CN115270601A - FDALM-based method and system for monitoring preparation process of ternary cathode material - Google Patents

FDALM-based method and system for monitoring preparation process of ternary cathode material Download PDF

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CN115270601A
CN115270601A CN202210720684.7A CN202210720684A CN115270601A CN 115270601 A CN115270601 A CN 115270601A CN 202210720684 A CN202210720684 A CN 202210720684A CN 115270601 A CN115270601 A CN 115270601A
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陈宁
谢沐言
陈嘉瑶
阳春华
桂卫华
胡福海
李彬艳
王凯
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Abstract

The invention discloses a method and a system for monitoring a preparation process of a ternary cathode material based on FDALM (fully drawn aluminum standard), which are applied to monitoring a sintering process of the ternary cathode material, wherein the sintering process of the ternary cathode material is a typical process industry, and the production process relates to a plurality of chemical reactions coupled with each other, including chemical combination, hydrolysis and side reactions. Firstly, deducing a factor FDALM modeling method by means of a factor modeling method on the basis of the technology of a dynamic autoregressive hidden variable model, wherein the factor FDALM modeling method models data with dynamic and multi-modal characteristics at the same time, and an improved EM algorithm is utilized 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 fault probability of the sample by means of a Bayesian inference technology; finally, simulation results compared with other models show that the proposed monitoring method can track modal fluctuations of the process.

Description

FDALM-based method and system for monitoring preparation process of ternary cathode material
Technical Field
The invention relates to the technical field of ternary cathode material preparation process fault detection, and particularly discloses a Factor Dynamic autoregressive hidden Variable Model (FDALM) -based ternary cathode material preparation process monitoring method and system.
Background
The preparation process of the ternary cathode material is a complex process in which substance transmission, energy exchange, heat convection, heat diffusion and other forms of mutual coupling occur simultaneously in a roller kiln. In order to simplify the system, the sintering process is divided into three temperature sections according to the development trend of temperature, namely a temperature rising section, a constant temperature section and a temperature lowering section, and corresponding oxygen and temperature are added into each temperature section according to the generated chemical reaction. Under the condition of specific temperature and oxygen, the materials can generate established reaction in the corresponding temperature zone. However, if the sintering system deviates from the set process, the product quality does not reach the standard or energy is wasted. Therefore, real-time monitoring is established for the sintering process to adjust the sintering system, and operators can be guided to adjust the operating parameters in real time.
However, chemical reactions occurring inside the roller kiln are related, so that data generated at the current moment are influenced by historical moment data, namely the data show high-order dynamic characteristics; in addition, the roller kiln runs continuously twenty-four hours a day, chemical reaction is particularly sensitive to temperature and raw material mixing ratio, and the process presents a plurality of stable working conditions due to the fact that the external environment temperature periodically changes, so that process data presents certain multi-modal characteristics. Therefore, a method for monitoring the preparation process of the ternary cathode material, which considers the high-order dynamic characteristics and the multi-modal characteristics of the process at the same time, is needed to ensure the stable operation of the preparation system of the ternary cathode material.
Therefore, the high-order dynamic characteristics and the multi-modal characteristics presented in the preparation process of the ternary cathode material cause low fault detection rate and high false alarm rate of the traditional monitoring method, and the method is a technical problem to be solved urgently at present.
Disclosure of Invention
The invention provides a method and a system for monitoring a preparation process of a ternary cathode material based on FDALM (fully drawn aluminum model), and aims to solve the technical problems of low fault detection rate and high false alarm rate of the traditional monitoring method due to high-order dynamic characteristics and multi-modal characteristics presented in the preparation process of the ternary cathode material.
The invention relates to a method for monitoring the preparation process of a ternary cathode material based on FDALM, which comprises the following steps:
data preparation and preprocessing, collecting historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003710970710000021
the m-dimensional process observation data is obtained, k is a time label, and T is the number of samples;
respectively identifying a time-lag coefficient L and a system factor K of the model by using a time-lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model, and initializing a model parameter thetaold；
Identifying relevant parameters of a factor dynamic autoregressive hidden variable model by adopting an improved EM algorithm;
defining the factor dynamic autoregressive hidden variable model under each sub-model state based on the obtained factor dynamic autoregressive hidden variable model
Figure BDA0003710970710000026
Statistics ofMeasuring and determining control thresholds for submodels
Figure BDA0003710970710000027
And a significance level α;
collecting online data x (k), k =1, 2., N as a test set of the model, and performing a standardization process;
detecting the test set based on the obtained factor dynamic autoregressive model, and calculating the test sample in each sub-mode
Figure BDA0003710970710000022
And fusing each sub-modality using Bayesian inference techniques
Figure BDA0003710970710000023
Statistics to obtain the posterior fault probability of the sample
Figure BDA0003710970710000024
Will be provided with
Figure BDA0003710970710000025
And comparing with the significance level alpha, and outputting a detection result.
Further, a time lag coefficient L and a system factor K of the model are respectively identified by using a time lag identification algorithm and a clustering algorithm, a factor dynamic autoregressive hidden variable model is established, and a model parameter theta is initializedoldComprises the following steps:
identifying to obtain a time lag coefficient L by a trend similarity algorithm;
the physical interpretation of the system factor K is the number of the types of data division, and the system factor K is obtained by identification through an affine clustering propagation algorithm based on a genetic algorithm;
and constructing a factor dynamic autoregressive hidden variable model by utilizing the preprocessed data set.
Further, the step of identifying relevant parameters of the factor dynamic autoregressive hidden variable model by using the improved EM algorithm comprises the following steps:
in the step E, reasonably estimating the posterior distribution of the expanded dynamic hidden variable expectation and the system factor K based on Bayesian filtering and smoothing;
in the step M, model parameters are updated by means of a method of maximizing a likelihood function, a Lagrange multiplier formula is constructed, and factor coefficients are constrained and updated by using factors in the step M.
Further, based on the obtained factor dynamic autoregressive hidden variable model, defining the factor dynamic autoregressive hidden variable model under each sub-mode
Figure BDA0003710970710000031
Statistics and determining control thresholds for submodels
Figure BDA0003710970710000032
And in the step of the significance level alpha, for the trained factor dynamic autoregressive hidden variable model, the hidden variable is a key variable for driving the operation of the dynamic change process, and the hidden variable of each sub-model can establish a corresponding hidden variable
Figure BDA0003710970710000033
The statistical quantity is calculated by the statistical quantity,
Figure BDA0003710970710000034
the statistic is calculated by the following formula:
Figure BDA0003710970710000035
wherein the content of the first and second substances,
Figure BDA0003710970710000036
t representing the kth sub-modality2The statistical quantity is calculated by the statistical quantity,
Figure BDA0003710970710000037
representing an implicit variable zt qWith respect to x1：t q，y1：t qCovariance, which represents the hidden variable zt qWith respect to x1：t q，y1：t qCovariance of E (z)t q|x1：t q，yl：t q) Representing hidden variables zt qWith respect to x1：t q，y1：t qThe condition of (2) is desired;
in order to fully utilize the key information of each mode, the monitoring results of each sub-mode are fused into fault probability by means of a Bayesian inference method, and the event probability that an observation sample fails in the kth mode is constructed as follows:
Figure BDA0003710970710000038
Figure BDA0003710970710000039
wherein the content of the first and second substances,
Figure BDA00037109707100000310
represents a prior probability of failure of the process data,
Figure BDA00037109707100000311
represents the prior probability that the process data is normal,
Figure BDA00037109707100000312
representing the conditional probability of the observation sample under the k modal fault condition;
Figure BDA00037109707100000313
representing the probability of the observed variable being observed in the k-th modality;
Figure BDA00037109707100000314
representing the conditional probability of the observation sample under the normal condition of the kth mode;
Figure BDA00037109707100000315
representing the conditional probability of the occurrence of the observation sample under the fault condition in the kth mode;
Figure BDA00037109707100000316
representing a process data failure prior probability;
Figure BDA00037109707100000317
representing the normal prior probability of the process data;
will be provided with
Figure BDA00037109707100000318
And
Figure BDA00037109707100000319
in combination with the significance level α, the following formula is defined:
Figure BDA00037109707100000320
Figure BDA00037109707100000321
wherein α represents a significance level; actual size is a balance between false positives and false negatives, failure probability for obtaining new data samples
Figure BDA0003710970710000041
Constructing the conditional probability of observing the occurrence of the sample under normal and fault conditions, and defining the following formula:
Figure BDA0003710970710000042
Figure BDA0003710970710000043
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003710970710000044
indicating the occurrence of the observed sample under normal conditions in the kth modeConditional probability of (d);
Figure BDA0003710970710000045
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure BDA0003710970710000046
is a control limit for each modality, the value of which is uniquely determined by the degree of freedom d and the significance level α of the submodel;
Figure BDA0003710970710000047
t representing the kth sub-modality2And (4) statistic amount.
Further, detecting the test set based on the obtained factor dynamic autoregressive model, and calculating the test sample under each sub-mode
Figure BDA0003710970710000048
And fusing each sub-modality using Bayesian inference techniques
Figure BDA0003710970710000049
Statistics to obtain the posterior fault probability of the sample
Figure BDA00037109707100000410
Will be provided with
Figure BDA00037109707100000411
Comparing with the significance level alpha, and outputting the detection result, after the probability of the fault of each local model of the observation data is determined, fusing the probability of the fault of each sub-model by using Bayesian inference technology to obtain the fault probability of the sample
Figure BDA00037109707100000412
Probability of failure of a sample
Figure BDA00037109707100000413
Calculated by the following formula:
Figure BDA00037109707100000414
wherein the content of the first and second substances,
Figure BDA00037109707100000415
denotes the failure probability of the sample, P (k | x)t) Factor k with respect to xtA posterior probability of (d);
Figure BDA00037109707100000416
indicating the relation to a new sample x under a factor mode ktThe posterior probability of failure of (1);
whether the system fails or not is judged by comparing the failure probability with the significance level alpha, and the judgment logic is shown as the following formula:
Figure BDA00037109707100000417
wherein the content of the first and second substances,
Figure BDA00037109707100000418
indicating the probability of failure of the sample and alpha indicating the level of significance.
Another aspect of the invention relates to a system for monitoring the preparation process of a ternary cathode material based on FDALM, comprising:
a preprocessing module for preparing and preprocessing data and collecting historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003710970710000051
the data are observed in an m-dimensional process, k is a time label, and T is the number of samples;
the establishing module is used for respectively identifying the time lag coefficient L and the system factor K of the model by using time lag identification and clustering algorithms, establishing a factor dynamic autoregressive hidden variable model and initializing model parameters thetaold；
The identification module is used for identifying relevant parameters of the factor dynamic autoregressive hidden variable model by adopting an improved EM algorithm;
a determining module for defining each sub-mode of the factor dynamic autoregressive hidden variable model based on the obtained factor dynamic autoregressive hidden variable model
Figure BDA0003710970710000052
Statistics and determining control thresholds for submodels
Figure BDA0003710970710000053
And a significance level α;
the collecting module is used for collecting online data x (k), wherein k =1, 2., N is used as a test set of the model and carrying out standardization processing;
a calculation module for detecting the test set based on the obtained factor dynamic autoregressive model and calculating the test sample in each sub-mode
Figure BDA0003710970710000054
And fusing each sub-modality using Bayesian inference techniques
Figure BDA0003710970710000055
Statistics to obtain the posterior fault probability of the sample
Figure BDA0003710970710000056
Will be provided with
Figure BDA0003710970710000057
And comparing with the significance level alpha, and outputting a detection result.
Further, the establishing module comprises:
the first acquisition unit is used for identifying and obtaining a time lag coefficient L through a trend similarity algorithm;
the second obtaining unit is used for obtaining a system factor K through affine clustering propagation algorithm identification based on a genetic algorithm, and the system factor K is physically interpreted as the number of types of data division;
and the first construction unit is used for constructing a factor dynamic autoregressive hidden variable model by utilizing the preprocessed data set.
Further, the identification module comprises:
the estimation unit is used for reasonably estimating the posterior distribution of the expansion dynamic hidden variable expectation and the system factor K based on Bayesian filtering and smoothing in the step E;
and the second construction unit is used for updating the model parameters by means of a method of maximizing a likelihood function in the step M, constructing a Lagrange multiplier formula and utilizing the factors in the step M to restrain and update the factor coefficients.
Further, in the determination module, for the trained factor dynamic autoregressive hidden variable model, hidden variables are key variables for driving the operation of the dynamic change process, and the hidden variables of each sub-mode can establish corresponding hidden variables
Figure BDA0003710970710000061
The statistical quantity is calculated by the statistical quantity,
Figure BDA0003710970710000062
the statistic is calculated by the following formula:
Figure BDA0003710970710000063
wherein the content of the first and second substances,
Figure BDA0003710970710000064
t representing the kth sub-modality2Statistic, E (z)t q|x1：t q，y1：t q)TRepresenting hidden variables zt qWith respect to x1：t q，y1：t qCovariance represents the hidden variable zt qWith respect to x1：t q，y1：t qCovariance of E (z)t q|x1：t q，yl：t q) Representing an implicit variable zt qAbout x1：t q，y1：t qThe condition of (2) is desired;
in order to fully utilize the key information of each mode, the monitoring results of each sub-mode are fused into fault probability by means of a Bayesian inference method, and the event probability that an observation sample fails in the kth mode is constructed as follows:
Figure BDA0003710970710000065
Figure BDA0003710970710000066
wherein the content of the first and second substances,
Figure BDA0003710970710000067
represents a prior probability of a failure of the process data,
Figure BDA0003710970710000068
represents a prior probability that the process data is normal,
Figure BDA0003710970710000069
representing the conditional probability of the observation sample under the k modal fault condition;
Figure BDA00037109707100000610
representing the probability of the observed variable being observed in the kth modality;
Figure BDA00037109707100000611
representing the conditional probability of the observation sample under the normal condition of the kth mode;
Figure BDA00037109707100000612
representing the conditional probability of the occurrence of the observation sample under the fault condition in the kth mode;
Figure BDA00037109707100000613
representing a process data failure prior probability;
Figure BDA00037109707100000614
representing the normal prior probability of the process data;
will be provided with
Figure BDA00037109707100000615
And
Figure BDA00037109707100000616
in combination with the significance level α, the following formula is defined:
Figure BDA00037109707100000617
Figure BDA00037109707100000618
wherein α represents a significance level; actual size is a balance between false positives and false negatives, failure probability for obtaining new data samples
Figure BDA00037109707100000619
Constructing the conditional probability of observing the occurrence of the sample under normal and fault conditions, and defining the following formula:
Figure BDA00037109707100000620
Figure BDA00037109707100000621
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003710970710000071
representing the conditional probability of observing the sample under normal conditions in the kth mode;
Figure BDA0003710970710000072
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure BDA0003710970710000073
is a control limit for each modality, the value of which is uniquely determined by the degree of freedom d and the significance level α of the submodel;
Figure BDA0003710970710000074
t representing the kth sub-modality2Statistics are obtained.
Furthermore, in the calculation module, after the probability of the fault of each local model of the observation data is determined, the probability of the fault of each sub-model is further fused by using a Bayesian inference technology to obtain the fault probability of the sample
Figure BDA0003710970710000075
Probability of failure of a sample
Figure BDA0003710970710000076
Calculated by the following equation:
Figure BDA0003710970710000077
wherein the content of the first and second substances,
Figure BDA0003710970710000078
denotes the failure probability of the sample, P (k | x)t) Factor k with respect to xtThe posterior probability of (d);
Figure BDA0003710970710000079
indicating the relation to a new sample x under a factor modality ktThe posterior probability of failure of (1);
whether the system fails or not is judged by comparing the failure probability with the significance level alpha, and the judgment logic is shown as the following formula:
Figure BDA00037109707100000710
wherein the content of the first and second substances,
Figure BDA00037109707100000711
indicating the probability of failure of the sample and alpha indicating the level of significance.
The beneficial effects obtained by the invention are as follows:
the invention provides a method and a system for monitoring the preparation process of a ternary cathode material based on FDALM (fully drawn alkaline metal-insulator-metal), which adopt data preparation and pretreatment to collect historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; respectively identifying a time lag coefficient L and a system factor K of the model by using a time lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model, and initializing a model parameter thetaold(ii) a Identifying relevant parameters of the dynamic autoregressive hidden variable model of the factor by adopting an improved EM (effective electromagnetic) algorithm; defining the factor dynamic autoregressive hidden variable model under each sub-model state based on the obtained factor dynamic autoregressive hidden variable model
Figure BDA00037109707100000712
Statistics and determining control thresholds for submodels
Figure BDA00037109707100000713
And a significance level α; collecting online data x (k), k =1, 2., N as a test set of models and performing a normalization process; detecting the test set based on the obtained factor dynamic autoregressive model, and calculating the test sample under each submode
Figure BDA00037109707100000714
And fusing each sub-modality using Bayesian inference techniques
Figure BDA00037109707100000715
Statistics to obtain the posterior fault probability of the sample
Figure BDA00037109707100000716
Will be provided with
Figure BDA00037109707100000717
And comparing with the significance level alpha, and outputting a detection result.
The FDALM-based method and system for monitoring the preparation process of the ternary cathode material are applied to monitoring the sintering process of the ternary cathode material, the sintering process of the ternary cathode material is a typical process industry, and the production process relates to a plurality of chemical reactions coupled with each other, including chemical combination, hydrolysis and side reactions. These reactions can lead to side reactions if the temperature is not well controlled, which are reversible, and thus, fluctuating changes in the external environment and materials can lead to the process being in a different steady state process. Leading to certain multimodal properties of the process. Meanwhile, the coupling of different temperature zones enables the data to be related before and after, namely the dynamic property of the process data is not negligible, so that the process data has complex characteristics. Firstly, deducing a factor FDALM modeling method by means of a factor modeling method on the basis of the technology of a dynamic autoregressive hidden variable model, wherein the factor FDALM modeling method models data with dynamic and multi-modal characteristics at the same time, and learns model parameters by utilizing an improved EM algorithm; 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 fault probability of the sample by means of a Bayesian inference technology; finally, simulation results compared with other models show that the monitoring method can track modal fluctuations of the process.
Drawings
Fig. 1 is a schematic flow chart of an embodiment of a method for monitoring a preparation process of a ternary cathode material based on FDALM according to the present invention;
FIG. 2 is a schematic flow diagram of an embodiment of process monitoring incorporating an FDALM model and Bayesian inference in the FDALM-based ternary positive electrode material preparation process monitoring method provided by the present invention;
FIG. 3 is a process data classification diagram of an embodiment of the FDALM-based method for monitoring the manufacturing process of a ternary positive electrode material provided in the present invention;
FIG. 4 is a schematic diagram of monitoring results of abnormal temperature rise faults of a temperature zone by different methods in the method for monitoring the preparation process of the FDALM-based ternary cathode material provided by the invention;
FIG. 5 is a schematic diagram of monitoring results of temperature abnormal drop faults of a temperature zone by different methods in the FDALM-based ternary cathode material preparation process monitoring method provided by the invention;
FIG. 6 is a schematic diagram of the monitoring results of the shutdown faults of the roller kiln according to different methods in the method for monitoring the preparation process of the FDALM-based ternary cathode material provided by the invention;
FIG. 7 is a functional block diagram of an embodiment of a FDALM-based ternary positive electrode material preparation process monitoring system provided in the present disclosure;
FIG. 8 is a functional block diagram of one embodiment of the setup module shown in FIG. 7;
FIG. 9 is a functional block diagram of the identification module shown in FIG. 7 according to an embodiment.
The reference numbers indicate:
10. a pre-processing module; 20. establishing a module; 30. an identification module; 40. a determining module; 50. A collection module; 60. a calculation module; 21. a first acquisition unit; 22. a second acquisition unit; 23. a first building element; 31. an estimation unit; 32. a second building element.
Detailed Description
In order to better understand the technical scheme, the technical scheme is described in detail in the following with reference to the attached drawings of the specification and specific embodiments.
As shown in fig. 1 to 6, a first embodiment of the present invention provides a method for monitoring a preparation process of a ternary cathode material based on FDALM, comprising the following steps:
step S100, data preparation and preprocessing, and historical data x collectedh(k) K =1, 2., T as a model training set, each sample was normalized; wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003710970710000091
and k is the time label and T is the sample number of the m-dimensional process observation data.
The data set used for model training and testing was collected from a production plant of some typical ternary cathode material. The sintering link of the ternary material is crucial to the performance of the battery material, so that the sintering process of the material needs to be accurately monitored, and the aims of ensuring the product quality and reducing the energy consumption are fulfilled. A total of 7 observation variables are selected, the first 6 variables are important temperature measurement data of the temperature rising region, and the last data is observation data representing the quality of the product and residual lithium. A total of 2200 consecutive time data are selected, and the sequence data factory always produces the same batch of battery materials, and the sampling period is 30min. The data set is preprocessed or standardized, and the standardization operation is as follows: the average value of the sample of the variable to which each element in the sample set belongs is subtracted, and then the average value is divided by the standard deviation of the sample, so that the average value of the data corresponding to each process variable and each key quality variable is 0, and the variance is 1.
Step S200, respectively identifying a time lag coefficient L and a system factor K of the model by using a time lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model, and initializing a model parameter thetaold。
The step S200 includes:
and step S210, identifying through a trend similarity algorithm to obtain a time lag coefficient L.
And S220, physically interpreting the system factor K into the number of the types of data division, and identifying the types of the data division through an affine clustering propagation algorithm based on a genetic algorithm.
And step S230, constructing a factor dynamic autoregressive hidden variable model by utilizing the preprocessed data set.
The time lag coefficient L is obtained by identifying through a trend similarity algorithm; the physical interpretation of the factor K is the number of the types of data division, and the factor K is obtained by affine clustering propagation algorithm identification based on a genetic algorithm.
Constructing a factor dynamic autoregressive hidden variable model by utilizing the preprocessed data set, and assuming that the data set meets the following relational expression:
Figure BDA0003710970710000101
in the formula (1), zt，k∈RdRepresenting an implicit variable describing the state of the system at the current time t under the mode k, ht，kH, an augmented hidden variable representing the hidden state composition of the states at time t and L previous times in the mode kt，k＝[zt， k Tzt-1，k T…zt-L+1，k T]T∈RdLAnd L is a time lag coefficient identified by a time lag identification algorithm. x is the number oft，k∈RvAnd d and v respectively represent dimensions of a hidden variable and an observed variable. A. Thek∈Rd×dLRepresenting a hidden variable h from augmentationt-1，kShifting to hidden variable z at presentt，kThe state transition matrix of (2). B isk∈Rv×dRepresenting an implicit variable zt，kDivergence to the observed variable xt，kThe divergence matrix of (1).
Figure BDA0003710970710000102
Respectively, the hidden variable of the mode k and the Gaussian noise of the observed variable. Assuming that the noises are independent of each other, the distributions obeyed are respectively
Figure BDA0003710970710000103
Zero mean gaussian distribution.
The model parameters Θ of the whole dynamic autoregressive hidden variable model are as follows:
Θ＝{Ak，Bk，μπ，k，∑π，k，∑z，k，∑x，k，P(k)|k＝1，2，…，K} (2)
in the formula (2), μπ，kSum sigmaπ，kRespectively for increasing hidden variable h at initial moment0，kMean and variance of gaussian distribution; sigmaz，k，∑x，kThe variance of Gaussian noise of an implicit variable and an observed variable respectively expressed as a mode k; p (k) is a factor coefficient in different modes.
And step S300, identifying relevant parameters of the factor dynamic autoregressive hidden variable model by adopting an improved EM algorithm.
Step S300 includes:
and S310, reasonably estimating the posterior distribution of the expanded dynamic hidden variable expectation and the system factor K based on Bayesian filtering and smoothing in the step E.
And S320, in the step M, updating the model parameters by means of a method of maximizing a likelihood function, constructing a Lagrange multiplier formula, and updating factor coefficients by using factor constraint in the step M.
The FDALM structure not only has unobservable hidden variables, but also needs to identify a system factor K and a corresponding factor coefficient. The traditional EM algorithm cannot meet the requirements, so by solving the model parameters with an improved EM algorithm: and E, reasonably estimating the posterior distribution of the expanded dynamic hidden variable expectation and the factor K based on Bayesian filtering and smoothing. In the step M, model parameters are updated by means of a method of maximizing a likelihood function, in addition, a Lagrange multiplier formula is constructed, and the factor number is updated by utilizing factor constraint in the step M.
In step E, model parameters { A }k，Bk，μπ，k，∑π，k，∑z，k，∑x，kP (K) | K =1,2, \8230;, K } is randomly initialized, where Ak＝[A1，k，A2，k，…，AL，k]. Expanding dynamic hidden variable expectation E by adopting Bayesian filtering and smoothingz(zt，k)、
Figure BDA0003710970710000111
And a posterior distribution P (k | x) of factor kt) An accurate estimation is performed, which is mainly disclosed as follows:
Figure RE-GDA0003859118450000112
in the formula (3), Ez(zt，k) Indicating that the sample information of the 1: T time is utilized to T timeEstimating the expectation of the hidden variable of the moment; x is a radical of a fluorine atom1：TRepresents 1: all samples at time T; thetaoldRepresenting a previous iteration parameter set;
Figure BDA0003710970710000113
respectively representing the k-th sub-modal hidden variable ht，kWith respect to observation sequence x1：TThe mean and variance of the posterior probability distribution of (a);
Figure BDA0003710970710000114
represents the k-th sub-modal hidden variable ht，kWith respect to observation sequence x1：TTransposing the mean of the posterior probability distribution of (1);
Figure BDA0003710970710000115
representing a k-th sub-modal lag i time hidden variable ht，kWith respect to observation sequence x1：TTransposing the mean of the posterior probability distribution of (1); a. Thei，kA state transition matrix representing hidden variables under the kth sub-modality at the lag i moment;
Figure BDA0003710970710000116
representing the covariance of the ith variable at time t-1 and the lag of the variable by time L;
Figure BDA0003710970710000121
representing the k-th sub-modal lag at time t-1, i, and the hidden variable ht，kWith respect to observation sequence x1：TThe mean of the posterior probability distribution of (1);
Figure BDA0003710970710000122
represents the k-th sub-modal lag L time hidden variable h at the time t-1t，kWith respect to observation sequence x1：TTransposing the mean of the posterior probability distribution;
Figure BDA0003710970710000123
represents the utilization of 1: estimating the covariance of the hidden variables at the time T by using the sample information at the time T;
Figure BDA0003710970710000124
indicates that with 1: estimating the covariance of hidden variables at the T moment and the T-i moment by the T moment sample information;
Figure BDA0003710970710000125
indicates that with 1: estimating covariance of hidden variables at T moment and T-L moment by sample information at T moment; m is a unit oft，kAnd Mt，kRespectively, the kth sub-modal hidden variable ht，kWith respect to observation sequence x1：TThe mean and variance of the posterior probability distribution of (a).
Another type of hidden variable is the posterior probability P (k | x) for factor kt) Wherein T =0,1, \8230;, T, the mathematical solution is shown below:
Figure BDA0003710970710000126
in the 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 in the kth modality; p (k) represents a factor coefficient; p (x)t) Representing an observed variable xtThe probability of occurrence.
In the step M, model parameters { A ] are carried out by utilizing the hidden variable expectation obtained in the step E and the posterior probability of the factor kk，Bk，μπ，k，∑π，k，∑z，k，∑x，kUpdate of P (K) | K =1,2, \8230;, K }:
Figure BDA0003710970710000127
Figure BDA0003710970710000128
Figure BDA0003710970710000129
Figure BDA00037109707100001210
Figure BDA00037109707100001211
Figure BDA0003710970710000131
in the formulas (5) to (10),
Figure BDA0003710970710000132
respectively representing the updated augmentation hidden variables h in the kth mode0Mean and variance of;
Figure BDA0003710970710000133
representing a state transition matrix, an observation matrix, an updating value of hidden variable variance and a corresponding transpose under the kth mode;
Figure BDA0003710970710000134
representing covariance estimation of an augmentation hidden variable at the t-1 moment in the kth mode;
Figure BDA0003710970710000135
representing covariance estimation of a t-moment hidden variable and a t-1 moment amplification hidden variable under a kth mode;
Figure BDA0003710970710000136
representing a covariance estimate of an initial augmented hidden variable in a kth mode;
Figure BDA0003710970710000137
representing covariance estimation of an implicit variable at lag i time in a kth mode; x is the number oftRepresenting an observed variable;
Figure BDA0003710970710000138
Ez(h0，k) Respectively representing the expectation of the hidden variable at the t moment and the initial augmentation hidden variable in the kth mode.
In order to update the factor coefficient P (k), since the factor involves more constraints, an optimization condition needs to be constructed separately for the factor. First, all terms related to P (k) are separated and expressed as follows:
Figure BDA0003710970710000139
in formula (11), g (k) represents a log-likelihood function with respect to the factor coefficient P (k); p (k | x)t) Represents the posterior probability of factor k; p (k) represents a factor coefficient.
Due to the presence of constraints
Figure BDA00037109707100001310
Introducing a Lagrange multiplier lambda and constructing a Lagrange function form as follows:
Figure BDA00037109707100001311
Figure BDA00037109707100001312
in equations (12) to (13), f (k) represents a lagrangian function constructed for updating the factor coefficient P (k); p (k | x)t) Represents the posterior probability of factor k; g (k) represents a log-likelihood function with respect to the factor coefficient P (k), and λ represents a Lagrangian multiplier.
And the two above two equations are accumulated for k terms (for k), resulting in:
Figure BDA0003710970710000141
in equation (14), P (k) represents a factor coefficient, and λ represents a lagrange multiplier.
Substituting the result back to equation 13 yields the result of the factor coefficient, as shown in the following equation:
Figure BDA0003710970710000142
in formula (15), P (k) represents a factor coefficient, P (k | x)t) Representing the posterior probability of factor k.
In the process of constructing the model, the maximum likelihood value obtained by calculating the new model parameter is compared with the corresponding maximum likelihood value of the original model parameter, if the error threshold value is met, the step S400 is entered, otherwise, the model parameter is continuously updated in an iterative manner. For example, after each M step, the new resulting model parameters ΘnewAnd old model parameter thetaoldComparing, if | | Θ is satisfiedold-ΘnewIf the | | is less than or equal to the sigma, the model training is finished and the step S400 is entered, otherwise, the model parameters are continuously updated according to the EM algorithm strategy of the step S300. Wherein σ is a threshold value of model convergence, and a model complete log-likelihood function is as follows:
Figure RE-GDA0003859118450000151
in formula (16), Q (Θ | Θ)old) Log-likelihood function InP (x) representing equivalent conversion of log-likelihood function to computational complete data1：T，z1-L：T| Θ) about a hidden variable z1-L：TThe condition of (2) is desired; in { P (k) P (x)1：T，z1-L：TI k) is to be In (x)1：T，z1-L：T，k|Θold) Displaying according to conditional probability; inP (k) is the log probability of modal factors; cons represents a constant;
Figure BDA0003710970710000152
Bkzt，kand others are part of a gaussian distribution after logarithmic expansion.
Step S400, based on the obtained factor dynamicsThe autoregressive hidden variable model is defined in each sub-model state of the factor dynamic autoregressive hidden variable model
Figure BDA0003710970710000153
Statistics and determining control thresholds for submodels
Figure BDA0003710970710000154
And significance level a.
It is necessary to define the model in each sub-modality
Figure BDA0003710970710000155
Statistics and determining control thresholds for submodels
Figure BDA0003710970710000156
And significance level a.
For the trained factor dynamic autoregressive hidden variable model, the hidden variables are key variables for driving the operation of the dynamic variation process, and the hidden variables of each sub-mode can establish corresponding
Figure BDA0003710970710000157
The statistical quantity is calculated according to the data,
Figure BDA0003710970710000158
the statistic is calculated by the following formula:
Figure BDA0003710970710000159
in the case of the formula (17),
Figure BDA00037109707100001510
t representing the kth sub-modality2Statistic, E (z)t q|x1：t q，y1：t q)TRepresenting an implicit variable zt qAbout x1：t q，y1：t qCovariance represents the hidden variable zt qAbout x1：t q，y1：t qCovariance of E (z)t q|xl：t q，yl：t q) Representing hidden variables zt qWith respect to x1：t q，y1：t qThe conditions of (a) are expected.
In order to fully utilize the key information of each mode, the monitoring results of each sub-mode are fused into fault probability by means of a Bayesian inference method, and the event probability that an observation sample fails in the kth mode is constructed as follows:
Figure BDA0003710970710000161
in the formula (18), the first and second groups,
Figure BDA0003710970710000162
represents a prior probability of failure of the process data,
Figure BDA0003710970710000163
represents a prior probability that the process data is normal,
Figure BDA0003710970710000164
representing the conditional probability of the occurrence of the observation sample under the k-th modal fault condition;
Figure BDA0003710970710000165
representing the probability of the observed variable being observed in the kth modality;
Figure BDA0003710970710000166
representing the condition probability of the observation sample under the normal condition of the kth mode;
Figure BDA0003710970710000167
representing the conditional probability of the occurrence of the observation sample under the fault condition in the kth mode;
Figure BDA0003710970710000168
representing a process data failure prior probability;
Figure BDA0003710970710000169
representing the normal prior probability of the process data.
Will be provided with
Figure BDA00037109707100001610
And
Figure BDA00037109707100001611
in combination with the significance level α, the following formula is defined:
Figure BDA00037109707100001612
in formula (19), α represents the significance level; the actual size is a balance between false positives and false negatives, the probability of failure in order to obtain a new data sample
Figure BDA00037109707100001613
Constructing the conditional probability of the observation sample under normal and fault conditions, and defining the following formula:
Figure BDA00037109707100001614
in the formula (20), in the following formula,
Figure BDA00037109707100001615
representing the conditional probability of observing the sample under normal conditions in the kth mode;
Figure BDA00037109707100001616
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure BDA00037109707100001617
is the control limit of each mode, whose value is given by the sum of the degrees of freedom d of the submodelsThe significance level alpha is uniquely determined;
Figure BDA00037109707100001618
t representing the kth sub-modality2Statistics are obtained.
Step S500, collecting online data x (k), k =1, 2., N as a test set of models, and performing a normalization process.
The data set used for model training and testing was collected from a production plant of some typical ternary positive electrode material. The sintering link of the ternary material is crucial to the performance of the battery material, so that the sintering process of the material needs to be accurately monitored, and the aims of ensuring the product quality and reducing the energy consumption are fulfilled. A total of 7 observation variables are selected, the first 6 variables are important temperature measurement data of the heating area, and the last data are observation data representing the residual lithium in the product quality. A total of 2200 consecutive moments of data were selected, and the sequence data factory produced the same batch of battery material all the time, with a sampling period of 30min. The data set is preprocessed or standardized, and the standardization operation is as follows: the average value of the sample of the variable to which each element in the sample set belongs is subtracted, and then the average value is divided by the standard deviation of the sample, so that the average value of the data corresponding to each process variable and each key quality variable is 0, and the variance is 1.
Step S600, detecting a test set based on the obtained factor dynamic autoregressive model, and calculating the test sample under each submode
Figure BDA0003710970710000171
And merging each sub-modality using Bayesian inference techniques
Figure BDA0003710970710000172
Statistics to obtain the posterior fault probability of the sample
Figure BDA0003710970710000173
Will be provided with
Figure BDA0003710970710000174
Comparison with significance level αAnd outputs the detection result.
After the probability of the fault of each local model of the observation data is determined, the probability of the fault of each sub-model is further fused by using a Bayesian inference technology to obtain the fault probability of the sample
Figure BDA0003710970710000175
Probability of failure of a sample
Figure BDA0003710970710000176
Calculated by the following formula:
Figure BDA0003710970710000177
in the case of the formula (21),
Figure BDA0003710970710000178
denotes the failure probability of the sample, P (k | x)t) Factor k is related to xtA posterior probability of (d);
Figure BDA0003710970710000179
indicating the relation to a new sample x under a factor modality ktThe posterior probability of failure.
Whether the system fails or not is judged by comparing the failure probability with the significance level alpha, and the judgment logic is shown as the following formula:
Figure BDA00037109707100001710
in the formula (22), the first and second groups,
Figure BDA00037109707100001711
indicating the probability of failure of the sample and alpha indicating the level of significance.
The method for monitoring the preparation process of the ternary cathode material based on the FDALM, provided by the embodiment, is applied to monitoring the sintering process of the ternary cathode material, the sintering process of the ternary cathode material is a typical process industry, and the production process involves a plurality of chemical reactions coupled with each other, including chemical combination, hydrolysis and side reactions. These reactions, if poorly controlled, lead to the occurrence of side reactions which are reversible and therefore fluctuating changes in the external environment and materials lead to the process being in a different steady state. Leading to certain multimodal properties of the process. Meanwhile, the coupling of different temperature zones enables the data to be related front and back, namely the dynamic property of the process data is not negligible, so that the process data has complex characteristics. Firstly, deducing a factor FDALM modeling method by means of a factor modeling method on the basis of the technology of a dynamic autoregressive hidden variable model, wherein the factor FDALM modeling method models data with dynamic and multi-modal characteristics at the same time, and learns model parameters by utilizing an improved EM algorithm; 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 fault probability of the sample by means of a Bayesian inference technology; finally, simulation results compared with other models show that the proposed monitoring method can track modal fluctuations of the process.
Referring to fig. 7 to 9, the present invention further provides a system for monitoring the preparation process of the FDALM-based ternary cathode material, which includes a preprocessing module 10, an establishing module 20, an identifying module 30, a determining module 40, a collecting module 50 and a calculating module 60, wherein the preprocessing module 10 is used for preparing and preprocessing data and collecting historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; wherein the content of the first and second substances,
Figure BDA0003710970710000181
the data are observed in the m-dimensional process, k is a time label, and T is the number of samples; the establishing module 20 is used for respectively identifying the time lag coefficient L and the system factor K of the model by using time lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model and initializing model parameters thetaold(ii) a An identification module 30 for identifying relevant parameters of the factor-dynamic autoregressive hidden variable model using the improved EM algorithm(ii) a A determining module 40, configured to define, based on the obtained factor dynamic autoregressive hidden variable model, a factor dynamic autoregressive hidden variable model in each sub-mode
Figure BDA0003710970710000182
Statistics and determining control thresholds for submodels
Figure BDA0003710970710000183
And a significance level α; a collecting module 50, configured to collect online data x (k), k =1,2, ·, N as a test set of the model, and perform a normalization process; a calculating module 60, configured to detect the test set based on the obtained factor dynamic autoregressive model, and calculate the test sample in each sub-mode
Figure BDA0003710970710000184
And fusing each sub-modality using Bayesian inference techniques
Figure BDA0003710970710000185
Statistics to obtain the posterior fault probability of the sample
Figure BDA0003710970710000186
Will be provided with
Figure BDA0003710970710000187
And comparing with the significance level alpha, and outputting a detection result.
Further, please refer to fig. 8, fig. 8 is a schematic functional module diagram of an embodiment of the establishing module shown in fig. 7, in this embodiment, the establishing module 20 includes a first obtaining unit 21, a second obtaining unit 22 and a first constructing unit 23, where the first obtaining unit 21 is configured to obtain the time lag coefficient L through a trend similarity algorithm; the second obtaining unit 22 is configured to obtain a system factor K through identification by an affine clustering propagation algorithm based on a genetic algorithm, where the system factor K is physically interpreted as a number of types of data division; the first constructing unit 23 is configured to construct a factor dynamic autoregressive hidden variable model by using the preprocessed data set.
Preferably, referring to fig. 9, fig. 9 is a functional module schematic diagram of an embodiment of the identification module shown in fig. 7, in this embodiment, the identification module 30 includes an estimation unit 31 and a second construction unit 32, where the estimation unit 31 is configured to reasonably estimate, at step E, the posterior distribution of the expanded dynamic hidden variable expectation and the system factor K based on bayesian filtering and smoothing; and the second construction unit 32 is configured to update the model parameters by using a method of maximizing a likelihood function in the step M, construct a lagrangian multiplier formula, and constrain and update the factor coefficients by using the factors in the step M.
Further, in the determining module 40, for the trained factor dynamic autoregressive hidden variable model, the hidden variables are key variables for driving the operation of the dynamic change process, and the hidden variables of each sub-model can establish corresponding
Figure BDA0003710970710000191
The statistical quantity is calculated by the statistical quantity,
Figure BDA0003710970710000192
the statistic is calculated by the following formula:
Figure BDA0003710970710000193
in the formula (23), the first and second groups,
Figure BDA0003710970710000194
t representing the kth sub-modality2Statistic, E (z)t q|x1：t q，y1：t q)TRepresenting hidden variables zt qAbout x1：t q，y1：t qCovariance, which represents the hidden variable zt qWith respect to x1：t q，y1：t qCovariance of E (z)t q|xl：t q，yl：t q) Representing hidden variables zt qAbout xl：t q，yl：t qThe conditions of (a) are expected.
In order to fully utilize the key information of each mode, the monitoring results of each sub-mode are fused into fault probability by means of a Bayesian inference method, and the event probability that an observation sample fails in the kth mode is constructed as follows:
Figure BDA0003710970710000195
in the case of the formula (24),
Figure BDA0003710970710000196
represents a prior probability of a failure of the process data,
Figure BDA0003710970710000197
represents a prior probability that the process data is normal,
Figure BDA0003710970710000201
representing the conditional probability of the occurrence of the observation sample under the k-th modal fault condition;
Figure BDA0003710970710000202
representing the probability of the observed variable being observed in the kth modality;
Figure BDA0003710970710000203
representing the condition probability of the observation sample under the normal condition of the kth mode;
Figure BDA0003710970710000204
representing the conditional probability of the occurrence of the observation sample under the fault condition in the kth mode;
Figure BDA0003710970710000205
representing a process data failure prior probability;
Figure BDA0003710970710000206
representing the normal prior probability of the process data;
will be provided with
Figure BDA0003710970710000207
And
Figure BDA0003710970710000208
in combination with the significance level α, the following formula is defined:
Figure BDA0003710970710000209
in formula (25), α represents the significance level; the actual size is a balance between false positives and false negatives, the probability of failure in order to obtain a new data sample
Figure BDA00037109707100002010
Constructing the conditional probability of the observation sample under normal and fault conditions, and defining the following formula:
Figure BDA00037109707100002011
in the formula (26), the first and second groups,
Figure BDA00037109707100002012
representing the conditional probability of observing the sample under normal conditions in the kth mode;
Figure BDA00037109707100002013
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure BDA00037109707100002014
is a control limit for each modality, the value of which is uniquely determined by the degree of freedom d and the significance level α of the submodel;
Figure BDA00037109707100002015
t representing the kth sub-modality2Statistics are obtained.
Further, in the calculation module 60, after the probability of the fault occurrence of each local model of the observation data is determined, the probability of the fault occurrence of each sub-model is further fused by using the bayesian inference technology to obtain the fault probability of the sample
Figure BDA00037109707100002016
Probability of failure of a sample
Figure BDA00037109707100002017
Calculated by the following formula:
Figure BDA00037109707100002018
in the formula (27), the first and second groups,
Figure BDA00037109707100002019
denotes the failure probability of the sample, P (k | x)t) Factor k is related to xtA posterior probability of (d);
Figure BDA00037109707100002020
indicating the relation to a new sample x under a factor modality ktThe posterior probability of failure.
Whether the system fails or not is judged by comparing the failure probability with the significance level alpha, and the judgment logic is shown as the following formula:
Figure BDA0003710970710000211
in the formula (28), the first and second groups,
Figure BDA0003710970710000212
indicating the probability of failure of the sample and alpha indicating the level of significance.
The FDALM-based ternary cathode material preparation process monitoring system provided in this embodiment is applied to monitoring of a sintering process of a ternary cathode material, the sintering process of the ternary cathode material is a typical process industry, and a production process involves numerous chemical reactions coupled to each other, including chemical combination, hydrolysis, and side reactions. These reactions can lead to side reactions if the temperature is not well controlled, which are reversible, and thus, fluctuating changes in the external environment and materials can lead to the process being in a different steady state process. Leading to certain multimodal properties of the process. Meanwhile, the coupling of different temperature zones enables the data to be related front and back, namely the dynamic property of the process data is not negligible, so that the process data has complex characteristics. Firstly, deducing a factor FDALM modeling method by means of a factor modeling method on the basis of the technology of a dynamic autoregressive hidden variable model, wherein the factor FDALM modeling method models data with dynamic and multi-modal characteristics at the same time, and learns model parameters by utilizing an improved EM algorithm; 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 fault probability of the sample by means of a Bayesian inference technology; finally, simulation results compared with other models show that the proposed monitoring system can track modal fluctuations of the process.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the invention. It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A method for monitoring the preparation process of a ternary cathode material based on FDALM is characterized by comprising the following steps:
data preparation and preprocessing, collecting historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003710970700000011
the data are observed in an m-dimensional process, k is a time label, and T is the number of samples;
respectively identifying a time lag coefficient L and a system factor K of the model by using a time lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model, and initializing a model parameter thetaold；
Identifying relevant parameters of the factor dynamic autoregressive hidden variable model by adopting an improved EM algorithm;
defining T of the factor dynamic autoregressive hidden variable model under each sub-model state based on the obtained factor dynamic autoregressive hidden variable modelk 2Statistics and determining control thresholds for submodels
Figure FDA0003710970700000012
And a significance level α;
collecting online data x (k), k =1, 2., N as a test set of models and performing a normalization process;
detecting the test set based on the obtained factor dynamic autoregressive model, and calculating the test sample under each submode
Figure FDA0003710970700000013
And fusing each sub-modality using Bayesian inference techniques
Figure FDA0003710970700000014
Statistics to obtain the posterior fault probability of the sample
Figure FDA0003710970700000015
Will be provided with
Figure FDA0003710970700000016
And comparing with the significance level alpha, and outputting a detection result.
2. The FDALM-based triad of claim 1The method for monitoring the preparation process of the meta-anode material is characterized in that a time lag coefficient L and a system factor K of a model are respectively identified by using a time lag identification and clustering algorithm, a factor dynamic autoregressive hidden variable model is established, and a model parameter theta is initializedoldComprises the following steps:
identifying and obtaining the time-lag coefficient L by a trend similarity algorithm;
identifying and obtaining a 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 types of data division;
and constructing a factor dynamic autoregressive hidden variable model by utilizing the preprocessed data set.
3. The FDALM-based ternary positive electrode material manufacturing process monitoring method of claim 2, wherein said step of identifying relevant parameters of said factorial dynamic autoregressive hidden variable model using a modified EM algorithm comprises:
in the step E, reasonably estimating the posterior distribution of the expanded dynamic hidden variable expectation and the system factor K based on Bayesian filtering and smoothing;
in the step M, model parameters are updated by means of a method of maximizing a likelihood function, a Lagrange multiplier formula is constructed, and factor constraint updating factor coefficients in the step M are utilized.
4. The FDALM-based ternary positive electrode material preparation process monitoring method of claim 1, wherein the factor dynamic autoregressive hidden variable model is defined based on the obtained factor dynamic autoregressive hidden variable model in each sub-mode
Figure FDA0003710970700000021
Statistics and determining control thresholds for submodels
Figure FDA0003710970700000022
And in the step of the significance level alpha, for the trained factor dynamic autoregressive hidden variable model, the hidden variable is a driving motionThe key variable of the operation of the state change process, namely the hidden variable of each sub-mode can establish the corresponding hidden variable
Figure FDA0003710970700000023
The statistical quantity is calculated by the statistical quantity,
Figure FDA0003710970700000024
the statistic is calculated by the following formula:
Figure FDA0003710970700000025
wherein the content of the first and second substances,
Figure FDA0003710970700000026
t representing the kth sub-modality2Statistic, E (z)t q|x1：t q，y1：t q)TRepresenting an implicit variable zt qWith respect to x1：t q，y1：t qCovariance, which represents the hidden variable zt qWith respect to x1：t q，y1：t qCovariance of E (z)t q|x1：t q，yl：t q) Representing hidden variables zt qWith respect to x1：t q，y1：t qThe conditions of (a);
in order to fully utilize the key information of each mode, the monitoring results of all the sub-modes are fused into fault probability by means of a Bayesian inference method, and the fault event probability of an observation sample in the kth mode is constructed as follows:
Figure FDA0003710970700000027
Figure FDA0003710970700000028
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003710970700000029
represents a prior probability of a failure of the process data,
Figure FDA00037109707000000210
represents a prior probability that the process data is normal,
Figure FDA00037109707000000211
representing the conditional probability of the occurrence of the observation sample under the k-th modal fault condition;
Figure FDA00037109707000000212
representing the probability of the observed variable being observed in the k-th modality;
Figure FDA00037109707000000213
representing the conditional probability of the observation sample under the normal condition of the kth mode;
Figure FDA00037109707000000214
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure FDA00037109707000000215
representing a process data failure prior probability;
Figure FDA00037109707000000216
representing the normal prior probability of the process data;
will be provided with
Figure FDA00037109707000000217
And
Figure FDA00037109707000000218
and level of significanceα in combination, defines the following equation:
Figure FDA0003710970700000031
Figure FDA0003710970700000032
wherein α represents a significance level; actual size is a balance between false positives and false negatives, failure probability for obtaining new data samples
Figure FDA0003710970700000033
Constructing the conditional probability of the observation sample under normal and fault conditions, and defining the following formula:
Figure FDA0003710970700000034
Figure FDA0003710970700000035
wherein the content of the first and second substances,
Figure FDA0003710970700000036
representing the conditional probability of the occurrence of the observation sample under normal conditions in the kth modality;
Figure FDA0003710970700000037
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure FDA0003710970700000038
is a control limit for each modality, the value of which is uniquely determined by the degree of freedom d and the significance level α of the submodel;
Figure FDA0003710970700000039
t representing the kth sub-modality2Statistics are obtained.
5. The FDALM-based ternary positive electrode material preparation process monitoring method of claim 1, wherein the FDALM-based ternary positive electrode material preparation process monitoring method is characterized in that a test set is detected based on the obtained factor dynamic autoregressive model, and the value of a test sample in each sub-mode is calculated
Figure FDA00037109707000000310
And fusing each sub-modality using Bayesian inference techniques
Figure FDA00037109707000000311
Statistics to obtain the posterior fault probability of the sample
Figure FDA00037109707000000312
Will be provided with
Figure FDA00037109707000000313
In the step of comparing with the significance level alpha and outputting the detection result, after the probability of the fault of each local model of the observation data is determined, the probability of the fault of each sub-model is further fused by using the Bayesian inference technology to obtain the fault probability of the sample
Figure FDA00037109707000000314
Probability of failure of a sample
Figure FDA00037109707000000315
Calculated by the following formula:
Figure FDA00037109707000000316
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00037109707000000317
denotes the failure probability of the sample, P (k | x)t) Factor k with respect to xtA posterior probability of (d);
Figure FDA00037109707000000318
indicating the relation to a new sample x under a factor modality ktThe posterior probability of failure of (1);
whether the system fails or not is judged by comparing the failure probability with the significance level alpha, and the judgment logic is shown as the following formula:
Figure FDA00037109707000000319
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00037109707000000320
indicating the probability of failure of the sample and alpha indicating the level of significance.
6. A FDALM-based ternary positive electrode material preparation process monitoring system is characterized by comprising:
a preprocessing module (10) for data preparation and preprocessing, for collecting historical data xh(k) K =1, 2., T as a model training set, each sample was normalized; wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003710970700000041
the data are observed in the m-dimensional process, k is a time label, and T is the number of samples;
the establishing module (20) is used for respectively identifying the time lag coefficient L and the system factor K of the model by using time lag identification and clustering algorithm, establishing a factor dynamic autoregressive hidden variable model and initializing model parameters thetaold；
An identification module (30) for identifying relevant parameters of the factor dynamic autoregressive hidden variable model by adopting an improved EM algorithm;
a determination module (40) for dynamically self-determining based on the derived factorsA regression hidden variable model for defining the factor dynamic autoregressive hidden variable model in each sub-model state
Figure FDA0003710970700000042
Statistics and determining control thresholds for submodels
Figure FDA0003710970700000043
And a significance level α;
a collection module (50) for collecting online data x (k), k =1, 2., N as a test set of models and performing a normalization process;
a calculation module (60) for detecting the test set based on the obtained factor dynamic autoregressive model and calculating the test sample in each sub-mode
Figure FDA0003710970700000044
And fusing each sub-modality using Bayesian inference techniques
Figure FDA0003710970700000045
Statistics to obtain the posterior fault probability of the sample
Figure FDA0003710970700000046
Will be provided with
Figure FDA0003710970700000047
And comparing with the significance level alpha, and outputting a detection result.
7. The FDALM-based ternary positive electrode material production process monitoring system of claim 6, wherein the establishing module (20) comprises:
a first obtaining unit (21) for identifying and obtaining the time lag coefficient L by a trend similarity algorithm;
the second obtaining unit (22) is used for obtaining a system factor K through affine clustering propagation algorithm identification based on a genetic algorithm, and the system factor K is physically interpreted as the number of types of data division;
and a first construction unit (23) for constructing a factor dynamic autoregressive hidden variable model by using the preprocessed data set.
8. The FDALM-based ternary positive electrode material production process monitoring system of claim 7, wherein the identification module (30) comprises:
the estimation unit (31) is used for reasonably estimating the expanded dynamic hidden variable expectation and the posterior distribution of the system factor K based on Bayesian filtering and smoothing in the step E;
and the second construction unit (32) is used for updating the model parameters by means of a method of maximizing the likelihood function in the step M, constructing a Lagrange multiplier formula and utilizing factors in the step M to restrain and update factor coefficients.
9. The FDALM-based ternary positive electrode material preparation process monitoring system of claim 6, wherein in the determining module (40), for the trained factor dynamic autoregressive hidden variable model, the hidden variables are key variables for driving the operation of the dynamic variation process, and the hidden variables of each sub-mode can establish a corresponding hidden variable
Figure FDA0003710970700000051
The statistical quantity is calculated by the statistical quantity,
Figure FDA0003710970700000052
the statistic is calculated by the following formula:
Figure FDA0003710970700000053
wherein the content of the first and second substances,
Figure FDA0003710970700000054
t representing the kth sub-modality2Statistic, E (z)t q|x1：t q，y1：t q)TRepresenting hidden variables zt qWith respect to x1：t q，y1：t qCovariance, which represents the hidden variable zt qWith respect to x1：t q，y1：t qCovariance of E (z)t q|x1：t q，yl：t q) Representing hidden variables zt qWith respect to x1：t q，y1：t qThe conditions of (a);
in order to fully utilize the key information of each mode, the monitoring results of all the submodes are fused into fault probability by means of a Bayesian inference method, and the probability of the fault event of the observation sample in the kth mode is constructed as follows:
Figure FDA0003710970700000055
Figure FDA0003710970700000056
wherein the content of the first and second substances,
Figure FDA0003710970700000057
represents a prior probability of a failure of the process data,
Figure FDA0003710970700000058
a priori probability of the process data being normal is represented,
Figure FDA0003710970700000059
representing the conditional probability of the occurrence of the observation sample under the k-th modal fault condition;
Figure FDA00037109707000000510
representing the probability of the observed variable being observed in the kth modality;
Figure FDA00037109707000000511
representing the conditional probability of the observation sample under the normal condition of the kth mode;
Figure FDA00037109707000000512
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure FDA00037109707000000513
representing a process data failure prior probability;
Figure FDA00037109707000000514
representing the normal prior probability of the process data;
will be provided with
Figure FDA00037109707000000515
And
Figure FDA00037109707000000516
in combination with the significance level α, the following formula is defined:
Figure FDA0003710970700000061
Figure FDA0003710970700000062
wherein α represents a significance level; actual size is a balance between false positives and false negatives, failure probability for obtaining new data samples
Figure FDA0003710970700000063
Constructing the conditional probability of the observation samples under normal and fault conditions, and defining the following formula:
Figure FDA0003710970700000064
Figure FDA0003710970700000065
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003710970700000066
representing the conditional probability of the observation sample under normal conditions in the kth mode;
Figure FDA0003710970700000067
representing the conditional probability of the occurrence of the observation sample under the fault condition of the kth mode;
Figure FDA0003710970700000068
is a control limit for each modality, the value of which is uniquely determined by the degree of freedom d and the significance level α of the submodel;
Figure FDA0003710970700000069
t representing the kth sub-modality2And (4) statistic amount.
10. The FDALM-based ternary positive electrode material preparation process monitoring system of claim 6, wherein in the calculation module (60), after the probability of the occurrence of the fault of each local model of the observed data is determined, the probability of the occurrence of the fault of each sub-model is further fused by using a Bayesian inference technology to obtain the fault probability of the sample
Figure FDA00037109707000000610
Probability of failure of a sample
Figure FDA00037109707000000611
Calculated by the following formula:
Figure FDA00037109707000000612
wherein the content of the first and second substances,
Figure FDA00037109707000000613
denotes the failure probability of the sample, P (k | x)t) Factor k with respect to xtA posterior probability of (d);
Figure FDA00037109707000000614
indicating the relation to a new sample x under a factor mode ktThe posterior probability of failure of (a);
and judging whether the system fails or not by comparing the failure probability with the significance level alpha, wherein the judgment logic is shown as the following formula:
Figure FDA00037109707000000615
wherein the content of the first and second substances,
Figure FDA00037109707000000616
indicating the probability of failure of the sample and alpha indicating the level of significance.
CN202210720684.7A 2022-06-23 2022-06-23 FDALM-based method and system for monitoring preparation process of ternary cathode material Pending CN115270601A (en)

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