Research on the Optimization of the Vibration Reduction Seat Based on Genetic Algorithm

Adopting the parallel mechanism as the main body of the seat and the active joints with spring damping elements as the vibration actuator, we established the damping seat model with the parallel mechanism of six degrees of freedom 3-PRPS. To achieve good damping effect, the damping space and flexibility of the mechanism were improved by affecting the velocity matrix with branched speed built by vectors. Optimal parameter values were obtained by genetic algorithm. Finally, results were synthesized and verified to provide an important theoretical basis for the practical application of the mechanism.


INTRODUCTION
As the new idea and breakthrough in the field of vibration, the multi-dimensional damping system based on parallel mechanism is of great applications and development value.Researches on the vibration of parallel mechanism around the world focused on the following aspects.Emdadul Hoque, Gexue R, Lvzhong M and Qizhi Y [1][2][3][4] replaced the traditional active vibration isolation system with the parallel mechanism and carried on the theoretical analysis and experimental verification.Thomas H, Lvzhong M and Wenjiang D [5][6][7] designed parameters of damping devices of the suspension system based on the parallel mechanism according to the sensitive frequency range of the human body and the natural frequency of the vehicle.Bing Li, Qizhi Y, Xiuxiang C and Peng Y [8][9][10][11][12] established the mechanism optimization design model with various constraints after analyzing a kinematic performance indicator of the parallel mechanism.To the mechanism, size parameters largely relate to the motion performance.The size optimization based on tasks in the multi-dimensional damping system of the parallel mechanism is of great significance.However, the size optimization of the damping of parallel mechanism in the task space has not been reported.
In this paper, compact, controllable and precise [13,14] parallel mechanism with six degrees of freedom 3-PRPS was the main body of the multi-dimensional vibration seat.The active joints were accompanied with spring damping elements to achieve energy absorption and dynamic adaptive balance, thus reducing the physical and psychological harm to drivers due to strong vibrations of agricultural vehicles and improving driving and riding comfort.Meanwhile, it was figured out that stability index limited the position and orientation of the mechanism's moving platform and that the optimization in the task space of the parallel mechanism was more practical, which provided significance in the engineering application of the mechanism.

The Establishment of 3-PRPS Parallel Mechanism
As shown in Fig. (1), the damping suspension of agricultural vehicles' seats adopted 3-PRPS parallel mechanism, which consisted of moving platform , fixed platform and symmetrical branches of the platforms with three identical structure parameters.And each branch was composed of .Both the moving platform and the fixed platform were equilateral triangles.The circumcircle radius of the moving platform was r and the inscribed circle radius of the fixed platform was R. According to the characteristics of 3-PRPS parallel mechanism, fixed coordinate system O-XYZ was established on the orthocenter of the fixed platform and moving coordinate system p-xyz was established on the orthocenter of the moving platform .
We installed spring and damping devices on the longitudinal moving pair of branch H and the contact position P between branched chain and the fixed platform.With elastic support, vertical rod length changes and horizontal movement of P could be realized, so that to realize the damping seat with six-dimensional direction.

The Solution of Speed and Acceleration of the Mechanism
According to the symmetry of 3-PRPS parallel mechanism, we studied a loop of the mechanism and established the single chain vector diagram of the mechanism as shown in Fig. (2).We can see: (1) (1) shows that: (2) In addition, the speed of can be expressed as: Wherein , ! p are respectively the linear and angular velocities of P in the moving platform.
Make , the velocity and acceleration of the position and orientation of the moving platform, then: where: They are respectively the input and output speed matrices of the mechanism.
, are respectively the first-order influence coefficient matrix and first-order and second-order influence coefficient matrix of input speed to moving platform velocity.

Optimization Model Establishment
Constraints of the intersection angle of the revolute pair Limit the vice rotation angle by defining the angle between the longitudinal connecting rod and the initial position .The maximum was and minimum was .should meet .Constraints of parameters of the mechanism: The constraints were shown as follows: (19)

Optimization Algorithm Selection
Genetic algorithm is a kind of machine learning technique, which relies on evolutionary theory.Unlike traditional optimization methods, genetic algorithm is a colony optimization technique.In the algorithm, individuals are often decoded by binary system.Individuals need to be decoded during fitness calculation.Fitness is an index for evaluating the advantage and disadvantage of a solution.According to Darwin's evolutionary theory, individuals with high fitness are more likely to be selected to generate the next generation.
. Suspension seat simulation model of the mechanism.
Based on the selected individuals, the next generation is generated by genetic operators.Each of the individual conducts cross over and mutation with another selected individual according to certain probability.The generated individuals become the candidate solutions for the next generation.This process is repeated for many generations to enable the population to evolve constantly, thus acquiring the solution of the optimization problem, as shown in Fig. (3).The genetic algorithm is characterized by: 1).Preserving a small number of elites in the population to the next generation.2).Automatically determining the size of the population according to the defined optimization problem.

RESULTS AND CONCLUSION
We chose q = 1.9 and k = 1 taking movement space and flexibility into account after optimization.

Simulation
From the above, we selected the mechanism parameter as , and .The model of the damping platform is shown in Fig. (4).
In order to verify the damping effect, we took the quality of the moving platform as 66,76,86,96,106kg respectively, added damping spring with stiffness coefficient and damping coefficient to the lateral movement joints and added damping spring with stiffness coefficient and damping coefficient to the longitudinal connecting rod movement joints.Then we exerted pulse force and pulse torque from , , to the center of moving platform.The amplitude of the force was .Torque amplitude was .The total time of the pulse was seconds.The pulse function was STEP (time,0,0, 0.1,600)+STEP (time,0.1,600,0.3,-600)+STEP ( time,0.3,-600,0.4,0).After the dynamics simulation at End Time=10 and steps=100.Through above parameters and in combination with a multibody dynamic model, we could obtain acceleration transfer characteristics in 3 perpendicular axial directions under different bearing qualities, as shown in Fig. (5).
(3) and derivative of the time to obtain: displacement of horizontal slider at the chain I and the length of longitudinal connecting rodDerive the time of (6) and make (4) and (5) simultaneously to obtain: unit vector of the sliding along the directions of and , then:
3).Providing 3 categories of cross over operations, i.e., single-point cross over, two-points cross over and uniform cross over.4).Mutating the individuals according to certain probability.And the parameter configuration of GA was as follows: Scale of sub-population: 20 Scale of total group：300 Total evolving algebra: 150 Crossover rate：0.7 Mutation probability: 0.01 Elite individual: 1 Fig. (5).Acceleration transfer characteristics of system in each Axial direction under different bearing qualities.