CN115097735A - Improved Adam optimization algorithm-based reaction kettle continuous stirring process identification method - Google Patents
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Abstract
The invention discloses an identification method of a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm, and belongs to the technical field of chemical engineering system identification. The technical scheme is as follows: a method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm comprises the following steps: step 1) establishing an input nonlinear Hammerstein-CARMA model in the continuous stirring process of a reaction kettle; and 2) constructing an identification process of the improved Adam optimization algorithm. The beneficial effects of the invention are as follows: the improved Adam optimization algorithm provided by the invention is an improved gradient optimization algorithm, has higher convergence speed and higher convergence precision compared with the traditional gradient optimization algorithm and the like, can be better suitable for modeling and parameter identification of a continuous stirring process of a reaction kettle, and has a certain engineering practical application value.
Description
Technical Field
The invention relates to the technical field of chemical engineering system identification, in particular to a method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm.
Background
With the development of society and science and technology, the parameter identification and control of chemical stirring reaction kettles gradually become a research hotspot in the field of chemical process control, and because the stirring reaction kettles often have the characteristics of nonlinearity, system dynamic complexity and the like, the identification accuracy of control parameters is often not high. Compared with other reaction kettles, the continuous stirring reaction kettle has many advantages, such as low investment rate, strong heat exchange capability and the like, and has high research value, so that a corresponding system model needs to be established for the continuous stirring process of the reaction kettle, and parameters of the established model need to be identified. For this reason, many researchers have proposed different identification methods, such as: least square algorithm, particle swarm algorithm, differential evolution algorithm and the like.
The least square algorithm has the problem of data saturation caused by the fact that the data quantity is increased in the process of tracking the time-varying parameters; the particle swarm algorithm is high in applicability in engineering application, but is sensitive, not strong in robustness, unstable and prone to have problems in convergence effect; the differential evolution algorithm is a novel genetic algorithm, has good global search capability and robustness, but requires certain experience for controlling variable parameter selection due to large calculated amount and large sensitivity to parameters.
How to solve the above technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm, wherein the improved Adam optimization algorithm provided by the invention is an improved gradient optimization algorithm, has higher convergence speed and higher convergence precision, is far smaller in calculated amount than an intelligent algorithm, is far better in calculation precision than a traditional gradient optimization algorithm, and can be better suitable for parameter identification of the continuous stirring process of the reaction kettle.
The invention is realized by the following measures: a method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm comprises the following steps:
step 1) establishing an input nonlinear Hammerstein-CARMA model of a reaction kettle in a continuous stirring process.
And 2) constructing an identification process of the improved Adam optimization algorithm.
As a further optimization scheme of the improved Adam optimization algorithm-based identification method for the continuous stirring process of the reaction kettle, the concrete modeling steps of the step 1) are as follows:
step 1-1) constructing an input nonlinear Hammerstein-CARMA model of a reaction kettle continuous stirring process: in equation (1), y (t) is the output of the system, w (t) is colored noise, and q (t) is the non-interference output of the system:
y(t)＝q(t)+w(t), (1)
wherein q (t) and w (t) are represented by:
A(z -1 )，B(z -1 ) And D (z) -1 ) Is about the backward shift operator z -1 The polynomial of (c):
step 1-2) according to the formulas (2) and (3), the relation between the output y (t) and the input u (t), the intermediate variable m (t), the non-interference output q (t) and the error v (t) can be obtained, wherein
q(t)＝[1-A(z -1 )]q(t)+[B(z -1 )-1]m(t)+m(t), (2)
The nonlinear part is defined as follows:
m(t)＝f(u(t))＝γ 1 f 1 (u(t))+γ 2 f 2 (u(t))+...+γ m f m (u(t)), (3)
wherein γ ═ γ 1 ,γ 2 ,...,γ m ] T ∈R m The parameter vector of the non-linear part, equation (2) can be re-expressed as:
wherein the parameter estimation vector and the system input and output data vector are respectively
As a further optimization scheme of the improved Adam optimization algorithm-based identification method for the continuous stirring process of the reaction kettle, the specific steps of the step 2) for constructing the identification process of the improved Adam optimization algorithm are as follows:
step 2-1), taking the input coolant flow as input data of a continuous stirring process model of the reaction kettle, and taking the concentration of the output fluid as output data;
step 2-2) defining fitness function
Wherein: l is the data length, t is the time,
is an estimated value of the system output, and y (t) is the actual output value of the system;
step 2-3) solving the gradient of the fitness function according to the formula (8):
step 2-4) solving improved parameter values zeta of first moment estimation and second moment estimation of the improved Adam algorithm according to the formula (9) 1 (t),ζ 2 (t)：
Wherein: w is the clipping parameter of the second moment estimation improvement parameter;
step 2-5) calculating the first moment estimation value and the second moment estimation value V (t) of the improved Adam optimization algorithm according to the formula (10), S (t):
wherein: beta is a 1 Is a control parameter of the first moment estimate, beta 2 Is a control parameter for the second moment estimation;
step 2-6) selecting a suitable convergence limiting parameter r (t) according to equation (11):
step 2-7) solving parameter estimation vector according to formula (12)
Wherein: ε is a constant avoiding a denominator of 0, usually taken to be 0.0001;
step 2-8) judging whether the maximum recursion times are reached, if not, jumping to the step 2-2) by the program, and if so, entering the step 2-9);
step 2-9) outputting the parameter estimation vector obtained by identification
And finishing the identification.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method establishes a model for identifying parameters in the continuous stirring process of the reaction kettle, takes the flow of input coolant as input data, and identifies the parameters of the model by utilizing an improved Adam optimization algorithm; as can be seen from fig. 4 and 5, the algorithm can identify the model parameters well.
(2) Compared with the Adam optimization algorithm, the improved Adam optimization algorithm adds a coefficient which is constantly changed according to recursion times to the second term in the first moment estimation formula, and limits the learning rate of the second moment estimation, and meanwhile, because the improved parameter values are self-adaptive, the influence of the former gradient data on the first moment estimation and the second moment estimation at the current moment can be weakened, so that the convergence speed can be improved; the improved Adam optimization algorithm can better identify the nonlinear system, the identification precision is higher, and the obtained estimation error is smaller; meanwhile, the identification method has better applicability to the continuous stirring process of the reaction kettle.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is an overall flow chart of the method for identifying the continuous stirring process of the reaction kettle based on the improved Adam optimization algorithm provided by the invention.
Fig. 2 is a schematic diagram of a continuous stirring process of a reaction kettle of the identification method of the continuous stirring process of the reaction kettle based on the improved Adam optimization algorithm provided by the invention.
FIG. 3 is a schematic diagram of a general model of an input nonlinear Hammerstein-CARMA system of the method for identifying a continuous stirring process of a reaction kettle by using an improved Adam optimization algorithm provided by the invention.
FIG. 4 is a schematic diagram of the error between the identification parameter and the true value according to the present invention.
FIG. 5 is a graph illustrating a comparison of actual output and fitted output obtained from the last one hundred recursions of the identified embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Example 1
Referring to fig. 1 to 5, the technical scheme provided by the invention is that a method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm comprises the following specific steps:
step 1) establishing an input nonlinear Hammerstein-CARMA model in the continuous stirring process of a reaction kettle;
and 2) constructing an identification process of an improved Adam optimization algorithm.
Specifically, the specific modeling steps of step 1) are as follows:
step 1-1) constructing an input nonlinear Hammerstein-CARMA model of a reaction kettle continuous stirring process: in equation (1), y (t) is the output of the system, w (t) is colored noise, and q (t) is the non-interference output of the system:
y(t)＝q(t)+w(t), (1)
wherein q (t) and w (t) are represented by:
A(z -1 )，B(z -1 ) And D (z) -1 ) Is about the backward shift operator z -1 The polynomial of (c):
step 1-2) according to the formulas (2) and (3), the relation between the output y (t) and the input u (t), the intermediate variable m (t), the non-interference output q (t) and the error v (t) can be obtained, wherein
q(t)＝[1-A(z -1 )]q(t)+[B(z -1 )-1]m(t)+m(t), (2)
The nonlinear part is defined as follows:
m(t)＝f(u(t))＝γ 1 f 1 (u(t))+γ 2 f 2 (u(t))+...+γ m f m (u(t)), (3)
wherein γ ═ γ 1 ,γ 2 ,...,γ m ] T ∈R m The parameter vector of the non-linear part, equation (2) can be re-expressed as:
wherein the parameter estimation vector and the system input and output data vector are respectively
Preferably, the specific steps of the step 2) to construct the identification process of the improved Adam optimization algorithm are as follows:
step 2-1), taking the input coolant flow as input data of a continuous stirring process model of the reaction kettle, and taking the concentration of the output fluid as output data;
step 2-2) defining a fitness function
Wherein: l is the data length, t is the time,
is an estimated value of the system output, and y (t) is the actual output value of the system; step 2-3) solving a gradient of the fitness function according to the formula (8):
step 2-4) solving first moment estimation and second moment of the improved Adam algorithm according to the formula (9)Estimated improved parameter value ζ 1 (t),ζ 2 (t)：
Wherein: w is the clipping parameter of the second moment estimation improvement parameter;
step 2-5) calculating first moment estimation and second moment estimation values V (t) of the improved Adam optimization algorithm according to the formula (10), S (t):
wherein: beta is a beta 1 Is a control parameter of the first moment estimate, beta 2 Is a control parameter for the second moment estimation;
step 2-6) selecting a suitable convergence limiting parameter r (t) according to equation (11):
step 2-7) solving parameter estimation vector according to formula (12)
Wherein: ε is a constant avoiding a denominator of 0, usually taken to be 0.0001;
step 2-8) judging whether the maximum recursion times are reached, if not, skipping the program to the step 2-2), and if so, entering the step 2-9);
step 2-9) outputting the parameter estimation vector obtained by identification
And finishing the identification.
The present invention is further described with reference to the drawings and examples, which are only for illustrating the present invention, but the scope of the present invention is not limited to the examples. The schematic diagram of the continuous stirring process of the reaction kettle used in this example is shown in FIG. 2. Wherein u (t) is the input coolant flow, and y (t) is the concentration of the output fluid after the stirring reaction is finished.
With the above mentioned general input nonlinear Hammerstein-CARMA model, the following model can be built for this example:
y(t)＝q(t)+w(t),
m(t)＝f(u(t))＝γ 1 f 1 (u(t))+γ 2 f 2 (u(t))＝1.15u(t)-0.51u 2 (t),
w(t)＝1+d 1 z -1 +d 2 z -2 ＝1+0.91z -1 -1.38z -2 ,
comparing the above model with step 1), it is possible to obtain
a 1 ＝0.7,a 2 ＝0.1,b 1 ＝1.8,b 2 ＝1.5,γ 1 ＝1.15,γ 2 ＝-0.51,d 1 ＝0.91,d 2 ＝-1.38,
Determining a fitness function for the above model
For use in the advanced Adam optimization algorithm, the fitness function is defined as follows:
in the formula (I), the compound is shown in the specification,
is the estimated value of the output, and y (t) is the actual value of the output.
In order to conveniently substitute the parameters to be identified into the improved Adam optimization algorithm, the parameters to be identified form a parameter vector η, and the parameters to be identified are as follows:
collecting input and output data according to the step 2-1);
obtaining a fitness function value according to the step 2-2)
Solving the gradient of the fitness function according to the step 2-3)
Calculating an improved optimization parameter zeta of the first moment estimate and the second moment estimate of the improved Adam optimization algorithm according to step 2-4) 1 (t),ζ 2 (t)；
Calculating first moment estimation and second moment estimation V (t), S (t) according to the step 2-5);
calculating and selecting a proper convergence limiting parameter r (t) according to the step 2-6);
solving parameter estimation vector according to step 2-7)
Completing the circulation according to the steps 2-8) and 2-9), and outputting the parameter estimation vector obtained by identification
And finishing the identification.
Wherein the parameter beta of the first moment estimation and the second moment estimation is set 1 ,β 2 The initial value of (c) and r (t) need to consider several problems: estimated beta of first moment 1 When the setting is too large, the convergence rate is increased, but the convergence accuracy is reduced, and the beta of the second moment estimation is reduced 2 When the setting is too large, the convergence speed becomes slow. To ensure
Convergence of, symmetric matrix
It is necessary to have all the eigenvalues in the unit circle, and a relatively conservative approach is to place an interval limit on the value of r (t). Therefore, the parameters are selected reasonably according to different systems.
The parameter identification result of the identification method of the continuous stirring process of the reaction kettle based on the improved Adam optimization algorithm is shown in FIG. 4, and the actual output and fitting output identification result pair is shown in FIG. 5. It can be seen that the method has high identification precision and small calculation dimensionality, so that the time required for convergence is fast, and the maximum recursion times can be reached only by needing less time. Meanwhile, the identification method has better applicability to a continuous stirring process model of the reaction kettle.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (3)
1. A method for identifying a continuous stirring process of a reaction kettle based on an improved Adam optimization algorithm is characterized by comprising the following steps:
step 1) establishing an input nonlinear Hammerstein-CARMA model in the continuous stirring process of a reaction kettle;
and 2) constructing an identification process of an improved Adam optimization algorithm.
2. The improved Adam optimization algorithm-based identification method for the continuous stirring process of the reaction kettle according to claim 1, wherein the modeling step of the step 1) is as follows:
step 1-1) constructing an input nonlinear Hammerstein-CARMA model of a reaction kettle continuous stirring process: in equation (1), y (t) is the output of the system, w (t) is colored noise, and q (t) is the non-interfering output of the system:
y(t)＝q(t)+w(t), (1)
wherein q (t) and w (t) are represented by:
A(z -1 )，B(z -1 ) And D (z) -1 ) Is about the backward shift operator z -1 The polynomial of (c):
step 1-2) according to the formulas (2) and (3), the relation between the output y (t) and the input u (t), the intermediate variable m (t), the non-interference output q (t) and the error v (t) can be obtained, wherein
q(t)＝[1-A(z -1 )]q(t)+[B(z -1 )-1]m(t)+m(t), (2)
The nonlinear part is defined as follows:
m(t)＝f(u(t))＝γ 1 f 1 (u(t))+γ 2 f 2 (u(t))+…+γ m f m (u(t)), (3)
wherein γ ═ γ 1 ,γ 2 ,...,γ m ] T ∈R m Non-linear partThe divided parameter vector, equation (2), can be re-expressed as:
wherein the parameter estimation vector and the system input and output data vector are respectively
3. The improved Adam optimization algorithm-based identification method for the continuous stirring process of the reaction kettle according to claim 1, wherein the step 2) of constructing the identification flow of the improved Adam optimization algorithm comprises the following steps:
step 2-1), taking the input coolant flow as input data of a continuous stirring process model of the reaction kettle, and taking the concentration of output fluid as output data;
step 2-2) defining fitness function
Wherein: l is the data length, t is the time,
is an estimated value of the system output, and y (t) is the actual output value of the system;
step 2-3) solving the gradient of the fitness function according to the formula (8):
step 2-4) solving improved parameter values zeta of first moment estimation and second moment estimation of the improved Adam algorithm according to the formula (9) 1 (t),ζ 2 (t)：
Wherein: w is the clipping parameter of the second moment estimation improvement parameter;
step 2-5) calculating the first moment estimation value and the second moment estimation value V (t) of the improved Adam optimization algorithm according to the formula (10), S (t):
wherein: beta is a 1 Is a control parameter of the first moment estimate, beta 2 Is a control parameter for the second moment estimation;
step 2-6) selecting a suitable convergence limiting parameter r (t) according to equation (11):
step 2-7) solving parameter estimation vector according to formula (12)
Wherein: ε is a constant avoiding a denominator of 0, usually taken to be 0.0001;
step 2-8) judging whether the maximum recursion times are reached, if not, skipping the program to the step 2-2), and if so, entering the step 2-9);
step 2-9) outputting the parameter estimation vector obtained by identification
And finishing the identification.
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