CN106407573A - A Pareto-based hydraulically damped rubber mount structure parameter multi-objective optimization method - Google Patents

Abstract

The invention discloses a Pareto-based multi-objective optimization method for liquid resistance mount structural parameters, which is characterized in that it comprises the following steps: 1) establishing a liquid resistance mount structural parameter multi-objective optimization model; 2) transforming according to the fuzzy penalty function method It is an unconstrained multi-objective optimization problem; 3) Pareto GA genetic algorithm is used to optimize the one-step multi-objective optimization problem; 4) The objective weight of each optimization objective is determined by the entropy weight method; 5) The Pareto optimal solution is based on the TOPSIS strategy Sets are prioritized to obtain the best structural scheme. The beneficial effects achieved by the present invention: the method can realize the automatic determination of the structural parameters of the liquid resistance mount, and meet the dynamic requirements of the liquid resistance mount "with high stiffness and large damping in the low frequency domain, and low stiffness and small damping in the high frequency domain", Make up for the shortcomings of adjusting design parameters by trial and error in the traditional design process, improve development efficiency, shorten development costs and development cycles.

Description

Pareto-based multi-objective optimization method for structural parameters of hydraulic mount

technical field

The invention relates to a Pareto-based multi-objective optimization method for structural parameters of liquid resistance mounts, and belongs to the technical field of automobile engine vibration reduction.

Background technique

Automobile engine hydraulic mount is an important vibration reduction and vibration isolation component on the automobile. It plays the role of fixing and supporting the powertrain of the locomotive, isolating the vibration caused by the engine itself and the impact of the road surface. In order to effectively isolate the transmission of the vibration caused by the main harmonic excitation of the reciprocating unbalanced inertial force in the high frequency band of the engine to the car body, improve ride comfort and reduce noise, especially cavity resonance, it is hoped that the suspension components have low stiffness and small damping characteristics; On the other hand, in order to suppress the excitation of the idling fluctuation torque main harmonic, which causes the powertrain to vibrate with a large amplitude near the resonance frequency, and to limit those quasi-static loads, such as starting, shifting, acceleration, braking, turning and unevenness The displacement of the powertrain caused by road impact and other loads, and the large-scale free vibration induced by it should be attenuated as soon as possible, and the suspension components should have high stiffness and large damping characteristics. These are the two basic and contradictory requirements put forward by the powertrain vibration isolation for the suspension components, that is, "high stiffness and large damping in the low frequency domain and low stiffness and small damping in the high frequency domain" are put forward for the powertrain suspension. These two basic but contradictory requirements.

The structural parameters of liquid resistance mounts are the main parameters that affect the vibration reduction performance of liquid resistance mounts. How to determine these parameters to obtain good vibration reduction performance has always been the difficulty and focus of mount design. The invention discloses a Pareto-based multi-objective optimization method for the structural parameters of the liquid resistance mount, which solves the problem that the structural parameters are difficult to determine in the design process of the existing liquid resistance mount, and satisfies the "low frequency domain of the liquid resistance mount with high stiffness and large Damping, high frequency domain has the dynamic requirements of low stiffness and small damping". The invention can effectively improve the dynamic characteristics of the liquid resistance mount, meet the dynamic characteristic requirements of the automobile engine mount system for the mount components, improve the development efficiency of the liquid resistance mount, and shorten the development cost and development period.

Contents of the invention

In order to solve the deficiencies in the prior art, the object of the present invention is to provide a Pareto-based multi-objective optimization method for the structural parameters of the liquid resistive mount, to realize the automatic determination of the structural parameters of the liquid resistive mount, and to meet the requirements of the low frequency domain of the liquid resistive mount. The dynamic requirements of high stiffness and large damping, low stiffness and low damping in the high frequency domain make up for the shortcomings of using trial and error methods to adjust design parameters in the traditional design process, improve development efficiency, and shorten development costs and development cycles.

In order to achieve the above object, the present invention adopts the following technical solutions:

A Pareto-based multi-objective optimization method for structural parameters of liquid resistance mounts is characterized in that it comprises the following steps:

1) Establish a multi-objective optimization model of hydraulic mount structure parameters, select the variables involved in the model and optimization objectives according to the actual situation, and establish constraints;

2) Transform the multi-objective optimization problem with constraints in step 1) into an unconstrained multi-objective optimization problem according to the fuzzy penalty function method, obtain the fitness value function of each optimization target, and form a new target optimization function;

3) Using the Pareto GA genetic algorithm to optimize the multi-objective optimization problem obtained in step 2), and obtain the Pareto optimal solution set;

4) Using the entropy weight method to determine the objective weight of each optimization objective;

5) Prioritize the Pareto optimal solution set based on the TOPSIS strategy to obtain the best structural scheme.

Further, the parameters involved in the step 1) are:

Rubber main spring dynamic stiffness K _r , rubber main spring damping B _r , volume stiffness K ₁ of the upper liquid chamber, inertia channel length l _i , inertia channel cross-sectional area A _i , inertial coefficient I _d of liquid flow in the decoupler and damping The coefficient B _d is the design variable;

The optimization goal is:

Peak frequency of dynamic stiffness of hydraulic mount under low-frequency and large-amplitude excitation;

The peak dynamic stiffness of the liquid resistance mount under low-frequency and large-amplitude excitation;

The peak value of the damping coefficient of the hydraulic mount under low-frequency and large-amplitude excitation;

The peak frequency of the dynamic stiffness of the hydraulic mount under high-frequency and small-amplitude excitation;

The peak dynamic stiffness of the liquid resistance mount under high-frequency and small-amplitude excitation;

The peak damping coefficient of a hydraulic mount under high-frequency, small-amplitude excitation.

Further, the new optimization objective function in step 2) is composed of the sum of the fuzzy penalty function determined by the discrete membership function and the normalized objective function.

Further, the step 3) specific steps are as follows:

301) Initialize the population M, and randomly generate a parent population P _t whose size is N;

302) Calculate the objective function value for the current population individual;

303) performing non-inferior hierarchical sorting on population individuals;

304) using binary tournament selection, crossover and mutation operations to generate N offspring populations Q _t ;

305) Population P _t and population Q _t are merged into R _t , R _t = P _t ∪ Q _t ;

306) Carry out objective function value calculation to the individual in the new population Rt;

307) Perform non-dominated sorting on population individuals;

308) Select the first N individuals to generate the parent population P _t+1 ;

309) If the convergence condition is reached (the fitness of the generated population is less than the set value), then terminate; otherwise, the number of iterations is increased by 1, and the step 302 is turned to);

310) Outputting the Pareto optimal solution set.

Further, the specific steps of said step 4) are as follows:

401) Standardize the Pareto optimal solution set data to obtain a standardized decision:

where f _ij represents the value of the jth optimization objective of the i-th candidate scheme, max{f _j } and min{f _j } represent the maximum and minimum values of the j-th evaluation index in all candidate schemes, and m is The number of options to be selected, n is the number of optimization objectives;

402) Process the decision matrix to obtain the matrix P=(p _ij ) _m×n ,

403) Calculate the information entropy of the indicator output

404) Calculate attribute objective weight vector

Further, the specific process of said step 5) is as follows:

501) standardize the decision matrix to get the normalized decision matrix Y=(y _ij ) _m×n ;

502) Calculate the weighted normalized decision matrix Z=(z _ij ) _m×n , where z _ij =w _j y _ij , 1≤i≤m, 1≤j≤n;

503) Determine positive ideal solution Z ⁺ and negative ideal solution Z ⁻ : in

504) Calculate each scheme ^to the Euclid distance of positive ideal solution Z ⁺ and negative ideal solution Z- with

505) Calculate the relative closeness of each scheme

506) Arranging the priority order of each scheme according to the relative closeness: the greater the relative closeness, the better, and the smaller the relative closeness, the worse.

The beneficial effects achieved by the present invention: the method can realize the automatic determination of the structural parameters of the liquid resistance mount, and meet the dynamic requirements of the liquid resistance mount "with high stiffness and large damping in the low frequency domain, and low stiffness and small damping in the high frequency domain", Make up for the shortcomings of adjusting design parameters by trial and error in the traditional design process, improve development efficiency, shorten development costs and development cycles.

Description of drawings

Fig. 1 is a flow chart of the multi-objective optimization method for the structural parameters of the hydraulic mount;

Fig. 2 is a structural schematic diagram of a liquid resistance suspension structure.

Meanings of reference signs in the figure:

1-Rubber main spring, 2-Metal skeleton, 3-Decoupling plate, 4-Flector seat, 5-Rubber base film, 6-Lower liquid chamber, 7-Inertia channel, 8-Upper liquid chamber, 9-Connecting bolts .

detailed description

The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

Step 1) Establish a multi-objective optimization model for the structural parameters of the fluid-resistance mount, and determine the design variables and optimization objectives.

Referring to Figure 2: the dynamic stiffness of the rubber main spring K _r , the damping of the rubber main spring B _r , the bulk stiffness of the upper liquid chamber K ₁ , the length of the inertial channel l _i , the cross-sectional area of the inertial channel A _i , and the inertia of the liquid flow in the decoupler Coefficient _Id and damping coefficient _Bd are design variables.

The peak frequency of the dynamic stiffness of the hydraulic mount under low-frequency and large-amplitude excitation;

The peak dynamic stiffness of the liquid resistance mount under low-frequency and large-amplitude excitation;

The peak value of the damping coefficient of the hydraulic mount under low-frequency and large-amplitude excitation;

The peak frequency of the dynamic stiffness of the hydraulic mount under high-frequency and small-amplitude excitation;

The peak dynamic stiffness of the liquid resistance mount under high-frequency and small-amplitude excitation;

The peak value of the damping coefficient of the hydraulic mount under high-frequency and small-amplitude excitation is the optimization target.

The design variables are x=(x ₁ ,x ₂ ,x ₂ ,x ₄ ,x ₅ ,x ₆ ,x ₇ )=(K _r ,B _r ,K ₁ ,l _i ,A _i ,I _d ,B _d ) , let η=8πμ, Wherein, μ is the viscosity coefficient of the liquid in the liquid resistance suspension. In this embodiment, the liquid in the liquid resistance suspension is ethylene glycol solution, and its viscosity coefficient is 21 mPa.s. The piston area A _p of the upper liquid chamber is 5.278×10 ^-3 m ² .

According to the design requirements of the OEM, combined with the ideal dynamic characteristics requirements of the powertrain engine mount system for the mount components, the results of the multi-body dynamics analysis of the mount system and the characteristics of the dynamic characteristics of the hydraulic mount, the hydraulic mount Setting the dynamic characteristics presents the following requirements:

(1) The peak frequency of dynamic stiffness of liquid resistance mount under low frequency and large amplitude excitation is 8Hz;

(2) The peak dynamic stiffness of the liquid resistance mount under low-frequency and large-amplitude excitation is 350N/mm;

(3) The peak damping coefficient of the liquid resistance mount under low frequency and large amplitude excitation is 8N.s/mm;

(4) The peak frequency of the dynamic stiffness of the liquid resistance mount under high-frequency and small-amplitude excitation is 90Hz;

(5) The peak dynamic stiffness of the liquid resistance mount under high-frequency and small-amplitude excitation is 320N/mm;

(6) The peak value of the damping coefficient of the liquid resistance mount under high-frequency and small-amplitude excitation is 3.5N.s/mm;

By analyzing the structure of the liquid resistance mount, the structural parameters of the liquid resistance mount are required to meet the following conditions:

(1) The length l _i of the inertia channel is less than the outer circumference of the diversion seat cover;

(2) Twice the diameter d _i of the inertial channel is less than the length l _i of the inertial channel.

Then the optimization objective of the multi-objective parameter optimization model of liquid resistance mount can be written as:

Wherein, ρ is the density of the liquid in the liquid resistance mount, and its value is 1.113×10 ³ kg/m ³ in this embodiment.

The constraint conditions of the optimization model of fluid resistance mount parameters are:

The mathematical model for the multi-objective parameter optimization of the dynamic characteristics of the hydraulic mount is as follows:

Step 2) Transform the original multi-objective optimization problem with constraints into an unconstrained multi-objective optimization problem according to the fuzzy penalty function method, and obtain the fitness value function of each individual. The specific process is as follows:

In the fuzzy environment, the constraints are defined by the fuzzy set _G in the definition domain, and μG represents the degree to which points satisfy the constraints.

Unlike the midpoint of the deterministic model, which is judged as an infeasible solution if it is outside the feasible region, after adopting fuzzy theory, the infeasible point can be accepted as an incompletely feasible solution.

According to fuzzy set theory, when a point is in the feasible region, its membership function μ _G (x) is equal to 1. In other cases, the membership function value is within the range of 0≤μ _G ≤1. The maximum violation degree of a point to L constraints is defined as μ _C (x), and expressed as:

Regularize the objective function:

For the minimization problem at the jth point in the fuzzy set the objective function considering the fuzzy penalty function for: Among them, R _k is the fuzzy penalty function determined by the discrete membership function, and f _j ′(x) is the objective function after normalization. The purpose of the normalization of the objective function is to determine the point state in the feasible domain. _Rk is expressed as

In the present invention, the penalty weight coefficient KD=10.

Step 3) Pareto GA genetic algorithm is used to optimize the multi-objective optimization problem of liquid resistance mount, and obtain the Pareto optimal solution set. The specific process is as follows:

Step S301, initialize the population M, and randomly generate a parent population P _t whose size is N=60;

Step S302, calculating the objective function value for the current population individual;

Step S303, performing non-inferior hierarchical sorting on the population individuals;

Step S304, using binary tournament selection, selecting a crossover probability of 0.5 and a mutation probability of 0.008, and the crossover and mutation operations generate N offspring populations Q _t ;

Step S305, the population P _t and the population Q _t are merged into R _t , R _t = P _t ∪ Q _t ;

Step S306, calculating the objective function value for the individual in the new population R _t ;

Step S307, perform non-dominated sorting on the population individuals;

Step S308, selecting the first N individuals to generate the parent population P _t+1 ;

Step S309, if the convergence condition is reached, then terminate; otherwise, increase the algebra by 1, and turn to step S302;

Step S310, outputting a Pareto optimal solution set.

Step 4), using the entropy weight method to determine the objective weight of each optimization objective, the process is as follows:

401) Standardize the Pareto optimal solution set data to obtain a standardized decision:

where f _ij represents the value of the jth optimization objective of the i-th candidate scheme, max{f _j } and min{f _j } represent the maximum and minimum values of the j-th evaluation index in all candidate schemes, and m is The number of options to be selected, n is the number of optimization objectives;

402) Process the decision matrix to obtain the matrix P=(p _ij ) _m×n ,

403) Calculate the information entropy of the indicator output

404) Calculate attribute objective weight vector

In the step 5), based on the TOPSIS strategy, the Pareto optimal solution set is prioritized to obtain the best hydraulic mount structure parameters, and the specific process is as follows:

501) standardize the decision matrix to get the normalized decision matrix Y=(y _ij ) _m×n ;

502) Calculate the weighted normalized decision matrix Z=(z _ij ) _m×n , where z _ij =w _j y _ij , 1≤i≤m, 1≤j≤n;

503) Determine positive ideal solution Z ⁺ and negative ideal solution Z ⁻ : Among them, w is an n-dimensional row vector, in

504) Calculate each scheme ^to the Euclid distance of positive ideal solution Z ⁺ and negative ideal solution Z- with

505) Calculate the relative closeness of each scheme

506) Arranging the priority order of each scheme according to the relative closeness: the greater the relative closeness, the better, and the smaller the relative closeness, the worse.

The above is only a preferred embodiment of the present invention, and it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.

Claims (6)

1. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto, is characterized in that, comprise the following steps：

1) set up Hydraulic Engine Mount structural parameters Model for Multi-Objective Optimization, according to the variable being related in actual conditions preference pattern and excellent Change target, and set up constraints；

2) according to Fuzzy Penalty Function method by step 1) in the multi-objective optimization question of Problem with Some Constrained Conditions be converted into unconfined many mesh Mark optimization problem, obtains the fitness value function of each optimization aim, forms new objective optimization function；

3) adopting Pareto GA genetic algorithm to step 2) multi-objective optimization question that obtains is optimized, and obtains Pareto Excellent disaggregation；

4) objective weight of each optimization aim is determined using the entropy method of weighting；

5) priority ordered is carried out based on TOPSIS strategy to Pareto optimal solution set and obtain optimal organization plan.

2. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto according to claim 1, it is special Levying is, described step 1) in the parameter that is related to be：

Rubber spring dynamic stiffness K_r, rubber spring damping B_r, upper liquid building volume stiffness K₁, inertia channel length l_i, inertia channel horizontal Sectional area A_i, in decoupler liquid flowing inertia coeffeicent I_dWith damped coefficient B_dFor design variable；

Optimization aim is：

Low frequency, the lower Hydraulic Engine Mount dynamic stiffness crest frequency of large amplitude excitation；

Low frequency, the dynamic stiffness peak value of the lower Hydraulic Engine Mount of large amplitude excitation；

Low frequency, the damped coefficient peak value of the lower Hydraulic Engine Mount of large amplitude excitation；

Hydraulic Engine Mount dynamic stiffness crest frequency under high frequency, little amplitude excitations；

The dynamic stiffness peak value of Hydraulic Engine Mount under high frequency, little amplitude excitations；

The damped coefficient peak value of Hydraulic Engine Mount under high frequency, little amplitude excitations.

3. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto according to claim 1, it is special Levying is, described step 2) in new optimization object function Fuzzy Penalty Function and through normalization determined by discrete membership function Object function sum afterwards is constituted.

4. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto according to claim 1, it is special Levying is, described step 3) comprise the following steps that：

301) initialize population M, random one size of generation is the parent population P of N_t；

302) target function value calculating is carried out to current population at individual；

303) population at individual is carried out with non-bad layer sorting；

304) binary algorithm of tournament selection, intersection and mutation operation is adopted to produce N number of progeny population Q_t；

305) population P_tWith population Q_tIt is incorporated into R_tIn, R_t=P_t∪Q_t；

306) target function value calculating is carried out to individuality in new population Rt；

307) non-dominated ranking is carried out to population at individual；

308) select top n individual generation parent population P_t+1；

309) if reaching the condition of convergence, terminate；Otherwise, iterations adds 1, turns step 302)；

310) export Pareto optimal solution set.

5. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto according to claim 1, it is special Levying is, described step 4) comprise the following steps that：

401) standardization is done to Pareto optimal solution set data, obtain specified decision：

1≤i≤m, 1≤j≤n, wherein f_ijRepresent j-th optimization aim of i-th optional program Numerical value, max { f_jAnd min { f_jRepresenting the maximum of jth item evaluation index and minimum of a value in all optional programs respectively, m is Optional program number, n is optimization aim number；

402) process decision matrix, obtain matrix P=(p_ij)_m×n,1≤i≤m,1≤j≤n；

403) comentropy of parameter output1≤i≤m,1≤j≤n；

404) computation attribute objective weight vector1≤i≤m,1≤j≤n.

6. a kind of Hydraulic Engine Mount structural parameters Multipurpose Optimal Method based on Pareto according to claim 5, it is special Levying is, described step 5) detailed process as follows：

501) standardization processing is made to decision matrix, obtain specified decision matrix Y=(y_ij)_m×n；

502) calculate weighted normal decision matrix Z=(z_ij)_m×n, wherein z_ij=w_jy_ij, 1≤i≤m, 1≤j≤n；

503) determine positive ideal solution Z⁺With minus ideal result Z^-：Wherein, the row vector that w ties up for n,Wherein

504) calculate each scheme to positive ideal solution Z⁺With minus ideal result Z^-Euclid distanceWith

505) calculate the relative similarity degree of each scheme1≤i≤m；

506) precedence of each scheme is arranged according to relative similarity degree：Relative similarity degree is more big then more excellent, and relative similarity degree is less Then more bad.