Issue 53

Y. Lu et alii, Frattura ed Integrità Strutturale, 53 (2020) 325-336; DOI: 10.3221/IGF-ESIS.53.25 327   ( ) 1, 2, , , 1, 2, , i i X X k k n i m = = = (2) The four factors selected in this article have different physical meanings, so the data dimensions are different. In order to facilitate the comparison between the factors, the data is first normalized. The normalization formula is as follows: min( ) ( ) , 1, 2, , max( ) min( ) i i X X x k i n X X − = = − (3) Calculate the correlation coefficient ( ) i k  between ( ) y k and ( ) i x k at time k , which yields: minmin ( ) ( ) maxmax ( ) ( ) ( ) ( ) ( ) maxmax ( ) ( ) i i i k i k i i i i k y k x k y k x k k y k x k y k x k    − + − = − + − (4) In the formula: k is the time;  is the resolution; the value range is (0,1) [19]; this article takes 0.8; minmin ( ) ( ) i i k y k x k − and maxmax ( ) ( ) i i k y k x k − are the minimum and maximum differences of the two levels, respectively. Since the correlation coefficient is the correlation degree between the comparison sequence and the reference sequence at each time, the value is too scattered to be detrimental to the overall comparison. Therefore, the average value of the comparison between the two columns i r is as follows: 1 1 ( ), 1, 2, , n i i k r k k n n  = = =  (5) The magnitude of the correlation characterizes the relative influence of the comparison sequence on the reference sequence. Establishment of GA-BPNN model The steps of predicting aluminum-steel CMT welding deformation by GA-BPNN are as follows: 1) Determine the structure of BPNN. This paper uses a parallel network structure, including the input layer, hidden layer and output layer. The number of input and output layers is determined by test parameters and evaluation indicators. The transfer function used in this paper is: 1 ( ) 1 x f x e − = + (6) This function maps the real field to the [0,1] space smoothly. In addition, the function is monotonically increasing, continuous and derivable, and the derivative form is very simple, which is a suitable function. 2) Initialize the weight coefficients connecting the input layer, hidden layer and output layer of the BPNN; 3) Code the chromosomes of the weight coefficients and set the GA parameters. In this paper, the individual coding length of the genetic algorithm is 21. The parameters of the genetic algorithm are set as follows: the population size is 10, the number of evolutions is 50, the crossover probability is 0.4, and the mutation probability is 0.2. 4) Design the fitness function and calculate the corresponding fitness value of current chromosomes. The fitness function is designed as: 1 ( ) n i i i F abs y o = = −  (7) ( n denotes the number of neurons in the output layer, i o and i y represent the predicted and actual outputs of the ith neuron, respectively)