A method for failure root cause ranking of a polyester fiber polymerization process

Abstract

The application relates to a fault root cause sorting method of a polyester fiber polymerization process, which comprises the following steps: (1) according to a normal historical data set of the polyester fiber polymerization process, variable pairs are combined two by two to determine whether there is an invariant relationship between two variables in each variable pair, and an invariant network of variables is constructed by combining all the invariant relationships among the variables; (2) a prediction model is respectively established for each variable pair with an invariant relationship in the invariant network of variables; (3) new data of the polyester fiber polymerization process are collected to obtain a set of variable fault invariant networks; (4) the invariant network of variables is extended into an invariant network of variable pairs; (5) a variable pair fault invariant network is obtained according to the set of variable fault invariant networks and the invariant network of variable pairs; and (6) according to fault propagation theory and invariant relationship disappearance, the possibility of whether a node in the invariant network of variable pairs is a root cause is sorted. The application can guide the search for the cause of fault generation in the polyester fiber polymerization process.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of big data fault analysis of chemical fiber production, and relates to a fault root cause sorting method for a polyester fiber polymerization process. BACKGROUND

[0002] Polyester fiber, commonly known as polyester (PET) fiber, is a synthetic fiber obtained by spinning polyester obtained by polycondensation of organic dibasic acid and dibasic alcohol. Due to the characteristics of high strength, good elastic recovery, good wrinkle resistance and good shape retention, polyester fiber is widely used in the fields of textile and industry.

[0003] With the development of society, people's requirements for polyester fiber are getting higher and higher. Finding the reason for unqualified product quality in the production process has attracted widespread attention. In the development of industrial informatization, a large number of sensors are arranged in the polyester fiber polymerization industrial process, and are matched with distributed control systems, monitoring and data acquisition systems, etc., for effectively capturing the dynamic evolution of the industrial process and timely detecting industrial faults. However, due to the interwoven feedback mechanism and complex transmission process in the polyester fiber polymerization process, the equipment, components and process variables in the process are coupled, forming a complex interrelated industrial network. This makes it difficult to identify the root cause of the fault in the polyester fiber polymerization process. Once a fault occurs in the process, the fault will spread from a certain link to the whole process or a key link, resulting in a decrease in product quality or damage to production equipment.

[0004] The polymerization process is the first step in the research of the whole polyester fiber production process, and the process variables and equipment coupling are complex, and the whole production industrial network is complex. The process includes esterification, pre-polymerization and final polymerization three stages. The variables collected by data acquisition can be divided into liquid level, pressure, temperature and current according to their properties. Under the assumption that the industrial raw materials have no quality problems, the polyester fiber polymerization process faults are mostly caused by equipment failure and power failure. The equipment failure is characterized by the abnormality of the physical quantity related to the function of the equipment, which is detected as the root cause. The power anomaly is characterized by the related current and the quantity affected by the current, which is detected as the fault root cause. At present, the fault root cause sorting algorithm is less applied to the related research of the polyester fiber polymerization process. The existing data-driven polyester fiber polymerization process industrial process fault root cause research often first mines the correlation information between variables to construct a causal topology graph, and then identifies the fault propagation path to realize the root cause diagnosis of the fault. However, it is difficult to achieve the expected effect in the face of non-stationary and nonlinear polyester fiber polymerization data, and false and redundant causal relationships are easily generated, which makes the causal graph constructed inaccurate and affects the identification of the fault propagation path and the positioning of the root cause. The invariant network model can analyze the root cause of the system fault without constructing a causal graph. It focuses on finding the pair-wise stable and significant dependency relationships between the components of the monitoring system to analyze the system state and perform subsequent reasoning. The pair-wise strong dependency relationship between the components is regarded as an invariant relationship, and the invariant network of the system is constructed by combining the invariant relationships learned from all components. The important practical value of the invariant network lies in that it provides important clues for the abnormal behavior of the system and the abnormal source by checking whether the existing invariant relationship disappears. However, the existing root cause sorting algorithm based on the invariant network ignores the nonlinearity of the data and the complexity of the disappearance of the invariant relationship, and they usually assume that the fault is stable and invariant, without considering the actual situation of fault propagation, and are not suitable for the polyester fiber polymerization production process.

[0005] Therefore, it is of great practical significance to develop an invariant network-based fault root cause sorting method that can identify the fault root cause in the polyester fiber polymerization production process. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art and provide a fault root cause sorting method for the polyester fiber polymerization process.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0008] A fault root cause sorting method for the polyester fiber polymerization process, comprising the following steps:

[0009] (1) According to the normal historical data set of the polyester fiber polymerization process, the variables are combined in pairs to judge whether there is an invariant relationship between the two variables in each variable pair, and all the invariant relationships between the variables are combined to construct a variable invariant network;

[0010] The nodes of the variable invariant network represent variables, and the edges represent invariant relationships between variables; when there is an invariant relationship between variables, there is an edge between the nodes corresponding to the two variables; otherwise, there is no edge;

[0011] (2) A prediction model is established for each pair of variables with an invariant relationship in the variable invariant network;

[0012] (3) New data of the polyester fiber polymerization process is collected to obtain a set G of variable fault invariant networks;

[0013] The set G of variable fault invariant networks is a set of variable fault invariant networks corresponding to each time point from t1 to t v ;

[0014] The expression form of the set G of variable fault invariant networks is as follows:

[0015]

[0016] In the formula:

[0017] u represents the number of edges in the variable invariant network, u = 1, 2,..., U;

[0018] T represents the time point, T = t1, t2,..., t v ;

[0019] represents the disappearance of the invariant relationship of the u-th edge in the variable invariant network at the time point T, 0 indicates that the invariant relationship has not disappeared, 1 indicates that the invariant relationship has disappeared;

[0020] (4) The variable invariant network is extended to a variable pair invariant network;

[0021] The nodes of the variable pair invariant network represent pairs of variables with an invariant relationship, and the edges represent invariant relationships between variable pairs; when there is an invariant relationship between variable pairs, there is an edge between the nodes corresponding to the two variable pairs; otherwise, there is no edge;

[0022] (5) A variable pair fault invariant network P is obtained according to the set G of variable fault invariant networks and the variable pair invariant network;

[0023] The expression form of the variable pair fault invariant network P is as follows:

[0024]

[0025] P z′zPz,z' represents the disappearance of the invariant relationship between the zth node and the z'th node in the invariant network, the disappearance of the invariant relationship is represented by 1, and the non-disappearance is represented by 0, P 11 , P 22 , …, P ZZ all equal to 1, when the transmission entropy between the zth node and the z'th node in the invariant network of the variable pair is greater than the set threshold, then P zz′ = P z′z = 1, otherwise, P zz′ = P z′z = 0;

[0026] (6) According to the fault propagation theory and the reconstruction of the disappearance of the invariant relationship, the possibility of whether the node in the invariant network of the variable pair is a root cause is sorted;

[0027] (6.1) Set the objective function, the expression is as follows:

[0028]

[0029] In the formula:

[0030] c is a regularization parameter in (0, 1); I n is a unit matrix; is the degree matrix of A; A i，j represents whether there is an invariant relationship between the ith node and the jth node in the invariant network of the variable pair, A i，j = 1 represents that there is, and A i，j = 0 represents that there is not;

[0031] e represents the possibility that the node in the invariant network of the variable pair is a fault root cause, e = [e1, e2, …, e i , …, e z ], e i represents the probability that the ith node in the invariant network of the variable pair is a fault root cause, e i , e i = 1 represents 100%, and e i = 0 represents 0%;

[0032] represents that the corresponding elements are multiplied one by one;

[0033] Q is the degree matrix of P; P is the fault invariant network of the variable pair;

[0034] λ is a hyperparameter for controlling the number of non-zero terms in e;

[0035] (6.2) iteratively update e to reach a set number of iterations to optimize the objective function according to the following formula:

[0036]

[0037] wherein:

[0038] are element operators;

[0039] 1 z represents a one-dimensional vector with length Z and all values being 1;

[0040] (6.3) sort the elements in the last updated e according to their size, select the first k largest elements, count the number of times each variable appears in the nodes in the invariant network corresponding to the first k largest elements, sort the variables according to the number of times, and select the first two variables with the highest frequency as the root cause.

[0041] As a preferred technical solution:

[0042] The method for sorting the root causes of the polyester fiber polymerization process according to the above-described method, in step (1), the method for determining whether there is an invariant relationship between the two variables in each variable pair is as follows: calculate the fitting degree F(θ) of the two variables in each variable pair, if F(θ) is greater than a set threshold value of 0.6, then the two variables in the variable pair have an invariant relationship; otherwise, the two variables in the variable pair do not have an invariant relationship; the calculation formula of F(θ) is as follows:

[0043]

[0044] wherein:

[0045] t is the time index;

[0046] N is the total number of samples in the historical fault-free data set;

[0047] y(t) is the value of Y at time t, Y is one of the time series variables in the variable pair;

[0048] is the prediction of y(t) by the ARX model, wherein, a1,..., a n , b0,..., b m are coefficients, a1,..., a n , b0,..., b mThe value of is obtained by least square fitting calculation, the least square fitting is polynomial fitting, the objective function is the residual sum of observation value and theoretical value, y(t-1) is the value of Y at t-1 time, y(t-n) is the value of Y at t-n time, x(t-k) is the value of X at t-k time, X is another time series variable in the variable pair, x(t-k-m) is the value of X at t-k-m time, n, m are the order of ARX model, k is the delay factor, 0≤n, m, k≤2, ε(t) is the noise at t time;

[0049] is the average value of Y.

[0050] The fault root cause ranking method of the polyester fiber polymerization process as described above, in step (2), the prediction model is the trained model;

[0051] Suppose that one variable pair with an invariant relationship in the invariant variable network is X * and Y * , the input of the model is X * , the detection value at the current time and the historical time, and Y * , the detection value at the current time and the historical time, the output of the model is X * , one-step prediction, and Y * , one-step prediction;

[0052] The model is composed of two LSTM models without connection relationship, the input of one LSTM model is X * , the detection value at the historical time, and Y * , the detection value at the current time and the historical time, the output is X * , one-step prediction, the input of the other LSTM model is X * , the detection value at the current time and the historical time, and Y * , the detection value at the historical time, the output is Y * , one-step prediction;

[0053] The training process is to continuously adjust the parameter batch, memory vector length and LSTM module number of the two LSTM models;

[0054] During the training process, when the prediction accuracy of the model does not improve in ten iterations, the training is terminated; otherwise, when the maximum number of iterations is reached, the training is terminated.

[0055] In the above-described method for ranking the root causes of failures in the polyester fiber polymerization process, in step (2), the memory vector length of the first two layers of each LSTM model is 80, the activation function is a linear activation function, and the fully connected layer and the linear activation layer keep the output dimension of the LSTM model consistent with the prediction step size; each LSTM model takes minimizing the sum of squares of the prediction error as the objective function, uses an adaptive matrix estimation optimizer to calculate the model gradient and update the model weights, and selects its default recommended value of 0.001 as the initial learning rate.

[0056] In the above-described method for ranking the root causes of failures in a polyester fiber polymerization process, in step (3), assuming that the variable pair corresponding to the u-th edge in the variable-invariant network is X′ and Y′, the process for determining the disappearance of the invariant relationship of the u-th edge in the variable-invariant network at time T is as follows:

[0057] (i) The corresponding Tl values ​​of X′ and Y′ in the new data of the polyester fiber polymerization process s The values ​​from time T to time T-1 are input into the corresponding prediction model, which outputs the predicted values ​​of X′ and Y′ at time T.

[0058] (ii) Calculate the prediction error values ​​of X′ and Y′ at time T respectively, and take the larger prediction error value as the residual d(T) of the invariant relationship at time T. Obtain the residuals of the invariant relationship at all times during the prediction process: d(t1), d(t2)...d(t) v );

[0059] (iii) Set an error smoothing window sh and perform an exponentially weighted average on the obtained invariant residuals to obtain the smoothed error ds(T), i.e., ds(t1), ds(t2)...ds(t). v );

[0060] (iv) Set a dynamic threshold window th, and combine the invariant relation residuals within a window to obtain multiple one-dimensional error vectors ds1 = [ds(t1), ds(t1+1), ..., ds(t1+th-1)], ds2 = [ds(t1+th), ds(t1+th+2), ..., ds(t1+2th-1)], ..., ds K =ds(t1+(W-1)th),…,ds(t1+Wth-1)],…,ds k =ds(t1+(w-1)th),…,ds(t v )];

[0061] (v) For each one-dimensional error vector, set a dynamic threshold γ to track the disappearance of continuous invariant relationships;

[0062] The principle for setting γ is: remove ds wall elements in ds max, where:

[0063] Δμ(ds W ) = μ(ds W ) - μ{ds W ∈ ds W | ds W < γ}, μ(ds W ) is the mean of the elements in ds W , μ{ds W ∈ ds W | ds W < γ} is the mean of the elements in ds W less than γ, {ds W ∈ ds W | ds W < γ} is the set of elements in ds W less than γ, and ds W is an element in ds W ;

[0064] Δδ(ds W ) = δ(ds W ) - δ{ds W ∈ ds W | ds W < γ}, δ(ds W ) is the standard deviation of the elements in ds W , δ{ds W ∈ ds W | ds W < γ} is the standard deviation of the elements in ds W less than γ;

[0065] | da W | is the number of elements in da W , da W = {ds W ∈ ds W | ds W > γ}, da W is the set of elements in ds W greater than γ, and ds seq is an element in da 2 ;

[0066] | E seq | 2 is the square of the number of elements in E seq , E seq is the largest contiguous interval of {da W ∈ da W}, da W is an element in da W ;

[0067] γ is an element in the candidate threshold vector γ, γ = μ(ds W )+ z ＊ δ(ds W ), where z ＊ is a one-dimensional vector, and z ＊ = (1, 2, …, 10);

[0068] When the time is the time corresponding to the E seq of each error one-dimensional vector, the element in the interval obtained by merging corresponds to the time, the invariant relationship of the u-th edge in the variable invariant network at the time disappears; otherwise, the invariant relationship of the u-th edge in the variable invariant network at the time does not disappear.

[0069] The fault root cause sorting method of the polyester fiber polymerization process as described above, in step (4), the extension method is: the variable invariant network contains Q' nodes, if there is an invariant relationship between nodes q and q', q'', there is no invariant relationship between nodes q and q''', there is no invariant relationship between nodes q' and q'', there is no invariant relationship between nodes q' and q''', and there is an invariant relationship between nodes q'' and q''', then q-q', q-q'', q'''-q'' are taken as three nodes in the variable pair invariant network, and there is an invariant relationship between q-q' and q-q'', there is an invariant relationship between q-q'' and q'''-q'', and there is no invariant relationship between q-q' and q'''-q'', that is, in the variable invariant network, the node set containing the invariant relationship with node q is {q', q',...}, then in the variable pair invariant network, q-q', q-q'', … are taken as variable pair nodes in the variable pair invariant network, and there is an invariant relationship between these variable pair nodes.

[0070] The fault root cause sorting method of the polyester fiber polymerization process as described above, in step (5), according to the set G of the variable fault invariant network, the invariant relationship disappearance of the z-th node in the variable pair invariant network from t1 to t v is determined to form a time sequence X'', and the invariant relationship disappearance of the z'-th node in the variable pair invariant network from t1 to t v is determined to form a time sequence Y''; the calculation formula of the transmission entropy T X″Y″ between the z-th node and the z'-th node in the variable pair invariant network is as follows:

[0071]

[0072] In the formula:

[0073] L indicates the total number of samples from t 1+τ to t v , and τ is the lag considered between the two time sequences.

[0074] y ″p denotes the set of elements in Y corresponding to time instants t-t to t-1.

[0075] x ″p denotes the set of elements in X corresponding to time instants t-t to t-1.

[0076] y ″t is the element in Y corresponding to time instant t.

[0077] x ″t is the element in X corresponding to time instant t.

[0078] f h denotes the kernel density estimation function, and h denotes the bandwidth.

[0079] The fault root cause ranking method of the polyester fiber polymerization process as described above, in step (5), the threshold value is set in the range of 0.08-0.12.

[0080] The principle of the application is as follows:

[0081] The polyester fiber polymerization process data has the characteristics of rich noise, long time span, nonlinearity, complex structure and strong correlation. The ARX model has limited ability to describe the nonlinear dynamic characteristics, so when facing the polyester fiber polymerization process data, the prediction performance is reduced, and the disappearance of the invariant relationship cannot be accurately tracked. The ability of LSTM in processing high complexity time sequence data makes it an ideal candidate for polyester fiber polymerization process data anomaly detection.

[0082] Compared with other neural networks, the LSTM model learns the relationship between past data values and current data values, and performs weighted self-loop of context through input gate, forgetting gate, output gate and memory unit, while forgetting non-important information, thereby effectively improving the processing ability of long sequence historical information. The above characteristics of LSTM have good tracking ability for the invariant relationship of the polyester fiber polymerization process system with information redundancy and multivariate dynamic coupling under complex working conditions.

[0083] Because the invariable relationship of a pair of variables is undirected, when determining whether it disappears, a bidirectional test is needed, that is, the failure of any variable in the two variables will lead to the disappearance of the invariable relationship. Therefore, an improved LSTM model is proposed and designed: two LSTM models are trained simultaneously to predict the residual error between the true value and the predicted value of the two variables at each time. The data of the polyester fiber polymerization process is rich in noise, complex and volatile, and has modal transition data mutations. The LSTM model that predicts by historical values cannot react in time when facing sudden data, resulting in a peak of residual error, thus incorrectly judging the disappearance of the invariable relationship. Therefore, the peak value is eliminated by using exponential weighted average smoothing error, and the residual error of adjacent time is also close, which is prepared for finding the continuous invariable relationship disappearance in the interval. If a fixed threshold is used, because the smoothed error may still fluctuate around the threshold, it is difficult to find a threshold that is continuous in each section of the long time series detection, so that the discontinuous invariable relationship disappearance cannot be obtained. Therefore, a dynamic threshold is introduced to track the continuous disappearance of the invariable relationship.

[0084] Beneficial effects:

[0085] (1) The present application proposes a fault root cause ranking method for the polyester fiber polymerization process, which improves the accuracy of detecting the disappearance of the invariable relationship by improving the LSTM model. The smoothed error and dynamic threshold are introduced to continuous invariable relationship disappearance, which is consistent with the actual situation of industrial process;

[0086] (2) The present application proposes a fault root cause ranking method for the polyester fiber polymerization process, which improves the robustness and accuracy of fault root cause ranking by studying the fault propagation in the disappearance of the invariable relationship. Through experimental verification, the method proposed by us has guiding effect on finding the causes of the faults generated in the actual production of the polyester fiber polymerization process. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 The flowchart of the present application;

[0088] Figure 2 The structure diagram of the improved LSTM model of the present application;

[0089] Figure 3 The schematic diagram of the polyester fiber polymerization process;

[0090] Figure 4 The flowchart of the polyester fiber polymerization process;

[0091] Figure 5 The relationship diagram of the variable types involved in the polyester fiber polymerization process;

[0092] Figure 6 The fault root cause ranking result method of the precondensation process;

[0093] Figure 7 An instance result method for failure root cause ranking for final polycondensation process. DETAILED DESCRIPTION

[0094] The application will be further described below in connection with specific embodiments. It should be understood that these embodiments are only used to illustrate the application and not used to limit the scope of the application. Furthermore, it should be understood that after reading the content of the application, those skilled in the art can make various modifications or changes to the application, and these equivalent forms also fall within the scope of the appended claims.

[0095] A failure root cause ranking method for a polyester fiber polymerization process, a flow chart of which is shown in Figure 1 The specific steps are as follows:

[0096] (1) According to the normal historical data set of the polyester fiber polymerization process, variable pairs are formed by two-by-two combination, it is judged whether there is an invariant relationship between the two variables in each variable pair, and the invariant relationships among all variables are combined to build a variable invariant network;

[0097] Because in the failure propagation process, the failure often propagates from one variable to another variable, therefore, the variable pairs are constructed; the invariant relationship is a stable and significant dependent relationship between two variables, which is used to analyze the system state and perform subsequent reasoning;

[0098] The variable invariant network is represented by a graph structure, the nodes in the graph structure represent variables, and the edges represent the invariant relationships between variables; when there is an invariant relationship between variables, there is an edge between the nodes corresponding to the two variables; otherwise, there is no edge;

[0099] The method for judging whether there is an invariant relationship between the two variables in each variable pair is as follows: the fitting degree F(θ) of the two variables in each variable pair is calculated, if F(θ) is greater than a set threshold value 0.6, then there is an invariant relationship between the two variables in the variable pair; otherwise, there is no invariant relationship between the two variables in the variable pair; the calculation formula of F(θ) is as follows:

[0100]

[0101] In the formula:

[0102] t is the time index;

[0103] N is the total number of samples of the historical failure-free data set;

[0104] y(t) is the value of Y at time t, Y is one of the time series variables in the variable pair;

[0105] is the prediction of y(t) by the ARX model, wherein a1,..., an b0,..., b m are coefficients, a1,..., a n b0,..., b m are obtained by least square fitting, the least square fitting is polynomial fitting, the objective function is the residual sum of squares of observed values and theoretical values, y(t-1) is the value of Y at time t-1, y(t-n) is the value of Y at time t-n, x(t-k) is the value of X at time t-k, X is another time series variable in the variable pair, x(t-k-m) is the value of X at time t-k-m, n, m are the order of ARX model, k is the delay factor, 0≤n, m, k≤2, ε(t) is the noise at time t;

[0106] is the mean value of Y;

[0107] (2) A nonlinear prediction model is established for each variable pair with an invariant relationship in the variable invariant network;

[0108] Because the data obtained in the polyester polyamide spinning process is highly nonlinear, the original ARX model is suitable for finding stable strong dependence relationships between variable pairs, but the overall prediction accuracy is low, and the invariant relationship cannot be accurately tracked, so a nonlinear prediction model is designed to track the invariant relationship;

[0109] The prediction model is the trained model;

[0110] Suppose that one variable pair with an invariant relationship in the variable invariant network is X * and Y * , then the input of the model is X * current and historical detection values and Y * current and historical detection values, and the output of the model is one-step prediction of X * and one-step prediction of Y * ;

[0111] As shown in Figure 2 , the model is composed of two LSTM models without connection relationship, the input of one LSTM model is X * historical detection values and Y * current and historical detection values, and the output is one-step prediction of X * , the input of the other LSTM model is X * current and historical detection values and Y * historical detection values, and the output is one-step prediction of Y * ;

[0112] The process of training is the process of continuously adjusting the parameters of the two LSTM models, the batch size, the length of the memory vector, and the number of LSTM modules;

[0113] During the training process, when the prediction accuracy of the model does not improve in ten iterations, the training is terminated; otherwise, when the maximum number of iterations (100 according to the experimental value in multiple data) is reached, the training is terminated;

[0114] The length of the memory vector of the first two layers of each LSTM model is 80 (this value is determined by experiment), and the activation function is linear activation function (LSTM model contains nonlinear relationship, therefore only linear activation function is selected to process the results of LSTM model, which meets the prediction task requirements), the output dimension of the LSTM model and the prediction step are consistent with the full connection layer and the linear activation layer;

[0115] Each LSTM model takes the sum of the squares of the prediction errors as the objective function, uses the adaptive matrix estimation (Adam) optimizer to calculate the model gradient and update the model weight, and selects the default recommended value 0.001 as the initial learning rate;

[0116] (3) Collect new data of the polyester fiber polymerization process to obtain the set G of variable fault invariant networks;

[0117] As shown in Figure 3 , the set G of variable fault invariant networks is the set of variable fault invariant networks corresponding to each time from t v to t

[0118] At a certain time such as T, there are two states of invariant relationship: the original invariant relationship still exists and the original invariant relationship disappears; the variable invariant network containing the invariant relationship at this time is called the variable fault invariant network at this time;

[0119] The expression form of the set G of variable fault invariant networks is as follows:

[0120]

[0121] In the formula:

[0122] u represents the number of edges in the variable invariant network, u = 1, 2,..., U;

[0123] T represents the time, T = t1, t2,..., t v ;

[0124] represents the disappearance of the invariant relationship of the u-th edge in the variable invariant network at time T, 0 indicates that the invariant relationship has not disappeared, A value of 1 indicates that the invariant relationship disappears;

[0125] Assuming the variable pair corresponding to the u-th edge in the variable-invariant network is X′ and Y′, the process for determining whether the invariant relationship of the u-th edge in the variable-invariant network disappears at time T is as follows:

[0126] (i) The corresponding Tl values ​​of X′ and r′ in the new data of the polyester fiber polymerization process s The values ​​from time T to time T-1 are input into the corresponding prediction model, which outputs the predicted values ​​of X′ and r′ at time T.

[0127] (ii) Calculate the prediction error values ​​(absolute values ​​of the difference between the true value and the predicted value) of X′ and Y′ at time T respectively. Since any abnormality in the variable pair will cause the invariant relationship to disappear, the larger prediction error value is taken as the residual d(T) of the invariant relationship at time T, and the residuals of the invariant relationship at all times during the prediction process are obtained as d(t1), d(t2)...d(t). v );

[0128] (iii) Due to noise, the invariant residuals fluctuate, and the LSTM model, which predicts based on historical values, cannot react promptly to sudden changes in data, leading to residual peaks and incorrect judgments that the invariant relationship has disappeared. Therefore, an error smoothing window sh (size 105) is set to perform an exponentially weighted average on the obtained invariant residuals to obtain the smoothed error ds(T), i.e., ds(t1), ds(t2)...ds(t... v );

[0129] (iv) Because faults often occur continuously, the disappearance of invariant relationships should also be continuous. Therefore, using a fixed threshold cannot meet the requirement of continuous disappearance of invariant relationships. To address this, a dynamic threshold is designed. Setting a dynamic threshold requires defining a dynamic threshold window and designing dynamic threshold rules. A dynamic threshold window th (size 100) is set, and the invariant relationship residuals within a window are combined to obtain multiple one-dimensional error vectors: ds1 = [ds(t1), ds(t1+1), ..., ds(t1+th-1)], ds2 = [ds(t1+th), ds(t1+th+2), ..., ds(t1+2th-1)], ..., ds K =ds(t1+(W-1)th),…,ds(t1+Wth-1)],…,ds k =ds(t1+(w-1)th),...,ds(t v )];

[0130] (v) For each one-dimensional error vector, set a dynamic threshold γ to track the disappearance of continuous invariant relationships;

[0131] The setting principle of γ is: remove all elements in ds W higher than γ, max, where:

[0132] Δμ(ds W ) = μ(ds W ) - μ{ds W ∈ ds W |ds W < γ}, μ(ds W ) is the mean of each element in ds W , Δμ(ds W ) / μ(ds W ) represents the mean reduction ratio of invariant relationship residuals after removing the invariant relationship residuals higher than the dynamic threshold, μ{ds W ∈ ds W |ds W < γ} is the mean of each element in ds W lower than γ, {ds W ∈ ds W |ds W < γ} is the set of elements in ds W lower than γ, and ds W is the element in ds W ;

[0133] Δδ(ds W ) = δ(ds W ) - δ{ds W ∈ ds W |ds W < γ}, δ(ds W ) is the standard deviation of each element in ds W , Aδ(ds W ) / δ(ds W ) represents the variance reduction ratio of invariant relationship residuals after removing the invariant relationship residuals higher than the dynamic threshold, δ{ds W ∈ ds W |ds W < γ} is the standard deviation of each element in ds W lower than γ;

[0134] |da W | is the number of elements in da W , da W = {ds W ∈ ds W |ds W > γ}, and da W is the set of elements in ds W greater than γ;

[0135] |Eseq | 2 is E seq the square of the number of elements in E seq is {da W ∈ da W} the largest continuous interval of da W is the element in da W ;

[0136] γ is the element in the candidate threshold vector γ, γ = μ(ds W ) + z ＊ δ(ds ＊ ), where z seq is a one-dimensional vector, and z z′z = (1, 2, …, 10);

[0137] When the time is the time corresponding to the element in the interval obtained by merging the E 11 corresponding to each error one-dimensional vector, the invariant relationship of the u-th edge in the variable-invariant network at this time disappears; otherwise, the invariant relationship of the u-th edge in the variable-invariant network at this time does not disappear;

[0138] The reason for setting the dynamic threshold as above is that the error selection basis is to select a threshold value in the candidate threshold set, so that after removing all values higher than the threshold value, the average value and the standard deviation of the error decrease by the maximum percentage, and the longest continuous interval of invariant relationship disappearance is retained as much as possible;

[0139] (4) extending the variable-invariant network into a variable pair-invariant network;

[0140] If an invariant relationship disappears, it means that at least one variable has failed, but it cannot be located which one, therefore, the research object of the present application is extended from a variable to a variable pair;

[0141] The nodes of the variable pair-invariant network represent variable pairs with invariant relationships, and the edges represent the invariant relationships between the variable pairs; when there is an invariant relationship between the variable pairs, there is an edge between the nodes corresponding to the two variable pairs; otherwise, there is no edge;

[0142] The extended method is: the variable-invariant network contains Q' nodes, if node q and node q', q'' have an invariant relationship, node q and node q''' do not have an invariant relationship, node q' and q'' do not have an invariant relationship, node q' and q''' do not have an invariant relationship, and node q'' and q''' have an invariant relationship, then q-q', q-q'', q'''-q'' are taken as three nodes in the variable pair-invariant network, and there is an invariant relationship between q-q' and q-q'', there is an invariant relationship between q-q'' and q'''-q'', and there is no invariant relationship between q-q' and q'''-q'', that is, in the variable-invariant network, the node set having an invariant relationship with node q is {q', q'',...}, then in the variable pair-invariant network, q-q', q-q'',... are taken as variable pair nodes in the variable pair-invariant network, and all these variable pair nodes contain an invariant relationship;

[0143] (5) Obtain the variable pair fault-invariant network P according to the variable fault-invariant network set G and the variable pair-invariant network;

[0144] The expression form of the variable pair fault-invariant network P is as follows:

[0145]

[0146] Wherein, P z′z represents the disappearance of the invariant relationship between the zth node and the z'th node in the variable pair-invariant network, and the invariant relationship disappearance is represented by 1 and the non-disappearance is represented by 0, P 11 , P 22 ,..., P ZZ are all equal to 1, when the transmission entropy between the zth node and the z'th node in the variable pair-invariant network is greater than the set threshold, then P zz′ = P z′z = 1, otherwise, P zz′ = P z′z = 0;

[0147] According to the variable fault-invariant network set G, the invariant relationship disappearance of the zth node in the variable pair-invariant network from t1 to t v is determined to form a time sequence X'', and the invariant relationship disappearance of the z'th node in the variable pair-invariant network from t1 to t v is determined to form a time sequence Y''; the calculation formula of the transmission entropy T X″Y″ between the zth node and the z'th node in the variable pair-invariant network is as follows:

[0148]

[0149] In the formula:

[0150] L represents the transmission entropy between the zth node and the z'th node from t 1+τ to tv Total number of samples at time t, τ is the lag of the influence between two time series, here is 2;

[0151] y ″p represents the set of elements in Y" corresponding to time t-τ to t-1;

[0152] x ″p represents the set of elements in X" corresponding to time t-τ to t-1;

[0153] y ″t is the element in Y" corresponding to time t;

[0154] x ″t is the element in X" corresponding to time t;

[0155] f h (·) represents the kernel density estimation function, h represents the bandwidth, which is 0.45, and the present application selects Gaussian kernel;

[0156] The reason for selecting transfer entropy is that in previous studies, transfer entropy has been proved to be a very useful tool for quantifying the directional causal influence of linear and nonlinear relationships, representing the average unpredictability of random variables and has been successfully applied in chemical processes; it is a measure of the uncertainty associated with random variables, if T X″Y″ is the information gain of X" to Y", if X" is the cause of Y", the information gain is larger, if X" is not the cause of Y", the information gain is less; here, X" is composed of the disappearance of invariance relationship at each time, if X" is the cause of the disappearance of invariance relationship of Y", then T X″Y″ is larger; if T X″Y″ is greater than the threshold value, it is considered that the invariance relationship disappearance of the variable pair to the node z has an impact on the invariance relationship disappearance of the variable pair to the node z', that is, the fault is transmitted from the variable pair node z to the variable pair node z', that is, the invariance relationship disappears between z and z';

[0157] (6) According to the fault propagation theory and the reconstruction of invariance relationship disappearance, the possibility of whether the node in the variable pair invariance network is the root cause is sorted;

[0158] (6.1) Set the objective function, the expression is as follows:

[0159]

[0160] In the formula:

[0161] c∈(0,1) is a regularization parameter, here is 0.2; I n is the unit matrix; is the degree matrix of A; A i，j represents whether there is an invariant relationship between the i-th node and the j-th node in the invariant network of variable pairs, A i，j = 1 represents that there is, A i，j = 0 represents that there is not;

[0162] e represents the possibility that a node in the invariant network of variable pairs is a root cause of failure, e = [e1, e2, …, e i , …, e z ], e i represents the probability that the i-th node in the invariant network of variable pairs is a root cause of failure, e i , e i = 1 represents a probability of 100%, e i = 0 represents a probability of 0%;

[0163] represents that the corresponding elements are multiplied one by one;

[0164] Q is the degree matrix of P; P is the invariant network of variable pairs failure;

[0165] λ is a hyperparameter for controlling the number of non-zero terms in e, which is 0.2 here;

[0166] The objective function is derived as follows:

[0167] First, the propagation of e to r is modeled. The modeling reason is that in the invariant network of variable pairs, the damage degree of adjacent nodes should be close, and whether the variable pair node is a root cause or not, the abnormal state of the variable pair node in the system after failure propagation is close;

[0168]

[0169] In the formula:

[0170] is the degree matrix of A;

[0171] c ∈ (0, 1) is a regularization parameter, which is 0.2 here;

[0172] r is the abnormal score vector of the initial failure e after propagation, r = [r1, r2, …, r i , …, r z ], r i represents the damage of the i-th node in the invariant network of variable pairs, r i , r i = 1 represents a damage degree of 100%, r i = 0 represents a damage degree of 0%;

[0173] Ai，j 1 means there is an invariant relationship between the variable pairs i, j, and 0 means there is no invariant relationship;

[0174] Then the above expression is simplified as:

[0175]

[0176] In the formula:

[0177] I n is a unit matrix;

[0178] is the standardization of the degree matrix A;

[0179] The optimal solution of the formula is:

[0180]

[0181] The fault invariant network is reconstructed using the anomaly score r of each variable pair:

[0182]

[0183] In the formula:

[0184] is the standardization of P, Q is the degree matrix of P;

[0185] denotes the multiplication of corresponding elements one by one;

[0186] Let The preliminary objective function is obtained:

[0187]

[0188] The L1 constraint is added to the optimization objective, and the final optimization objective function is obtained;

[0189] (6.2) Update e according to the following formula until the set number of iteration updates is reached to optimize the objective function, wherein the number of iteration updates is set to 100:

[0190]

[0191] In the formula:

[0192] are element operators;

[0193] 1 z denotes a one-dimensional vector with a length of Z and all values of 1;

[0194] (6.3) Sort the elements in e obtained by the last update by size, select the largest kth elements, count the number of times each variable appears in the nodes in the variable pair invariant network corresponding to the kth elements, sort the variables by the number of times, and select the top 2 variables with the highest frequency as the root cause.

[0195] Example 1

[0196] In the pre-polycondensation process, 13 variables are selected, including current, liquid level, pressure and temperature, as shown in the pre-polycondensation process of Figure 4 , wherein TIC is temperature adjustment, PIT is pressure, LIT is liquid level, TE indicates temperature, LIC is liquid level adjustment, PIC is frequency adjustment, II is current, NI is torque, SI is valve speed, the following numbers are sensor numbers, ZCP91 is the production line name, 1R211 is the number of esterification kettle, 1R311 is the number of pre-polycondensation kettle, 1R321 is the number of final polycondensation kettle, and the relationship between the physical quantities is as shown in Figure 5 . Two variables are combined to form a variable pair, and based on the collected fault-free historical data, an ARX model and a fitting degree are used to obtain a variable invariant network containing 13 variables and 24 nodes, and a prediction model of each variable is obtained by training a nonlinear model. According to whether there is an invariant relationship between the variables in the variable invariant network and the prediction model of each variable, the invariant relationship disappearance residual of the historical data to be studied is obtained. The invariant relationship disappearance residual is smoothed and a dynamic threshold is used to determine the invariant relationship disappearance of each variable at each time to obtain the variable fault invariant network at each time. According to the variable invariant network, the variable pair invariant network containing 24 nodes and 204 edges is extended. Through the variable fault invariant network at each time, the variable pair fault invariant network is converted into a variable pair fault invariant network using transmission entropy. Finally, by simulating fault propagation and invariant relationship disappearance reconstruction, the final result is that the first cause of the fault is the pressure (PIT_0512) in the low polymer conveying process, and the second is the pressure (PIC_0608) under the pre-polycondensation kettle.

[0197] The experimental results are analyzed. According to the pre-polycondensation process, it is analyzed that the equipment is abnormal. When the low polymer is sent into the pre-polycondensation kettle, the pressure fault causes the pressure to rise, causing the pressure of the pre-polycondensation kettle to rise and gradually spread. In the case of normal pressure pump current and material indicators, it is possible that the pre-polycondensation kettle has a problem with the air vent, causing the pressure in the kettle and the pressure in the conveying pipeline to fail. As can be seen from Figure 6 , the two pressures have a great influence on each other, and there is a causal relationship between the faults, but the change in pressure will not affect the change in temperature in a short period of time, which is consistent with Figure 5 .

[0198] Example 2

[0199] The final condensation process is shown in Figure 4 The relationship between each physical quantity is shown in Figure 5 Among the 16 variables selected in the final condensation process, 1 current, 3 liquid level, 4 pressure and 7 temperature, etc. 13 variables are combined into pairs of variables. According to the collected fault-free historical data, the invariance network containing 13 nodes and 28 edges is obtained by ARX model and fitting degree, and the prediction model of each variable is obtained by training the nonlinear model. According to whether there is an invariance relationship between the variables in the invariance network and the prediction model of each variable, the invariance relationship disappearance residual of the historical data to be studied is obtained. Smooth the invariance relationship disappearance residual and use the dynamic threshold to determine the invariance relationship disappearance of each variable at each time to obtain the variable fault invariance network at each time. According to the variable invariance network, the variable pair invariance network containing 28 nodes and 224 edges is extended. Through the variable fault invariance network at each time, the transmission entropy is used to convert the variable fault invariance network into the variable pair fault invariance network. Finally, through the simulation of fault propagation and invariance relationship disappearance reconstruction, the experimental results show that the first cause of the fault is the current of the final condensation kettle stirrer (II_0710), and the second is the liquid level of the final condensation kettle (LIT_0705).

[0200] As shown in Figure 7 First, the two causes detected are close in the process, and then according to the process of final condensation, it can be analyzed that the sudden increase of the stirrer current directly leads to the uneven density of the material in the final condensation kettle, and the increase of the material conveying speed makes the liquid level of the pre-condensation kettle drop, and then gradually expand the existing causal relationship. Similarly, the current and the liquid level will not affect the temperature, which is consistent with the relationship between the variables of the reaction. Figure 5 ​

Claims

1. A method for sequencing the root causes of failures in a polyester fiber polymerization process, characterized in that, Includes the following steps: (1) Based on the normal historical dataset of the polyester fiber polymerization process, pair variables are formed, and it is determined whether there is an invariant relationship between the two variables in each pair. Combine all the invariant relationships between the variables to construct a variable invariant network. In an invariant network, nodes represent variables, and edges represent invariant relationships between variables. When an invariant relationship exists between variables, there is an edge between the nodes corresponding to the two variables; otherwise, there is no edge. (2) Establish prediction models for each pair of variables with invariant relationships in the variable-invariant network; (3) Collect new data on the polyester fiber polymerization process to obtain the set G of variable fault invariant networks; The set G of variable fault-invariant networks is from time t1 to t2. v The set of variable fault-invariant networks corresponding to each time step within a given time step; The set G of variable fault-invariant networks is expressed as follows: In the formula: u represents the edge number in the variable-invariant network, u = 1, 2, ..., U; T represents time, T = t1, t2, ..., t v ; This represents the situation where the invariant relation of the u-th edge in a variable-invariant network disappears at time T. A value of 0 indicates that the invariant relationship has not disappeared. A value of 1 indicates that the invariant relationship disappears; (4) Extend the variable-invariant network into a variable-pair-invariant network; In a variable-pair invariant network, nodes represent variable pairs that have an invariant relationship, and edges represent the invariant relationship between variable pairs. When there is an invariant relationship between two variable pairs, there is an edge between the nodes corresponding to the two variable pairs; otherwise, there is no edge. (5) Obtain the variable pair fault invariant network P based on the set G of variable fault invariant networks and the variable pair invariant network; The variables in the fault-invariant network P are expressed as follows: Among them, P z'z This indicates the disappearance of the invariant relation between the z-th node and the z'-th node in an invariant network. The disappearance of the invariant relation is represented by 1, and the continued existence by 0. P 11 P 22 ... P ZZ Both are equal to 1. When the transmission entropy between the z-th node and the z'-th node in the invariant network is greater than a set threshold, then P... zz' =P z'z =1, otherwise P zz' =P z'z =0; (6) Based on the fault propagation theory and the reconstruction of invariant relations, the probability of whether a node in the variable-pair invariant network is the root cause is ranked. (6.1) Set the objective function, with the following expression: In the formula: c∈(0,1) is the regularization parameter; I n It is the identity matrix; It is the degree matrix of A; A i,j Indicates whether there is an invariant relationship between the i-th node and the j-th node in an invariant network. A i,j =1 indicates existence, A i,j =0 indicates that it does not exist; e represents the probability that a variable is a root cause of failure in a node in an invariant network, e = [e1, e2, ..., e] i ,…,e Z ], e i Let e ​​represent the probability that the i-th node in an invariant network is the root cause of the failure. i The value range of is [0,1], e i =1 represents a probability of 100%, e i =0 represents a probability of 0%; This indicates that corresponding elements are multiplied one by one; Q is the degree matrix of P; P is a fault-invariant network with variable pairs. λ is a hyperparameter used to control the number of non-zero terms in e; (6.2) Iterate and update e according to the following formula until the set number of iterations is reached to optimize the objective function: In the formula: These are all element-matter operators; 1 Z This represents a one-dimensional vector of length Z with all values ​​being 1. (6.3) Sort the elements in e obtained from the last update by size, select the largest kth elements, count the number of times each variable in the nodes of the invariant network corresponding to the first kth elements appears, sort each variable by the number of times, and select the two variables with the highest frequency as the root cause.

2. The method for troubleshooting the failure root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (1), the method for determining whether there is an invariant relationship between the two variables in each variable pair is as follows: calculate the goodness of fit F(θ) between the two variables in each variable pair. If F(θ) is greater than the set threshold of 0.6, then there is an invariant relationship between the two variables in the variable pair; otherwise, there is no invariant relationship between the two variables in the variable pair. The formula for calculating F(θ) is as follows: In the formula: t is the time exponent; N is the total number of samples in the historical fault-free dataset; y(t) is the value of Y at time t, where Y is a time series variable in the variable pair; It is the ARX model's prediction of y(t). Where a1,...,a n ,b0,...,b m Let a1,...,a be the coefficients. n ,b0,...,b m The values ​​of are obtained by least squares fitting, which is a polynomial fitting. The objective function is the sum of the residuals between the observed and theoretical values. y(t-1) is the value of Y at time t-1, y(tn) is the value of Y at time tn, x(tk) is the value of X at time tk, X is the other time series variable in the variable pair, x(tkm) is the value of X at time tkm, n,m are the order of the ARX model, k is the delay factor, 0≤n,m,k≤2, and ε(t) is the noise at time t. It is the average value of Y.

3. The method for troubleshooting the failure root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (2), the prediction model is the trained model; Assume that there exists an invariant relationship between a pair of variables, X, in the variable-invariant network. * and Y * Then the input of the model is X. * The detection values ​​at the current time and historical time and Y * The model outputs X, which is the detection value at the current time and in historical time. * One-step prediction and Y * A one-step prediction; The model consists of two unconnected LSTM models, one of which takes X as input. * Historical moment detection values ​​and Y * The detection values ​​at the current time and historical time are output as X. * One step of prediction, the input of another LSTM model is X. * Current and historical detection values ​​and Y * The detection value at a historical moment is output as Y. * A one-step prediction; The training process involves continuously adjusting the parameter batch size, memory vector length, and number of LSTM modules of the two LSTM models. During training, training terminates when the model's prediction accuracy does not improve within ten iterations; conversely, training terminates when the maximum number of iterations is reached.

4. The method for troubleshooting the failure root cause of a polyester fiber polymerization process according to claim 3, characterized in that, In step (2), the memory vector length of the first two layers of each LSTM model is 80, the activation function is linear activation function, and the fully connected layer and linear activation layer keep the output dimension of the LSTM model consistent with the prediction step size; each LSTM model takes minimizing the sum of squares of the prediction error as the objective function, uses an adaptive matrix estimation optimizer to calculate the model gradient and update the model weights, and selects its default recommended value of 0.001 as the initial learning rate.

5. The method for troubleshooting the root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (3), assuming that the variable pair corresponding to the u-th edge in the variable-invariant network is X′ and Y′, the process of determining the disappearance of the invariant relationship of the u-th edge in the variable-invariant network at time T is as follows: (i) The corresponding Tl values ​​of X′ and Y′ in the new data of the polyester fiber polymerization process s The values ​​from time T to time T-1 are input into the corresponding prediction model, which outputs the predicted values ​​of X′ and Y′ at time T. (ii) Calculate the prediction error values ​​of X′ and Y′ at time T respectively, and take the larger prediction error value as the residual d(T) of the invariant relationship at time T. Obtain the residuals of the invariant relationship at all times during the prediction process: d(t1), d(t2)...d(t) v ); (iii) Set an error smoothing window sh and perform an exponentially weighted average on the obtained invariant residuals to obtain the smoothed error ds(T), i.e., ds(t1), ds(t2)...ds(t) v ); (iv) Set a dynamic threshold window th, and combine the invariant relation residuals within a window to obtain multiple one-dimensional error vectors ds1 = [ds(t1), ds(t1+1), ..., ds(t1+th-1)], ds2 = [ds(t1+th), ds(t1+th+2), ..., ds(t1+2th-1)], ..., ds K =ds(t1+(W-1)th),...,ds(t1+Wth-1)],...,ds k =ds(t1+(w-1)th),...,ds(t v )]; (v) For each one-dimensional error vector, set a dynamic threshold γ to track the disappearance of continuous invariant relationships; The principle for setting γ is: remove ds W After all elements higher than γ, Maximum, of which: Δμ(ds W )=μ(ds W )-μ{ds W ∈ds W |ds W <γ},μ(ds W ) is ds W The mean of all elements in μ, ds W ∈ds W |ds W <γ} is ds W The mean of all elements less than γ, {ds W ∈ds W |ds W <γ} is ds W The set of elements less than γ, ds W For ds W Elements in; Δδ(ds W )=δ(ds W )-δ{ds W ∈d W |ds W <γ},δ(ds W ) is ds W The standard deviation of each element in the δ{ds} W ∈ds W |ds W <γ} is ds W The standard deviation of each element smaller than γ; |da W |for da W Number of inner elements, da W ={ds W ∈ds W |ds W >γ}, da W For ds W The set of elements greater than γ; |E seq | 2 It is E seq The square of the number of inner elements, E seq is {da W ∈da W The maximum continuous interval of}, da W for da W Elements in; The value of γ is an element in the candidate threshold vector γ, where γ = μ(ds) W )+z*δ(ds W ), where z* is a one-dimensional vector, and z* = (1, 2, ..., 10); When the time is E corresponding to each one-dimensional error vector seq When the elements in the merged interval correspond to a specific time, the invariant relation of the u-th edge in the variable-invariant network disappears at that time; otherwise, the invariant relation of the u-th edge in the variable-invariant network does not disappear at that time.

6. The method for troubleshooting the failure root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (4), the expansion method is as follows: The variable invariant network contains Q' nodes. If node q has an invariant relationship with nodes q' and q″, node q does not have an invariant relationship with node q”', node q' does not have an invariant relationship with q”, node q' does not have an invariant relationship with q”', and node q” does have an invariant relationship with q”', then q-q', qq”, and q”'-q” are taken as three nodes in the variable pair invariant network. There is an invariant relationship between q-q' and qq”, an invariant relationship between qq” and q”'-q”, and no invariant relationship between q-q' and q”'-q”. That is, in the variable invariant network, the set of nodes with an invariant relationship with node q is {q', q”, ...}. Then, in the variable pair invariant network, q-q', qq”, ... are taken as variable pair nodes in the variable pair invariant network, and there is an invariant relationship between these variable pair nodes.

7. The method for troubleshooting the root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (5), the values ​​from t1 to t2 of the z-th node in the variable fault invariant network are determined based on the set G of the variable fault invariant network. v The disappearance of invariant relationships is used to form a time series X, and the variable's relationship with the z'th node in the invariant network from t1 to t2 is determined. v The disappearance of invariant relationships forms the time series Y”; the transmission entropy T between the z-th node and the z'-th node in the invariant network. X”Y” The calculation formula is as follows: In the formula: L refers to t 1+τ Time to t v The total number of samples at time point τ is the lag factor that is considered in the influence between the two time series. y” p Let Y be the set of elements from time t-τ to time t-1. x” p Let X” represent the set of elements from time t-τ to time t-1. y” t It is the element corresponding to time t in Y”; x” t It is the element corresponding to time t; f h (·) represents the kernel density estimation function, and h represents the bandwidth.

8. The method for troubleshooting the failure root cause of a polyester fiber polymerization process according to claim 1, characterized in that, In step (5), the set threshold value ranges from 0.08 to 0.12.

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