the mean
of each group follows
Let ; thus, .
For m groups, an unbiased estimate of
is obtained by
Furthermore, the
of a whole is obtained according to
As a result, the proof is completed.
The lemma shows that the performance of the board can be obtained through the combination of different groups. For a board tunnel, this means the total probability of healthy model can be combined with different input signals.