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CN-115422815-B - Parameter estimation method, system, device and storage medium of nonlinear diffusion model

CN115422815BCN 115422815 BCN115422815 BCN 115422815BCN-115422815-B

Abstract

The invention discloses a parameter estimation method, a system, a device and a storage medium of a nonlinear diffusion model, wherein the parameter estimation method comprises the steps of constructing a space basis function according to a data snapshot of a system aiming at a nonlinear Fisher type diffusion system applied to a heating and cooling process of an iron rod, utilizing an orthogonal decomposition method to separate space-time variables, utilizing a discrete experience interpolation method to carry out sparse sampling on nonlinear items to obtain optimal low-order approximation of a high-order system, initializing a particle swarm to obtain n particles corresponding to m-dimensional solution vectors of a low-order time sequence model, calculating self fitness of each particle according to a calculation formula and an objective function of parameters to be identified, carrying out iteration and optimization on each particle, outputting the position of the particle with a global optimal value, adding a non-Gaussian Levy process into a traditional particle swarm algorithm, avoiding the particle swarm from being concentrated in the same direction prematurely through random jump of the Levy process, and increasing mutual learning capability among the particles.

Inventors

  • GE FUDONG
  • Hu Yuanye

Assignees

  • 中国地质大学（武汉）

Dates

Publication Date
20260505
Application Date
20220818

Claims (8)

  1. 1. The parameter estimation method of the nonlinear diffusion model is applied to the thermal diffusion process of heating and cooling of the iron rod and is characterized by comprising the following steps of: S 100 , constructing a low-order time sequence model of a nonlinear thermal diffusion process of the iron rod; s 110 , constructing a nonlinear Fisher type diffusion system model, and determining parameters to be identified; the nonlinear Fisher type diffusion system model is as follows: Wherein: As the coefficient of the axial energy dispersion, The density of the iron rod is the density of the iron rod, Represents the specific heat capacity of the material, Indicating temperature Is used for the speed of change of (a), Represents the heat transfer coefficient of the rod surface of the iron rod, Is the space-time temperature distribution of the iron rod, Represents the variation amount with respect to temperature and time, Is the second derivative of temperature with respect to spatial distribution, Representing the distribution position of the temperature, and t represents time; The parameters to be identified comprise axial energy dispersion coefficient Heat transfer coefficient with the surface of iron rod ; S 120 , constructing an output data snapshot of the nonlinear Fisher type diffusion system, and constructing an optimal space basis function of the nonlinear Fisher type diffusion system; The optimal spatial basis function of the nonlinear Fisher type diffusion system is as follows: Wherein: a snapshot of the system being constructed is presented, Is the characteristic vector after the characteristic decomposition of the system snapshot, For the corresponding characteristic value(s), Representing the selection of the largest of these Reconstructing the system by the individual space base; A step S 130 of projecting the nonlinear component into a subspace to approximate the nonlinear component to reconstruct a nonlinear term; the expression of the nonlinear term is expressed as: constructing an identity matrix to project the nonlinear term, which satisfies the following conditions: Wherein: Is a system snapshot built from nonlinear terms, Represents the unit matrix of the matrix of units, Representing the transpose of the identity matrix, The characteristic quantity representing the non-linear term, Spatial components representing nonlinear terms; Calculating the optimal weight coefficient, which is expressed as: Reconstructing the nonlinear term, wherein the expression of the reconstructed nonlinear term is as follows: Step S 140 , performing inner product on all terms of the nonlinear Fisher diffusion system model and an optimal space basis function of the system simultaneously to obtain a low-order approximation of a high-order system, wherein the low-order approximation form of the high-order system is as follows: Wherein: the time component obtained by decomposing the temperature distribution of the iron rod is shown, Is the corresponding spatial component of the signal, And As an unknown parameter of the system, Representing a nonlinear term of the system; And S 200 , carrying out parameter identification on an equivalent low-order time sequence model of the nonlinear Fisher type diffusion system, introducing a Levy process to iterate and optimize each particle, and outputting the position of the particle with the global optimal value after reaching the iteration termination condition.
  2. 2. The method for estimating parameters of a nonlinear diffusion model according to claim 1, wherein in step S 200 , the specific step of performing parameter identification on an equivalent low-order time sequence model of a nonlinear Fisher-type diffusion system includes: Step S 210 , initializing a particle swarm to obtain a corresponding low-order time sequence model Maintaining solution vectors The particles are subjected to calculation according to a calculation formula and an objective function of parameters to be identified, and self fitness of each particle is calculated; step S 220 , obtaining corresponding opposite individuals of the particles, and calculating the fitness of each particle Fitness of the particles The calculation formula of (2) is as follows: Wherein: representing the spatial dimension and the temporal dimension of the data respectively, Is the value of the parameter to be determined for the system, Is the position information corresponding to the optimal adaptability in the particle updating process; Is the true temperature of the system and, Is the estimated temperature of the system; step S 230 , comparing the self fitness of each particle, and selecting the optimal fitness value from the current individual and the opposite individual Individual to obtain global optimum of the whole population of particles Individual optimum value Each particle is updated according to a position updating formula; Step S 240 , introducing a non-Gaussian process Levy distribution to update the position of the particles; Step S 250 , updating the historical individual optimal fitness and the global fitness of the particles, and determining the optimal position of the particles; Step S 260 , carrying out iteration and optimization, and outputting a global optimal value after reaching the iteration termination condition The position of the particle is the model identification parameter of the nonlinear diffusion model.
  3. 3. The method for estimating parameters of a nonlinear diffusion model according to claim 2, wherein in step S 220 , the calculation method of the inverse individual selection is: wherein c is a random number within (0, 1), The number of particles and the dimensions respectively, 、 Respectively the first Minimum and maximum values in the dimension are set, Represents the current first The particles are at the first Temperature estimates in the individual dimensions are used, For the number of iterations, Representing the current particle 。
  4. 4. A method for estimating parameters of a nonlinear diffusion model in accordance with claim 3, wherein in step S 250 , the Levy process update formula for updating each particle according to the location update formula is: wherein S represents compliance parameters of Is a distribution of Levy of (c), And The normal distribution is satisfied, , And Wherein: respectively random variables And Is a function of the variance of (a), Is the value parameter of Levy distribution, Is a gamma function.
  5. 5. The method according to claim 4, wherein in step S 250 , the particle position and velocity update formula is specifically: Wherein: 、 、 as the weight factor of the weight factor, For the dot-product symbol, Is the individual optimum value in the iteration of the particle, Is the global optimum in the iteration of the particle, Is the flight speed of the particles during each iteration, Is the position of the particle during each iteration, The random value is hopped to update the velocity of the particle on behalf of the Levy process.
  6. 6. A parameter estimation system of a nonlinear diffusion model, using the parameter estimation method of a nonlinear diffusion model according to any one of claims 1 to 5, characterized in that the system comprises: The model construction module is configured to construct a low-order time sequence model of the nonlinear diffusion process of the iron rod; and the parameter identification module is configured for carrying out parameter identification on an equivalent low-order time sequence model of the nonlinear Fisher type diffusion system.
  7. 7. Parameter estimation device of a nonlinear diffusion model, characterized by comprising a computer readable storage medium storing a computer program and a processor, said computer program realizing the parameter estimation method of a nonlinear diffusion model according to any one of claims 1-5 when read and run by said processor.
  8. 8. A computer-readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements a method for estimating parameters of a nonlinear diffusion model in accordance with any one of claims 1-5.

Description

Parameter estimation method, system, device and storage medium of nonlinear diffusion model Technical Field The present invention relates to the field of automatic control technologies, and in particular, to a method, a system, an apparatus, and a storage medium for estimating parameters of a nonlinear diffusion model. Background Nonlinear diffusion systems have been widely used to describe the reaction diffusion phenomena commonly found in nature and engineering, such as thermal conduction, thermonuclear reactions, neurophysiology, chemical reactions, nuclear reactions, etc., and are most remarkable in that the change of system state is not only time-dependent, but also closely related to spatial position, and further has the characteristic of space-time coupling. Therefore, how to identify the coefficients of the nonlinear diffusion system through data driving to establish a nonlinear diffusion system model capable of accurately describing the reaction diffusion process is very important. The conventional parameter estimation problem is mainly focused on the situation of a normal differential equation, and the characteristic that a nonlinear structure and spatial information are mutually coupled in a nonlinear diffusion system makes the solution of the parameter estimation problem require huge calculation capacity and an accurate calculation method. Because parameter estimation is an important link of system modeling, the system modeling is a key scientific problem which is primarily solved by researching a controlled object based on a system control theory. In recent years, a Particle Swarm Optimization (PSO) algorithm developed has attracted a lot of attention because of advantages such as easy implementation, high accuracy and fast convergence speed, and has demonstrated its superiority in solving practical problems. However, in the prior art, aiming at a nonlinear Fisher type diffusion system model of iron rod heating, cooling and other processes, a constant inertia coefficient in a classical Particle Swarm Optimization (PSO) algorithm is adopted, so that a search strategy of the algorithm is prone to being in a local defect, the complexity of system modeling is increased, and the computational complexity of nonlinear terms is also increased. Disclosure of Invention The invention provides a parameter estimation method, a system, a device and a storage medium of a nonlinear diffusion model, which can greatly simplify the complexity of system modeling by deducing a low-order model of the nonlinear diffusion process in the iron rod reaction process, and can enhance the searching capability of particles, jump out of local optimum and enhance the mutual learning capability among particles by adding a Levy random process in a traditional particle swarm optimization algorithm. In order to solve the above problems, the present invention provides a parameter estimation method of a nonlinear diffusion model, which is applied to a thermal diffusion process of heating and cooling an iron rod, the parameter estimation method comprising: S 100, constructing a low-order time sequence model of a nonlinear thermal diffusion process of the iron rod; And S 200, carrying out parameter identification on an equivalent low-order time sequence model of the nonlinear Fisher type diffusion system, introducing a Levy process to iterate and optimize each particle, and outputting the position of the particle with the global optimal value after reaching the iteration termination condition. Further, in step S 100, the low-order time sequence model for constructing the nonlinear diffusion model of the iron rod specifically includes: s 110, constructing a nonlinear Fisher type diffusion system model, and determining parameters to be identified; The nonlinear Fisher type diffusion system model is as follows: Wherein alpha is an axial energy dispersion coefficient, d is the density of the iron rod, s is the specific heat capacity, v is the change speed of temperature, beta is the rod surface heat transfer coefficient of the iron rod, T is the space-time temperature distribution of the iron rod, Representing the variation with respect to temperature, time, T xx is the second derivative of temperature with respect to spatial distribution, x represents the location of the distribution of temperature, and T represents time. The parameters to be identified comprise an axial energy dispersion coefficient alpha and a rod surface heat transfer coefficient beta of the iron rod; s 120, constructing an output data snapshot of the nonlinear Fisher type diffusion system, and constructing an optimal space basis function of the nonlinear Fisher type diffusion system; The optimal spatial basis function of the nonlinear Fisher type diffusion system is as follows: Wherein y i represents a constructed system snapshot, u i (x) is a feature vector of the system snapshot after feature decomposition, sigma i is a corresponding feature value, phi (x) represen