Entropy weight analysis method

The entropy weighting method is based on the variation degree of the feature parameters, and obtains the entropy weight of each feature parameter through the information entropy, and then obtains the weight of each feature parameter.22. The greater the difference of an indicator, the smaller the entropy weight, which indicates that the greater the amount of information provided by the indicator, the greater the role it plays in the evaluation. , and the larger the weight, which provides a basis for an overall analysis. Evaluation. The process of calculating the entropy weight of the input parameter is as follows: calculate the entropy value under this output parameter according to formula (1):

$$ e_{j} = – frac{1}{ln n}y_{ij}^{^{prime}} mathop sum limits_{i = 1}^{m} y_{ij}^ {^{first}} $$

(1)

In formula (1),({ }y_{ij}^{^{prime}} = frac{{y_{ij} }}{{mathop sum nolimits_{i = 1}^{m} y_{ij} }} )is the proportion of I sample data under I characteristic parameter, ({text{y}}_{ij}) is a data sample, m is the number of sample data, not is the number of feature parameters;

According to the entropy value of each index calculated according to formula (1), their weight is calculated according to formula (2):

$$ q_{j} = frac{{1 – e_{j} }}{{n – mathop sum nolimits_{j = 1}^{n} e_{j} }} $$

(2)

In the formula (2), not is the number of characteristic parameters; ({text{e}}_{j}) is the entropy weight of I feature parameter; (q_{j}) is the weight value of the feature parameter j obtained by the entropy method.

GA-BP algorithm model

Genetic Algorithm (GA) has strong macro search and global optimization capabilities, which can solve local minimal network problems and improve network performance. Currently, GA is commonly used to optimize BP neural network23. The flowchart of the GA-BP algorithm is shown in Fig. 1, and the specific steps are as follows.

  1. (1)

    Population initialization

Figure 1

Flowchart of the GA-BP neural network.

Determine the population number, evolution times, population size, crossover probability and mutation probability, and build the initial population.

  1. (2)

    Initialize the BP network model

Set the input layer node, the output layer node and the hidden layer node of the neural network according to the training set data, where the hidden layer node is obtained by the empirical formula (3).

$$ {text{L}} = sqrt {m + n} + l $$

(3)

In the formula, m is the number of input layer nodes, n is the number of output layer nodes, which is an arbitrary constant between1.10.

  1. (3)

    Determine fitness function

Fitness refers to the degree to which each individual in the measurement group is close to the optimal solution in the optimization calculation and predicts the absolute value of the error between the expected outputs and the calculation formula for the fitness value individual as formula (4):

$$ {text{F}} = {text{k}}left( {mathop sum limits_{i = 1}^{n} absleft( {y_{i} – o_{i} } right)} right) $$

(4)

In the formula, not is the number of training samples, (y_{i}) is the actual value of I BP neural network node, ( o_{i}) is the planned release of the I node; ({text{k}}) is the coefficient, usually (frac{1}{n}).

  1. (4)

    Select the operation

The roulette method is used to select the chromosome with the best fitness calculated by formula (2) from the current population for the copy operation, and this process generates a new population. Among them, the probability of selecting each individual is calculated by the formula (5):

$$ p_{i} = {text{F}}left( {x_{i} } right)/mathop sum limits_{1}^{n} Fleft( {x_{i} } right) $$

(5)

In the formula, not is the number of individual populations; Does the individual (x_{i}) fitness value calculated by formula (4).

  1. (5)

    Cross operation

Using the real number crossover method, the crossover operation between the ({text{k}}) chromosome (a_{k}) and the I chromosome (a J}) at office I is represented by formula (6):

$$ left{ {begin{array}{*{20}c} {a_{kj} = a_{kj} left( {1 – b} right) + a_{lj} b} { a_{lj} = a_{lj} left( {1 – b} right) + a_{kj} b} end{array} } right. $$

(6)

In this formula includes a random number and ({text{b}} in left[ {0,1} right]).

  1. (6)

    Mutation Operation

Selection of I gene I individual to mutate to obtain a whole new individual, the method is illustrated by the formula (7):

$$ left{ {begin{array}{*{20}c} {a_{ij} = a_{ij} + left( {a_{ij} – a_{max } } right) times fleft( g right) ,r > 0.5} {a_{ij} = a_{ij} + left( {a_{min } – a_{ij} } right) times fleft( g right) ,r le 0.5} end{array} } right. $$

(seven)

In this formula, (a_{max }) and (a_{min }) are the upper and lower bounds of the gene (a_{ij}), ( fleft( g right) = r_{2} left[ {left( {1 – g} right)/G_{max } } right]^{2}), ( r_{2}) is a random number, ({text{g}}) is evolutionary algebra, (G_{max }) is the maximum number of evolutions; (r) is a random number and ( r in left( {0,1} right)).

  1. (seven)

    Calculate fitness

Replace the original chromosome with the new chromosome to calculate the new individual fitness. If the ability meets the condition, proceed to step (8); otherwise, skip to step (3) to continue calculating fitness.

  1. (8)

    Form

Once the performance metrics are achieved, the optimal weights and thresholds are assigned to the BP neural network, and the training set is used to train the network until the defined error requirements are met.

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