A ternary cathode material preparation process monitoring method and system based on FDALM

Abstract

The present invention discloses a ternary cathode material preparation process monitoring method and system based on FDALM, which is applied to the monitoring of the sintering process of ternary cathode materials. The sintering process of ternary cathode materials is a typical process industry, and the production process involves many mutually coupled chemical reactions, including combination, hydrolysis and side reactions. Firstly, based on the technology of dynamic autoregressive latent variable model, with the help of factor modeling method, a factor FDALM modeling method is derived. The factor FDALM modeling method models data with both dynamic and multimodal characteristics, and uses an improved EM algorithm to learn model parameters; then, in order to give full play to the process output of each factor model, the statistical values of the sub-models are fused into the posterior failure probability of the sample with the help of Bayesian inference technology; finally, the simulation results compared with other models show that the proposed monitoring method is capable of tracking the modal fluctuations of the process.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection in the preparation process of ternary cathode materials, and in particular discloses a method and system for monitoring the preparation process of ternary cathode materials based on a Factor Dynamic Autoregression Latent Variable Model (FDALM). Background Art

[0002] The preparation of ternary cathode materials involves a complex process within a roller hearth kiln, with multiple interconnected processes simultaneously occurring, including material transfer, energy exchange, heat convection and diffusion. To simplify the system, the sintering process is divided into three temperature zones based on temperature trends: a heating zone, a constant temperature zone, and a cooling zone. Each zone incorporates oxygen and temperature adjustments tailored to the chemical reactions occurring. Under specific temperature and oxygen conditions, the materials undergo the desired reactions in the corresponding temperature zones. However, deviations from the set sintering schedule can result in substandard product quality and energy waste. Therefore, real-time monitoring of the sintering process is implemented to adjust the sintering schedule, providing real-time guidance to operators on adjusting operating parameters.

[0003] However, the chemical reactions occurring within the roller hearth kiln are interconnected, so the data generated at the current moment is influenced by historical data, resulting in high-order dynamic characteristics. Furthermore, the roller hearth kiln operates 24 hours a day, and the chemical reactions are particularly sensitive to temperature and the raw material mixing ratio. The periodic fluctuations in the external ambient temperature cause the process to exhibit multiple stable operating conditions, resulting in multimodal characteristics in the process data. Therefore, a monitoring method for the ternary cathode material preparation process that simultaneously considers both the high-order dynamic characteristics and multimodal characteristics of the process is urgently needed to ensure the smooth operation of the ternary cathode material preparation system.

[0004] Therefore, due to the high-order dynamic characteristics and multimodal characteristics of the preparation process of ternary positive electrode materials, the traditional monitoring methods have low fault detection rate and high false alarm rate, which is a technical problem that needs to be solved urgently. Summary of the Invention

[0005] The present invention provides a ternary cathode material preparation process monitoring method and system based on FDALM, aiming to solve the technical problems of low fault detection rate and high false alarm rate of traditional monitoring methods due to the high-order dynamic characteristics and multimodal characteristics of the ternary cathode material preparation process.

[0006] One aspect of the present invention relates to a method for monitoring the preparation process of a ternary cathode material based on FDALM, comprising the following steps:

[0007] Data preparation and preprocessing, collect historical data xh (k), k = 1, 2, .., T is used as the model training set, and each sample is standardized; where, is the m-dimensional process observation data, k is the time label, and T is the number of samples;

[0008] The time lag coefficient L and system factor K of the model are identified by using time lag identification and clustering algorithm respectively, and the factor dynamic autoregressive latent variable model is established to initialize the model parameters Θ old ;

[0009] The improved EM algorithm is used to identify the relevant parameters of the factor dynamic autoregressive latent variable model;

[0010] Based on the obtained factor dynamic autoregressive latent variable model, define the factor dynamic autoregressive latent variable model under each sub-mode Statistics, and determine the control threshold of the sub-model and significance level α;

[0011] Collect online data x(k), k = 1, 2, .., N as the test set of the model and perform normalization;

[0012] The test set is tested based on the obtained factor dynamic autoregressive model, and the test samples under each sub-modality are calculated. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

[0013] Furthermore, the time lag identification and clustering algorithms are used to identify the time lag coefficient L and system factor K of the model respectively, and a factor dynamic autoregressive latent variable model is established to initialize the model parameters Θ old The steps include:

[0014] The time lag coefficient L is obtained by identifying the trend similarity algorithm;

[0015] The physical interpretation of the system factor K is the number of categories of data partitioning, which is identified by the affine cluster propagation algorithm based on the genetic algorithm;

[0016] Using the preprocessed data set, a factor dynamic autoregressive latent variable model is constructed.

[0017] Furthermore, the steps of using the improved EM algorithm to identify relevant parameters of the factor dynamic autoregressive latent variable model include:

[0018] In the E-step, a reasonable estimation is made of the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing;

[0019] In the M step, the model parameters are updated by maximizing the likelihood function, the Lagrange multiplier formula is constructed, and the factor coefficients are updated using the factor constraints in the M step.

[0020] Furthermore, based on the obtained factor dynamic autoregressive latent variable model, the factor dynamic autoregressive latent variable model under each sub-mode is defined. Statistics, and determine the control threshold of the sub-model In the steps of the significance level α, for the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable that drives the dynamic change process. The latent variable of each sub-modal can establish the corresponding Statistics, The statistic is calculated using the following formula:

[0021]

[0022] in, represents the T2 statistic of the kth sub-mode, represents the latent variable z t q About x 1：t q ,y 1：t q The transpose of the conditional expectation, covariance represents the latent variable z t q About x 1：t q ,y 1：t q The covariance of E(z t q |x 1：t q ,y l：t q ) represents the latent variable z t q About x 1：t q ,y 1：t q The conditional expectation of

[0023] In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows:

[0024]

[0025]

[0026] in, represents the prior probability of process data failure, represents the prior probability that the process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; represents the prior probability of process data failure; represents the normal prior probability of process data;

[0027] Will and Combined with the significance level α, the following formula is defined:

[0028]

[0029]

[0030] Where α represents the significance level; the actual size is the balance between false positives and false negatives. In order to obtain the failure probability of a new data sample Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula:

[0031]

[0032]

[0033] in, represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

[0034] Furthermore, the test set is tested based on the obtained factor dynamic autoregressive model, and the test samples under each sub-modality are calculated. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will In the step of comparing with the significance level α and outputting the test results, after the probability of failure of each local model is determined, the Bayesian inference technology is further used to fuse the failure probability of each sub-modal to obtain the failure probability of the sample. Failure probability of the sample Calculated by the following formula:

[0035]

[0036] in, represents the failure probability of the sample, P(k|x t ) Factor k about x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability of

[0037] By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula:

[0038]

[0039] in, represents the failure probability of the sample, and α represents the significance level.

[0040] Another aspect of the present invention relates to a ternary cathode material preparation process monitoring system based on FDALM, comprising:

[0041] The preprocessing module is used for data preparation and preprocessing. h (k), k = 1, 2, .., T is used as the model training set, and each sample is standardized; where, is the m-dimensional process observation data, k is the time label, and T is the number of samples;

[0042] Establish a module for identifying the lag coefficient L and system factor K of the model using time lag identification and clustering algorithms, establish a factor dynamic autoregressive latent variable model, and initialize the model parameters Θ old ;

[0043] Identification module, used to identify relevant parameters of the factor dynamic autoregressive latent variable model using an improved EM algorithm;

[0044] Determination module, used to define the dynamic autoregressive latent variable model of each sub-mode based on the obtained factor dynamic autoregressive latent variable model Statistics, and determine the control threshold of the sub-model and significance level α;

[0045] The collection module is used to collect online data x(k), k = 1, 2, ..., N as the test set of the model and perform normalization processing;

[0046] The calculation module is used to detect the test set based on the obtained factor dynamic autoregressive model and calculate the test sample under each sub-modality. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

[0047] Furthermore, the building blocks include:

[0048] A first acquisition unit is used to obtain a time lag coefficient L by identifying a trend similarity algorithm;

[0049] The second acquisition unit is used to identify and obtain the system factor K through an affine clustering propagation algorithm based on a genetic algorithm. The system factor K is physically interpreted as the number of categories of data division;

[0050] The first construction unit is used to construct a factor dynamic autoregressive latent variable model using the preprocessed data set.

[0051] Furthermore, the identification module includes:

[0052] The estimation unit is used to reasonably estimate the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing in the E step;

[0053] The second construction unit is used to update the model parameters in the M step by using the method of maximizing the likelihood function, construct a Lagrange multiplier formula, and update the factor coefficients using the factor constraints in the M step.

[0054] Furthermore, in the determination module, for the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable driving the operation of the dynamic change process, and the latent variable of each sub-modality can establish the corresponding Statistics, The statistic is calculated using the following formula:

[0055]

[0056] in, represents the T2 statistic of the kth submode, E(z t q |x 1：t q ,y 1：t q ) Trepresents the latent variable z t q About x 1：t q ,y 1：t q The transpose of the conditional expectation, covariance represents the latent variable z t q About x 1：t q ,y 1：t q The covariance of E(z t q |x 1：t q ,y l：t q ) represents the latent variable z t q About x 1：t q ,y 1：t q The conditional expectation of

[0057] In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows:

[0058]

[0059]

[0060] in, represents the prior probability of process data failure, represents the prior probability that the process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; represents the prior probability of process data failure; represents the normal prior probability of process data;

[0061] Will and Combined with the significance level α, the following formula is defined:

[0062]

[0063]

[0064] Where α represents the significance level; the actual size is the balance between false positives and false negatives. In order to obtain the failure probability of a new data sample Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula:

[0065]

[0066]

[0067] in, represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

[0068] Furthermore, in the calculation module, after the probability of failure of each local model is determined, the Bayesian reasoning technology is further used to fuse the failure probability of each sub-modal to obtain the failure probability of the sample. Failure probability of the sample Calculated by the following formula:

[0069]

[0070] in, represents the failure probability of the sample, P(k|x t ) Factor k about x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability of

[0071] By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula:

[0072]

[0073] in, represents the failure probability of the sample, and α represents the significance level.

[0074] The beneficial effects achieved by the present invention are:

[0075] The present invention provides a ternary cathode material preparation process monitoring method and system based on FDALM, which uses data preparation and preprocessing to collect historical data x h(k), k = 1, 2, .., T as the model training set, and standardize each sample; use the time lag identification and clustering algorithms to identify the model's time lag coefficient L and system factor K respectively, establish a factor dynamic autoregressive latent variable model, and initialize the model parameters Θ old ; Use the improved EM algorithm to identify the relevant parameters of the factor dynamic autoregressive latent variable model; Based on the obtained factor dynamic autoregressive latent variable model, define the factor dynamic autoregressive latent variable model under each sub-mode Statistics, and determine the control threshold of the sub-model and significance level α; collect online data x(k), k = 1, 2, .., N as the test set of the model and perform standardization; test the test set based on the obtained factor dynamic autoregressive model and calculate the test sample under each sub-modality And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

[0076] The FDALM-based ternary cathode material preparation process monitoring method and system provided by the present invention are applied to the monitoring of the sintering process of ternary cathode materials. The sintering process of ternary cathode materials is a typical process industry, and the production process involves many mutually coupled chemical reactions, including combination, hydrolysis and side reactions. If the temperature of these reactions is not well controlled, side reactions will occur. These side reactions are reversible. Therefore, the fluctuations in the external environment and materials will cause the process to be in different steady-state processes. This causes the process to have certain multimodal characteristics. At the same time, the coupling of different temperature zones causes the data to be correlated before and after, that is, the dynamic nature of the process data cannot be ignored, which makes the process data present complex characteristics. Based on the technology of dynamic autoregressive latent variable models, this paper first uses factor modeling methods to derive a factor FDALM modeling method. This factor FDALM modeling method models data with both dynamic and multimodal characteristics and uses an improved EM algorithm to learn model parameters. Then, to fully utilize the process output of each factor model, the statistical values of the sub-models are fused into the posterior failure probability of the sample with the help of Bayesian inference technology. Finally, simulation results compared with other models show that the proposed monitoring method is capable of tracking modal fluctuations of the process. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 A schematic flow chart of an embodiment of a method for monitoring the preparation process of a ternary cathode material based on FDALM provided by the present invention;

[0078] Figure 2 A flow chart of an embodiment of process monitoring combining the FDALM model and Bayesian reasoning in the FDALM-based ternary cathode material preparation process monitoring method provided by the present invention;

[0079] Figure 3 A process data classification diagram of an embodiment of the FDALM-based ternary cathode material preparation process monitoring method provided by the present invention;

[0080] Figure 4 Schematic diagram of monitoring results of abnormal temperature rise in temperature zone using different methods in the FDALM-based ternary cathode material preparation process monitoring method provided by the present invention;

[0081] Figure 5 Schematic diagram of monitoring results of abnormal temperature drop in temperature zone using different methods in the FDALM-based ternary cathode material preparation process monitoring method provided by the present invention;

[0082] Figure 6 Schematic diagram of monitoring results of roller kiln shutdown failure using different methods in the FDALM-based ternary cathode material preparation process monitoring method provided by the present invention;

[0083] Figure 7 This is a functional block diagram of an embodiment of a ternary cathode material preparation process monitoring system based on FDALM provided by the present invention;

[0084] Figure 8 for Figure 7 Schematic diagram of functional modules of an embodiment of a building module shown in FIG;

[0085] Figure 9 for Figure 7 FIG. 1 is a functional module diagram of an embodiment of an identification module shown in FIG.

[0086] Description of Figure Numbers:

[0087] 10. Preprocessing module; 20. Establishment module; 30. Identification module; 40. Determination module; 50. Collection module; 60. Calculation module; 21. First acquisition unit; 22. Second acquisition unit; 23. First construction unit; 31. Estimation unit; 32. Second construction unit. DETAILED DESCRIPTION

[0088] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0089] like Figures 1 to 6As shown, the first embodiment of the present invention proposes a method for monitoring the preparation process of a ternary cathode material based on FDALM, comprising the following steps:

[0090] Step S100: Data preparation and preprocessing: collect historical data x h (k), k = 1, 2, .., T is used as the model training set, and each sample is standardized; where, is the m-dimensional process observation data, k is the time label, and T is the number of samples.

[0091] The dataset used for model training and testing was collected from a typical ternary cathode material production plant. The sintering process of ternary materials is crucial to battery material performance, so accurate monitoring of the sintering process is essential to ensure product quality while reducing energy consumption. A total of seven observation variables were selected: the first six are critical temperature measurements in the heating zone, and the last is an observation of residual lithium, which characterizes product quality. A total of 2,200 consecutive moments of data were selected. This sequence of data represents the factory consistently producing the same batch of battery materials, with a sampling period of 30 minutes. The dataset was preprocessed, or normalized, by subtracting the sample mean of each element from the sample set and then dividing by the sample standard deviation. This ensures that the data corresponding to each process variable and key quality variable have a mean of 0 and a variance of 1.

[0092] Step S200: Use time lag identification and clustering algorithms to identify the time lag coefficient L and system factor K of the model respectively, establish a factor dynamic autoregressive latent variable model, and initialize the model parameters Θ old .

[0093] Step S200 includes:

[0094] Step S210: Obtain the time lag coefficient L by identifying through a trend similarity algorithm.

[0095] Step S220 : The physical interpretation of the system factor K is the number of categories of data division, which is identified by an affine clustering propagation algorithm based on a genetic algorithm.

[0096] Step S230: Using the preprocessed data set, construct a factor dynamic autoregressive latent variable model.

[0097] The time lag coefficient L is identified by the trend similarity algorithm. The physical interpretation of the factor K is the number of categories of data division, which is identified by the affine clustering propagation algorithm based on the genetic algorithm.

[0098] Using the preprocessed data set, a factor dynamic autoregressive latent variable model is constructed, assuming that the data set satisfies the following relationship:

[0099]

[0100] In formula (1), z t，k ∈R d represents the hidden variable describing the state of the system in mode k at the current time t, h t，k The augmented latent variable h represents the hidden state of the state at time t and the previous L moments under mode k. t，k =[z t， k T z t-1，k T …z t-L+1，k T ] T ∈R dL , L is the time delay coefficient obtained by the time delay identification algorithm. t，k ∈R v A represents the system observation variable composed of process variables and quality variables under mode k at time t, d and v represent the dimensions of latent variables and observation variables respectively. k ∈R d×dL Indicates that from the augmented latent variable h t-1，k Transfer to the current hidden variable z t，k The state transition matrix of B. k ∈R v×d represents the latent variable z t，k Diverge to the observed variable x t，k The divergence matrix of . are the Gaussian noises of the latent variables and observed variables of mode k respectively. Assuming that the noises are independent of each other, the distributions they obey are The zero-mean Gaussian distribution.

[0101] The model parameter Θ of the entire dynamic autoregressive latent variable model is:

[0102] Θ={A k , B k , μ π，k ,∑ π，k ,∑ z，k ,∑ x，k ,P(k)|k=1,2,…,K} (2)

[0103] In formula (2), μ π，k and Σ π，k are the augmented latent variables h at the initial moment 0，k The mean and variance of the Gaussian distribution; ∑ z，k ,∑ x，k They are respectively represented as the variance of the Gaussian noise of the latent variable and the observed variable of mode k; P(k) is the factor coefficient under different modes.

[0104] Step S300: using an improved EM algorithm to identify relevant parameters of a factor dynamic autoregressive latent variable model.

[0105] Step S300 includes:

[0106] Step S310: In step E, a reasonable estimate is made of the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing.

[0107] Step S320: In the M step, the model parameters are updated by using the method of maximizing the likelihood function, a Lagrange multiplier formula is constructed, and the factor coefficients are updated using the factor constraints in the M step.

[0108] Because the FDALM structure not only involves unobservable latent variables but also requires identification of the system factor K and its corresponding coefficients, the traditional EM algorithm cannot meet this requirement. Therefore, a modified EM algorithm is employed to solve the model parameters. In the E-step, Bayesian filtering and smoothing are used to reasonably estimate the expected value of the extended dynamic latent variables and the posterior distribution of the factor K. In the M-step, the model parameters are updated by maximizing the likelihood function. Furthermore, a Lagrange multiplier formula is constructed to update the coefficients using the factor constraints in the M-step.

[0109] In step E, the model parameters {A k , B k , μ π，k ,∑ π，k ,∑ z，k ,∑ x，k , P(k)|k=1,2,…,K} are randomly initialized, where A k =[A 1，k , A 2，k ,…,A L，k ]. Using Bayesian filtering and smoothing to expand the dynamic latent variable expectation E z (z t，k ), And the posterior distribution of factor k P(k|x t ) to make an accurate estimate, the main disclosures are as follows:

[0110]

[0111] In formula (3), E z (z t，k ) indicates that the expected value of the latent variable at time t is estimated using the sample information at time 1:T; x 1：T Represents 1: all samples at time T; Θ old Represents the parameter set of the previous iteration; Represent the kth submodal latent variable ht，k About the observation sequence x 1：T The mean and variance of the posterior probability distribution of ; represents the kth submodal latent variable h t，k About the observation sequence x 1：T The transpose of the mean of the posterior probability distribution of ; represents the latent variable h at the kth submodal lag i t，k About the observation sequence x 1：T The transpose of the mean of the posterior probability distribution of A i，k represents the state transfer matrix of the latent variable under the kth sub-mode at lag i; represents the covariance between the i-th variable at time t-1 and the variable lagged by L times; represents the latent variable h of the kth submode at time t-1 and lag i t，k About the observation sequence x 1：T The mean of the posterior probability distribution of ; represents the latent variable h of the kth submode at time t-1, which is lagged by L. t，k About the observation sequence x 1：T The transpose of the mean of the posterior probability distribution of ; Indicates that the covariance of the latent variable at time t is estimated using the sample information at time 1:T; Indicates that the covariance of latent variables at time t and time ti is estimated using the sample information at time 1:T; Indicates that the covariance of latent variables at time t and time tL is estimated using the sample information at time 1:T; m t，k and M t，k are the kth submodal latent variables h t，k About the observation sequence x 1：T The mean and variance of the posterior probability distribution of .

[0112] Another type of latent variable is the posterior probability P(k|x t ), where t = 0, 1, ..., T, the mathematical solution is as follows:

[0113]

[0114] In formula (4), P(k|x t ) represents the posterior probability of factor k; P(x t |k) represents the conditional probability of the observed variable under the kth mode; P(k) represents the factor coefficient; P(x t ) represents the observed variable x t Probability of occurrence.

[0115] In the M step, the model parameters {A k , B k , μ π，k ,∑ π，k ,∑ z，k ,∑ x，k , P(k)|k=1,2,…,K}update:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] In formulas (5) to (10), Respectively represent the mean and variance of the updated augmented latent variable h0 under the kth mode; Represents the state transfer matrix, observation matrix, latent variable variance update value and corresponding transpose under the kth mode; represents the covariance estimate of the augmented latent variable at time t-1 under the kth mode; represents the covariance estimate of the latent variable at time t and the augmented latent variable at time t-1 under the k-th mode; represents the covariance estimate of the initial augmented latent variable under the kth mode; represents the covariance estimate of the latent variable under the kth mode at lag i; x t represents the observed variable; E z (h 0，k ) represent the expectations of the latent variables and the initial augmented latent variables at time t under the k-th mode, respectively.

[0123] To update the factor coefficient P(k), since the factor involves more constraints, it is necessary to construct optimization conditions for it separately. First, all terms related to P(k) are separated and expressed as follows:

[0124]

[0125] In formula (11), g(k) represents the log-likelihood function of the factor coefficient P(k); P(k|x t ) represents the posterior probability of factor k; P(k) represents the factor coefficient.

[0126] Due to the constraints Introducing the Lagrange multiplier λ, constructing it into the form of Lagrange function, as shown below:

[0127]

[0128]

[0129] In formulas (12) to (13), f(k) represents the Lagrangian function constructed to update the factor coefficient P(k); P(k|x t ) represents the posterior probability of factor k; g(k) represents the log-likelihood function of the factor coefficient P(k), and λ represents the Lagrange multiplier.

[0130] And add the k terms on both sides of the above two equations (for k), and we get:

[0131]

[0132] In formula (14), P(k) represents the factor coefficient, and λ represents the Lagrange multiplier.

[0133] Substituting the result back into Formula 13 yields the factor coefficient, as shown in the following formula:

[0134]

[0135] In formula (15), P(k) represents the factor coefficient, P(k|x t ) represents the posterior probability of factor k.

[0136] In the process of building the model, the maximum likelihood values of the new model parameters are calculated and compared with the corresponding maximum likelihood values of the original model parameters. If the error threshold is met, the process proceeds to step S400, otherwise the model parameters are iteratively updated. For example, after each M steps, the new model parameters Θ are new and old model parameters Θ old Compare, if satisfy ||Θ old -Θ new If ||≤σ, the model training is complete and the process proceeds to step S400. Otherwise, the model parameters are updated according to the EM algorithm strategy of step S300. Where σ is the threshold for model convergence, and the complete log-likelihood function of the model is as follows:

[0137]

[0138] In formula (16), Q(Θ|Θ old ) means converting the log-likelihood function into the log-likelihood function InP(x1：T , z 1-L：T |Θ) About the latent variable z 1-L：T The conditional expectation of In{P(k)P(x 1：T , z 1-L：T |k)} is In(x 1：T , z 1-L：T , k|Θ old ) is expanded according to the conditional probability formula; InP(k) is the logarithm of the modal factor probability; cons represents a constant; B k z t，k and other items are all parts of the logarithmic expansion of the Gaussian distribution.

[0139] Step S400: Based on the obtained factor dynamic autoregressive latent variable model, define the factor dynamic autoregressive latent variable model under each sub-mode Statistics, and determine the control threshold of the sub-model and significance level α.

[0140] It is necessary to define the model under each sub-mode Statistics, and determine the control threshold of the sub-model and significance level α.

[0141] For the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable that drives the dynamic change process. The latent variable of each sub-modal can establish the corresponding Statistics, The statistic is calculated using the following formula:

[0142]

[0143] In formula (17), represents the T2 statistic of the kth submode, E(z t q |x 1：t q ,y 1：t q ) T represents the latent variable z t q About x 1：t q ,y 1：t q The transpose of the conditional expectation, covariance represents the latent variable z t q About x 1：t q ,y 1：t q The covariance of E(zt q |x l：t q ,y l：t q ) represents the latent variable z t q About x 1：t q ,y 1：t q conditional expectation of .

[0144] In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows:

[0145]

[0146] In formula (18), represents the prior probability of process data failure, represents the prior probability that the process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; represents the prior probability of process data failure; represents the prior probability that the process data is normal.

[0147] Will and Combined with the significance level α, the following formula is defined:

[0148]

[0149] In formula (19), α represents the significance level; the actual size is the balance between false positives and false negatives, in order to obtain the failure probability of new data samples Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula:

[0150]

[0151] In formula (20), represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

[0152] Step S500: Collect online data x(k), k=1, 2, .., N as a test set of the model and perform standardization.

[0153] The dataset used for model training and testing was collected from a typical ternary cathode material production plant. The ternary material sintering process is crucial to battery material performance, so accurate monitoring of the sintering process is essential to ensure product quality while reducing energy consumption. A total of seven observation variables were selected: the first six are critical temperature measurements in the heating zone, and the last is an observation of residual lithium, which characterizes product quality. A total of 2,200 consecutive moments of data were selected. This sequence of data represents the factory's consistent production of the same batch of battery materials, with a sampling period of 30 minutes. The dataset was preprocessed or normalized. Normalization involves subtracting the sample mean of each element in the sample set from the corresponding variable and then dividing by the sample standard deviation, ensuring that the data corresponding to each process variable and key quality variable have a mean of 0 and a variance of 1.

[0154] Step S600: Test the test set based on the obtained factor dynamic autoregressive model and calculate the test sample under each sub-modality. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

[0155] After the probability of failure of each local model is determined, the Bayesian inference technology is further used to fuse the failure probability of each sub-modal to obtain the failure probability of the sample. Failure probability of the sample Calculated by the following formula:

[0156]

[0157] In formula (21), represents the failure probability of the sample, P(k|x t ) Factor k about x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability.

[0158] By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula:

[0159]

[0160] In formula (22), represents the failure probability of the sample, and α represents the significance level.

[0161] The FDALM-based ternary cathode material preparation process monitoring method provided in the present embodiment is applied to the monitoring of the sintering process of ternary cathode materials. The sintering process of ternary cathode materials is a typical process industry, and the production process involves numerous mutually coupled chemical reactions, including combination, hydrolysis and side reactions. If these reactions are not well controlled by temperature, side reactions will occur. These side reactions are reversible. Therefore, the fluctuations in the external environment and materials will cause the process to be in different steady-state processes. This results in certain multimodal characteristics in the process. At the same time, the coupling of different temperature zones causes the data to be correlated before and after, that is, the dynamic nature of the process data cannot be ignored, so that the process data presents complex characteristics. Based on the dynamic autoregressive latent variable model technology, the present invention first uses factor modeling methods to derive a factor FDALM modeling method. This factor FDALM modeling method models data with both dynamic and multimodal characteristics and uses an improved EM algorithm to learn model parameters. Then, to fully utilize the process output of each factor model, the statistical values of the sub-models are fused into the posterior failure probability of the sample with the help of Bayesian inference technology. Finally, simulation results compared with other models show that the proposed monitoring method is capable of tracking the modal fluctuations of the process.

[0162] Please see Figures 7 to 9 The present invention also provides a ternary cathode material preparation process monitoring system based on FDALM, which includes a pre-processing module 10, a building module 20, an identification module 30, a determination module 40, a collection module 50 and a calculation module 60. The pre-processing module 10 is used for data preparation and pre-processing, and collects the historical data x h (k), k = 1, 2, .., T is used as the model training set, and each sample is standardized; where, is the m-dimensional process observation data, k is the time label, and T is the number of samples; a module 20 is established to use the time lag identification and clustering algorithms to identify the time lag coefficient L and system factor K of the model respectively, establish a factor dynamic autoregressive latent variable model, and initialize the model parameters Θ old; Identification module 30, for identifying the relevant parameters of the factor dynamic autoregressive latent variable model using the improved EM algorithm; determination module 40, for defining the factor dynamic autoregressive latent variable model under each sub-mode based on the obtained factor dynamic autoregressive latent variable model Statistics, and determine the control threshold of the sub-model and significance level α; a collection module 50 is used to collect online data x(k), k = 1, 2, .., N as a test set of the model and perform standardization processing; a calculation module 60 is used to detect the test set based on the obtained factor dynamic autoregressive model and calculate the test sample under each sub-modality. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

[0163] Further, see Figure 8 , Figure 8 for Figure 7 , in which the functional module diagram of an embodiment of the establishment module 1 is shown. In this embodiment, the establishment module 20 includes a first acquisition unit 21, a second acquisition unit 22 and a first construction unit 23, wherein the first acquisition unit 21 is used to obtain the lag coefficient L by identifying the trend similarity algorithm; the second acquisition unit 22 is used to obtain the system factor K by identifying the affine clustering propagation algorithm based on the genetic algorithm, and the system factor K is physically interpreted as the number of categories of data division; the first construction unit 23 is used to use the preprocessed data set to construct a factor dynamic autoregressive latent variable model.

[0164] Preferably, see Figure 9 , Figure 9 for Figure 7 , in which the identification module 30 includes an estimation unit 31 and a second construction unit 32, wherein the estimation unit 31 is used to reasonably estimate the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing in the E step; the second construction unit 32 is used to update the model parameters in the M step by means of the method of maximizing the likelihood function, construct the Lagrange multiplier formula, and update the factor coefficients using the factor constraints in the M step.

[0165] Furthermore, in the determination module 40, for the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable driving the operation of the dynamic change process, and the latent variable of each sub-modality can establish the corresponding Statistics, The statistic is calculated using the following formula:

[0166]

[0167] In formula (23), represents the T2 statistic of the kth submode, E(z t q |x 1：t q ,y 1：t q ) T represents the latent variable z t q About x 1：t q ,y 1：t q The transpose of the conditional expectation, covariance represents the latent variable z t q About x 1：t q ,y 1：t q The covariance of E(z t q |x l：t q ,y l：t q ) represents the latent variable z t q About x l：t q ,y l：t q conditional expectation of .

[0168] In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows:

[0169]

[0170] In formula (24), represents the prior probability of process data failure, represents the prior probability that the process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; represents the prior probability of process data failure; represents the normal prior probability of process data;

[0171] Will and Combined with the significance level α, the following formula is defined:

[0172]

[0173] In formula (25), α represents the significance level; the actual size is the balance between false positives and false negatives, in order to obtain the failure probability of a new data sample Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula:

[0174]

[0175] In formula (26), represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

[0176] Furthermore, in the calculation module 60, after the probability of failure of each local model is determined, the Bayesian reasoning technology is further used to fuse the failure probability of each sub-modal to obtain the failure probability of the sample. Failure probability of the sample Calculated by the following formula:

[0177]

[0178] In formula (27), represents the failure probability of the sample, P(k|x t ) Factor k about x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability.

[0179] By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula:

[0180]

[0181] In formula (28), represents the failure probability of the sample, and α represents the significance level.

[0182] The FDALM-based ternary cathode material preparation process monitoring system provided in this embodiment is applied to the monitoring of the sintering process of ternary cathode materials. The sintering process of ternary cathode materials is a typical process industry, and the production process involves many mutually coupled chemical reactions, including combination, hydrolysis and side reactions. If these reactions are not well controlled by temperature, side reactions will occur. These side reactions are reversible. Therefore, the fluctuations in the external environment and materials will cause the process to be in different steady-state processes. This results in certain multimodal characteristics in the process. At the same time, the coupling of different temperature zones causes the data to be correlated before and after, that is, the dynamic nature of the process data cannot be ignored, which makes the process data present complex characteristics. Based on the technology of dynamic autoregressive latent variable models, this paper first uses factor modeling methods to derive a factor FDALM modeling method. This factor FDALM modeling method models data with both dynamic and multimodal characteristics and uses an improved EM algorithm to learn model parameters. Then, to fully utilize the process output of each factor model, the statistical values of the sub-models are fused into the posterior failure probability of the sample with the help of Bayesian inference technology. Finally, simulation results compared with other models show that the proposed monitoring system is capable of tracking modal fluctuations of the process.

[0183] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such changes and modifications as fall within the scope of the claims and their equivalents.

Claims

1. A ternary cathode material preparation process monitoring method based on FDALM, characterized in that: The following steps are involved: Data preparation and preprocessing, collect historical data x h (k), k=1,2,..,T is used as the model training set, and each sample is standardized; is the m-dimensional process observation data, k is the time label, and T is the number of samples; The time lag coefficient L and system factor K of the model are identified by using time lag identification and clustering algorithm respectively, and the factor dynamic autoregressive latent variable model is established to initialize the model parameters Θ old Specifically, the method includes: obtaining the time lag coefficient L through a trend similarity algorithm, obtaining the system factor K through an affine clustering propagation algorithm based on a genetic algorithm, wherein the system factor K is physically interpreted as the number of categories of data division, and constructing a factor dynamic autoregressive latent variable model using the preprocessed data set; An improved EM algorithm is used to identify the relevant parameters of the factor dynamic autoregressive latent variable model; Based on the obtained factor dynamic autoregressive latent variable model, define the factor dynamic autoregressive latent variable model under each sub-mode Statistics, and determine the control threshold of the sub-model and significance level α; Online data x(k), k = 1, 2, ..., N, is collected as the test set for the model and standardized. The data set used for model training and testing comes from the production workshop of ternary cathode materials. Seven observation variables are selected, and the first six variables are temperature measurement data in the heating zone. The test set is tested based on the obtained factor dynamic autoregressive model, and the test samples under each sub-modality are calculated. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

2. The FDALM-based ternary cathode material preparation process monitoring method according to claim 1, characterized in that: The step of using the improved EM algorithm to identify relevant parameters of the factor dynamic autoregressive latent variable model includes: In the E-step, a reasonable estimation is made of the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing; In the M step, the model parameters are updated by maximizing the likelihood function, the Lagrange multiplier formula is constructed, and the factor coefficients are updated using the factor constraints in the M step.

3. The FDALM-based ternary cathode material preparation process monitoring method according to claim 1, characterized in that: Based on the obtained factor dynamic autoregressive latent variable model, the factor dynamic autoregressive latent variable model is defined under each sub-mode. Statistics, and determine the control threshold of the sub-model In the steps of the significance level α, for the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable that drives the dynamic change process. The latent variable of each sub-modal can establish the corresponding Statistics, The statistic is calculated using the following formula: in, represents the T2 statistic of the kth submode, E(z t q |x 1:t q ,y 1:t q ) T represents the latent variable z t q About x 1:t q ,y 1:t q The transpose of the conditional expectation of represents the latent variable z t q About x 1:t q ,y 1:t q The covariance of E(z t q |x 1:t q ,y 1:t q ) represents the latent variable z t q About x 1:t q ,y 1:t q The conditional expectation of In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows: in, represents the prior probability of the kth modal process data failure, represents the prior probability that the kth modal process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; Will and Combined with the significance level α, the following formula is defined: Where α represents the significance level; the actual size is the balance between false positives and false negatives, in order to obtain the failure probability of a new data sample Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula: in, represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

4. The method for monitoring the preparation process of a ternary cathode material based on FDALM according to claim 1, wherein: The test set is tested based on the obtained factor dynamic autoregressive model, and the test samples under each sub-modality are calculated. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will In the step of comparing with the significance level α and outputting the test results, after the probability of failure of each local model is determined, the Bayesian inference technology is further used to fuse the failure probability of each sub-modal to obtain the failure probability of the sample. Failure probability of the sample Calculated by the following formula: in, represents the failure probability of the sample, P(k|x t ) represents the factor k with respect to x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability of By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula: in, represents the failure probability of the sample, and α represents the significance level.

5. A ternary cathode material preparation process monitoring system based on FDALM, characterized in that: include: The preprocessing module (10) is used for data preparation and preprocessing, and collects historical data x h (k), k=1,2,..,T is used as the model training set, and each sample is standardized; is the m-dimensional process observation data, k is the time label, and T is the number of samples; Establish module (20) for identifying the time lag coefficient L and system factor K of the model using time lag identification and clustering algorithm, establish factor dynamic autoregressive latent variable model, and initialize model parameters Θ old Specifically, the method includes: obtaining the time lag coefficient L through a trend similarity algorithm, obtaining the system factor K through an affine clustering propagation algorithm based on a genetic algorithm, wherein the system factor K is physically interpreted as the number of categories of data division, and constructing a factor dynamic autoregressive latent variable model using the preprocessed data set; an identification module (30), configured to identify relevant parameters of the factor dynamic autoregressive latent variable model using an improved EM algorithm; Determination module (40), for defining the factor dynamic autoregressive latent variable model under each sub-mode based on the obtained factor dynamic autoregressive latent variable model Statistics, and determine the control threshold of the sub-model and significance level α; A collection module (50) is used to collect online data x(k), k = 1, 2, .., N as a test set for the model and perform standardization processing, wherein the data set used for model training and testing comes from the production workshop of ternary cathode materials, and 7 observation variables are selected, and the first 6 variables are temperature measurement data in the heating zone; The calculation module (60) is used to detect the test set based on the obtained factor dynamic autoregressive model and calculate the test sample under each sub-modality. And use Bayesian inference technology to fuse each submodality Statistics, get the sample posterior failure probability Will Compare with the significance level α and output the test results.

6. The FDALM-based ternary cathode material preparation process monitoring system according to claim 5, characterized in that: The identification module (30) comprises: An estimation unit (31) is used to reasonably estimate the posterior distribution of the extended dynamic latent variable expectation and the system factor K based on Bayesian filtering and smoothing in the E step; The second construction unit (32) is used to update the model parameters in the M step by using the method of maximizing the likelihood function, construct a Lagrange multiplier formula, and update the factor coefficients using the factor constraints in the M step.

7. The FDALM-based ternary cathode material preparation process monitoring system according to claim 5, characterized in that: In the determination module (40), for the trained factor dynamic autoregressive latent variable model, the latent variable is the key variable that drives the operation of the dynamic change process. The latent variable of each sub-modality can establish the corresponding Statistics, The statistic is calculated using the following formula: in, represents the T2 statistic of the kth submode, E(z t q |x 1:t q ,y 1:t q ) T represents the latent variable z t q About x 1:t q ,y 1:t q The transpose of the conditional expectation of represents the latent variable z t q About x 1:t q ,y 1:t q The covariance of E(z t q |x 1:t q ,y 1:t q ) represents the latent variable z t q About x 1:t q ,y 1:t q The conditional expectation of In order to make full use of the key information of each mode, the monitoring results of each sub-mode are integrated into the fault probability with the help of Bayesian inference method, and the event probability of failure of the observation sample under the kth mode is constructed as follows: in, represents the prior probability of the kth modal process data failure, represents the prior probability that the kth modal process data is normal, represents the conditional probability of the observed sample occurring under the kth modal fault condition; represents the probability of the observed variable being observed under the kth mode; represents the conditional probability of the observed sample occurring under normal conditions of the kth mode; Will and Combined with the significance level α, the following formula is defined: Where α represents the significance level; the actual size is the balance between false positives and false negatives, in order to obtain the failure probability of a new data sample Construct the conditional probability of the observed samples occurring under normal and fault conditions and define the following formula: in, represents the conditional probability of the observed sample occurring under normal conditions under the kth mode; represents the conditional probability of the observed sample occurring under the fault condition under the kth mode; is the control limit of each mode, and its value is uniquely determined by the degree of freedom d and significance level α of the sub-model; represents the T2 statistic of the kth submodality.

8. The FDALM-based ternary cathode material preparation process monitoring system according to claim 5, characterized in that: In the calculation module (60), after the probability of failure of each local model is determined, the Bayesian reasoning technology is further used to fuse the probability of failure of each sub-modal to obtain the failure probability of the sample Failure probability of the sample Calculated by the following formula: in, represents the failure probability of the sample, P(k|x t ) represents the factor k with respect to x t The posterior probability of Represents the new sample x under factor mode k t The posterior failure probability of By comparing the failure probability with the significance level α, we can determine whether the system has failed. The judgment logic is shown in the following formula: in, represents the failure probability of the sample, and α represents the significance level.

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