A Fault Diagnosis Method Based on Bottleneck State Observer and Distribution Optimization

Abstract

The present application relates to a fault diagnosis method based on a bottleneck state observer and distribution optimization, the method comprising: S1: collecting data to be diagnosed of a three-tank system; S2: inputting the data to be diagnosed into a trained bottleneck state observer, predicting output data starting at the current moment, and calculating the residual between the output data starting at the current moment and the actual output data; S3: inputting the residual starting at the current moment into a trained flow model, mapping an approximate normal distribution of the residual; calculating T based on the residual of the approximate normal distribution. 2 Statistics; S4: Based on the T 2 Statistics determine the fault diagnosis results. This method generates residuals based on the bottleneck state observer and uses a flow model to simplify the residual distribution, accurately captures the system dynamics and optimizes the threshold setting, which is conducive to improving the accuracy of industrial fault diagnosis.

Description

Technical Field

[0001] The present application relates to the technical field of industrial fault diagnosis, and in particular to a fault diagnosis method based on bottleneck state observer and distribution optimization. Background Art

[0002] At present, traditional industrial fault diagnosis methods can be divided into model-based and data-driven methods; model-based methods rely on accurate modeling of the system's physical process, but have difficulty handling complex and nonlinear systems. In contrast, data-driven methods do not rely on physical models and can learn and reason through a large amount of historical data, thus becoming the current development trend of industrial fault diagnosis technology; data-driven fault diagnosis methods can be roughly divided into shallow learning and deep learning. Shallow learning methods are often used to deal with simple nonlinear problems. For large-scale complex system modeling and big data analysis, there are defects such as insufficient feature extraction capabilities and low fault detection accuracy. Deep learning methods achieve automatic feature extraction through a multi-layer network structure and can capture complex patterns and relationships from large amounts of data.

[0003] Although deep learning has shown great potential in industrial fault diagnosis, there are certain problems such as insufficient mechanism constraints and low reliability. In addition, the distribution of residual statistics of deep networks is complex, and valuable information is easily lost when statistical compression is performed on them, which causes the threshold to be set too high, resulting in false alarms and missed faults. Summary of the invention

[0004] Based on this, it is necessary to provide a fault diagnosis method based on bottleneck state observer and distribution optimization, which includes:

[0005] S1: Collecting the data to be diagnosed of the three-water tank system, wherein the data to be diagnosed includes the water level of the first water tank, the water level of the second water tank, the water level of the third water tank, the flow rate of the first water inlet, and the flow rate of the second water inlet;

[0006] S2: input the data to be diagnosed into the trained bottleneck state observer, predict the output data starting from the current moment, and calculate the residual between the output data starting from the current moment and the actual output data;

[0007] S3: Input the residual starting from the current moment into the trained flow model to map the approximate normal distribution of the residual; calculate T based on the residual of the approximate normal distribution 2 Statistics;

[0008] S4: Based on the T 2 Statistics determine the fault diagnosis results.

[0009] Preferably, the bottleneck state observer is composed of two fully connected neural networks connected in series, the first fully connected neural network is used to predict the current state data of the system, and the second fully connected neural network is used to predict the output data at the next moment;

[0010] The training process of the bottleneck state observer is:

[0011] Step 1.1: Collect normal data of the three-tank system;

[0012] Step 1.2: The normal data includes n Normal data samples at consecutive moments are sampled by sliding window. q Normal data samples at consecutive moments, q Much smaller than n , and move the front q- The input data and real output data of the normal data samples at one continuous moment are passed through the first fully connected neural network in the bottleneck state observer, and the state data of the system in the current window is output; the state data in the current window and the first q The input data of the normal data sample passes through the second fully connected neural network in the bottleneck state observer to obtain the first q The predicted output data of normal data samples;

[0013] Step 1.3: Calculate the q The second residual between the predicted output data and the true output data of the normal data samples;

[0014] Step 1.4: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second normal data sample to the q+ 1 normal data sample at a continuous moment, and execute steps 1.2 to 1.3;

[0015] Step 1.5: Repeat steps 1.2 to 1.4 until the maximum number of sliding windows is reached, and the first q The second residual between the predicted output data and the true output data of the normal data samples;

[0016] Step 1.6: Take minimizing the second residual as the training objective and perform multiple rounds of training until the maximum set number of times is reached to obtain a trained bottleneck state observer.

[0017] Preferably, minimizing the second residual is expressed as:

[0018] ;

[0019] ;

[0020] in, N Indicates the maximum number of sliding windows; Indicates w The second sliding window q The actual output data of normal data samples; represents the second fully connected neural network; represents the network parameters of the second fully connected neural network; represents the first fully connected neural network; represents the network parameters of the first fully connected neural network; Indicates w Second sliding window middle front q- Input data of normal data samples at 1 continuous moment; Indicates w Second sliding window middle front q- The actual output data of a normal data sample at 1 continuous moment; Indicates w The second sliding window q Input data of normal data samples; n represents the number of normal data samples; Δ q Represents the sliding window step size.

[0021] Preferably, the process of predicting the output data starting at the current moment includes:

[0022] Step 2.1: The data to be diagnosed includes The data samples to be diagnosed at consecutive moments are sampled by sliding window. q The data samples to be diagnosed at consecutive moments, q Much smaller than , will t Before the moment q- The input data and real output data of the data samples to be diagnosed at 1 continuous moment are the first fully connected neural network in the trained bottleneck state observer, and the prediction system t Status data at the moment; the mapping formula is:

[0023] ;

[0024] ;

[0025] ;

[0026] in, Indicates t Before q- Input data of the data sample to be diagnosed at 1 continuous moment; Indicatest Before q- The actual output data of the data sample to be diagnosed at one continuous moment; Indicates the three-tank system t Status data at the moment; Indicates the direction of mapping to the right; Indicates t-q+ Input data of the data sample to be diagnosed at time 1; Indicates t-q+ Input data of the data sample to be diagnosed at time 2; Indicates t- Input data of the data sample to be diagnosed at time 1; Indicates t-q+ The actual output data of the data sample to be diagnosed at time 1; Indicates t-q+ The actual output data of the data sample to be diagnosed at time 2; Indicates t- The actual output data of the data sample to be diagnosed at time 1;

[0027] Step 2.2: t Status data at the moment and t The input data of the data sample to be diagnosed at time t is passed through the second fully connected neural network in the trained bottleneck state observer to predict the system t Output data at the moment; the mapping formula is:

[0028] ;

[0029] in, Indicates t Input data of the data sample to be diagnosed at time; Indicates the three-tank system t The predicted output data at the moment;

[0030] Step 2.3: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second data sample to be diagnosed to the q+ 1 continuous moment of the data sample to be diagnosed, and execute steps 2.1-2.2 to predict the system t+ Output data at time 1;

[0031] Step 2.4: Repeat steps 2.1 to 2.3 until the number of sliding windows reaches Second, get the t The predicted output data of the three-tank system starts at time; The time range representing the future direction is calculated as:

[0032] ;

[0033] in, Indicates the number of samples of data to be diagnosed in the data to be diagnosed.

[0034] Preferably, the residual is calculated as:

[0035] ;

[0036] ;

[0037] ;

[0038] in, Indicates t The residual at the start of time; Indicates t The real output data of the three-tank system starts at every moment; Indicates t The predicted output data of the three-tank system starts at time; Indicates t The actual output data of the three-tank system at each moment; A time horizon indicating future direction; Indicates The actual output data of the three-tank system at each moment; Indicates The actual output data of the three-tank system at each moment; Indicates t Predicted output data of the three-tank system at time instant; Indicates Predicted output data of the three-tank system at time instant; Indicates Predicted output data for the three-tank system at time instant.

[0039] Preferably, the flow model is a nonlinear independent component estimation model, which is formed by stacking multiple additive coupling layers and is used to convert the complex distribution of residuals starting from the current moment into an approximate normal distribution to obtain residuals of an approximate normal distribution.

[0040] Preferably, it also includes:

[0041] In the training process of the nonlinear independent component estimation model, in order to maximize the log-likelihood of the second residual, the nonlinear independent component estimation model is trained by minimizing the second norm in the latent representation after the second residual is transformed by mapping, so that the model learns the mapping rule from the complex distribution to the approximate normal distribution;

[0042] The calculation formula for the log-likelihood of the second residual is:

[0043] ;

[0044] in, The second residual The log-likelihood of ; The second residual The latent representation after the mapping transformation; represents the log probability that the latent variable follows an approximately normal distribution; Represents the mapping rule from complex distribution to approximate normal distribution; Indicated by w The first window in each window starts q The second residual calculated from normal data samples;

[0045] Since the learning goal is that the latent variables follow an approximate normal distribution, the logarithmic probability calculation formula of the latent variables is:

[0046] ;

[0047] in, d Represents the dimensionality of the latent variable.

[0048] Preferably, the T 2 The statistical determination of fault diagnosis results includes:

[0049] When the T 2 Statistics less than or equal to T 2 When the statistic threshold is reached, the nonlinear system is judged to be fault-free;

[0050] When the T 2 Statistics greater than T 2 When the statistic threshold is reached, the nonlinear system is judged to be faulty and an alarm is issued.

[0051] Preferably, T 2 The process of statistical thresholding is:

[0052] Will be w The first window in each window starts q The second residual calculated from the normal data samples is converted into the second residual of approximate normal distribution through the nonlinear independent component estimation model;

[0053] T is calculated based on the dimension of the second residual that follows an approximately normal distribution. 2 The statistical threshold is calculated as follows:

[0054] ;

[0055] in, Indicates the T² statistic threshold; Indicates the false alarm rate Next Distribution critical value; m represents the dimension of the second residual; N Indicates the maximum number of sliding windows.

[0056] Preferably, t The approximate normal distribution of the residual starting at time is expressed as: ;in, Indicates t The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; Indicates The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; represents the time frame of the future direction; T represents transposition;

[0057] Calculate T based on the approximate normal distribution of the residuals 2 Statistics, calculated as:

[0058] ;

[0059] ;

[0060] ;

[0061] in, Indicates T 2 Statistics; represents the mean calculated from the data mapped by the second residual through the nonlinear independent component estimation model; Indicated by w In the window q The second residual calculated from the normal data samples is mapped to the data by the nonlinear independent component estimation model; Indicated by data With the mean The calculated covariance matrix; Indicates t + k- The residuals at time 1 are mapped to the data using a nonlinear independent component estimation model.

[0062] Beneficial effects: This method generates residuals based on the bottleneck state observer and uses the flow model to simplify the residual distribution, accurately captures the system dynamics and optimizes the threshold setting, which is beneficial to improving the accuracy of industrial fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0064] Figure 1 This is a flow chart of a fault diagnosis method based on bottleneck state observer and distribution optimization in an embodiment of the present application.

[0065] Figure 2 This is a schematic diagram of the structure of the three water tank systems in the embodiment of the present application.

[0066] Figure 3 Schematic diagram of training loss during the bottleneck state observer training process of an embodiment of the present application.

[0067] Figure 4 This is a schematic diagram of the residual distribution of the bottleneck state observer after the samples in the embodiment of the present application are trained.

[0068] Figure 5 A schematic diagram of training loss during the flow model training process of an embodiment of the present application.

[0069] Figure 6 This is a schematic diagram of residual distribution optimization according to an embodiment of the present application. DETAILED DESCRIPTION

[0070] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0071] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0072] like Figure 1 As shown, this embodiment provides a fault diagnosis method based on bottleneck state observer and distribution optimization, the method comprising:

[0073] S1: Collect the data to be diagnosed of the three-water tank system, wherein the data to be diagnosed are the water level of the first water tank, the water level of the second water tank, the water level of the third water tank, the flow rate of the first water inlet, and the flow rate of the second water inlet, and the data to be diagnosed include normal data samples and fault data samples.

[0074] In this embodiment, three water tanks are connected in series to form a three-tank system (TTS), which is a typical nonlinear process during operation. Its structure is as follows: Figure 2 shown. Figure 2 In the TTS system, the control variables are the flow rate V1 of the first water inlet and the flow rate V2 of the second water inlet. The flow rates from tank 1 to tank 2 and from tank 3 to tank 2 are V 12 、V 32 , transported through the connecting pipes under the water tanks. The water levels of the three water tanks are measured by sensors, and the water levels of the first water tank, the second water tank, and the third water tank are recorded as H 1. H 2. H 3.

[0075] S2: Input the data to be diagnosed into the trained bottleneck state observer, predict the output data starting from the current moment, and calculate the residual between the output data starting from the current moment and the actual output data.

[0076] The bottleneck state observer is a network structure based on subspace identification and observability theory, combining the functions of a state observer and a predictor. The core idea is to extract key state information from the system's historical input and output data through a state observer, and then predict the system's future output based on the system's state information and future inputs. The model is implemented through a fully connected neural network, has strong modeling capabilities and prediction accuracy, and has broad application prospects in system identification and fault diagnosis tasks.

[0077] In this embodiment, the introduction of the bottleneck state observer can effectively compress high-dimensional features and improve computing efficiency. Based on the observability theory of the model, the state representation of the bottleneck state observer can directly correspond to the state of the physical system, which helps engineers better understand and analyze the causes of system failures.

[0078] Specifically, the bottleneck state observer is composed of two fully connected neural networks connected in series, the first fully connected neural network is used to predict the current state data of the system, and the second fully connected neural network is used to predict the output data at the next moment;

[0079] The training process of the bottleneck state observer is:

[0080] Step 1.1: Collect normal data of the three-tank system;

[0081] The input data in the normal data of the TTS system is represented as: ; The output data is expressed as: ; Each process variable is expressed as: .

[0082] Step 1.2: The normal data includes n Normal data samples at consecutive moments are sampled by sliding window. q Normal data samples at consecutive moments, q Much smaller than n , and move the front q- The input data and real output data of the normal data samples at one continuous moment are passed through the first fully connected neural network in the bottleneck state observer, and the state data of the system in the current window is output; the state data in the current window and the first q The input data of the normal data sample passes through the second fully connected neural network in the bottleneck state observer to obtain the first q The predicted output data of normal data samples;

[0083] Step 1.3: Calculate the q The second residual between the predicted output data and the true output data of the normal data samples;

[0084] Step 1.4: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second normal data sample to the q+ 1 normal data sample at a continuous moment, and execute steps 1.2 to 1.3;

[0085] Step 1.5: Repeat steps 1.2-1.4 until the maximum number of sliding windows is reached, and the first q The second residual between the predicted output data and the true output data of the normal data samples;

[0086] Step 1.6: Take minimizing the second residual as the training goal, perform multiple rounds of training until the maximum set number of times is reached, and obtain the trained bottleneck state observer, whose training loss is as follows Figure 3 As shown, the number of normal data samples for training the bottleneck state observer is n s =16008, the batch size is P =16, the sliding window size is q =4, each sliding window step is Δ q =1.

[0087] Furthermore, minimizing the second residual is expressed as:

[0088] ;

[0089] ;

[0090] in, N Indicates the maximum number of sliding windows; Indicates w The second sliding window q The actual output data of normal data samples; represents the second fully connected neural network; represents the network parameters of the second fully connected neural network; represents the first fully connected neural network; represents the network parameters of the first fully connected neural network; Indicates w Second sliding window middle front q- Input data of normal data samples at 1 continuous moment; Indicates w Second sliding window middle front q- The actual output data of a normal data sample at 1 continuous moment; Indicates w The second sliding window q Input data of normal data samples; n represents the number of normal data samples; Δ q Represents the sliding window step size.

[0091] Furthermore, the process of predicting the output data starting from the current moment includes:

[0092] Step 2.1: The data to be diagnosed includes The data samples to be diagnosed at consecutive moments are sampled by sliding window. q The data samples to be diagnosed at consecutive moments, q Much smaller than , will t Before the moment q- The input data and real output data of the data samples to be diagnosed at 1 continuous moment are the first fully connected neural network in the trained bottleneck state observer, and the prediction system t Status data at the moment; the mapping formula is:

[0093] ;

[0094] ;

[0095] ;

[0096] in, Indicates t Before q- Input data of the data sample to be diagnosed at 1 continuous moment; Indicates t Before q- The actual output data of the data sample to be diagnosed at one continuous moment; Indicates the three-tank system t Status data at the moment; Indicates the direction of mapping to the right; Indicates t-q+ Input data of the data sample to be diagnosed at time 1; Indicates t-q+ Input data of the data sample to be diagnosed at time 2; Indicates t- Input data of the data sample to be diagnosed at time 1; Indicates t-q+ The actual output data of the data sample to be diagnosed at time 1; Indicates t-q+ The actual output data of the data sample to be diagnosed at time 2; Indicates t- The actual output data of the data sample to be diagnosed at time 1;

[0097] Step 2.2: t Status data at the moment and t The input data of the data sample to be diagnosed at time t is passed through the second fully connected neural network in the trained bottleneck state observer to predict the system t Output data at the moment; the mapping formula is:

[0098] ;

[0099] in, Indicates t Input data of the data sample to be diagnosed at time; Indicates the three-tank system t The predicted output data at the moment;

[0100] Step 2.3: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second data sample to be diagnosed to the q+ 1 continuous moment of the data sample to be diagnosed, and execute steps 2.1-2.2 to predict the system t+ Output data at time 1;

[0101] Step 2.4: Repeat steps 2.1 to 2.3 until the number of sliding windows reaches Second, get the t The predicted output data of the three-tank system starts at time; The time range representing the future direction is calculated as:

[0102] ;

[0103] in, Indicates the number of samples of data to be diagnosed in the data to be diagnosed.

[0104] Calculate the residual between the predicted output data at the next moment and the actual output data. The distribution of the residual is as follows: Figure 4 As shown; the residual calculation formula is:

[0105] ;

[0106] ;

[0107] ;

[0108] in, Indicates t The residual at the start of time; Indicates t The real output data of the three-tank system starts at every moment; Indicates t The predicted output data of the three-tank system starts at time; Indicates t The actual output data of the three-tank system at each moment; A time horizon indicating future direction; Indicates The actual output data of the three-tank system at each moment; Indicates The actual output data of the three-tank system at each moment; Indicates t Predicted output data of the three-tank system at time instant; Indicates Predicted output data of the three-tank system at time instant; Indicates Predicted output data for the three-tank system at time instant.

[0109] S3: Input the residual starting from the current moment into the trained flow model to map the approximate normal distribution of the residual; calculate T based on the residual of the approximate normal distribution 2 Statistics.

[0110] Specifically, flow-based models are a type of generative model that can transform complex data distributions into simple data distributions (such as standard normal distribution) through reversible transformations. The key feature of flow models is the reversibility of the generation process and probability calculation, that is, a series of certain transformations can be used to generate simple distribution samples from complex distribution samples, and vice versa; its basic goal is to find a To the latent space The reversible mapping function f , distribute complex data Convert to a simpler distribution that is tractable (such as the standard normal distribution) ,Right now:

[0111] ;

[0112] in, z It is the data in the latent space, corresponding to the data mapped by the nonlinear independent component estimation model, which obeys a simple distribution (such as the standard normal distribution ); x It is the data space The data sample corresponds to the residual starting from the current moment .because f It is reversible, and when generating new data, we only need to sample from the latent space z , and then through the inverse mapping You can generate x According to the rate of change formula, the mapping in the flow model f The probability density function of is:

[0113] ;

[0114] in, is the determinant of the Jacobian matrix in the flow model, which represents the mapping f For volume changes in data space; Represents partial derivative; the training goal of the flow model is to learn the mapping by maximizing the log likelihood in this formula f , the log-likelihood function It is expressed as:

[0115] ;

[0116] in, is the log probability of a near normal distribution, is the logarithm of the Jacobian.

[0117] Furthermore, in order to ensure the mapping fThe Jacobian determinant is reversible and easy to calculate. This embodiment uses a nonlinear independent component estimation model (NICE, one of the flow models) to perform a reversible affine transformation, that is, to convert the complex distribution of the residual into an approximate normal distribution, and obtain an approximate normal distribution of the residual. NICE can calculate the Jacobian determinant at a very low computational cost without losing the generation capability. The nonlinear independent component estimation model is formed by stacking multiple additive coupling layers. For the approximate normal distribution z , each additive coupling layer converts the vector z Split into two complementary parts z 1 and z 2, and only a portion of them ( z 2) transform one part while keeping the other part ( z 1) unchanged, that is:

[0118] x 1= z 1;

[0119] x 2= z 2+ m ( z 1);

[0120] in, m ( z 1) is based on z 1Calculate the additive transformation function; x 1 refers to t The residual of the moment; x 2 refers to the t+ The residual starting at time 1.

[0121] This form of coupling layer is reversible, and its inverse transformation is:

[0122] z 1 =x 1;

[0123] z 2= x 2- m ( z 1).

[0124] The Jacobian determinant in NICE is:

[0125] ;

[0126] Where I represents the identity matrix; since z 1 =x 1 is unchanged, and z2 is transformed only by addition, so the Jacobian in NICE is a unit triangular determinant with a determinant value of 1. In addition, the cross-stacked approach is used to approximate any complex probability distribution, and the expression of the first additive coupling layer is:

[0127] ;

[0128] ;

[0129] The expression of the second additive coupling layer is:

[0130] ;

[0131] ;

[0132] The expression of the third additive coupling layer is:

[0133] ;

[0134] ;

[0135] in, Represents the data space in the first additive coupling layer The first data sample of Represents the first data in the latent space; Represents the data space in the first additive coupling layer The second data sample of Represents the second data in the latent space; m ( z 1) is based on z 1Calculate the additive transformation function; Represents the data space in the second additive coupling layer The first data sample of ; Represents the data space in the second additive coupling layer The second data sample of ; is based on Computed additive transformation function; Represents the data space in the third additive coupling layer The first data sample of ; Represents the data space in the third additive coupling layer The second data sample of ; is based on The additive transformation function to compute.

[0136] By analogy, , according to the inverse transformation and the chain rule, Therefore, even when facing high-dimensional input data, the density function calculation of the transformation can be very efficient, without calculating complex determinants, which simplifies the training process.

[0137] Similarly, NICE is trained by maximizing the log-likelihood of the residual. Its goal is to learn a reversible transformation that can generate the target data distribution. Since the Jacobian determinant of NICE is 1, This item is 0; in the training process of the nonlinear independent component estimation model, in order to maximize the log-likelihood of the second residual, the nonlinear independent component estimation model is trained by minimizing the second norm in the potential representation of the second residual after the mapping transformation, so that it learns the mapping rule from the complex distribution to the approximate normal distribution; the training loss of the nonlinear independent component estimation model is as follows Figure 5 As shown, the approximate normal distribution of the residual after mapping is as follows Figure 6 shown.

[0138] The calculation formula for the log-likelihood of the second residual is:

[0139] ;

[0140] in, The second residual The log-likelihood of ; The second residual The latent representation after the mapping transformation; represents the log probability that the latent variable follows an approximately normal distribution; Represents the mapping rule from complex distribution to approximate normal distribution; Indicated by w The first window in each window starts q The second residual calculated from normal data samples;

[0141] Since the learning goal is that the latent variables follow an approximate normal distribution, the logarithmic probability calculation formula of the latent variables is:

[0142] ;

[0143] in, d Represents the dimensionality of the latent variable.

[0144] S4: Based on the T 2 Statistics determine fault diagnosis results, including:

[0145] When the T 2 Statistics less than or equal to T 2 When the statistic threshold is reached, the nonlinear system is judged to be fault-free;

[0146] When the T 2 Statistics greater than T2 When the statistic threshold is reached, the nonlinear system is judged to be faulty and an alarm is issued.

[0147] The T² statistic, also known as Hotelling's T² Test Statistic, is a statistical test method for multivariate data analysis. It is widely used to detect whether a data set deviates from a normal distribution, and is particularly suitable for fault monitoring and anomaly detection tasks. As the core of the Hotelling's T² test, the T² statistic is mainly used to evaluate whether the observed data deviates significantly from the known multivariate mean. Specifically, the Hotelling's T² statistic can effectively identify outliers in multivariate data, and by measuring the degree of deviation between data points and the mean, it provides a powerful tool for fault detection.

[0148] In this embodiment, T 2 The process of statistical thresholding is:

[0149] The first by the w The first window in each window starts q The second residual calculated from the normal data samples is converted into the second residual of approximate normal distribution through the nonlinear independent component estimation model;

[0150] T is calculated based on the dimension of the second residual that follows an approximately normal distribution. 2 The statistical threshold is calculated as follows:

[0151] ;

[0152] in, Indicates the T² statistic threshold; Indicates the false alarm rate ( is a hyperparameter that can be set according to actual conditions) Distribution critical value; m represents the dimension of the second residual; N Indicates the maximum number of sliding windows.

[0153] Further, t The approximate normal distribution of the residual starting at time is expressed as: ;in, Indicates t The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; Indicates The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; represents the time frame of the future direction; T represents transposition;

[0154] Calculate T based on the approximate normal distribution of the residuals 2Statistics, calculated as:

[0155] ;

[0156] ;

[0157] ;

[0158] in, Indicates T 2 Statistics; represents the mean calculated from the data mapped by the second residual through the nonlinear independent component estimation model; Indicated by w In the window q The second residual calculated from the normal data samples is mapped to the data by the nonlinear independent component estimation model; Indicated by data With the mean The calculated covariance matrix; Indicates t + k- The residuals at time 1 are mapped to the data using a nonlinear independent component estimation model.

[0159] 301×5 normal samples and 1600×5 fault samples (the fault is introduced at the 300th point, and time 0 is the initial state) in the three-tank system are collected and used as the data to be diagnosed (test set) to verify the performance of the model. The description of the fault types in the TTS simulation is shown in Table 1;

[0160] Table 1 is a description table of fault types in TTS simulation;

[0161] ;

[0162] The test results are shown in Table 2;

[0163] Table 2 is the test set fault detection result table;

[0164] ;

[0165] As can be seen from Table 2, this method transforms complex distribution into simple approximate normal distribution by introducing flow model, which improves the problem that the distribution of deep network residual statistics in the existing technology is complex, and valuable information is easily lost when statistical compression is performed on it, which leads to high threshold setting and causes false alarm and omission of faults.

[0166] The fault diagnosis method based on bottleneck state observer and distribution optimization provided in this embodiment collects the data to be diagnosed of the three-tank system; then, the data to be diagnosed is input into the trained bottleneck state observer, the output data starting from the current moment is predicted, and the residual between the output data starting from the current moment and the real output data is calculated; then, the residual starting from the current moment is input into the trained flow model to map the approximate normal distribution of the residual; finally, T is calculated based on the residual of the approximate normal distribution. 2 Statistics; Based on the T 2 Statistics determine the fault diagnosis results. This method integrates the observability of the target system, subspace identification theory and the nonlinear fitting ability of deep networks, constructs a deep bottleneck observer model to accurately capture the system dynamics, and forms a residual generation model based on the deep bottleneck state observer, which helps to enhance the reliability and accuracy of fault diagnosis; based on this, the flow model is introduced to convert the complex unknown distribution of residual data into a simple Gaussian distribution, reducing the information loss caused by dimension compression using statistical methods, thereby improving the accuracy of fault diagnosis.

[0167] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0168] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A fault diagnosis method based on bottleneck state observer and distribution optimization, characterized in that: include: S1: Collecting the data to be diagnosed of the three-water tank system, wherein the data to be diagnosed includes the water level of the first water tank, the water level of the second water tank, the water level of the third water tank, the flow rate of the first water inlet, and the flow rate of the second water inlet; S2: input the data to be diagnosed into the trained bottleneck state observer, predict the output data starting from the current moment, and calculate the residual between the output data starting from the current moment and the actual output data; The process of predicting the output data starting from the current moment includes: By sampling the data samples to be diagnosed at several historical continuous moments in the data to be diagnosed through sliding windows, and passing the input data and the real output data in the data samples to be diagnosed at several historical continuous moments through the first fully connected neural network in the trained bottleneck state observer, the state data of the system at the current moment is predicted; The state data of the system at the current moment and the input data of the data sample to be diagnosed at the current moment are passed through the second fully connected neural network in the trained bottleneck state observer to predict the output data of the system at the current moment; With a sliding window step size of 1, slide the window to sample in the future until the number of sliding windows reaches Second-rate, Represents the time range of the future direction, and obtains the predicted output data of the three-tank system starting from the current moment; The difference between the actual output data starting from the current moment and the output data starting from the current moment is taken as the residual; S3: Input the residual starting from the current moment into the trained flow model to map the approximate normal distribution of the residual; calculate T based on the residual of the approximate normal distribution 2 Statistics; The flow model is a nonlinear independent component estimation model, which is formed by stacking multiple additive coupling layers and is used to convert the complex distribution of residuals starting from the current moment into an approximate normal distribution to obtain a residual of an approximate normal distribution; In the training process of the nonlinear independent component estimation model, in order to maximize the log-likelihood of the second residual, the nonlinear independent component estimation model is trained by minimizing the second norm in the latent representation after the second residual is transformed by mapping, so that it learns the mapping rule from the complex distribution to the approximate normal distribution; The calculation formula for the log-likelihood of the second residual is: ； in, The second residual The log-likelihood of ; The second residual The latent representation after the mapping transformation; represents the log probability that the latent variable follows an approximately normal distribution; Represents the mapping rule from complex distribution to approximate normal distribution; Indicated by w The first window in each window starts q The second residual calculated from normal data samples; Since the learning goal is that the latent variables follow an approximate normal distribution, the logarithmic probability calculation formula of the latent variables is: ； in, d represents the dimension of the latent variable; S4: Based on the T 2 Statistics determine the fault diagnosis results.

2. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 1 is characterized in that: The bottleneck state observer is composed of two fully connected neural networks in series, the first fully connected neural network is used to predict the current state data of the system, and the second fully connected neural network is used to predict the output data at the next moment; The training process of the bottleneck state observer is: Step 1.1: Collect normal data of the three-tank system; Step 1.2: The normal data includes n Normal data samples at consecutive moments are sampled by sliding window. q Normal data samples at consecutive moments, q Less than n , and move the front q- The input data and real output data of the normal data samples at one continuous moment are passed through the first fully connected neural network in the bottleneck state observer, and the state data of the system in the current window is output; the state data in the current window and the first q The input data of the normal data sample passes through the second fully connected neural network in the bottleneck state observer to obtain the first q The predicted output data of normal data samples; Step 1.3: Calculate the q The second residual between the predicted output data and the true output data of the normal data samples; Step 1.4: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second normal data sample to the q +1 normal data sample at consecutive moments, and execute steps 1.2-1.3; Step 1.5: Repeat steps 1.2 to 1.4 until the maximum number of sliding windows is reached, and the first q The second residual between the predicted output data and the true output data of the normal data samples; Step 1.6: Take minimizing the second residual as the training objective and perform multiple rounds of training until the maximum set number of times is reached to obtain a trained bottleneck state observer.

3. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 2 is characterized in that: Minimizing the second residual is expressed as: ； ； in, N Indicates the maximum number of sliding windows; Indicates w The second sliding window q The actual output data of normal data samples; represents the second fully connected neural network; represents the network parameters of the second fully connected neural network; represents the first fully connected neural network; represents the network parameters of the first fully connected neural network; Indicates w Second sliding window middle front q- Input data of normal data samples at 1 continuous moment; Indicates w Second sliding window middle front q- The actual output data of a normal data sample at 1 continuous moment; Indicates w The second sliding window q Input data of normal data samples; n represents the number of normal data samples; Δ q Represents the sliding window step size.

4. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 2 is characterized in that: The process of predicting the output data starting from the current moment specifically includes: Step 2.1: The data to be diagnosed includes l The data samples to be diagnosed at consecutive moments are sampled by sliding window. q The data samples to be diagnosed at consecutive moments, q Much smaller than l , will t Before the moment q- The input data and real output data of the data samples to be diagnosed at 1 continuous moment are the first fully connected neural network in the trained bottleneck state observer, and the prediction system t Status data at the moment; the mapping formula is: ； ； ； in, Indicates t Before the moment q- Input data of the data sample to be diagnosed at 1 continuous moment; Indicates t Before the moment q- The actual output data of the data sample to be diagnosed at one continuous moment; Indicates the three-tank system t Status data at the moment; Indicates the direction of mapping to the right; Indicates tq +1 Input data of the data sample to be diagnosed at time; Indicates tq + Input data of the data sample to be diagnosed at time 2; Indicates t- Input data of the data sample to be diagnosed at time 1; Indicates tq The actual output data of the data sample to be diagnosed at time +1; Indicates tq The actual output data of the data sample to be diagnosed at time +2; Indicates t- The actual output data of the data sample to be diagnosed at time 1; Step 2.2: t Status data at the moment and t The input data of the data sample to be diagnosed at time t is passed through the second fully connected neural network in the trained bottleneck state observer to predict the system t Output data at the moment; the mapping formula is: ； in, Indicates t Input data of the data sample to be diagnosed at time; Indicates the three-tank system t The predicted output data at the moment; Step 2.3: Set the sliding window size to q , sliding window step length Δ q =1, sampling the second data sample to be diagnosed to the q +1 continuous moment of the data sample to be diagnosed, and execute steps 2.1-2.2, the prediction system t Output data at time +1; Step 2.4: Repeat steps 2.1 to 2.3 until the number of sliding windows reaches Second, get the t The predicted output data of the three-tank system starts at time; The time range representing the future direction is calculated as: ； in, l Indicates the number of samples of data to be diagnosed in the data to be diagnosed.

5. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 1 is characterized in that: The residual is calculated as: ； ； ； in, Indicates t The residual at the start of time; Indicates t The real output data of the three-tank system starts at every moment; Indicates t The predicted output data of the three-tank system starts at time; Indicates t The actual output data of the three-tank system at each moment; A time horizon indicating future direction; Indicates The actual output data of the three-tank system at each moment; Indicates The actual output data of the three-tank system at each moment; Indicates t Predicted output data of the three-tank system at time instant; Indicates Predicted output data of the three-tank system at time instant; Indicates Predicted output data for the three-tank system at time instant.

6. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 1 is characterized in that: Get T 2 The process of statistical thresholding is: Will be w The first window in each window starts q The second residual calculated from the normal data samples is converted into the second residual of approximate normal distribution through the nonlinear independent component estimation model; T is calculated based on the dimension of the second residual that follows an approximately normal distribution. 2 The statistical threshold is calculated as follows: ； in, Indicates the T² statistic threshold; Indicates the false alarm rate Next Distribution critical value; m represents the dimension of the second residual; N Indicates the maximum number of sliding windows.

7. The fault diagnosis method based on bottleneck state observer and distribution optimization according to claim 6 is characterized in that: No. t The approximate normal distribution of the residual starting at time is expressed as: ;in, Indicates t The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; Indicates The residuals at the moment are mapped to the data by the nonlinear independent component estimation model; represents the time frame of the future direction; T represents transposition; Calculate T based on the approximate normal distribution of the residuals 2 Statistics, calculated as: ； ； ； in, Indicates T 2 Statistics; represents the mean calculated from the data mapped by the second residual through the nonlinear independent component estimation model; Indicated by w In the window q The second residual calculated from the normal data samples is mapped to the data by the nonlinear independent component estimation model; Indicated by data With the mean The calculated covariance matrix; Indicates t+k- The residuals at time 1 are mapped to the data using a nonlinear independent component estimation model.

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