Iterative estimation method for rapidly identifying crystallization process model parameters

Abstract

The chemical industry is an important pillar of national economy, and the requirements of the fields of biological pharmacy and food additives for high-purity crystal products are gradually increased. L-glutamic acid is used as a key raw material, the crystal quality and yield are affected in the solution crystallization process, and a traditional control strategy has the problems of poor batch repeatability and high energy consumption. Under the background of intelligent manufacturing, construction of a crystallization kinetic model is the key of process optimization, but modeling based on a physical equation faces challenges due to time variation and strong nonlinearity of crystallization reaction. According to the method, a Wiener nonlinear L-glutamic acid solution crystallization process model based on a nonlinear basis function and a static nonlinear function is taken as a research object, and a momentum-based two-stage gradient iteration algorithm is provided to estimate model parameters. The system is decomposed into two subsystems through the hierarchical principle, gradient descent is accelerated through a momentum method, and the convergence speed is increased. The invention aims to realize effective identification of the parameters by using an iterative estimation method for rapidly identifying the parameters of the model.

Description

Technical Field

[0001] The present invention relates to a method for identifying a Wiener nonlinear L-glutamic acid solution crystallization process model based on a momentum-based two-stage gradient iteration algorithm. Background Art

[0002] The chemical industry is an important pillar of the national economy, and the demand for high-purity crystalline products in the fields of biopharmaceuticals and food additives is increasing. As the core raw material for food flavor enhancers and pharmaceutical intermediates, the solution crystallization process of L-glutamic acid directly affects crystal morphology, particle size distribution, and product yield. Traditional crystallization processes mostly rely on empirical control strategies, suffering from problems such as poor repeatability between batches and high energy consumption. With the development of intelligent manufacturing technology, constructing an accurate crystallization kinetics model has become the key to realizing process optimization and control. However, the crystallization reaction mechanism with time-varying characteristics and strong nonlinearity makes the modeling method based on physical equations face challenges such as complex parameters and insufficient real-time performance.

[0003] Existing research mostly uses Hammerstein-Wiener type nonlinear block structure models to describe the crystallization process, but its parameter identification is often restricted by problems such as gradient disappearance and local convergence. Traditional gradient descent algorithms are prone to falling into suboptimal solutions when dealing with the multi-peak optimization objectives of crystallization reactions, while methods such as extended Kalman filtering result in a decrease in identification accuracy due to sensor noise and process disturbances. In addition, the multi-stage characteristics of the crystallization process (such as nucleation, growth, and coalescence stages) require the identification algorithm to have the ability to dynamically adjust. The present invention introduces a momentum factor to accelerate gradient convergence for the Wiener nonlinear model structure; combines the hierarchical principle to decompose the system into two subsystems, and finally realizes the rapid and effective identification of L-glutamic acid crystallization kinetic parameters. Summary of the Invention

[0004] The present invention aims to identify the parameters of a Wiener nonlinear L-glutamic acid solution crystallization process model using a momentum-based two-stage gradient iteration algorithm.

[0005] The solution at the technical level is as follows: According to the momentum theory and the hierarchical principle, parameter estimation of the Wiener nonlinear L-glutamic acid solution crystallization process model is realized.

[0006] 1) Construct a parameter identification model for the Wiener nonlinear output error L-glutamic acid solution crystallization process:

[0007] The first step: Construct a Wiener nonlinear L-glutamic acid solution crystallization process identification model based on a static nonlinear function composed of nonlinear basis functions as shown in the appendix Figure 2 as follows:

[0008] Step 2: Referring to the established model structure, construct the Wiener linear dynamical sub-model expression for the crystallization process of L-glutamic acid solution as follows: The expression of the static non-linear function is as follows:

[0009] After organizing the above equations, the complete Wiener non-linear output error model expression for the crystallization process of L-glutamic acid solution is obtained as follows: c(t) = f(x(t))+v(t). (6) Let γ1=1 and organize (1) to get: x(t)=[1 - A(z)]x(t)+B(z)w(t), (7) Then substitute (7) into (6) to get:

[0010] where w(t) is the wavelength sequence where the characteristic absorption peaks of the L-glutamic acid solution mainly concentrate, x t is the intermediate variable, c(t) is the concentration of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data, and v(t) is the white noise in the identification process.

[0011] Step 3: Construct the Wiener non-linear output error identification model for the L-glutamic acid cooling crystallization process as follows:

[0012] 2) Design the two-stage gradient iteration parameter identification algorithm flow based on momentum:

[0013] Step 1: Start the parameter identification algorithm;

[0014] Step 2: Let the iteration number k = 0 and set the initial values;

[0015] Step 3: Obtain the wavelength sequence where the characteristic absorption peaks of the L-glutamic acid solution mainly concentrate as the input data, and the concentration of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data as the output data;

[0016] Step 4: Construct and

[0017] Step 5: Construct and

[0018] Step 6: Calculate

[0019] Step 7: Define two gradient directions F s , F γ and two correction vectors C s , C γ ;

[0020] Step 8: Determine μ s , μ γ and η s , η γ ;

[0021] Step 9: Update F s , F γ , C s , C γ ,

[0022] If then k = k + 1; Otherwise, obtain and end the process.

[0023] The definitions of the variables are as follows:

[0024] Define the input w(t) and the output c(t);

[0025] Define the data group composed of its input as W(L) and the data group composed of its output as Y(L), where L is the data length;

[0026] Define and as the relevant information vectors;

[0027] Define θ s , θ γ as the parameter vectors;

[0028] Define as the estimated values of θ s , θ γ at the k-th iteration respectively;

[0029] are respectively the estimated values at the k-th iteration; Denote Φ s (t), Φ γ (t) as the estimated values at the k-th iteration.

[0030] 3) According to the parameter estimation method of the Wiener nonlinear output error model based on the L-glutamic acid cooling crystallization process, the finally derived two-stage gradient iteration estimation algorithm based on momentum is:

[0031] Define Y(L) as follows: Y(L) = [c(1),c(2),...,c(L)] T , (11)

[0032] Define and as follows:

[0033] Define and as follows:

[0034] Define F s,k , F γ,k , C s,k and C γ,k as follows: C s,k = η s C s,k-1 -μ s F s,k , (18) C γ,k = η γ C γ,k-1 -μ γ F γ,k , (19)

[0035] Define and as follows:

[0036] Define as follows:

[0037] Define μ s and μ γ as follows: BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention will be further described below in conjunction with the drawings and example simulations.

[0039] Figure 1 is an infrared spectrogram of an aqueous solution of L-glutamic acid.

[0040] Figure 2 is a structural diagram of a Wiener nonlinear crystallization process model of an L-glutamic acid solution based on a nonlinear basis function and a static nonlinear function.

[0041] Figure 3 represents the random ATR-FTIR spectral data of L-glutamic acid (1200 - 1800 cm -1 ) used by the model for experiments.

[0042] Figure 4 represents the solution concentration during the cooling crystallization process of L-glutamic acid used by the model for experiments.

[0043] Figure 5 is the error curve graph of the identified parameters a1, a2, b1, b2, γ2, γ3 after using this algorithm.

[0044] Figure 6 is the comparison curve and its error graph of the predicted solution concentration during the cooling crystallization process of L-glutamic acid and the actual solution concentration during the cooling crystallization process of L-glutamic acid obtained by using this algorithm. Detailed implementation method

[0045] Specific implementation steps of the algorithm:

[0046] 1) Start the identification algorithm, let k = 1, and set the initial values: as a random vector;

[0047] 2) Obtain the wavelength sequence w(t) where the characteristic absorption peaks of the L-glutamic acid solution are mainly concentrated as the input data, and the concentration c(t) of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data as the output data;

[0048] 3) Obtain

[0049] respectively through Equation (14) and Equation (15).

[0050] 4) Obtain

[0050] respectively through Equation (12) and Equation (13).

[0051] 5) Calculate

[0051] through Equation (22). s , μ γ and η s , η γ ;

[0052] 7) Refresh the

[0053] estimated by iteration through Equations (16) - (21). 8) If then k = k + 1, and repeat steps three to nine, otherwise, obtain and to end the process.

[0054] The present invention has accurate calculation and is applicable to parameter identification of the Wiener nonlinear crystallization process model of L-glutamic acid solution.

Claims

1. The present invention aims to use an iterative estimation method for quickly identifying the parameters of the crystallization process model to effectively identify the parameters of the Wiener nonlinear L-glutamic acid solution crystallization process model. It is characterized in that, First, a Wiener nonlinear identification model for the L-glutamic acid solution crystallization process based on a static nonlinear block composed of nonlinear basis functions and is constructed as shown in Figure 2 of the attached drawings: Then, referring to the established model structure, the expression of the Wiener linear dynamic sub-model for the L-glutamic acid solution crystallization process is constructed as follows: The expression of the static nonlinear function is as follows: After arranging the above equations, the expression of the complete Wiener nonlinear output error model for the L-glutamic acid solution crystallization process is obtained as follows: c(t) = f(x(t)) + v(t). (6) where \(w(t)\) is the wavelength sequence where the characteristic absorption peaks of the L-glutamic acid solution are mainly concentrated, \(x\) t is an intermediate variable, \(c(t)\) is the concentration of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data, and \(v(t)\) is white noise during the identification process. Let γ1 = 1 and arrange equation (1) to get: x(t) = [1 - A(z)]x(t) + B(z)w(t), (7) Then substitute equation (7) into equation (6) to get: Subsequently, the Wiener nonlinear output error identification model for the L-glutamic acid cooling crystallization process is obtained:

2. For the iterative identification algorithm described in claim 1, design a two-stage gradient iterative parameter identification algorithm based on momentum as follows: The first step: Start the parameter identification algorithm; The second step: Let the iteration number k = 0 and set the initial values; The third step: Obtain the wavelength sequence w(t) where the characteristic absorption peaks of the L-glutamic acid solution are mainly concentrated as the input data, and the concentration c(t) of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data as the output data; Step 4: Construct and Step 5: Construct and Step 6: Calculate Step 7: Define two gradient directions F s , F γ and two correction vectors C s , C γ ; Step 8: Determine μ s , μ γ and η s , η γ ; Step 9: Update F s , F γ , C s , C γ , Step 10: If then k = k + 1; otherwise, obtain and end the process. The definitions of the variables are as follows: Define the input quantity w(t) and the output quantity c(t); Define the data group composed of its inputs as W(L) and the data group composed of its outputs as Y(L), where L is the data length; Definition and are relevant information vectors; Define θ s , θ γ is the parameter vector; Definition are θ s , θ γ the estimated value of the k-th iteration; respectively the estimated value of the k-th iteration denote Φ s (t), Φ γ (t) the estimated value at the k-th iteration According to the parameter estimation method for constructing the Wiener nonlinear output error model based on the L-glutamic acid cooling crystallization process described in claim 2, the finally derived two-stage gradient iterative estimation algorithm based on momentum is: Y(L) = [c(1), c(2),..., c(L)] T , (11) C s,k = η s C s,k-1 - μ s F s,k , (18) C γ,k = η γ C γ,k-1 - μ γ F γ,k , (19) The specific steps of the above algorithm: 1) Start the identification algorithm, let k = 1, and set the initial values: is a random vector; 2) Obtain the wavelength sequence w(t) where the characteristic absorption peaks of the L-glutamic acid solution are mainly concentrated as the input data, and the concentration c(t) of the L-glutamic acid cooling crystallization process solution corresponding to the spectral data as the output data; 3) Obtain respectively through Equation (14) and Equation (15) 4) Obtain respectively through Equation (12) and Equation (13) 5) Calculate through formula (22) 6) Determine μ s , μ γ and η s , η γ ; 7) Refresh and iterate the estimated values through equations (16)-(21). 8) If then k = k + 1, and repeat steps three to nine. Otherwise, obtain and end the process.

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