Fault monitoring method and system based on hierarchical time sequence analysis

Abstract

The invention discloses a fault monitoring method and system based on hierarchical time sequence analysis, and solves the problem of how to implement time sequence change characteristic analysis of data from two angles of linearity and nonlinearity, thereby performing fault monitoring on the operation state of an industrial process on the basis of comprehensively analyzing time sequence change characteristics. Hierarchical time sequence analysis related to the method sequentially comprises linear time sequence analysis and nonlinear time sequence analysis, and various improved schemes about the linear time sequence analysis are disclosed, so that comprehensive learning of data time sequence characteristic representation is realized, and the sensitivity of fault monitoring is improved. Based on the same inventive concept, the invention further discloses a fault monitoring system based on hierarchical time sequence analysis, which comprises a hardware module consisting of a data acquisition unit, a data operation unit, a monitoring display unit and a fault alarm, and a software module stored with a program for realizing linear time sequence analysis and nonlinear time sequence analysis. And finally, verifying and explaining the effectiveness of the method through the embodiment.

Description

Technical Field

[0001] The present invention relates to the technical field of data-driven fault monitoring, and particularly to a fault monitoring method and system based on hierarchical time series analysis. Background Art

[0002] Modern industrial processes represented by process industrial processes all require real-time monitoring of their operating states to promptly detect faults or abnormalities occurring during the production process. Data-driven fault monitoring is a rapidly developing research field. With the increasing complexity of modern industrial production and the continuous expansion of process scale, traditional monitoring methods often struggle to meet the requirements of real-time, accuracy, and comprehensiveness. Therefore, using data-driven methods to implement fault monitoring has become an inevitable trend. With the widespread application of Internet of Things technology and advanced sensor technology in modern industrial processes, the data measured in real time by sensors during production operation has important value and can provide useful data information for real-time monitoring of abnormalities or faults.

[0003] The Chinese invention patent with the application number 202310219496.0 discloses a process industrial process monitoring method based on a time series autoencoder, which uses the constructed time series autoencoder to perform time series feature representation learning on industrial process data, thereby monitoring faults through the error change of data reconstruction. The Chinese invention patent with the application number 202311675238.X discloses a fault monitoring model combining local adaptive standardization, variational autoencoder, and GRU units, which also implements fault monitoring from the perspective of analyzing the time series characteristics of data. In addition, the Chinese invention patent with the application number 202411288685.4 discloses a fault monitoring method and system based on spatio-temporal feature attention fusion. This method represents and learns the change characteristics of data through feature analysis at two levels of time and space, thereby improving the sensitivity of fault monitoring.

[0004] A paper titled "Improved Two-Step Dynamic Slow Feature Analysis Algorithm and Its Fault Detection Model" published in the journal "Journal of Yunnan University (Natural Sciences Edition)" in 2024 improved the two-step dynamic slow feature analysis algorithm and verified the effectiveness of using the time series correlation features of data to implement fault monitoring. Thus, it can be seen that analyzing the time series change characteristics of data is an effective way for the industrial and academic circles to solve the problem of data-driven fault monitoring.

[0005] However, considering the complex coupling characteristics of various links in the actual industrial process, the corresponding sampling data will have both linear and nonlinear relationships in the sequence of time series. Analyzing the linear or nonlinear time series characteristics unilaterally cannot comprehensively describe the time series change characteristics of the data. Since the data-driven fault monitoring targets the normal working condition data when implementing feature analysis, how to comprehensively represent the change characteristics of the learning data is the basic way to ensure the performance of fault monitoring. However, the fault monitoring methods involved in the above patent technical materials and scientific research papers all analyze and extract the time series change characteristics of the data from a single perspective of linear or nonlinear, and the comprehensiveness of the time series feature representation still needs to be further improved. Summary of the Invention

[0006] The main technical problem to be solved by the present invention is: how to analyze the time series change characteristics of the data from two perspectives of linear and nonlinear, so as to perform reliable and effective fault monitoring on the operating state of the industrial process on the basis of comprehensively analyzing the time series change characteristics.

[0007] The technical solution adopted by the present invention to solve the above problems is: a fault monitoring method and system based on hierarchical time series analysis; wherein, the implementation process of a fault monitoring method based on hierarchical time series analysis involved in the present invention includes the following steps 1 to 3.

[0008] Step 1: Collect N groups of data during the normal operation of the industrial process, and after implementing standardization processing, obtain a training data set.

[0009] Step 2: Perform hierarchical time series analysis on the training data set to obtain a linear transformation matrix W, a linear loading matrix P, a nonlinear transformation function and a time series regression matrix V for calculating the fault index; wherein, can perform a nonlinear transformation on any given residual vector .

[0010] Step 3: After setting the threshold of the fault index, repeat the following steps 3-1 to 3-2 at the sampling time interval.

[0011] Step 3-1: Obtain a group of data of the industrial process at the latest sampling moment t, perform standardization processing on it, and then calculate the corresponding fault index

[0012] Step 3-2: Judge whether is greater than If not, the industrial process is operating normally; if so, a fault occurs.

[0013] In the above implementation steps, the key core technology of the method of the present invention lies in the hierarchical timing analysis implemented in step 2, which successively includes linear timing analysis and non-linear timing analysis; first, the purpose of the linear timing analysis is to obtain the linear transformation matrix W and the linear load matrix P, so that the linear score matrix S and the residual matrix can be calculated according to S = X T W and calculate the linear score matrix S and the residual matrix respectively wherein, each column vector in the matrix X is composed of each group of data in the training data set, and any linear transformation vector w in W satisfies the following condition ①:

[0014] wherein, X τ =[x τ ,x τ+1 ,…,x τ+N-d-1 T , X d+1 =[x d+1 ,x d+2 ,…,x N T , the superscript T represents the transpose of a matrix or vector, β τ represents the timing weight, x τ ,x τ+1 ,…,x τ+N-d-1 respectively represent the column vectors of the τ-th, τ+1-th, to τ+N-d-1-th columns in X, N is equal to the total number of column vectors in X, the timing order d is an integer not less than 2 and not greater than 10, and the timing number τ = 1, 2, …, d.

[0015] Then, perform non-linear timing analysis on , and use the gradient descent method to train and obtain the coefficient matrix in and the bias vector b, as well as the timing regression matrix V; wherein, tanh represents the hyperbolic tangent function, represents any residual vector in

[0016] wherein, respectively represent the i+d-th, i+d-1-th, i+d-2-th, to i-th residual vectors in

[0017] ​​It can be seen that the hierarchical timing analysis involved in the present invention includes a timing analysis process in two stages, namely: first, linear timing analysis is performed, and then non-linear feature analysis is implemented to comprehensively represent the linear and non-linear timing change features in the normal operating condition data, overcoming the defect that the traditional method only focuses on the timing change feature analysis of a single aspect.

[0018] In addition, when calculating the fault index, it is necessary to sequentially pass through u = x T W, and e = h - V T z Φ to calculate the corresponding linear feature vector u, residual vector non-linear feature vector h, and regression error vector e, and then calculate the fault index according to where x represents a column vector composed of any set of data after standardization processing, Λ 1 = S T S(N - 1), Λ 2 = H T H(N - 1), non-linear score matrix α 1 α, 2 α 3 and α are three weighting coefficients,

[0019] respectively representing the residual vectors corresponding to the column vectors at the previous 1, previous 2, and up to the previous d sampling moments of x. From the formula for calculating the fault index T it can be seen that the fault index calculates the weighted sum of the squared Mahalanobis distances corresponding to the linear feature vector u = x W and the non-linear feature vector

[0020] Comprehensively and fully utilizes the feature components extracted by linear timing analysis and non-linear timing analysis to monitor the change of data, so as to detect faults in time. T XX T w = 1, so that the Lagrange multiplier method can be used for solution, that is: first construct the following Lagrange function J:

[0021] Then, after making the partial differential equations of J with respect to w and λ equal to 0, the following two equalities can be obtained:

[0022] in, β=[β 1 ,β 2 ,…,β d ] T .

[0023] For those skilled in the art, the above formula ④ defines a generalized eigenvalue problem, while the above formula ⑤ defines the equation relationship between β and w; in addition, since the above formula ① is for solving the minimum value problem, the w in the above formula ④ is equivalent to the eigenvector corresponding to the minimum eigenvalue λ.

[0024] Since d time series weights β are required to solve the generalized eigenvalue problem in equation ④ above, 1 ,β 2 ,…,β d , and when calculating β through the above formula ⑤, w needs to be known. Therefore, the calculation of these two equations is coupled with each other and can only be calculated by iteration.

[0025] In summary, the present invention preferably implements linear timing analysis according to steps A1 to A4 as shown below to obtain a linear transformation matrix W and a linear load matrix P.

[0026] Step A1, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps A1-1 to A1-2 until w converges.

[0027] Step A1-1, follow calculate After that, set Among them, the d data in β are recorded as d time series weights β 1 ,β 2 ,…,β d .

[0028] Step A1-2, follow the and Calculate separately and G, and then solve the eigenvalue problem Gv = λLv, and then find the eigenvector v corresponding to the smallest eigenvalue λ. Update w; where L = XX T .

[0029] Step A3: X=X-ps T After updating X, return to step A1 to continue solving the next linear transformation vector and linear load vector.

[0030] Step A4. After respectively and correspondingly combining the obtained several linear transformation vectors and linear load vectors into \(W\) and \(P\), then update \(W\) according to \(W = W(P T W) -1 Update \(W\).

[0031] As another improvement of the present invention, linear time series analysis can also be implemented according to Steps B1 to B5 as shown below to obtain a linear transformation matrix \(W\), a linear score matrix \(S\), and a linear load matrix \(P\).

[0032] Step B1. Determine corresponding near neighborhoods for each column vector in \(X\) to calculate the near neighborhood weight matrix \(M\) corresponding to \(X\), so as to calculate the near neighborhood reconstruction error matrix \(Y\) according to \(Y = X(I - M)\).

[0033] Step B2. After initializing the linear transformation vector \(w\) to be equal to any non - zero vector, then repeatedly execute the following Steps B2 - 1 to B2 - 2 until \(w\) converges.

[0034] Step B2 - 1. Calculate Calculate After that, set where, \(d\) data in \(β\) are denoted as \(d\) time series weights \(β 1 ,β 2 ,…,β d .

[0035] Step B2 - 2. Calculate and respectively to calculate and \(G\) respectively, then solve the eigenvector \(v\) corresponding to the smallest eigenvalue \(λ\) in the generalized eigenvalue problem \(Gv = λLv\), and update \(w\) according to ; where, \(L = YY T .

[0036] Step B3. Calculate the linear score vector \(s\) and the linear load vector \(p\) successively according to \(s = X T w\) and \(p = Xs T / (s T s)\), and then execute Step B4.

[0037] Step B4. Update \(X\) through \(X = X - ps T and then return to Step B2 to continue solving the next linear transformation vector and linear load vector.

[0038] Step B5. After respectively and correspondingly combining the obtained several linear transformation vectors and linear load vectors into \(W\) and \(P\), then update \(W\) according to \(W = W(P T W) -1 Update \(W\).

[0039] The difference between this improved technical solution and the above steps A1 to A4 is that: first, the neighbor reconstruction implementation process in step B1 is added; second, the generalized eigenvalue problem is transformed into Gv = λYY T v. The generalized eigenvalue problem actually comes from using the Lagrange multiplier method to solve the minimization problem shown below: swt T X(IM)(IM) T X T w=w T YY T w=1

[0040] The above constraints w T YY T In fact, w=1 further takes into account the spatial neighbor distribution relationship of the data through neighbor domain reconstruction. Therefore, the improved scheme involving the use of steps B1 to B5 can take into account the neighbor relationship of the spatial distribution of the data while implementing linear time series analysis, thereby being able to more comprehensively implement linear time series analysis from the two perspectives of time series and spatial neighbor distribution, which is conducive to extracting more useful feature components for subsequent fault monitoring.

[0041] As another improvement of the linear timing analysis implementation scheme in the present invention, the linear timing analysis can also be implemented according to steps C1 to C4 as shown below to obtain the linear transformation matrix W, the linear score matrix S, and the linear load matrix P.

[0042] Step C1, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps C1-1 to C1-2 until w converges.

[0043] Step C1-1, follow calculate Reset Afterwards, through Update β; the d data in β are recorded as d time series weights β 1 ,β 2 ,…,β d .

[0044] Step C1-2, follow the formula and Calculate separately G, and L, and then solve the eigenvalue problem Gv = λLv, the eigenvector v corresponding to the largest eigenvalue λ, according to Update w.

[0045] Step C2: According to s=X Tw and p = Xs T (s T After calculating the linear score vector s and the linear loading vector p in sequence, step C3 is executed.

[0046] Step C3: Update X by X = X - ps T and then return to step C1 to continue solving for the next linear transformation vector and the linear loading vector p.

[0047] Step C4: After respectively corresponding and merging the obtained several linear transformation vectors and linear loading vectors into W and P, then according to W = W(P T W) -1 Update W.

[0048] The implementation schemes related to steps C1 to C4 above are derived from solving the following minimization problem with additional constraints and :

[0049] Due to the existence of the two newly added constraints, the following equation holds:

[0050] Therefore, the objective function to be minimized in the above formula ⑦ is equivalent to the following maximized objective function:

[0051] Using the Lagrange multiplier method can also achieve the solution of the above formula ⑨ with two additional constraints: and ; By first constructing the Lagrangian function and then setting its partial differential equations with respect to w and β = [β 1 ,β 2 ,…,β d T equal to 0, two equations as shown below can be equivalently deduced:

[0052] The two equations in the above formula ⑩ are respectively used in steps C1-1 and C1-2.

[0053] The minimization problem with constraints defined in the above formula ⑦ aims to minimize the prediction error of the time series autoregressive model, so as to analyze and extract the characteristic components that can best describe the time series prediction relationship. From this perspective, this improved implementation scheme of linear time series analysis has stronger interpretability for the dynamic changes of time series when analyzing and extracting linear time series features, and is more conducive to subsequent fault monitoring.

[0054] ​It should be noted that the above three improved implementation schemes for linear timing analysis all involve updating X by X = X - ps T to continue solving the next linear transformation vector different from the previously solved one. The advantage of this implementation is that it can ensure that the obtained multiple linear score vectors are orthogonal to each other, and can avoid redundancy between linear timing features.

[0055] To solve for multiple linear transformation vectors, updating X by X = X - ps T is not the only optional solution. It is also possible not to execute X = X - ps T , but instead require that the linear transformation vectors are orthogonal to each other. In view of this, the present invention adjusts the above three improved implementation schemes for linear timing analysis. The specific adjustment scheme is as follows: First, replace the generalized eigenvalue problem Gv = λLv solved in step A1-2, step B2-2, or step C1-2 with the eigenvalue problem where, is a matrix formed by combining the obtained linear transformation vectors. If no linear transformation vectors have been obtained yet, then

[0056] Secondly, cancel the operation of updating X by X = X - ps T and at the same time cancel the operation of updating W according to W = W(P T W) -1 .

[0057] The multiple linear transformation vectors obtained by solving the eigenvalue problem are orthogonal to each other, and can achieve the same linear timing analysis goal from different levels, achieving a similar feature extraction effect.

[0058] In addition, the above step A1-2, step B2-2, or step C1-2 all involve solving the generalized eigenvalue problem Gv = λLv, and only focus on solving the eigenvector corresponding to one eigenvalue, that is, the smallest eigenvalue or the largest eigenvalue. To avoid redundant calculations and speed up the implementation of linear timing analysis, the present invention preferably solves the eigenvector corresponding to the largest or smallest eigenvalue in the generalized eigenvalue problem Gv = λLv according to the following steps D1 to D4.

[0059] Step D1: Perform singular value decomposition on L to obtain L = UAU T ; where A represents a diagonal matrix composed of non-zero singular values corresponding to L, and U is a unitary matrix obtained by singular value decomposition of L.

[0060] Step D2: Set C = UA -0.5 , and according to G = CT After the GC updates G, solve the eigenvector ε corresponding to the largest or smallest eigenvalue in the eigenvalue problem Gε = λε.

[0061] Step D3: After setting v = Cε, the eigenvector v to be solved in the original generalized eigenvalue problem Gv = λLv can be obtained.

[0062] As a further improvement of the fault monitoring method involved in the present invention, it is preferably to set three weighting coefficients α according to the following steps E1 to E3 1 , α 2 and α 3 .

[0063] Step E1: According to Calculate the linear monitoring index φ 1 (x) corresponding to any column vector x in X, and then record the standard deviation of these linear monitoring indexes as γ 1 , thereby setting α 1 = 1 / γ 1 ; where u = x T W.

[0064] Step E2: According to Calculate the non-linear monitoring index φ 2 (x) corresponding to any column vector x in X, and then record the standard deviation of these non-linear monitoring indexes as γ 2 , thereby setting α 2 = 1 / γ 2 ; where,

[0065] Step E3: According to φ 3 (x) = e T e Calculate the error monitoring index φ 3 (x) corresponding to any column vector x in X, and then record the standard deviation of these error monitoring indexes as γ 3 , thereby setting α 3 = 1 / γ 3 ; where e = h - V T z Φ .

[0066] Finally, based on the same inventive concept, the present invention also discloses a fault monitoring system based on hierarchical time series analysis, including a hardware module and a software module; wherein, the hardware module is composed of a data acquisition unit, a data operation unit, a monitoring display unit and a fault alarm, and the function introductions of each component unit are as follows.

[0067] The data acquisition unit will obtain a set of data at the latest sampling moment according to the sampling time interval of the industrial process and immediately send it to the data operation unit; the data operation unit first performs standardization processing on the received data, and then successively passes through u = x T W, and e = h - V T z Φ to calculate the corresponding linear feature vector u, residual vector nonlinear feature vector h, and regression error vector e, and then calculate the fault index and immediately send the fault index to the monitoring and display unit; where x represents the column vector composed of the data received by the data operation unit.

[0068] After receiving the fault index , the monitoring and display unit first determines whether it is greater than the threshold If so, trigger the fault alarm; if not, keep the fault alarm silent; then use the specific value as the vertical axis data and the latest sampling moment as the horizontal axis data to draw the corresponding monitoring curve, and at the same time display the threshold in the form of a horizontal line.

[0069] The software module stores programs for performing linear time series analysis and nonlinear time series analysis, and can, according to the initialization instruction, execute steps 1 to 2, and then send the obtained linear transformation matrix W, linear score matrix S, linear loading matrix P, nonlinear transformation function and time series regression matrix V to the data operation unit for storage, and at the same time send the set threshold to the monitoring and display unit for storage.

[0070] It can be seen that the functions implemented by the hardware module of this fault monitoring system are to perform real-time monitoring of faults according to steps 3-1 to 3-2; while the software module is mainly responsible for training the corresponding parameters for the calculation of the data operation unit and judging whether there is a fault; of course, the most critical programs for linear time series analysis and nonlinear time series analysis are also stored in the software module.

[0071] As an improvement to the above fault monitoring system, the program for linear time series analysis stored in the software module can execute the implementation schemes for performing the above various linear time series analyses. Since different linear time series analyses can achieve different effects, writing corresponding programs according to the implementation steps of different linear time series analyses can be applicable to the fault monitoring tasks of different industrial objects, thereby ensuring the applicable range of the fault monitoring system.

[0072] As another improvement to the above fault monitoring system, the data acquisition unit in the hardware module stores the data at the previous sampling moment. When a certain data acquisition fails at the latest sampling moment, the corresponding data at the previous sampling moment stored is immediately used as the data for which the acquisition fails.

[0073] Since signal transmission may sometimes be affected by the on-site measurement environment, there is a small probability of data acquisition failure. Using the corresponding data at the previous sampling moment as a substitute can effectively address the problem of data acquisition failure. The reason for using the corresponding data at the previous sampling moment is that when the industrial process is running smoothly, the data at two consecutive sampling moments is very close, which can minimize the negative impact of the replacement deviation. Brief Description of the Drawings

[0074] Figure 1 It is the flowchart of the implementation of the fault monitoring method involved in the present invention.

[0075] Figure 2 It is a schematic diagram of the magnesium melting smelting process.

[0076] Figure 3 It is a schematic diagram of the details of the fault monitoring of the fault monitoring method involved in the present invention.

[0077] Figure 4 It is the implementation process of the linear time series analysis used in the second embodiment.

[0078] Figure 5 It is the fault monitoring schematic diagram corresponding to the second embodiment.

[0079] Figure 6 It is the implementation process of the linear time series analysis used in the third embodiment.

[0080] Figure 7 It is the fault monitoring schematic diagram corresponding to the third embodiment.

[0081] Figure 8 It is the fault monitoring schematic diagram corresponding to the fourth embodiment.

[0082] Figure 9 It is the schematic diagram of the composition structure of the fault monitoring system involved in the present invention. Detailed Embodiment

[0083] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0084] The present invention first discloses a fault monitoring method based on hierarchical time series analysis, and its implementation process is as Figure 1 shown. To test and verify the effectiveness of this fault monitoring method, it is applied to Figure 2The shown magnesium smelting process solves the problem of its fault monitoring.

[0085] As Figure 2 The shown magnesium smelting process produces refractory magnesium oxide, which is a basic material for metallurgical, chemical and other industrial processes. Figure 2 Some main equipment units of the magnesium smelting process are shown in [reference]. The smelting process involves the use of an electric arc furnace, which includes a control center, a furnace body, an electrode lifting mechanism, a power supply, and a raw material feeder. When magnesium oxide is smelted in the furnace, the feeder evenly feeds the raw materials into the furnace, and the power supply system provides a large current to form a high-temperature electric arc between the two electrodes. The raw materials are melted and purified to magnesium oxide at ultra-high temperature. The process object can measure the three-phase current, voltage, and power in real time at each sampling moment, and these power data can provide valuable information to be mined for monitoring its operating state.

[0086] Apply the fault monitoring method disclosed in the present invention to the fault monitoring task of the magnesium smelting process. The implementation process includes the following steps 1 to 3.

[0087] Step 1: Collect data during the normal operation of the industrial process. After implementing standardization processing, a training data set is obtained. Here, we collected data at 1000 consecutive sampling moments, and the corresponding training data set consists of 1000 groups of data after standardization processing.

[0088] Step 2: Perform hierarchical time series analysis on the training data set to obtain a linear transformation matrix W, a linear loading matrix P, a non-linear transformation function and a time series regression matrix V; where can perform a non-linear transformation on any given residual vector

[0089] The hierarchical time series analysis in the above step 2 includes linear time series analysis and non-linear time series analysis in sequence; first, the purpose of the linear time series analysis is to obtain W and P, so that the linear score matrix S and the residual matrix T W and can be calculated respectively; where each column vector in the matrix X is composed of each group of data in the training data set, and any linear transformation vector w in W satisfies the foregoing condition ①. Then, perform non-linear time series analysis on using the gradient descent method to train and obtain the coefficient matrix in and the bias vector b, as well as the time series regression matrix V; where tanh represents the hyperbolic tangent function, represents any residual vector in ​​

[0090] Step 3: Set the threshold of the fault index After that, repeat the following Steps 3-1 to 3-2 at the sampling time interval. In this step, we use the kernel density estimation method to set the threshold of the anomaly index, and the confidence limit is set to be equal to 99%.

[0091] Step 3-1: Obtain a set of data of the industrial process at the latest sampling moment t, perform standardization processing on it, and then calculate the corresponding fault index

[0092] Step 3-2: Judge whether it is greater than If not, the industrial process is operating normally; if so, a fault occurs

[0093] In this embodiment, when calculating the fault index corresponding to any given column vector x, it is necessary to successively pass through u = x T W, and e = h - V T z Φ to calculate the corresponding linear eigenvector u, residual vector nonlinear eigenvector h, and regression error vector e, and then calculate the fault index according to Calculate the fault index where three weighting coefficients α 1 , α 2 and α 3 are all equal to 1 to balance the monitoring weights of the changes of various different types of characteristic components.

[0094] It should be noted that after obtaining the fault indexes corresponding to the column vectors in X, the maximum value of them can be directly determined as the threshold, which is the simplest and most direct way to determine the threshold; of course, the average value of the largest multiple anomaly indexes can also be taken as the threshold. Therefore, the kernel density estimation method used in this embodiment is only a specific illustration of the anomaly detection method involved in the present invention, rather than a limitation on the technical solution of the present invention.

[0095] Plot the fault indexes corresponding to another 500 sets of data of the magnesium smelting process at the latest 500 sampling moments in Figure 3 Since the threshold no longer changes once it is determined, so Figure 3 the horizontal line in represents the threshold

[0096] From Figure 3It can be found that from the 151st latest sampling time, the corresponding fault indicators are mostly located at Figure 2 Above the middle horizontal line, that is, greater than the threshold, the fault is detected promptly and accurately.

[0097] The second embodiment of the present invention is as follows Figure 4 The implementation flow shown in the figure is used to implement linear timing analysis, including steps A1 to A4 shown below:

[0098] Step A1, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps A1-1 to A1-2 until w converges.

[0099] Step A1-1, follow calculate After that, set Among them, the d data in β are recorded as d time series weights β 1 ,β 2 ,…,β d .

[0100] Step A1-2, follow the and Calculate separately and G, and then solve the eigenvalue problem Gv = λLv, and then find the eigenvector v corresponding to the smallest eigenvalue λ. Update w; where L = XX T .

[0101] Step A2: According to s=X T w and p = Xs T / (s T s) After calculating the linear score vector s and the linear load vector p in sequence, execute step A3.

[0102] Step A3: X=X-ps T After updating X, return to step A1 to continue solving the next linear transformation vector and linear load vector.

[0103] Step A4: After the obtained linear transformation vectors and linear load vectors are respectively merged into W and P, the linear transformation vectors are respectively merged into W=W(P T W) -1 Update W.

[0104] Since 9 data can be measured at each sampling moment in the magnesium smelting process, namely three-phase current, voltage and electric power, in this embodiment, we merge the obtained 3 linear transformation vectors and 3 linear load vectors into W and P respectively.

[0105] Based on the linear time series analysis implemented in the above steps A1 to A4, and fault monitoring is performed on the data of the same 500 latest sampling moments. The corresponding details of the fault monitoring are as Figure 5 shown. Compared with the fault monitoring effect in Figure 3 , there is a slight improvement in the fault monitoring result in Figure 5 , further improving the sensitivity of the fault monitoring.

[0106] The third embodiment of the present invention implements the linear time series analysis according to the implementation process as Figure 6 shown, including the following steps B1 to B5.

[0107] Step B1: Determine the corresponding neighborhood for each column vector in X to calculate the neighborhood weight matrix M corresponding to X, and then calculate the neighborhood reconstruction error matrix Y according to Y = X(I - M).

[0108] Step B2: After initializing the linear transformation vector w to any non-zero vector, repeatedly execute the following steps B2-1 to B2-2 until w converges.

[0109] Step B2-1: Calculate and then set , where the d data in β are denoted as d time series weights β , β 1 , β 2 , …, β d .

[0110] Step B2-2: Calculate and respectively to calculate and G, and then solve the eigenvector v corresponding to the smallest eigenvalue λ in the generalized eigenvalue problem Gv = λLv, and update w according to ; where L = YY T .

[0111] Step B3: Calculate the linear score vector s and the linear loading vector p in sequence according to s = X T w and p = Xs T / (s T s), and then execute Step B4.

[0112] Step B4: Update X through X = X - ps T , and then return to Step B2 to continue solving the next linear transformation vector and linear loading vector.

[0113] Step B5: After merging the obtained several linear transformation vectors and linear loading vectors into W and P respectively, then according to W = W(P T W) -1Update W. Here, three linear transformation vectors are also combined to obtain W, and three linear load vectors are combined to obtain P.

[0114] Based on the above steps B1 to B5, perform linear time series analysis, and perform fault monitoring on the data at the same 500 latest sampling moments. The corresponding details of the fault monitoring are as Figure 7 shown in the right figure in Figure 3 and Figure 5 . Compared with the fault monitoring effects in Figure 7 , the sensitivity of the fault monitoring in

[0115] is further improved. This is mainly due to the fact that the implementation scheme of this linear time series analysis takes into account the spatial neighborhood distribution characteristics. Figure 8 The fourth embodiment of the present invention performs linear time series analysis according to the above-mentioned steps C1 to C4, and the corresponding details of the fault monitoring are as Figure 5 shown, and the sensitivity of its fault monitoring is comparable to the fault monitoring effect shown in

[0116] In the fifth embodiment of the present invention, the execution process of the time series analysis in any one of the above-mentioned second to fourth embodiments is replaced. Specifically: First, replace the implementation process of solving the generalized eigenvalue problem Gv = λLv with: solving the eigenvalue problem where is a matrix combined by the obtained linear transformation vectors. If no linear transformation vectors have been obtained yet, then Secondly, cancel the operation of updating X by X = X - ps T and at the same time cancel the operation of updating W according to W = W(P T W) -1 .

[0117] Based on the replaced linear time series analysis, a fault monitoring effect similar to that in Figure 3 , Figure 5 , Figure 7 and Figure 8 can be obtained, so it will not be elaborated here.

[0118] In the above embodiments, the eigenvector corresponding to the largest or smallest eigenvalue in the generalized eigenvalue problem Gv = λLv can also be solved according to the above-mentioned steps D1 to D3 to improve the efficiency of data operation processing.

[0119] In addition, in the above embodiments, α 1 = α 2 = α 3= 1, without considering the differences in the changes of different characteristic components. To address this issue, the above embodiments can also refer to the foregoing steps E1 to E3 to set three weighting coefficients α 1 , α 2 and α 3 .

[0120] Based on the same inventive concept as the foregoing fault monitoring method, the present invention also provides a fault monitoring system accordingly. Its structural composition is as shown in Figure 9 , including a software module and a hardware module composed of a data acquisition unit, a data operation unit, a monitoring display unit, and a fault alarm.

[0121] In the fault monitoring system shown in Figure 9 , the data acquisition unit will, according to the sampling time interval of the industrial process, acquire the data at the latest sampling moment in real time and immediately send it to the data operation unit; the data operation unit first performs standardization processing on the received data, and then successively calculates the corresponding linear feature vector u, residual vector T , and e = h - V T z Φ to calculate the corresponding linear feature vector u, residual vector non - linear feature vector h, and regression error vector e. Then, according to calculate the fault index and immediately send the fault index to the monitoring display unit; after receiving the fault index , the monitoring display unit first determines whether it is greater than the threshold If so, trigger the fault alarm; if not, keep the fault alarm silent; then use the specific value of as the vertical - axis data and the latest sampling moment as the horizontal - axis data to draw the corresponding monitoring curve, and at the same time display the threshold in the form of a horizontal line.

[0122] Figure 7 The software module shown in stores programs for performing linear time - series analysis and non - linear time - series analysis, and can, according to the initialization instruction, execute steps 1 to 2, and then send the obtained linear transformation matrix W, linear score matrix S, linear loading matrix P, non - linear transformation function and time - series regression matrix V to the data operation unit for storage, and at the same time send the set threshold

[0123] to the monitoring display unit for storage.

[0124] Finally, as another improved implementation solution of the fault monitoring system, the data acquisition unit in the hardware part stores the data of the previous sampling moment. When the acquisition of a certain data at the latest sampling moment fails, the corresponding data of the previous sampling moment stored is immediately used as the data for which the acquisition fails.

[0125] The explanatory description of the technical solution disclosed by the present invention in conjunction with the accompanying drawings is illustrative rather than restrictive. The technical solution disclosed by the present invention is not limited to the above-mentioned embodiments. Modifications made without departing from the purpose of the technical solution disclosed by the present invention and within the scope protected by the claims all fall within the protection scope of the present invention.

Claims

1. A fault monitoring method based on hierarchical timing analysis, comprising the following steps 1 to 3: Step 1: Collect data during normal operation of the industrial process, and obtain a training data set after standardization. Step 2: Perform hierarchical time series analysis on the training data set to obtain the linear transformation matrix W, linear load matrix P, and nonlinear transformation function for calculating the fault index. and the time series regression matrix V; where, For any given residual vector Implement nonlinear transformations; Step 3: Set the threshold of the fault indicator Then, repeat the following steps 3-1 to 3-2 according to the sampling time interval; Step 3-1, obtain a set of data of the industrial process at the latest sampling time t, perform standardization on it, and then calculate the corresponding fault index Step 3-2: Judgment Is it greater than If not, the industrial process is operating normally; if yes, a fault has occurred; The characteristic is that: the hierarchical timing analysis implemented in step 2 includes linear timing analysis and nonlinear timing analysis in sequence; firstly, the purpose of the linear timing analysis is to obtain W and P, so that S=X T W and Calculate the linear score matrix S and the residual matrix respectively Among them, each column vector in the matrix X is composed of each group of data in the training data set, and any linear transformation vector w in W satisfies the following condition ①: Among them, X τ =[x τ ,x τ+1 ,…,x τ+N-d-1 ] T , X d+1 =[x d+1 ,x d+2 ,…,x N ] T , the superscript T represents the transpose of a matrix or vector, β τ represents the time series weight, x τ ,x τ+1 ,…,x τ+N-d-1 denote the column vectors of the τth, τ+1th, to τ+Nd-1th columns in X, respectively, N is equal to the total number of column vectors in X, the time series order d is equal to an integer not less than 2 and not greater than 10, and the time series number τ=1,2,…,d; Then, yes Implement nonlinear timing analysis and use gradient descent to train The coefficient matrix in and the bias vector b, and the time series regression matrix V; where tanh represents the hyperbolic tangent function, express For any residual vector in , the optimization objective used in the training process is as follows: in, Respectively The residual vectors of the i+dth, i+d-1th, i+d-2th, to the ith column in , numbered i=1,2,…,Nd; When calculating the fault index, it is necessary to sequentially pass u=x T W. and e=hV T z Φ Calculate the corresponding linear eigenvector u and residual vector After the nonlinear feature vector h and the regression error vector e, we can Calculating Failure Indicators Where x represents a column vector of any set of data after standardization, Λ1=S T S / (N-1), Λ2=H T H / (N-1), nonlinear scoring matrix α1, α2 and α3 are three weighting coefficients, They represent the residual vectors corresponding to the column vectors of the sampling time points one, two, and d before x, respectively.

2. A fault monitoring method according to claim 1, characterized in that: The steps of implementing the linear timing analysis include the following steps A1 to A4: Step A1, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps A1-1 to A1-2 until w converges; Step A1-1: Follow calculate After that, set Among them, the d data in β are recorded as d time series weights β1, β2, …, β d ; Step A1-2, follow the and Calculate separately and G, and then solve the eigenvalue problem Gv = λLv, and then find the eigenvector v corresponding to the smallest eigenvalue λ. Update w; where L = XX T ; Step A2: According to s=X T w and p = Xs T / (s T s) After calculating the linear score vector s and the linear load vector p in sequence, executing step A3; Step A3: X=X-ps T After updating X, return to step A1 to continue solving the next linear transformation vector and linear load vector; Step A4: After the obtained linear transformation vectors and linear load vectors are respectively merged into W and P, W=W(P T W) -1 Update W.

3. A fault monitoring method according to claim 1, characterized in that: The process of implementing the linear timing analysis includes the following steps B1 to B5: Step B1, determining a corresponding nearest neighbor domain for each column vector in X to calculate a nearest neighbor weight matrix M corresponding to X, thereby calculating a nearest neighbor reconstruction error matrix Y according to Y=X(IM); Step B2, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps B2-1 to B2-2 until w converges; Step B2-1, follow calculate After that, set Among them, the d data in β are recorded as d time series weights β1, β2, …, β d ; Step B2-2: Follow the steps below: and Calculate separately and G, and then solve the eigenvalue problem Gv = λLv, and then find the eigenvector v corresponding to the smallest eigenvalue λ. Update w; where L = YY T ; Step B3: According to s=X T w and p = Xs T / (s T s) After calculating the linear score vector s and the linear load vector p in sequence, execute step B4; Step B4: X=X-ps T After updating X, return to step B2 to continue solving the next linear transformation vector and linear load vector; Step B5: After the obtained linear transformation vectors and linear load vectors are respectively merged into W and P, W=W(P T W) -1 Update W.

4. A fault monitoring method according to claim 1, characterized in that: The process of implementing the linear timing analysis includes steps C1 to C4: Step C1, after initializing the linear transformation vector w to be equal to any non-zero vector, repeat the following steps C1-1 to C1-2 until w converges; Step C1-1, follow calculate Reset Afterwards, through Update β; the d data in β are recorded as d time series weights β1, β2, …, β d ; Step C1-2, follow the formula and Calculate separately G, and L, and then solve the eigenvalue problem Gv = λLv, the eigenvector v corresponding to the largest eigenvalue λ, according to Update w; Step C2: According to s=X T w and p = Xs T / (s T s) After calculating the linear score vector s and the linear load vector p in sequence, executing step C3; Step C3: X=X-ps T Update X, and then return to step C1 to continue solving the next linear transformation vector and linear load vector p; Step C4: After the obtained linear transformation vectors and linear load vectors are respectively merged into W and P, W=W(P T W) -1 Update W.

5. A fault monitoring method according to any one of claims 2 to 4, characterized in that: First, replace the implementation process of solving the generalized eigenvalue problem Gv = λLv with: Solving the eigenvalue problem in, is a matrix formed by combining the obtained linear transformation vectors. If no linear transformation vectors have been obtained, then Secondly, cancel the execution by X = X-ps T Update the operation of X and cancel the execution according to W = W (P T W) -1 Update the operation of W.

6. A fault monitoring method according to any one of claims 2 to 4, characterized in that: Solve the eigenvector corresponding to the maximum or minimum eigenvalue in the generalized eigenvalue problem Gv=λLv according to steps D1 to D3 shown below: Step D1: Perform singular value decomposition on L to obtain L = UAU T ; Where A represents the diagonal matrix composed of non-zero singular values ​​corresponding to L, and U is the unitary matrix obtained by singular value decomposition of L; Step D2: Set C = UA -0.5 , and according to G=C T After GC updates G, it solves the eigenvalue problem Gε=λε and finds the eigenvector ε corresponding to the maximum or minimum eigenvalue; Step D3: After setting v=Cε, the eigenvector v to be solved in the original generalized eigenvalue problem Gv=λLv can be obtained.

7. A fault monitoring method according to any one of claims 1 to 4, characterized in that: The three weighting coefficients α1, α2 and α3 are set according to steps E1 to E3 as shown below: Step E1: According to φ1(x)=uΛ1 -1 u T After calculating the linear monitoring index φ1(x) corresponding to any column vector x in X, the standard deviation of these linear monitoring indicators is recorded as γ1, so as to set α1 = 1 / γ1; Where u = x T W; Step E2: According to φ2(x)=h T Λ2 -1 After calculating the nonlinear monitoring index φ2(x) corresponding to any column vector x in X, the standard deviation of these nonlinear monitoring indicators is recorded as γ2, so as to set α2 = 1 / γ2; where, Step E3, Step E3, according to φ3(x)=e T After calculating the error monitoring index φ3(x) corresponding to any column vector x in X, the standard deviation of these error monitoring indicators is recorded as γ3, so as to set α3 = 1 / γ3; where e = hV T z Φ .

8. A fault monitoring system based on hierarchical timing analysis, comprising a software module and a hardware module consisting of a data acquisition unit, a data calculation unit, a monitoring display unit and a fault alarm; wherein: The data acquisition unit will obtain a set of data at the latest sampling time according to the sampling time interval of the industrial process and send it to the data operation unit immediately; The data operation unit first performs standardization on the received data, and then passes u=x T W. and e=hV T z Φ Calculate the corresponding linear eigenvector u and residual vector After the nonlinear feature vector h and the regression error vector e, according to Calculating Failure Indicators And immediately send the fault indicator Send to the monitoring display unit; The monitoring display unit receives the fault indicator After that, first determine whether it is greater than the threshold If yes, the fault alarm is triggered; if no, the fault alarm is kept silent; then The specific value is the vertical axis data, and the latest sampling time is the horizontal axis data, and the corresponding monitoring curve is drawn. Displayed in horizontal lines; The software module is characterized in that the software module stores a program for executing linear timing analysis and nonlinear timing analysis, and can execute steps 1 to 2 according to the initialization instruction, and then obtain the linear transformation matrix W, linear score matrix S, linear load matrix P, nonlinear transformation function and the time series regression matrix V are sent to the data operation unit for storage, and the set threshold Send to the monitoring display unit for storage.

9. A fault monitoring system according to claim 8, characterized in that: The linear timing analysis program stored in the software module can execute the implementation process of the linear timing analysis described in claims 2 to 6.

10. A fault monitoring system according to claim 8 or 9, characterized in that: The data acquisition unit in the hardware module stores the data of the previous sampling moment. When the acquisition of a certain data at the latest sampling moment fails, the corresponding data stored at the previous sampling moment is immediately used as the data that failed to be acquired.

Images