Process industry system simulation method based on state space model
By introducing state-space models based on multinomial and Dirichlet distributions, and combining variational Bayesian inference and Kalman filtering techniques, the problems of unknown time delays and non-Gaussian noise in process industries are solved, achieving high-precision model parameter identification and state estimation.
Patent Information
- Application Number
- CN202511163050.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-19
- Publication Date
- 2025-11-14
AI Technical Summary
Existing technologies in the process industry suffer from unknown time delays and non-Gaussian interference noise, leading to inaccurate model parameter estimation and affecting the robustness and accuracy of the model.
A state-space model-based approach is adopted, which introduces a multinomial distribution to model random time delays, uses the Dirichlet distribution to characterize the time delay prior information, and uses a variational Bayesian inference framework and Kalman filtering technique to identify unknown parameters and estimate the state, thereby constructing a robust probabilistic model.
Achieving high-precision parameter identification for process industry system models under non-Gaussian noise and unknown time delay conditions improves the model's anti-interference performance and accuracy.
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Figure CN120949680A_ABST
Abstract
Description
Technical Field
[0001] This application relates to a simulation method for process industry systems based on a state-space model, belonging to the field of process industry system modeling technology. Background Technology
[0002] In process industries (such as chemical, pharmaceutical, metallurgical, and energy industries), accurate modeling and simulation of complex production processes are the core foundation for achieving efficient control, optimized operation, and fault diagnosis. State-space models, due to their ability to clearly describe the dynamic evolution of internal system state variables over time and their ease of integration with control system design (such as model predictive control (MPC) and optimal control), have become one of the widely adopted mainstream dynamic modeling frameworks in this field.
[0003] Existing technologies typically establish linear or near-linear state-space models based on physical mechanism analysis and system identification methods. These models simulate the system's state and output response under various inputs and disturbances, providing predictive insights for operators and core model support for advanced control algorithms. However, existing technologies face significant challenges in application, particularly in the accuracy of model parameter estimation. Unknown time delays and non-Gaussian noise severely limit model performance.
[0004] Process industries commonly exhibit inherent time delays in processes such as material transfer, heat conduction, and chemical reactions. These time delays are often difficult to measure accurately or know in advance. Existing identification methods (such as subspace identification, prediction error methods, and maximum likelihood estimation) often assume that the time delay is known or zero, or incorporate it as a parameter to be estimated into the model structure. However, in complex systems, time delays may vary with operating conditions and are difficult to model accurately. When the model does not accurately include or incorrectly estimates time delays, it leads to a structural mismatch between the state equation and the output equation, resulting in systematic biases in the identified model parameters, which fail to reflect the true dynamic characteristics.
[0005] The process industry environment is complex, and measurement data is often contaminated by various non-ideal factors, such as intermittent sensor failures, valve stickiness, pulses and spikes caused by material blockage / leakage, and asymmetric random disturbances. These disturbances often exhibit significant non-Gaussian characteristics (e.g., heavy-tailed distribution, skewed distribution, and impulse characteristics). Classical identification algorithms (such as least squares-based algorithms, standard Kalman filters, and their derivatives) are mostly based on the strong assumption that process noise w and measurement noise v are zero-mean Gaussian white noise. When the actual noise is non-Gaussian, the identified model has poor robustness. When simulating real operating data containing non-Gaussian noise, the prediction error (especially the peak error) will increase significantly, and the model confidence will decrease. Summary of the Invention
[0006] To address the problem of inaccurate parameter estimation in process industry system models under unknown time delays and non-Gaussian interference noise, this application provides a simulation method for process industry systems based on a state-space model.
[0007] This application discloses a simulation method for a process industry system based on a state-space model. The process industry system is a time-delay industrial system. The simulation method includes:
[0008] S1. Establish a linear time-delay state-space model of the process industry system, in which the control variables and state variables of the process industry system constitute the state variables, and the sensor measurement values are the output variables.
[0009] S2. Under the probabilistic framework, a multinomial distribution is introduced to model the random time delay between the state variables and output variables of the time-delay state-space model, and the Dirichlet distribution is used to characterize the time delay prior information to determine the probability distribution of the unknown parameters in the time-delay state-space model.
[0010] S3. Based on the variational Bayesian inference framework and the probability distribution of unknown parameters, the unknown parameters in the linear time-delay state-space model are identified according to the existing control quantities and sensor acquisition quantities of the process industry system, and the posterior distribution of the unknown parameters is obtained.
[0011] S4. Simulate the process industry system using a linear time-delay state-space model with identified unknown parameters.
[0012] The beneficial effects of this application are as follows: Based on the variational Bayesian inference framework, this application introduces a multinomial distribution to model the random time delay between the system input and output, and utilizes the Dirichlet distribution to characterize the time delay prior information of the process industry system. Simultaneously, it employs generalized inverse Gaussian and gamma distributions to construct a robust probabilistic model to adapt to the non-Gaussian noise of the process industry system. This application constructs an iteratively convergent identification algorithm by jointly inferring the system state, model parameters, and time delay distribution, and using the mean-field variational method for approximate derivation. Furthermore, it utilizes Kalman filtering and Kalman smoothing techniques to estimate the system's hidden state, exhibiting good robustness and anti-interference performance. Simulation experiments show that this method can still achieve high-precision identification of process industry system model parameters under non-Gaussian noise, unknown time delays, and unknown state conditions. This invention is of great significance for realizing accurate modeling, control, and health monitoring of time-delay industrial systems under highly dynamic and multi-interference conditions. Attached Figure Description
[0013] Figure 1 This is a schematic diagram of a chemical reactor system.
[0014] Figure 2 This is a diagram showing the comparison between the model's simulation output and the actual output. Detailed Implementation
[0015] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.
[0017] The present application will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the application.
[0018] The process industry system in this embodiment is a time-delay process industry system. The simulation method for the process industry system based on the state-space model includes:
[0019] Step 1: Establish a linear time-delay state-space model for the process industry system. The control variables and state variables of the process industry system form a state vector, and sensor measurements are output variables. The linear time-delay state-space model is as follows:
[0020]
[0021] in, Let these represent the system's state vector and output variable, respectively. It is the sampling time. To delay time, Indicates state noise. Let A represent the measurement noise, C represent the system matrix, and C represent the observation matrix.
[0022] Step 2: Within the probabilistic framework, a multinomial distribution is introduced to model the random time delay between the state vector and output variable in the time-delay state-space model. The Dirichlet distribution is used to characterize the time delay prior information, and the probability distribution of unknown parameters in the time-delay state-space model is determined. Time delays in the process industry (such as sensor transmission delays and reaction process lags) are usually discrete and bounded. This implementation quantifies the uncertainty of time delay values through a multinomial distribution, avoids assuming fixed time delays, introduces Dirichlet priors for non-Gaussian discrete modeling, and explicitly assigns a probability to each possible time delay value, thereby improving computational efficiency and robustness.
[0023] Step 3: Based on the variational Bayesian inference framework and the probability distribution of unknown parameters, the unknown parameters in the linear time-delay state-space model are identified according to the existing control quantities and sensor acquisition quantities of the process industry system, and the posterior distribution of the unknown parameters is obtained. Step 3 adopts variational Bayesian to efficiently jointly estimate all unknown quantities, output the posterior distribution, quantify the estimation uncertainty, and robustly handle non-Gaussian interference noise.
[0024] Step 4: Simulate the process industry system using a state-space model with identified unknown parameters.
[0025] In this embodiment, within a probabilistic framework, a statistical characterization of the state and output of the time-delay state-space model is established, and the probability distribution of unknown parameters is determined. Step 2 specifically includes:
[0026] Step 21: Measure the noise It is non-Gaussian white noise, which follows a Laplace distribution:
[0027]
[0028] in For position parameters, For the scale parameter. Introduce latent variables. Measure noise The Laplace distribution function can be rewritten as:
[0029]
[0030]
[0031] in, The mean is Covariance is Gaussian distribution, latent variables It follows an exponential distribution with a parameter of 1. For position parameters, For scale parameters;
[0032] Step 22, State Noise It is Gaussian white noise with a mean of 0 and a covariance of . Gaussian distribution:
[0033] ;
[0034] Step 23, State Vector The joint probability density function is:
[0035]
[0036] in, This represents the state variables at N time points. Initial state The probability density function, whose mean is The covariance is Gaussian distribution; for The probability density function, whose mean is The covariance is Gaussian distribution;
[0037] Step 24, Output Vector and order ,but The joint probability density function is:
[0038]
[0039] in, This represents the sensor measurements at N time points, where k ranges from 1 to N. for The probability density function, whose mean is The covariance is Gaussian distribution; Indicates a time-delay indicator auxiliary variable;
[0040] Step 25: Determine the probability distribution of the time-delay state-space model parameters as follows:
[0041] Unknown parameters include the system matrix. and observation matrix State vector and parameters System matrix Observation matrix , The probability distributions are as follows:
[0042] ;
[0043]
[0044] ;
[0045] ;
[0046] ;
[0047] ;
[0048] ;
[0049] ;
[0050]
[0051] Among them, the system matrix each line It follows a pattern with a mean of 0 and a covariance of . Gaussian distribution;
[0052] , These represent the dimensions of the state vector and the observation vector, respectively.
[0053] Observation matrix each line It follows a pattern with a mean of 0 and a covariance of . Gaussian distribution;
[0054] Precision parameters Each row of elements Obtain the parameter as gamma distribution,
[0055] Precision parameters Each row of elements Obtain the parameter as The gamma distribution;
[0056] Precision parameters Each row of elements Obtain the parameter as gamma distribution,
[0057] Precision parameters Each row of elements Obtain the parameter as The gamma distribution;
[0058] It is a time-delay distributed parameter The multinomial distribution;
[0059] A time-delay indicator auxiliary variable;
[0060] parameter It controls the delay probability distribution at time k. Dirichlet distribution parameters;
[0061] It is a parameter The Dirichlet distribution;
[0062] These are normalization parameters. The superscript dd indicates the corresponding parameter for the delay time, and D indicates the maximum time delay length.
[0063] Auxiliary variables It follows an exponential distribution with a parameter of 1;
[0064] , This is a hyperparameter.
[0065] Step 3 of this implementation method is based on the variational Bayesian inference framework. It identifies the unknown parameters in the linear time-delay state-space model based on the existing control quantities and sensor data collected by the process industry system, and obtains the approximate posterior distribution of the unknown parameters.
[0066] First, a mathematical description of the model identification problem is established, and the specific process is as follows:
[0067] The mathematical description of the model identification problem in this application can be expressed as: given the measurement output And introduce latent variables Joint estimation of system matrix based on Bayesian framework and observation matrix Unknown parameters and system state and parameters .
[0068] Then, the approximate posterior distribution of the unknown parameters is obtained using mean-field theory. The specific process is as follows:
[0069] All unknown parameters obtained from the previous iteration can be labeled as And there are Based on mean-field theory, the joint probability density function of all unknown parameters can be approximated as:
[0070]
[0071] Among them, for The approximate posterior distribution; For the system matrix The approximate posterior distribution of ; the other terms in the above formula are the approximate posterior distributions of the corresponding parameters.
[0072] The KL divergence is used to measure the distance between the approximate posterior distribution and the true posterior distribution. By minimizing this distance, the formula for calculating the log-posterior distribution with any unknown parameters can be obtained. The first in The unknown parameters are ,but The log-posterior distribution can be calculated as follows:
[0073] Formula 1
[0074] in, This indicates the evaluation of the function within the angle brackets. Dividing variables The expected value of all variables other than the given variable is given, with `const` representing a constant term. The representation of `const` differs depending on the specific variable being solved for. Irrelevant constant terms. These terms may take different forms when different variables are updated, but they have no effect on the current variable in the optimization objective (variational lower bound), so they can be uniformly regarded as constant terms and ignored.
[0075] Output and all unknown parameters The joint probability density function can be calculated as follows:
[0076]
[0077] Based on Equation 1, combined with the joint probability density function of the state vector and the output vector... The joint probability density functions are obtained respectively. posterior distribution , , , , , , , , , And obtain the covariance matrix and mean of the corresponding posterior distribution;
[0078] Determine if the stopping condition is met; if so, output the current condition. , , , , , , , , , The covariance matrix and mean, if not, the current , , , , , , , , , The mean is marked as Then, use Formula 1 for the next iteration.
[0079] The stopping condition in this implementation can be set to the number of iterations reaching a set upper limit, or the relative change of the current parameter estimate relative to the parameter estimate obtained in the previous iteration being less than an arbitrarily small constant.
[0080] The key to the variational method is the assumption that the variational distribution can be decomposed into several approximate posterior distributions, which greatly simplifies the optimization problem. The KL divergence is minimized by iteratively optimizing each approximate posterior distribution. The specific iterative steps typically involve:
[0081] renew When other parameters are fixed, the probability distribution of other parameters is obtained, and the calculation is performed using Formula 1. During the calculation, if the parameters have been updated, the probability distribution of the updated parameters is used; if they have not been updated, the result of the previous iteration is used.
[0082] This implementation method is a joint estimation, which iteratively estimates each parameter simultaneously. Variational Bayes solves the problems of state estimation and parameter identification affected by unknown time delays, and state estimation and time delay estimation affected by non-Gaussian noise.
[0083] Formula 1 is the formula for calculating the log-posterior distribution of any unknown parameter. From this, the system matrix can be derived. The posterior distribution is:
[0084]
[0085] The covariance matrix is:
[0086]
[0087] The mean vector is:
[0088]
[0089] in, This indicates the expected value of the function enclosed in angle brackets with respect to its variables. express The Row elements;
[0090] The posterior distribution of the observation matrix C is:
[0091]
[0092] The covariance matrix is:
[0093]
[0094] The mean vector is:
[0095]
[0096] in, for The Row element.
[0097] parameter The posterior distribution is:
[0098]
[0099] in: Represents the gamma distribution. express The shape parameters of the gamma distribution, ;
[0100] express The velocity parameters of the gamma distribution, Indicates to The initial prior strength, ,
[0101] For the system matrix The Line number Column elements;
[0102] The posterior distribution of γ is:
[0103]
[0104] in: express The shape parameters of the gamma distribution, express The velocity parameters of the gamma distribution, Indicates to The initial prior strength, , Observation matrix The Line number Column elements;
[0105] The posterior distribution is:
[0106]
[0107] in: express The shape parameters of the gamma distribution, , express The velocity parameters of the gamma distribution, Yes The initial prior strength; ;
[0108] The posterior distribution is a gamma distribution:
[0109]
[0110] in: express The shape parameters of the gamma distribution, express velocity parameters of the gamma distribution
[0111]
[0112]
[0113] The posterior distribution is:
[0114]
[0115] in: This represents the generalized inverse Gaussian distribution. Represents the linear weight parameters in the GIG distribution. This represents the inverse weight parameter in the GIG distribution. The exponential parameter representing the GIG distribution;
[0116]
[0117]
[0118]
[0119] express The row element;
[0120] The posterior distribution is:
[0121]
[0122] Where: calculation When calculating the posterior distribution, use Updated value , The time delay distribution parameters corresponding to the updated delay time dd;
[0123] .
[0124] The posterior distribution is:
[0125]
[0126] Among them, calculation When calculating the posterior distribution, use Updated value , ;
[0127] State vector The log-posterior distribution is in the form of:
[0128]
[0129] in: The result obtained from Formula 1 The corresponding constant term;
[0130] intermediate variable matrix intermediate variable matrix ;
[0131] Construct augmented state-space models with deterministic parameters having the same log-posterior distribution form:
[0132]
[0133]
[0134] in: , , , For the system matrix A and state noise Output variables Observation matrix C, measurement noise augmented forms;
[0135] , ,
[0136]
[0137] , , It is the identity matrix. It is a zero vector. It is a zero matrix. This indicates the vertical connection of the input parameters. and They represent and Cholesky decomposition, express Cholesky decomposition;
[0138] For the augmented state-space model, Kalman filtering and Kalman smoothing are used to smooth the state vector. Perform estimation and convert the state vector The covariance matrix is used as a measure of uncertainty in the state estimation, and the state vector is obtained. .
[0139] Example:
[0140] This embodiment uses a chemical reactor system to verify the validity of this application. The experimental setup diagram of this system is shown below. Figure 1 As shown, its dynamic characteristics can be described by a mechanistic model:
[0141]
[0142]
[0143] in, q(t) is the concentration of reactant A, in mol / L; q(t) is the feed flow rate, in mol / L; T(t) is the reaction temperature, in K. This refers to the coolant temperature, expressed in Kelvin (K). This represents the cooling water flow rate, expressed in L / min.
[0144] In this embodiment, the feed flow rate q(t) and coolant temperature are selected. The concentration of reactant A is the input variable. For output variables; due to the use of a concentration sensor to measure the concentration of reactant A. Since there is a measurement delay during the measurement process, the chemical reactor system can be described by a time-delay state-space model.
[0145] Identification data was obtained by simulating the aforementioned mechanism model, and the linear time-delay state-space model of the chemical reactor system was identified using the method of this application. A comparison between the simulation output of the identified model and the output of the real system is shown below. Figure 2 As shown in the figure, the fitting error between the simulation output of the identified model and the actual system output is very small. Verification results demonstrate that the method proposed in this application exhibits good identification performance under conditions of non-Gaussian noise, unknown time delay, and unknown state.
[0146] While this application has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other embodiments.
Claims
1. A simulation method for process industry systems based on a state-space model, characterized in that, The process industry system is a time-delay industry system, and the simulation method includes: S1. Establish a linear time-delay state-space model of the process industry system, in which the control variables and state variables of the process industry system constitute the state variables, and the sensor measurement values are the output variables. S2. Under the probabilistic framework, a multinomial distribution is introduced to model the random time delay between the state variables and output variables of the time-delay state-space model, and the Dirichlet distribution is used to characterize the time delay prior information to determine the probability distribution of the unknown parameters in the time-delay state-space model. S3. Based on the variational Bayesian inference framework and the probability distribution of unknown parameters, the unknown parameters in the linear time-delay state-space model are identified according to the existing control quantities and sensor acquisition quantities of the process industry system, and the posterior distribution of the unknown parameters is obtained. S4. Simulate the process industry system using a linear time-delay state-space model with identified unknown parameters.
2. The process industry system simulation method based on state-space model according to claim 1, characterized in that, The linear time-delay state-space model is as follows: in, These represent the system's state variables and output variables, respectively. It is the sampling time. To delay time, Indicates state noise. Let A represent the measurement noise, C represent the system matrix, and C represent the observation matrix.
3. The process industry system simulation method based on state-space model according to claim 2, characterized in that, Unknown parameters include the system matrix. and observation matrix State vector and parameters ; State vector The joint probability density function is: in, This represents the state variables at N time points. Initial state The probability density function, whose mean is The covariance is Gaussian distribution; for The probability density function, whose mean is The covariance is Gaussian distribution; Output vector ,but The joint probability density function is: in, This represents the sensor measurements at N time points, where k ranges from 1 to N. for The probability density function, whose mean is The covariance is Gaussian distribution; Indicates a time-delay indicator auxiliary variable; ; System Matrix Observation matrix , The probability distributions are as follows: ; ; ; ; ; ； ； Among them, the system matrix each line It follows a pattern with a mean of 0 and a covariance of . Gaussian distribution; , These represent the dimensions of the state variables and the observation vector, respectively. Observation matrix each line It follows a pattern with a mean of 0 and a covariance of . Gaussian distribution; Precision parameters Each row of elements Obtain the parameter as gamma distribution, Precision parameters Each row of elements Obtain the parameter as The gamma distribution; Precision parameters Each row of elements Obtain the parameter as gamma distribution, Precision parameters Each row of elements Obtain the parameter as The gamma distribution; It is a time-delay distributed parameter The multinomial distribution; A time-delay indicator auxiliary variable; parameter It controls the delay probability distribution at time k. Dirichlet distribution parameters; It is a parameter The Dirichlet distribution; These are normalization parameters. The superscript dd indicates the corresponding parameter for the delay time, and D indicates the maximum time delay length. Auxiliary variables It follows an exponential distribution with a parameter of 1; , This is a hyperparameter.
4. The process industry system simulation method based on state-space model according to claim 3, characterized in that, S3 includes: S31. Mark the mean of the parameters obtained in the previous iteration as... , The Middle The unknown parameters are , The log-posterior distribution is: Formula 1 in, This indicates the evaluation of the function within the angle brackets. Dividing variables The expected value of all other variables except for the constant term; Output vector and The joint probability density function is: S32. Based on Formula 1, combined with the joint probability density function of the state vector X and the output vector... The joint probability density functions are obtained respectively. posterior distribution , , , , , , , , , And obtain the covariance matrix and mean of the corresponding posterior distribution; S33. Determine if the convergence condition is met. If not, go to S31 to proceed to the next iteration. If yes, output the current... , , , , , , , , , The covariance matrix and mean.
5. The process industry system simulation method based on state-space model according to claim 4, characterized in that, System Matrix The posterior distribution is: The covariance matrix is: The mean vector is: in, This indicates the expected value of the function enclosed in angle brackets with respect to its variables. express The Row elements; The posterior distribution of the observation matrix C is: The covariance matrix is: The mean vector is: in, for The Row element.
6. The process industry system simulation method based on state-space model according to claim 5, characterized in that, parameter The posterior distribution is: in: Represents the gamma distribution. express The shape parameters of the gamma distribution, ; express The velocity parameters of the gamma distribution, Indicates to The initial prior strength, , For the system matrix The Line number Column elements; The posterior distribution of γ is: in: express The shape parameters of the gamma distribution, express The velocity parameters of the gamma distribution, Indicates to The initial prior strength, , Observation matrix The Line number Column elements; The posterior distribution is: in: express The shape parameters of the gamma distribution, , express The velocity parameters of the gamma distribution, Yes The initial prior strength; ; The posterior distribution is a gamma distribution: in: express The shape parameters of the gamma distribution, express velocity parameters of the gamma distribution The posterior distribution is: in: This represents the generalized inverse Gaussian distribution. Represents the linear weight parameters in the GIG distribution. This represents the inverse weight parameter in the GIG distribution. The exponential parameter representing the GIG distribution; express The row element; The posterior distribution is: Where: calculation When calculating the posterior distribution, use Updated value , The time delay distribution parameters corresponding to the updated delay time dd; . The posterior distribution is: Among them, calculation When calculating the posterior distribution, use Updated value , .
7. The process industry system simulation method based on state-space model according to claim 6, characterized in that, State vector The log-posterior distribution is in the form of: in: The result obtained from Formula 1 The corresponding constant term; intermediate variable matrix intermediate variable matrix ; Construct augmented state-space models with deterministic parameters having the same log-posterior distribution form: in: , , , For the system matrix A and state noise Output variables Observation matrix C, measurement noise augmented forms; ， ， , , It is the identity matrix. It is a zero vector. It is a zero matrix. This indicates the vertical connection of the input parameters. and They represent and Cholesky decomposition, express Cholesky decomposition; For the augmented state-space model, Kalman filtering and Kalman smoothing are used to smooth the state vector. Perform estimation and convert the state vector The covariance matrix is used as a measure of uncertainty in the state estimation, and the state vector is obtained. .
8. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the process industry system simulation method based on the state-space model as described in any one of claims 1 to 7.
9. A process industry system simulation device based on a state-space model, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the process industry system simulation method based on the state-space model as described in any one of claims 1 to 7.
10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the process industry system simulation method based on a state-space model as described in any one of claims 1 to 7.