Parameter optimization method of viscoelastic unit

Abstract

The invention provides a parameter optimization method, system and equipment for a viscoelastic unit and a medium, and the method comprises the steps: S1, constructing a dynamic model of the viscoelastic unit of a rubber bushing, determining unknown parameters according to the dynamic model, setting particle swarm parameters, and randomly generating a plurality of particles and corresponding positions and iteration speeds; s2, calculating the particle fitness of each particle, and taking the maximum particle fitness as the particle individual optimal fitness; s3, updating the position of each particle according to the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness, and then repeating the steps S2-S3 until the particle individual optimal fitness does not change any more; and S4, taking the value of the position of the particle corresponding to the optimal fitness of the particle individual as the value of the unknown parameter. The method solves the problems that in the prior art, complex nonlinear dynamic changes are difficult to process, and convergence performance is poor.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rubber bushing simulation, and in particular to a parameter optimization method, system, device and medium of a viscoelastic unit. BACKGROUND

[0002] Rubber bushings are particularly widely used in automobile chassis, especially in the suspension part. Rubber bushings can provide flexible connection for two connected parts to reduce wear and tear between the two parts and improve the service life of the parts. In many chassis of pure electric vehicles, most of the parts that need to be connected by hinges are replaced by rubber bushings, which can improve the service life of the parts. Compared with hinges, rubber bushings have the advantages of lower cost and lighter weight, which can reduce manufacturing cost and reduce vehicle weight. Since the lightweight of the whole vehicle is also a focus of current research, the rubber bushing has the advantage of small weight. It is found that the rubber filling material of the rubber bushing will exhibit Payne effect and dynamic stiffness will change with the change of excitation frequency and amplitude under cyclic loading, which is the dynamic viscoelastic property of the rubber bushing. The dynamic stiffness of the rubber bushing changes with the change of loading frequency and amplitude under dynamic loading, which is nonlinear, making the high-precision parameter identification of the model face many challenges. If the optimization ability of the identification algorithm itself is not strong, it will lead to the decrease of the precision of the model, and the research on the parameter identification algorithm is meaningful in improving the precision of the model.

[0003] The parameter of the viscoelastic unit of the rubber bushing is too much and the calculation is large, and the viscoelastic unit parameter identification is identified by algorithm. Common algorithms include least square method and particle swarm optimization (PSO) algorithm, etc. There are some limitations: the calibration method based on the least square method requires known performance curve and explicit mathematical expression, which is suitable for systems with known input-output relationship, but it is difficult to fully capture the dynamic behavior of the complex nonlinear and multivariable coupled rubber bushing dynamics model; the parallel computing characteristic of PSO algorithm is strong, because the update of particles is independent of each other and can be performed simultaneously, which has certain advantages in solving large-scale problems, however, PSO algorithm may face the problem of premature convergence, that is, stagnation near the local optimal solution, which makes it difficult to further find the global optimal solution, resulting in poor convergence performance. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a parameter optimization method of a viscoelastic unit, which solves the problems of difficult to handle complex nonlinear dynamic changes and poor convergence performance in the prior art.

[0005] According to an embodiment of the present application, a parameter optimization method of a viscoelastic unit comprises: S1: a dynamic model of the rubber bushing viscoelastic unit is constructed, unknown parameters are determined according to the dynamic model, particle swarm parameters are set, and a plurality of particles and corresponding positions and iteration speeds are randomly generated; S2: particle fitness of each particle is calculated, and the maximum particle fitness is taken as the particle individual optimal fitness; S3: the position of each particle is updated according to the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness, and then steps S2-S3 are repeated until the particle individual optimal fitness no longer changes; S4: the value of the position of the particle corresponding to the particle individual optimal fitness is taken as the value of the unknown parameter.

[0006] Preferably, the dynamic model is as follows: wherein, is the viscoelastic force at time t, is the fractional derivative operator at time t, is the amplitude at time t, , is the order of the fractional derivative, is the elastic modulus of the model, is the viscosity coefficient of the model, , all are unknown parameters.

[0007] Preferably, the method for updating the position of each particle according to the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness comprises: updating a learning factor and an inertia weight according to the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness; updating the iteration speed according to the updated learning factor and inertia weight; each particle adds the current position to the iteration speed to obtain the updated position of each particle.

[0008] Preferably, if the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness is less than 1, the updated position of each particle needs to be multiplied by the ratio . If the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness is greater than 1, when updating the learning factor and the inertia weight, the learning factor and the inertia weight need to be multiplied by the ratio .

[0009] Preferably, the calculation formula of the particle fitness is as follows: wherein, is the actual dynamic stiffness corresponding to the i th particle under the parameter; is the actual dynamic stiffness corresponding to the i th particle under the parameter; is the simulated dynamic stiffness corresponding to the i th particle under the parameter calculated by the dynamic model of the rubber bushing.

[0010] Preferably, when calculating the particle fitness, the error rate between the simulated dynamic stiffness and the actual dynamic stiffness must be less than or equal to 0.1.

[0011] In another aspect, according to the embodiment of the present application, a parameter optimization system of a viscoelastic unit is also provided, which uses the above-mentioned parameter optimization method of a viscoelastic unit, and comprises: a model construction module, which is configured to construct a dynamic model of a rubber bushing viscoelastic unit and determine unknown parameters; a parameter preset module, which is configured to set particle swarm parameters and randomly generate a plurality of particles and corresponding positions and iteration speeds; an optimization module, which is configured to calculate particle fitness of each particle and historical optimal fitness of the particle swarm, and perform parameter optimization according to the particle fitness of each particle and the historical optimal fitness of the particle swarm.

[0012] In another aspect, according to the embodiment of the present application, a computer is also provided, which comprises at least one processor and a memory, the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the above-mentioned parameter optimization method of a viscoelastic unit.

[0013] In another aspect, according to the embodiment of the present application, a storage medium is also provided, which is a computer readable storage medium, and the storage medium stores a computer program, and the computer program can be executed by one or more processors to implement the above-mentioned parameter optimization method of a viscoelastic unit.

[0014] Compared with the prior art, the present application has the following beneficial effects: The present application constructs a dynamic model of a rubber bushing viscoelastic unit, determines unknown parameters according to the dynamic model, clearly defines unknown parameters that need to be optimized, sets particle swarm parameters, randomly generates a plurality of particles and corresponding positions and iteration speeds, updates the position of each particle through the ratio of the individual optimal fitness of the particle to the historical optimal fitness of the particle swarm, dynamically updates and avoids the problem of falling into a local optimal solution, improves convergence performance, and then takes the value of the position of the corresponding particle of the individual optimal fitness of the particle as the value of the unknown parameter. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is the parameter optimization flowchart of the embodiment of the present application.

[0016] Figure 2 A structure simplified force diagram of a rubber bushing dynamics model of an embodiment of the present application.

[0017] Figure 3 A comparison chart of the optimization ability of the present application and the PSO algorithm of an embodiment of the present application. DETAILED DESCRIPTION

[0018] The technical solutions in the present application will be further described below with reference to the drawings and embodiments.

[0019] As shown in the drawings, Figure 1 an embodiment of the present application proposes a parameter optimization method of a viscoelastic unit, comprising: S1: constructing a dynamics model of a rubber bushing viscoelastic unit, and determining unknown parameters according to the dynamics model, setting particle swarm parameters, and randomly generating a plurality of particles and corresponding positions and iteration speeds; The present application takes a FFD (Frequncy-dependent) viscoelastic unit rubber bushing dynamics model as an example. For the establishment of the rubber bushing dynamics model, generally, the model is established by stress or force superposition based on the Boltzmann superposition principle, and the dynamics model of the rubber bushing is divided into an elastic unit, a friction hysteresis unit and a viscoelastic unit for separate modeling according to the mechanical properties possessed by the rubber bushing.

[0020] As shown in the drawings, Figure 2 , the unit of the elastic force is . the unit of the friction hysteresis unit force is . the unit of the viscoelastic force is . the unit of the response force of the entire parameterized model is .

[0021] The polynomial spring can change the highest degree or coefficient to adapt to the nonlinearity of the elastic unit, and the mechanical expression thereof is: the unit of the force of the elastic unit is . Under the action of a sinusoidal excitation with an amplitude of , the amplitude of the elastic unit is: The elastic unit does not consider friction, so there is no energy loss.

[0022] The expression of the friction unit model is as follows: the amplitude is Under the sinusoidal excitation of , the amplitude of the friction hysteresis module is: In the formula: , is the energy lost in one cycle, in units of .

[0023] During the test process, the rubber bushing is divided into static loading test and dynamic loading test, which respectively provide static stiffness and dynamic stiffness data. The static loading test data will be used to identify the parameters of the friction unit and the viscoelastic unit. The static loading data is generally a smooth curve and is not difficult to identify. The least squares method is used for identification. The dynamic stiffness data is used to identify the viscoelastic unit model parameters.

[0024] FFD viscoelastic element model, the relationship between force and displacement is: in, is the viscoelastic force at time t, is the fractional derivative operator at time t, is the amplitude at time t, 、 is the order of the fractional derivative, ranging from (0,1); is the elastic modulus of the model, is the viscosity coefficient of the model, 、 All are unknown parameters.

[0025] The fractional derivative operator is as follows: The complex stiffness of FFD in the frequency domain is derived as: The above formula can be further used to deduce that the amplitude Under the sinusoidal excitation, the amplitude of the real and imaginary parts of the response force and They are: Dynamic stiffness of rubber bushing The calculation formula is as follows: The above formula can be used to determine 、 All are unknown parameters.

[0026] Then, the particle swarm optimization algorithm is set up, and a plurality of particles and corresponding positions and iteration speeds are randomly generated, wherein the position of the particle is the unknown parameter.

[0027] S2: Calculate the particle fitness of each particle, and take the maximum particle fitness as the particle individual optimal fitness; First, the particle fitness of each particle is calculated by the following formula: Wherein, is the number of particles; is the actual dynamic stiffness under the parameters corresponding to the i-th particle; is the simulated dynamic stiffness of the i-th particle under the parameters corresponding to the i-th particle calculated by the bushing dynamic model.

[0028] In addition, in order to ensure that the fitted data and the data during the model calculation cannot have too large an error, the constraint is established: Then, the maximum particle fitness is selected as the particle individual optimal fitness.

[0029] S3: Update the position of each particle according to the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness, and then repeat steps S2-S3 until the particle individual optimal fitness no longer changes; In the initial state, the particle swarm historical optimal fitness is the same as the current particle individual optimal fitness, so the ratio of the particle individual optimal fitness to the particle swarm historical optimal fitness is 1, but as the number of iterations increases, the particle swarm historical optimal fitness will be completely different from the current particle individual optimal fitness, In order to enable the particle to adaptively adjust the weight and learning factor during the optimization process according to the change degree of the current optimal fitness of the particle swarm to the historical optimal fitness, the ratio of the optimal fitness to the historical optimal fitness is set as a reference, and the expression is: Wherein, and respectively represent the position of the particle individual optimal fitness and the position of the particle swarm historical optimal fitness. When is less than 1, it represents that the current particle swarm optimal fitness is better than the historical optimal fitness, and the search in the space is continued, otherwise the search is avoided to avoid falling into local optimum.

[0030] When is less than 1, the learning factor inertia weight updating formula is as follows: In the formula is the total number of iterations; is the current iteration number; 、 and is the learning factor; is the inertia weight; 、 、 and They are the initial values ​​set for the corresponding variables. 、 、 as well as The final values ​​set for the corresponding variables.

[0031] The corresponding speed update iterative formula is: In the formula, and is the current particle’s velocity and position; 、 and The range of random numbers is (0,1); the range of particle speed and position is [ ], the range of particle position in the formula is [ ]; is the position of the random particle in the current particle swarm.

[0032] The initial values ​​of the above algebraic expressions are as follows: The particle position update formula is: This will increase the search space.

[0033] when When it is greater than 1, it is necessary to jump out of the space. The update formula of the learning factor and inertia weight is as follows: The particle update speed is the same as formula 4, and the particle position update formula is: According to the above rules, multiple iterations are performed until the individual optimal fitness of the particle no longer changes. The position of each particle is updated by the ratio of the individual optimal fitness of the particle and the historical optimal fitness of the particle group, so as to achieve dynamic update and avoid falling into the problem of local optimal solution, improve convergence performance, and then the value of the particle position corresponding to the individual optimal fitness of the particle is used as the value of the unknown parameter; Figure 3 As shown, the parameter optimization capability of the present invention (MPSO) is significantly superior to that of the conventional PSO algorithm. In another aspect, the embodiment of the present application also provides a parameter optimization system of a viscoelastic unit, which uses the parameter optimization method of the viscoelastic unit as described above, and comprises: a model construction module, which is configured to construct a dynamic model of the rubber bushing viscoelastic unit and determine unknown parameters; a parameter preset module, which is configured to set particle swarm parameters and randomly generate a plurality of particles and corresponding positions and iteration speeds; an optimization module, which is configured to calculate particle fitness of each particle and historical optimal fitness of the particle swarm, and perform parameter optimization according to the particle fitness of each particle and the historical optimal fitness of the particle swarm.

[0034] In another aspect, the embodiment of the present application also provides a computer, which comprises at least one processor and a memory, the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the parameter optimization method of the viscoelastic unit as described above.

[0035] In another aspect, the embodiment of the present application also provides a storage medium, which is a computer readable storage medium, and the storage medium stores a computer program, and the computer program can be executed by one or more processors to implement the parameter optimization method of the viscoelastic unit as described above.

[0036] Finally, it should be explained that the above embodiments are only used to illustrate the technical solutions of the present application but not limit the present application, and although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the present application, and all of them should be covered in the scope of the claims of the present application.

Claims

1. A method for optimizing parameters of a viscoelastic element, characterized by: include: S1: Construct a dynamic model of the rubber bushing viscoelastic unit and determine the unknown parameters based on the dynamic model. At the same time, set the particle swarm parameters and randomly generate multiple particles and their corresponding positions and iteration speeds. S2: Calculate the fitness of each particle and take the maximum fitness as the optimal fitness of the particle; S3: Update the position of each particle according to the ratio of the individual particle's optimal fitness to the particle swarm's historical optimal fitness, and then repeat steps S2-S3 until the individual particle's optimal fitness no longer changes; S4: The value of the particle position corresponding to the optimal fitness of the particle individual is used as the value of the unknown parameter.

2. The method for optimizing parameters of a viscoelastic element according to claim 1, wherein: The kinetic model is as follows: in, is the viscoelastic force at time t, is the fractional derivative operator at time t, is the amplitude at time t, 、 is the order of the fractional derivative, is the elastic modulus of the model, is the viscosity coefficient of the model, 、 All are unknown parameters.

3. The method for optimizing parameters of a viscoelastic element according to claim 1, wherein: Methods for updating the position of each particle based on the ratio of the individual particle's optimal fitness to the particle swarm's historical optimal fitness include: Update the learning factor and inertia weight according to the ratio of the optimal fitness of the individual particle and the historical optimal fitness of the particle swarm; Update the iteration speed according to the updated learning factor and inertia weight; Each particle accumulates its current position and iterative velocity to obtain the updated position of each particle.

4. The method for optimizing parameters of a viscoelastic element according to claim 3, wherein: If the ratio of the optimal fitness of the individual particle to the historical optimal fitness of the particle swarm is When it is less than 1, the position of each particle after update must be consistent with the ratio multiplication; If the ratio of the optimal fitness of the individual particle to the historical optimal fitness of the particle swarm is When it is greater than 1, when updating the learning factor and inertia weight, both the learning factor and the inertia weight need to be compared with the ratio Multiply.

5. The method for optimizing parameters of a viscoelastic element according to claim 1, wherein: The calculation formula of the particle fitness is as follows: in, is the number of particles; is the actual dynamic stiffness under the parameters corresponding to the i-th particle; The simulated dynamic stiffness of the parameters corresponding to the i-th particle calculated for the bushing dynamic model.

6. The method for optimizing parameters of a viscoelastic element according to claim 5, wherein: When calculating particle fitness, the error rate between the simulated dynamic stiffness and the actual dynamic stiffness must be less than or equal to 0.

1.

7. A parameter optimization system for a viscoelastic element, characterized by: The system uses a parameter optimization method for a viscoelastic unit according to any one of claims 1 to 6, comprising: A model building module, wherein the model building module is used to build a dynamic model of the rubber bushing viscoelastic unit and determine unknown parameters; A parameter preset module, which is used to set particle swarm parameters and randomly generate multiple particles and their corresponding positions and iteration speeds; The optimization module is used to calculate the particle fitness of each particle and the historical optimal fitness of the particle swarm, and perform parameter optimization based on the particle fitness of each particle and the historical optimal fitness of the particle swarm.

8. A computer, characterized in that: The system comprises at least one processor and a memory, wherein the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the parameter optimization method for a viscoelastic element according to any one of claims 1 to 6.

9. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. The computer program can be executed by one or more processors to implement the parameter optimization method for a viscoelastic element according to any one of claims 1 to 6.

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