Adaptive state estimation method based on fixed structure parameterization decision

Abstract

The invention discloses an adaptive state estimation method based on fixed structure parameterization decision, which comprises the following steps of: converting the problem of simultaneous implementation of online adaptive overcoming and online state estimation of uncertainty of a chemical and biological process into an online design problem of fixed structure parameterization; through application of the single-layer neural network, the ideal design of the parameterized state estimator of the fixed structure is approximated, and ideal estimator parameters approximated by the single-layer neural network are obtained; and updating ideal estimator parameters approximated by the single-layer neural network by using a gradient descent method. According to the method, aiming at the complexity of a chemical and biological process state estimation problem, the idea of fixed structure parameterization (FSP) decision is utilized, the ideal design of a state estimator is directly approximated through a single-layer neural network, the problem is converted into a relatively simple online parameter identification problem, and a gradient descent method capable of ensuring convergence is adopted, so that the state estimation accuracy is improved. Therefore, the purposes of online overcoming of process uncertainty and online estimation of state variables are indirectly achieved.

Description

Technical Field

[0001] The invention relates to the field of chemical bioengineering, and in particular to an adaptive state estimation method based on fixed structure parameterized decision. Background Art

[0002] In recent years, with the continuous expansion of the scale of my country's manufacturing industry, the production process and links have become increasingly complex. How to deal with the complex dynamics of the production process has become an increasingly urgent problem to be solved. Compared with general mechanical manufacturing processes, chemical and biological processes involve more complex physical changes at the first principle level. The difficulty of observation and control required for their automation is higher. In particular, the urgent demand for more product types, shorter cycles and lower costs has brought them highly elastic and flexible characteristics, which has brought greater challenges to the automation of chemical and biological processes. As one of the typical propositions in production process automation, the state estimation problem has always been a hot research field in the field of chemical and biological engineering. The state estimation problem is a method to study the method of estimating the internal state of a dynamic system based on available measurement data. The data obtained by measuring the input and output of the process can only reflect the external characteristics of the system, while the dynamic laws of the process need to be described by internal state variables. Due to the difficulty of observation caused by the complexity of chemical and biological processes, their internal state variables are usually not directly measured, and the first principle modeling of the dynamic laws of the process itself is very difficult, and there is a large process uncertainty. All these make the state estimation problem of chemical and biological processes still one of the difficulties in the field of production process automation.

[0003] There have been many studies on the state estimation problem of chemical and biological processes, and the design method based on Bayesian filtering theory is still the mainstream idea. The representative algorithms under this design idea include traditional Kalman filtering (KF), extended Kalman filtering (EKF), unscented Kalman filtering (UKF), cubature Kalman filtering (CKF), quadrature Kalman filtering (QKF), central difference Kalman filtering (CDKF), Gaussian mixture filtering (GSF), strong tracking filtering (STF), particle filtering (PF), etc. These methods are based on the first principle model and perform numerical simplification methods such as linearization. The process uncertainty is generally treated as random noise, or an adaptive mode is adopted, that is, the process state to be estimated and the process uncertainty are integrated into the augmented process state, and then the state estimation algorithm is designed with the Bayesian filtering theory as a guide. However, the methods are either very harsh in terms of automation theory such as the stability and convergence of the state estimation error, or they cannot be explained. The fixed structure parameterization design concept (FSP) that has emerged in recent years is also used in state estimation. This concept directly assumes the existence of an ideal perfect estimator and uses fixed structure parameterization forms such as neural networks to approximate this perfect estimator. However, it relies on a large amount of data - the "correct answer" - to train the approximate expression of the perfect estimator offline, and only the last trained design is applied online, which greatly limits the promotion and application of this method in actual industrial scenarios with small cycles and high immediacy requirements.

[0004] The difficulties of adaptive state estimation of existing chemical and biological processes lie in the following three aspects:

[0005] (1) The process is complex and highly nonlinear. Even if the given model on which the traditional state estimation method is based is completely accurate, it still needs to perform numerical approximation under strong assumptions, which greatly affects the estimation accuracy.

[0006] (2) The difficulty of first-principles modeling of the process is high, and the resulting model mismatch leads to large uncertainty, that is, the accuracy of the above-mentioned "given model" is also poor, which further deteriorates the estimation accuracy and easily makes the state estimation process unstable.

[0007] (3) The design of traditional adaptive methods requires online identification of process uncertainties based on process state variables. However, in the state estimation problem, the process state variables are not completely known and are also variables to be identified online, making the design of traditional adaptive state estimation methods very difficult. Summary of the invention

[0008] The purpose of the present invention is to provide an adaptive state estimation method based on fixed structure parameterized decision making in view of the complexity of the state estimation problem of chemical and biological processes, so as to ensure that the estimated value of the state variable eventually converges to a satisfactory range near the true value.

[0009] To achieve the above object, the technical solution of the present invention is:

[0010] An adaptive state estimation method based on fixed structure parameterized decision, comprising:

[0011] The problem of overcoming the uncertainty of chemical and biological processes online adaptively and simultaneously performing online state estimation is transformed into an online design problem with fixed structural parameters;

[0012] By using a single-layer neural network, the ideal design of a fixed-structure parameterized state estimator is approximated, and the ideal estimator parameters of the single-layer neural network approximation are obtained;

[0013] Update the ideal estimator parameters for a single-layer neural network approximation using gradient descent.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] In view of the complexity of the state estimation problem of chemical and biological processes, the present invention utilizes the idea of ​​fixed structure parameterization (FSP) decision-making, directly approximates the ideal design of the state estimator through a single-layer neural network, transforms the problem into a relatively simple online parameter identification problem, and adopts a gradient descent method that can ensure convergence, thereby indirectly achieving the purpose of overcoming process uncertainty online and estimating state variables online, ensuring that the estimated value of the state variable eventually converges to a satisfactory range near the true value. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flowchart of an adaptive state estimation method based on fixed structure parameterized decision-making provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0017] Example:

[0018] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0019] See also Figure 1 As shown, this embodiment provides an adaptive state estimation method based on fixed structure parameterized decision, including:

[0020] 101. The problem of overcoming the uncertainty of chemical and biological processes online adaptation and online state estimation is transformed into an online design problem with fixed structure parameters.

[0021] In this way, the design difficulties caused by the unknown state variables required for direct process uncertainty identification are avoided, and the difficulty of the problem is reduced at the methodological level.

[0022] 102. Through the use of a single-layer neural network, the ideal design of a fixed-structure parameterized state estimator is approximated, and the ideal estimator parameters of the single-layer neural network approximation are obtained.

[0023] In this way, the original nonlinear process state estimation problem is transformed into a linear problem with uncertain parameters (LIPs), which further reduces the difficulty of solving the problem.

[0024] 103. The ideal estimator parameters of a single-layer neural network approximation are updated using gradient descent to ensure the uniform ultimate boundedness (UUB) of state and parameter estimates during the solution process.

[0025] In a specific embodiment, the above step 101 includes:

[0026] The specific mathematical expression of chemical and biological processes is as follows:

[0027] x(t+1)=G(x(t))+f(x(t))+w(t)

[0028] y(t)=Hx(t)+v(t)

[0029] where x∈R n×1 is the state variable vector of the process, G is the known dynamics of the process, f is the unknown nonlinear function, t is the discrete time point, y∈R m×1 is the real-time measurable output, H is the measurement constant matrix, w and v are the state space noise and measurement noise respectively, both of which obey the normal distribution with an expectation of 0 and a constant standard deviation. The system meets the observability condition when f is known. Chemical and biological processes such as continuous stirring reaction process, fermentation process, fluidized catalytic cracking process, chaotic chemical reaction process, homopolymerization reaction process all conform to this abstract mathematical form. The state estimation problem is how to accurately estimate the process state variable x based on the real-time measurable output y when the nonlinear function f is unknown.

[0030] Bypassing the identification of the uncertain dynamics f, the estimation of the state variables is expressed as And the design of the state estimation method is generalized as:

[0031] Where F is the fixed structure parameterization (FSP) estimator, which is an unknown function.

[0032] The design of F takes the following form:

[0033] F=F(z(t))

[0034] z(t+1) is the process information available at time t+1, such as earlier state variable estimates and can measure the output [y(t),...,y(td y )], etc. x With d y Can be used as a tunable non-negative parameter.

[0035] The purpose of designing the state estimation method is to estimate the state variables at time t+1. It can be as close to the true state x(t+1) as possible, that is, solve the following minimization problem Σ:

[0036]

[0037] It can be seen that the most ideal effect of the state estimation method design is to make Right now:

[0038]

[0039] Wherein, F0 represents the most ideal state estimator design; the present invention regards F0 as a function to be identified online.

[0040] In a specific embodiment, the above step 102 includes:

[0041] Use a single-layer neural network to approximate F0:

[0042] F0(z(t))=S T (z(t))W

[0043] In the above approximate form, W∈R nl×1 is the unknown constant weight vector to be identified, S∈R nl×n The basis function matrix is ​​as follows:

[0045]

[0046] in, is a bounded basis vector, that is, there exists a constant L>0 such that For the convenience of expression, F0(z(t)) and S(z(t)) in the following mathematical expressions are abbreviated as F0(t) and S(t), respectively.

[0047] The estimated value of the constant weight vector W is expressed as Then the corresponding estimate of the true state x(t+1) is It can be expressed as:

[0048]

[0049] Then the estimation problem of the true state x(t+1) can be converted into an online identification problem of the constant weight vector W.

[0050] The minimization problem Σ is transformed into:

[0051]

[0052] Since the state x(t+1) cannot be directly observed, the present invention modifies the minimization problem Σ into the minimization problem Σ based on the directly observable output y(t+1). H :

[0053]

[0054] According to the premise that both noise w and v obey the normal distribution with expectation 0 and constant standard deviation and the system satisfies the observability condition when f is known, it can be known that Σ and Σ H equivalence.

[0055] In a specific embodiment, the above step 103 includes:

[0056] For the minimization problem Σ H , using the following gradient descent method, incrementally iteratively update in the time direction

[0057] η(t) is a time-varying learning rate that satisfies:

[0058]

[0059] To ensure the algorithm is uniformly eventually bounded (UUB)

[0060] According to the updated The state estimate for the next moment can be calculated

[0061]

[0062] The cycle repeats itself.

[0063] In summary, the present invention aims at the state estimation problem of chemical and biological processes, proposes an idea based on fixed structure parameterization (FSP) decision-making, transforms the problem into a relatively simple single-layer neural network model identification problem, and adopts an identification algorithm that can ensure convergence, thereby indirectly achieving the purpose of online overcoming process uncertainty and online estimation of state variables. In theory, the consistent ultimate boundedness (UUB) of state estimation and parameter estimation in the solution process can be guaranteed.

[0064] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. An adaptive state estimation method based on fixed structure parameterized decision, characterized in that: include: The problem of overcoming the uncertainty of chemical and biological processes online adaptively and simultaneously performing online state estimation is transformed into an online design problem with fixed structural parameters; By using a single-layer neural network, the ideal design of a fixed-structure parameterized state estimator is approximated, and the ideal estimator parameters of the single-layer neural network approximation are obtained; Update the ideal estimator parameters for a single-layer neural network approximation using gradient descent.

2. The adaptive state estimation method based on fixed structure parameterized decision according to claim 1, characterized in that: The problem of overcoming the uncertainty of chemical and biological processes online adaptively and simultaneously performing online state estimation is converted into an online design problem of fixed structure parameterization, including: The specific mathematical expression of chemical and biological processes is as follows: x(t+1)=G(x(t))+f(x(t))+w(t) y(t)=Hx(t)+v(t) where x∈R n×1 is the state variable vector of the process, G is the known dynamics of the process, f is the unknown nonlinear function, t is the discrete time point, y∈R m×1 In order to measure the output in real time, H is the measurement constant matrix, w and v are the state space noise and measurement noise respectively, both of which obey the normal distribution with expectation of 0 and constant standard deviation; The estimate of the state variables is expressed as And the design of the state estimation method is generalized as: Where F is a fixed structure parameterized estimator and is an unknown function.

3. The adaptive state estimation method based on fixed structure parameterized decision according to claim 2, characterized in that: make Right now: Where F0 represents the optimal state estimator design; F0 is regarded as the function to be identified online, and z(t+1) is the process information available at time t+1, such as the earlier state variable estimate and can measure the output [y(t),...,y(td y )],d x With d y Can be used as a tunable non-negative parameter.

4. The adaptive state estimation method based on fixed structure parameterized decision according to claim 3, characterized in that: The ideal design of the fixed structure parameterized state estimator is approximated by using a single-layer neural network to obtain the ideal estimator parameters of the single-layer neural network approximation, including: Use a single-layer neural network to approximate F0: F0(z(t))=S T (z(t))W; In the above approximate form, W∈R nl×1 is the unknown constant weight vector to be identified, S∈R nl×n The basis function matrix is ​​as follows: in, is a bounded basis vector, that is, there exists a constant L>0 such that 5. The adaptive state estimation method based on fixed structure parameterized decision according to claim 4, characterized in that: The estimated value of the constant weight vector W is expressed as Then the corresponding estimate of the true state x(t+1) is is expressed as: Then the estimation problem of the true state x(t+1) is transformed into the online identification problem of the constant weight vector W; Among them, F0(t) is the abbreviation of F0(z(t)), and S(t) is the abbreviation of S(z(t)).

6. The adaptive state estimation method based on fixed structure parameterized decision according to claim 5, characterized in that: The minimization problem Σ is transformed into:

7. The adaptive state estimation method based on fixed structure parameterized decision according to claim 6, characterized in that: Based on the directly observable output y(t+1), the minimization problem Σ is modified to the minimization problem Σ H :

8. The adaptive state estimation method based on fixed structure parameterized decision according to claim 7, characterized in that: The method of updating the ideal estimator parameters of the single-layer neural network approximation using the gradient descent method includes: For the minimization problem Σ H , using the following gradient descent method, incrementally iteratively update in the time direction 9. The adaptive state estimation method based on fixed structure parameterized decision according to claim 8, characterized in that: η is a time-varying learning rate that satisfies: To ensure the consistent eventual boundedness of the algorithm.

10. The adaptive state estimation method based on fixed structure parameterized decision according to claim 9, characterized in that: According to the updated The state estimate for the next moment can be calculated The cycle repeats itself.

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