Optimization evaluation group of gear modification parameters based on genetic algorithm

1) Decoding

According to the encoding mode, the chromosome bit string is decoded to obtain the shape modification quantity is, is δ, IC, IC δ, LS, LS δ, LB, LB δ.

2) Define fitness function

Genetic algorithm uses fitness function to evaluate the quality of a solution. The larger the fitness is, the better the solution quality is. The fitness function should be defined before the realization of genetic algorithm. Generally speaking, there are two ways to choose: one is to consider the impact on the gear teeth from the minimum; the other is to consider the transmission error fluctuation of the gear from the minimum. Because there is no vibration when the transmission error of the gear is constant, it is reasonable to evaluate the group by taking the reciprocal of the transmission error fluctuation (peak to peak) as the adaptive value. The fitness function is defined as follows:

3) Fitness calculation

Arrange the chromosomes according to the size of the fitness value, so as to prepare for the next selection. The fitness function (3.28) can calculate the fitness of the chromosome. The fitness value of each chromosome is calculated and the decoding result of the first step above is substituted into the simulation model to calculate the maximum and minimum value of the transfer error

4) Selection operator

The selection operation is based on the fitness of the individual to determine the individuals inherited to the next generation. First, delete the unqualified individuals in the population, and then add the qualified individuals to form a new population. At this time, fitness proportional selection can be used for individual selection, which is a basic selection method. In the new group, the expected value of each individual selected is related to the proportion of their fitness and group average fitness, which can be realized by roulette. For an individual population with a given size of N, the probability that the individual is selected is:

That is to say, the proportion of each individual’s fitness value in the total of the group’s fitness value is calculated to represent the probability that the individual is selected in the selection process.

5) Apply crossover operator

The crossover operation randomly matches the individuals in the group to exchange some of their chromosomes with a certain probability to get new individuals. The individuals in the parent group were duplicated and randomly paired for cross operation. A pair of individuals to mate were selected by multi-point crossing method, and three crossing positions were randomly selected. The continuous exchange of variables between intersections, but not before the first intersection. That is, exchange between the first intersection and the second intersection, exchange after the fourth intersection, and do not exchange the rest. After crossing, two new progenies are generated, and finally n individuals are generated to form the progeny group.