A Multi-Field State Estimation Method for Composite Material Curing Based on Kalman Filtering

Abstract

This invention provides a multi-field state estimation method for composite material curing based on Kalman filtering, specifically including the following steps: Step 1, constructing a curing kinetic model, a heat conduction model, and a stress-strain model, and constructing a state vector based on the curing kinetic model, heat conduction model, and stress-strain model; Step 2, using Kalman filtering to estimate the state based on the curing kinetic model, heat conduction model, stress-strain model, and state vector.

Description

Technical Field

[0001] This invention relates to the field of composite material curing prediction, and in particular to a multi-field state estimation method for composite material curing based on particle swarm optimization Kalman filtering. Background Technology

[0002] The curing process of composite materials is a crucial step in manufacturing high-performance products, typically involving multi-field coupling effects such as temperature, degree of cure, and stress-strain fields. Currently, commonly used curing monitoring methods mainly rely on point measurements using thermocouples or fiber optic sensors, which are difficult to implement for large-area, real-time, full-field monitoring and are susceptible to noise interference. Existing technologies have attempted to use curing kinetic models combined with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) for state estimation. However, because model parameters (such as activation energy, rate constant, and thermal conductivity) are usually determined empirically or through single experimental calibration, their accuracy is limited, and their adaptability to complex process conditions is poor. Furthermore, with the application of visible light imaging and thermal imaging technologies in non-destructive testing, a mature and stable solution for effectively integrating large-scale spatiotemporal imaging data into the state estimation framework remains lacking. Therefore, a new method that integrates kinetic simulation, intelligent optimization algorithms, and non-contact detection is urgently needed to achieve high-precision, multi-spatiotemporal, and multi-field state estimation of the composite material curing process. Summary of the Invention

[0003] The main objective of this invention is to provide a multi-field state estimation method for composite material curing based on Kalman filtering, which can estimate multiple parameters of composite materials during the curing process.

[0004] To achieve the above objectives, the technical solution adopted by this invention is: a multi-field state prediction method for composite material curing based on Kalman filtering, specifically including the following steps: Step 1: Construct a curing kinetics model, a heat conduction model, and a stress-strain model, and then construct a state vector based on the curing kinetics model, heat conduction model, and stress-strain model. Step 2: State estimation is performed using Kalman filtering based on the curing kinetics model, heat conduction model, stress-strain model, and state vector.

[0005] Preferably, step one specifically includes the following steps: Step 11: Construct a curing kinetic model, the expression of which is: (1), in, For time, Let be the reaction order. The reaction rate constant is temperature-dependent. The expression is: (2), in, Pre-exponential factor, The activation energy of the reaction. The gas constant is For temperature; Step 12: Construct a heat conduction model, the expression of which is: (3), in, Thermal conductivity, For density, For specific heat capacity, The curing reaction is exothermic. The expression is: (4), in, The total exothermic enthalpy of reaction per unit mass of composite material. The curing reaction rate is related to the value in formula (1). The meaning is the same; Step 12: Construct the stress-strain model, with the following expression: (5), in, For stress, For total strain, Thermal strain caused by temperature To cure shrinkage strain, The elastic modulus varies with the degree of cure; Step 13: Construct the state vector : .

[0006] Preferably, step two specifically includes the following steps: Step 21: Based on the state vector at time k-1 The state vector at time k Making a prediction involves the following steps: Step 211, Substituting into formula (2) yields Then Substituting into formula (1) yields ; Step 212, corresponding Substituting into formula (4) yields Then Substituting into formula (3) yields ; Step 213, Substitution , Substitution and , will get Substituting into formula (5), we get ; Step 214: Predicted state vector .

[0007] Preferably, step two further includes the following steps: Step 22: Based on the predicted state vector The update process includes the following steps: Step 221: Predict the error covariance matrix at time k: (6), in, The error covariance matrix at time k is the result of the prediction. Let be the error covariance matrix at time k-1. State transition function Jacobi, The process noise covariance matrix; Step 222: Calculate the Kalman gain at time k. : (7), in, To observe the noise covariance matrix, Observation matrix Jacobi, , To observe noise; Step 223: Update the state vector at time k: (8), in, This is a nonlinear observation function that maps the surface temperature and defect information of the composite material to a state vector. Step 224: Update the error covariance matrix : (9), in, Let be the Jacobian of the observation matrix.

[0008] Preferably, the process noise covariance matrix The observation noise covariance matrix R is obtained by optimizing the particle swarm optimization algorithm. The specific steps are as follows: Step S1, Parameter Encoding and Particle Initialization: Step S11: Optimize the parameters of the Kalman filter. , which serves as the optimization objective for particle swarm optimization; Step S12: Define the position and velocity of the particle: In the D-dimensional search space, the first... The position of each particle is represented as , corresponding to a group The parameter combination, the speed is expressed as ; Step S13: Initialize the position and velocity of the particle swarm, and simultaneously set the initial values ​​of the inertial weights and the learning factor. Maximum number of iterations ; Step S2: Introduce adaptive inertia weights The calculation formula is as follows: (10) in, For maximum inertia weight, For minimum inertia weight, This represents the current iteration number. This represents the maximum number of iterations. Step S3: Iteratively update the particle's velocity and position: In each iteration, the particle is based on its individual best historical position. and the global optimal position of the group Update speed and position according to the following formula: Speed ​​updates: (11), Location update: (12), in, For the first The first particle The speed of each iteration For the first The first particle The position of the next iteration. , A random number between 0 and 1; Step S4: Construct a fitness function to evaluate the merits of the parameters, which includes the following steps: Step S41: Use the root mean square error (RMSE) as the fitness evaluation index, with the following formula: (13) in, The state estimate is obtained through Kalman filtering. Here, N is the reference value and the number of samples. Step S42: For each particle obtained... The parameter combination is input into the Kalman filter algorithm to calculate the RMSE between the estimated result and the reference measurement value. The RMSE value is used as the fitness of the particle. The smaller the RMSE, the better the parameter combination. Step S5, Global Optimization, specifically includes the following steps: Step S51: Compare the fitness of all particles, obtain the particle with the lowest fitness, and update the optimal position of the individual based on the particle with the lowest fitness. and the global optimal position ; Step S52: Return to step S2 until the maximum number of iterations is reached. At this point, the globally optimal position corresponding This is the optimal parameter combination.

[0009] Compared with the prior art, the present invention has the following beneficial effects: This invention establishes a curing kinetics model, a heat conduction model, and a stress-strain model, and uses Kalman filtering to estimate the state of the composite material during the curing process. In the estimation process, only the surface temperature of the composite material during the curing process needs to be obtained to estimate the state of multiple parameters of the entire composite material curing process. Attached Figure Description

[0010] Figure 1 This is a flowchart of state estimation according to the present invention. Detailed Implementation

[0011] The following description is intended to disclose the invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art.

[0012] A method for predicting the multi-field state of composite material curing based on Kalman filtering specifically includes the following steps: Step 1: Establish the curing kinetics model, heat conduction model, and stress-strain model, and construct the state vector based on the curing kinetics model, heat conduction model, and stress-strain model: Constructing a curing kinetic model: During the curing process of composite materials, thermosetting resins undergo polymerization and crosslinking reactions under the influence of temperature and photoinitiators. The reaction process is typically expressed as the degree of curing. Indicates the degree of curing. This value describes the degree of transformation of a material from an unreacted state to a fully cured state, and ranges from 0 to 1. The curing reaction rate is not only related to the reaction mechanism but also affected by temperature changes. Therefore, a curing kinetic model needs to be established to describe the change in the degree of curing over time. A curing kinetic equation based on the Kamal-Sourour type is adopted, and its expression is: (1), in, For time, Let be the reaction order. The reaction rate constant is a temperature-dependent constant that varies with temperature and is thus described by the Arrhenius equation. The relationship between temperature and temperature is expressed as follows: (2), in, Pre-exponential factor, The activation energy of the reaction. The gas constant is Let be the temperature. The reaction rate constant can be calculated using the above formula. The curing reaction rate is obtained by substituting the values ​​into the curing kinetic equation. This reaction rate is used not only to calculate the change in curing degree over time, but also for calculating the exothermic reaction in the subsequent heat conduction model.

[0013] Constructing a heat conduction model: During the curing process of composite materials, the resin polymerization reaction releases a large amount of heat. Therefore, the internal temperature field of the material is affected not only by the external environment but also by the heat released during the curing reaction. Temperature changes further affect the reaction rate, thus forming a kinetic-heat conduction coupled process. To describe the spatial distribution and temporal variation of temperature within the composite material, a three-dimensional transient heat conduction equation is used for heat conduction modeling, the expression of which is: (3), in, Thermal conductivity, For density, For specific heat capacity, The curing reaction is exothermic. It is a temperature gradient, reflecting the rate of change of temperature along a spatial direction. It is a three-dimensional spatial differential operator. It is directly related to the curing reaction rate, and can be expressed as: (4), in, The total exothermic enthalpy of reaction per unit mass of composite material. The curing reaction rate is related to the value in formula (1). They express the same meaning.

[0014] By solving the heat conduction equation, the internal temperature field T of the material can be obtained. This temperature field result is then fed back to the curing kinetics model as input to update the reaction rate, thus realizing the coupled calculation between kinetics and heat conduction.

[0015] Constructing a stress-strain model: During the curing process of composite materials, not only do temperature changes occur within the material, but volume shrinkage also occurs due to the resin crosslinking reaction, while temperature changes also induce thermal expansion. These factors work together to generate stress and deformation within the material. To describe the mechanical response of the material during curing, a simplified constitutive coupling relationship is introduced: (5), in, For stress, For total strain, Thermal strain caused by temperature To cure shrinkage strain, The elastic modulus varies with the degree of cure. The model takes temperature field and degree of cure as inputs and outputs material stress. The temperature field is calculated using a heat conduction model, while the degree of cure is calculated using a curing kinetics model.

[0016] Constructing the State Vector: To achieve a unified estimation of the multiphysics field in the composite material curing process, physical quantities such as temperature, degree of curing, and stress / strain are uniformly represented as the system state vector, and the state vector is constructed and defined at each point of the spatial discrete grid: .

[0017] Step 2: Based on the curing kinetics model, heat conduction model, stress-strain model, and state vector, Kalman filtering is used for state estimation. The Kalman filtering includes a prediction step and an update step. The prediction step is performed first, followed by the update step. Specifically, it includes the following steps: Step 21, Prediction: Based on the state vector at time k-1 The state vector at time k Making a prediction involves the following steps: Step 211, Substituting into formula (2) yields Then Substituting into formula (1) yields ; Step 212, corresponding Substituting into formula (4) yields Then Substituting into formula (3) yields ; Step 213, Substitution , Substitution and , will get Substituting into formula (5), we get ; Step 214: Predicted state vector ; Step 22, Update: Based on the predicted state vector The update process includes the following steps: Step 221: Predict the error covariance matrix at time k: (6), in, The error covariance matrix at time k is the result of the prediction. Let be the error covariance matrix at time k-1. State transition function Jacobi, Let be the covariance matrix of the process noise, and be the state transition function. Used to describe the state vector from time k-1 The state vector at time k is derived through a coupled model of solidification kinetics, heat conduction, and stress-strain. The nonlinear mapping relationship , This is process noise; Step 222: Calculate the Kalman gain at time k. : (7), in, To observe the noise covariance matrix, Observation matrix Jacobi, , To observe noise; Step 223: Update the state vector at time k: (8), in, The nonlinear observation function maps the surface temperature and defect information of the composite material to the state vector. The surface temperature of the composite material is obtained using a thermal imager. The effect of the model established in this patent is that after obtaining the surface temperature of the composite material, multiple parameters can be estimated by substituting the surface temperature into the model. Step 224: Update the error covariance matrix : (9), in, Let be the Jacobian of the observation matrix.

[0018] In the steps above, For the current moment, , The set total number of iterations.

[0019] Furthermore, the process noise covariance matrix The observation noise covariance matrix R is obtained by optimizing the particle swarm optimization algorithm. The specific steps are as follows: Step S1, Parameter Encoding and Particle Initialization: Step S11: Optimize the parameters of the Kalman filter. , which serves as the optimization objective for particle swarm optimization; Step S12: Define the position and velocity of the particle: In the D-dimensional search space, the first... The position of each particle is represented as , corresponding to a group The parameter combination, the speed is expressed as ; Step S13: Initialize the position and velocity of the particle swarm, and simultaneously set the initial values ​​of the inertial weights and the learning factor. Maximum number of iterations Algorithm parameters, etc.

[0020] Step S2: Introduce adaptive inertia weights: To balance the algorithm's global and local search capabilities, an adaptive inertia weight formula is used to adjust the inertia weights during the iteration process. : (10) in, For maximum inertia weight, For minimum inertia weight, This represents the current iteration number. This represents the maximum number of iterations. Step S3: Iteratively update the particle's velocity and position: In each iteration, the particle is based on its individual best historical position. and the global optimal position of the group Update speed and position according to the following formula: Speed ​​updates: (11), Location update: (12), in, For the first The first particle The speed of each iteration For the first The first particle The position of the next iteration. , A random number between 0 and 1; Step S4: Construct a fitness function to evaluate the merits of the parameters, which includes the following steps: Step S41: Use the root mean square error (RMSE) as the fitness evaluation index, with the following formula: (13) in, The state estimate is obtained through Kalman filtering. Here, N is the reference value and the number of samples. Step S42: For each particle obtained... The parameters are input into the Kalman filter algorithm, and the RMSE between the filtered estimation result and the reference measurement value is calculated. The RMSE value is used as the fitness of the particle. The smaller the RMSE, the better the parameter combination.

[0021] Step S5, Global Optimization, specifically includes the following steps: Step S51: Compare the fitness of all particles, obtain the particle with the lowest fitness, and update the optimal position of the individual based on the particle with the lowest fitness. and the global optimal position ; Step S52: Return to step S2 until the maximum number of iterations is reached. At this point, the globally optimal position corresponding This is the optimal parameter combination; The optimal and Input the Kalman filter module to perform adaptive optimization of the filter parameters.

[0022] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A multi-field state estimation method for composite material curing based on Kalman filtering, characterized in that, Specifically, the steps include the following: Step 1: Construct a curing kinetics model, a heat conduction model, and a stress-strain model, and then construct a state vector based on the curing kinetics model, heat conduction model, and stress-strain model. Step 2: State estimation is performed using Kalman filtering based on the curing kinetics model, heat conduction model, stress-strain model, and state vector.

2. The method according to claim 1, characterized in that, Step one specifically includes the following steps: Step 11: Construct a curing kinetic model, the expression of which is: （1）， in, For time, The reaction order is... The reaction rate constant is temperature-dependent. The expression is: （2）， in, Pre-exponential factor, The activation energy of the reaction. The gas constant is For temperature; Step 12: Construct a heat conduction model, the expression of which is: （3）， in, Thermal conductivity, For density, For specific heat capacity, The curing reaction is exothermic. The expression is: （4）， in, The total exothermic enthalpy of reaction per unit mass of composite material. The curing reaction rate is related to the value in formula (1). The meaning is the same; Step 12: Construct the stress-strain model, with the following expression: （5）， in, For stress, For total strain, Thermal strain caused by temperature To cure shrinkage strain, The elastic modulus varies with the degree of cure; Step 13: Construct the state vector : 。 3. The method according to claim 2, characterized in that, Step two specifically includes the following steps: Step 21: Based on the state vector at time k-1 The state vector at time k Making a prediction involves the following steps: Step 211, Substituting into formula (2) yields Then Substituting into formula (1) yields ; Step 212, corresponding Substituting into formula (4) yields Then Substituting into formula (3) yields ; Step 213, Substitution , Substitution and , will get Substituting into formula (5), we get ; Step 214: Predicted state vector .

4. The method according to claim 3, characterized in that, Step two also includes the following steps: Step 22: Based on the predicted state vector The update process includes the following steps: Step 221: Predict the error covariance matrix at time k: （6）， in, The error covariance matrix at time k is the result of the prediction. Let be the error covariance matrix at time k-1. State transition function Jacobi, The process noise covariance matrix; Step 222: Calculate the Kalman gain at time k. : （7）， in, To observe the noise covariance matrix, Observation matrix Jacobi, , To observe noise; Step 223: Update the state vector at time k: （8）， in, This is a nonlinear observation function that maps the surface temperature and defect information of the composite material to a state vector. Step 224: Update the error covariance matrix : （9）， in, Let be the Jacobian of the observation matrix.

5. The method according to claim 3, characterized in that, The process noise covariance matrix The observation noise covariance matrix R is obtained by optimizing the particle swarm optimization algorithm. The specific steps are as follows: Step S1, Parameter Encoding and Particle Initialization: Step S11: Optimize the parameters of the Kalman filter. , which serves as the optimization objective for particle swarm optimization; Step S12: Define the position and velocity of the particle: In the D-dimensional search space, the first... The position of each particle is represented as , corresponding to a group The parameter combination, the speed is expressed as ; Step S13: Initialize the position and velocity of the particle swarm, and simultaneously set the initial values ​​of the inertial weights and the learning factor. Maximum number of iterations ; Step S2: Introduce adaptive inertia weights The calculation formula is as follows: （10）， in, For maximum inertia weight, For minimum inertia weight, This represents the current iteration number. This represents the maximum number of iterations. Step S3: Iteratively update the particle's velocity and position: In each iteration, the particle is based on its individual best historical position. and the global optimal position of the group Update speed and position according to the following formula: Speed ​​updates: (11), Location update: (12)， in, For the first The first particle The speed of the next iteration For the first The first particle The position of the next iteration. , A random number between 0 and 1; Step S4: Construct a fitness function to evaluate the merits of the parameters, which includes the following steps: Step S41: Use the root mean square error (RMSE) as the fitness evaluation index, with the following formula: (13) in, The state estimate is obtained through Kalman filtering. Here, N is the reference value and the number of samples. Step S42: For each particle obtained... The parameter combination is input into the Kalman filter algorithm to calculate the RMSE between the estimated result and the reference measurement value. The RMSE value is used as the fitness of the particle. The smaller the RMSE, the better the parameter combination. Step S5, Global Optimization, specifically includes the following steps: Step S51: Compare the fitness of all particles, obtain the particle with the lowest fitness, and update the optimal position of the individual based on the particle with the lowest fitness. and global optimal position ; Step S52: Return to step S2 until the maximum number of iterations is reached. At this point, the globally optimal position corresponding This is the optimal parameter combination.

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