A Method and System for Filling Missing Parameters in Water-Cooled Cables Based on an Improved WOA Algorithm

Abstract

This invention relates to the field of data imputation technology, and particularly to a method and system for imputing missing parameters in water-cooled cables based on an improved WOA algorithm. The method includes: constructing a dataset of the operating status of water-cooled cables; imputing missing data using the BA imputation method to obtain BA imputation estimates; calculating the most correlated column data using the GRA correlation coefficient method; calculating the most correlated row correlation coefficient using the Pearson correlation coefficient method; deriving the Pearson correlation coefficient estimate of the missing data based on the equation between the most correlated row correlation coefficient and the missing data; constructing a target weight function for the missing data, the Pearson correlation coefficient estimate, and the BA imputation estimate; and optimizing the weight coefficients of the two estimates using an improved WOA algorithm. This invention addresses the problem that during process adjustments in electric arc furnace operation, voltage and current data can fluctuate significantly, and simple missing data processing methods cannot meet the accuracy requirements for dataset imputation.

Description

Technical Field

[0001] This invention relates to the field of data completion technology, and in particular to a method and system for completing missing parameters in water-cooled cables based on an improved WOA algorithm. Background Technology

[0002] Water-cooled cables are devices used to transmit electrical energy and cool thermal energy. They consist of an inner layer of wires and an outer layer of cooling pipes, and the temperature of the cable is reduced by circulating water. In electric arc furnace steelmaking, water-cooled cables can control the position and temperature of the electric arc, so that the steel is heated evenly in the furnace, while also protecting the cable from overheating. Water-cooled cables are prone to damage due to harsh working environments, and early replacement of water-cooled cables can improve production efficiency. Therefore, the prediction of the lifespan of water-cooled cables is of research significance.

[0003] Predicting the lifespan of water-cooled cables requires collecting complete data on the cables during operation. However, data loss due to sensor malfunctions, transmission failures, or process operations can cause significant problems in predicting the lifespan of water-cooled cables. Accurate correction of missing data has a major impact on the accuracy of the lifespan prediction. Therefore, it is extremely important to accurately fill in the missing data collected during the operation of water-cooled cables.

[0004] Currently, missing data imputation methods are mainly divided into two categories: single imputation and multiple imputation. Single imputation mainly includes mean, median, and mode imputation methods. These methods are simple to calculate, but using a single value to imputate greatly reduces the randomness of the data and results in the loss of a large amount of data information. Multiple imputation methods mainly include calorie imputation, nearest neighbor imputation, spatial interpolation, and Bayesian methods. Each method has its own advantages and disadvantages, and the imputation effect varies depending on the type of data object. Due to process adjustments during the operation of electric arc furnaces, voltage and current data will fluctuate significantly, and simple missing data processing methods cannot meet the accuracy requirements of dataset imputation. Summary of the Invention

[0005] To address the shortcomings of existing methods, this invention employs the BA algorithm to first obtain an estimated value, then uses the GRA correlation coefficient method to determine the most relevant attribute of the missing data, uses the K-means algorithm to cluster the most relevant column data, and uses the Pearson correlation coefficient method to determine the most relevant row within each group. An equation is constructed between the maximum correlation coefficient and the missing data to obtain an estimated value for the missing data. A target weight function is then constructed, relating the missing data to the two estimated values. An improved WOA algorithm is used to optimize the weight values ​​of the target weight function, outputting the optimal weight coefficient and calculating the missing data imputation value.

[0006] The technical solution adopted in this invention is: a method for filling missing parameters in water-cooled cables based on an improved WOA algorithm, comprising the following steps:

[0007] Step 1: Collect data on the water-cooled cables of the electric arc furnace and construct a data set on the operating status of the water-cooled cables;

[0008] Furthermore, the data for water-cooled cables includes: voltage, current, temperature, and circulating water flow rate.

[0009] Step 2: Impute the missing data using the BA imputation method to obtain the BA imputation estimate;

[0010] Furthermore, the formula for filling in the BA estimate is:

[0011]

[0012] Where, x A and x B The values ​​of t are the values ​​before and after the missing attribute data, respectively. A and t B These represent the times before and after the missing attribute data.

[0013] Step 3: Calculate the correlation coefficient between the column containing the missing data and other attribute data using the GRA method to determine the column with the highest correlation; then, use the K-means algorithm to cluster the data in the column with the highest correlation.

[0014] Step 4: Calculate the correlation coefficient between the row containing the missing data and other rows within the group using the Pearson correlation coefficient method to obtain the maximum row correlation coefficient;

[0015] Step 5: Based on the equation between the maximum row correlation coefficient and the missing data, derive the estimated value of the Pearson correlation coefficient for the missing data.

[0016] Furthermore, the equation for the maximum row correlation coefficient and missing data is as follows:

[0017]

[0018] Where, r max Let be the maximum row correlation coefficient, t be the time when the missing data occurs, j be the data attribute in R, and n be the total number of all attributes in R. Let be the mean of all data at time t. Let x be the mean of all data at time t′. tj For attribute j at time t, x t′j Let j be the data of attribute j at time t′.

[0019] Step 6: Construct the target weight function for the missing data and the Pearson correlation coefficient estimate and the BA imputation estimate;

[0020] Furthermore, the formula for the objective weight function is:

[0021] y = ρx BA +θx C (3)

[0022] Where y represents the imputed value for missing data, and x represents the imputed value for missing data. BA Fill in the estimated value for BA, x C The values ​​are estimated using the Pearson correlation coefficient method, where ρ and θ are the weighting coefficients of the two estimates, respectively.

[0023] Step 7: Optimize the weight coefficients of the two estimates using an improved WOA algorithm;

[0024] Further improvements to the WOA algorithm include:

[0025] Step 71: Set the WOA population size, maximum number of iterations, initial position range, step size, inertia weight, and diffusion parameters, and randomly generate the initial population;

[0026] Step 72: Calculate the fitness function value for each individual;

[0027] Step 73: Determine the current optimal solution;

[0028] Step 74: Update the position of individual whales using Levi's flight; use adaptive weight coefficients to update the adaptive weights based on the optimal solutions of historical iterations and the current optimal solution;

[0029] Furthermore, the formula for the adaptive weighting coefficient is:

[0030]

[0031] Where t is the current iteration number, T max X represents the maximum number of iterations. * (t) represents the best current whale position; X rand (t) represents a randomly selected whale individual in the current population; X(t+1) represents the updated whale position; D ′ denoted by ; D is the distance between the whale and its prey when surrounding the prey; b is a constant with a logarithmic spiral shape; l is a random number between [-1, 1]; A is a coefficient vector; p is the heuristic probability.

[0032] Step 75: Update the fitness function value and the optimal solution. Stop updating when the maximum number of iterations is met or when an optimal solution that meets the conditions is found.

[0033] Furthermore, the data filling system based on the improved WOA includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement a water-cooled cable missing parameter filling method based on the improved WOA algorithm.

[0034] The beneficial effects of this invention are:

[0035] 1. When faced with the complex process of electric arc furnace operation, using only single or multiple fillers to fill missing data is one-sided and cannot accurately reflect the working status of the electric arc furnace. The method of the present invention can take into account both the temporal nature of missing data and the differences in process adjustments. The filled data can more accurately reflect the working status of the secondary side water-cooled cable of the electric arc furnace.

[0036] 2. The improved WOA algorithm can further enhance its search capabilities, improve global search capabilities, avoid getting trapped in local optima, and help to accurately search for weight coefficients. Attached Figure Description

[0037] Figure 1 This is a flowchart of the water-cooled cable missing parameter filling method based on the improved WOA algorithm of the present invention;

[0038] Figure 2 This is a flowchart of the improved WOA optimization weight coefficients of the present invention;

[0039] Figure 3 This is a comparison chart of the missing data filling effect of the present invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0041] like Figure 1 As shown, the method for filling missing parameters in water-cooled cables based on the improved WOA algorithm includes the following steps:

[0042] Step 1: Collect data on the water-cooled cables of the operating electric arc furnace;

[0043] The collected data includes: voltage, current, temperature, and circulating water flow rate;

[0044] A dataset R representing the operating status of a water-cooled cable is constructed. Dataset R consists of a time series and four vectors Y1, Y2, Y3, and Y4, representing voltage, current, temperature, and circulating water flow rate, respectively. The dataset is composed of s-dimensional vectors, x... ij This represents the missing data in the i-th row and j-th column (1≤i≤s, 1≤j≤4);

[0045] Step 2: Impute the missing data using the BA method to obtain an estimated value;

[0046] For the estimated value of missing data at time t, x BA From the two time points t before and after the missing data column B t A (t B <t<t A ) Corresponding missing attribute data x B x A The estimated value is obtained, as shown in formula (1):

[0047]

[0048] Step 3: Calculate the correlation coefficient between the column containing the missing data and other attribute data using the GRA method to determine the column with the highest correlation; then, use the K-means algorithm to cluster the data in the column with the highest correlation.

[0049] Step 4: Calculate the correlation coefficient between the row containing the missing data and other rows within the group using the Pearson correlation coefficient method to obtain the maximum row correlation coefficient;

[0050] Step 5: Based on the maximum row correlation coefficient r max The equation with the missing data is used to derive the Pearson correlation coefficient estimate x for the missing data. C ;

[0051] The equation for the maximum row correlation coefficient and missing data is:

[0052]

[0053] Where, r max Let be the maximum row correlation coefficient, t be the time when the missing data occurs, j be the data attribute in R, and n be the total number of all attributes in R. Let be the mean of all data at time t. Let x be the mean of all data at time t′. tj For attribute j at time t, x t′j Given the data of attribute j at time t′, calculate x in reverse. tj The estimated value is x C ;

[0054] Step 6: Construct the target weight function for the missing data and the two estimates. The target weight function is shown in formula (3):

[0055] y = ρx BA +θx C (3)

[0056] Where y represents the imputed value for missing data, and x represents the imputed value for missing data. BA Fill in the estimated value for BA, x C The values ​​are estimated using the Pearson correlation coefficient method, where ρ and θ are the weighting coefficients of the two estimates (0 < ρ < 1, 0 < θ < 1, ρ + θ = 1).

[0057] Step 7: Optimize the weight coefficients by improving the WOA algorithm (ALWOA, Adaptive Levy Flight Whale Optimization Algorithm). Use the whale position X(t) as the weight coefficient ρ for searching. After obtaining the optimal ρ value, obtain the θ value by ρ+θ=1, and fill in the missing data.

[0058] Step 71: Set the WOA population size, maximum number of iterations, initial position range, step size, inertia weight, and diffusion parameters, and randomly generate the initial population;

[0059] Step 72: Calculate the fitness function value for each individual;

[0060] Step 73: Determine the current optimal solution;

[0061] Step 74: Using the idea of ​​Levi's flight, update the position of individual whales to enhance the global search capability, as shown in formula (4):

[0062]

[0063] Where X(t) is the position of an individual whale; α is the random step size; C is the coefficient vector; X rand (t) represents a randomly selected whale individual in the current population;

[0064] An iterative search is performed, using an adaptive weight coefficient method, which updates the adaptive weights based on the optimal solutions of previous iterations and the current optimal solution;

[0065] The formula is shown in (5):

[0066]

[0067] in, The adaptive weights for prey position gradually increase with the number of iterations. As the whale approaches the prey, smaller weights are used to change the prey's position, greatly improving the algorithm's local optimization ability. t represents the current iteration number, T... max X represents the maximum number of iterations. * (t) represents the best current whale position; X rand (t) represents a randomly selected whale individual in the current population; X(t+1) represents the updated whale position; D ′denoted by , where represents the distance between the whale and its prey; D is the distance between the whale and prey when surrounding the prey; b is a constant with a logarithmic spiral shape; l is a random number between [-1, 1]; A is a coefficient vector; p is the heuristic probability when t < 0.5 × T. max =0.7, t≥0.5×T max The value is 0.4.

[0068] Step 75: Update the fitness function value and the optimal solution until the maximum number of iterations is reached or an optimal solution that meets the conditions is found. The constraints are shown in formula (6):

[0069] S = min|yQ j | (6)

[0070] Where y represents the imputed value for missing data, and Q... j The value of the same attribute for the most relevant row within the group containing the missing data;

[0071] When the number of iterations reaches its maximum value or the condition is met, the optimal weight coefficient of the objective function is determined, the value of the missing data is calculated and filled in.

[0072] Figure 3 This is a comparison chart of the missing data filling effect of the present invention. Partial current data during the operation of the electric arc furnace was selected, and the real data was removed. The estimated values ​​obtained by the method of the present invention (ALWOA algorithm) were compared with the WOA algorithm, AWOA algorithm, and LWOA algorithm and the real values. The results show that the ALWOA algorithm is more accurate in estimating values ​​than other algorithms.

[0073] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for filling missing parameters in water-cooled cables based on an improved WOA algorithm, characterized in that, Includes the following steps: Step 1: Construct a dataset of the operating status of water-cooled cables; Step 2: Impute the missing data using the BA imputation method to obtain the BA imputation estimate; The formula for filling in the BA estimate is: in, and These represent the values ​​of the missing attribute data at the time points before and after the missing data. and These represent the times before and after the missing attribute data; Step 3: Calculate the correlation coefficient between the column containing the missing data and other attribute data using the GRA method to determine the column with the highest correlation; then, use the K-means algorithm to cluster the data in the column with the highest correlation. Step 4: Calculate the correlation coefficient between the row containing the missing data and other rows within the group using the Pearson correlation coefficient method, and obtain the maximum row correlation coefficient; Step 5: Based on the equation between the maximum row correlation coefficient and the missing data, derive the estimated value of the Pearson correlation coefficient for the missing data. The equation for the maximum row correlation coefficient and missing data is: in, The maximum row correlation coefficient, The time at which the missing data is located. For data attributes in R, The total number of all attributes in R. for The mean of all data at time 1. for The mean of all data at time 1. For attributes Corresponding time Data, For attributes exist Data at any given time; Step 6: Construct the target weight function for the missing data and the Pearson correlation coefficient estimate and the BA imputation estimate; The formula for the objective weight function is: in, Fill in missing values ​​for the data. Fill in the estimated values ​​for BA. The value is estimated using the Pearson correlation coefficient method. These are the weighting coefficients for the two estimates, respectively; Step 7: Optimize the weight coefficients of the two estimates by improving the WOA algorithm.

2. The method for filling missing parameters in water-cooled cables based on the improved WOA algorithm according to claim 1, characterized in that, The data for water-cooled cables include: voltage, current, temperature, and circulating water flow rate.

3. The method for filling missing parameters in water-cooled cables based on the improved WOA algorithm according to claim 1, characterized in that, The improvements to the WOA algorithm specifically include: Step 71: Set the WOA population size, maximum number of iterations, initial position range, step size, inertia weight, and diffusion parameters, and randomly generate the initial population; Step 72: Calculate the fitness function value for each individual; Step 73: Determine the current optimal solution; Step 74: Update the position of individual whales using Levi's flight; use adaptive weight coefficients to update the adaptive weights based on the optimal solutions of historical iterations and the current optimal solution; Step 75: Update the fitness function value and the optimal solution. Stop updating when the maximum number of iterations is met or when an optimal solution that meets the conditions is found.

4. The method for filling missing parameters in water-cooled cables based on the improved WOA algorithm according to claim 3, characterized in that, The formula for the adaptive weighting coefficient is: in, This represents the current iteration number. This represents the maximum number of iterations. This indicates the best location for the whale at present; This represents a randomly selected individual whale from the current population; Indicates the updated whale location; Indicates the distance between the whale and its prey; D The distance between the whale and its prey when surrounding them; It is a constant for the shape of the logarithmic spiral; yes A random number between [a certain range]; For coefficient vectors; This is a heuristic probability.

5. A data completion system based on an improved WOA, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the water-cooled cable missing parameter filling method based on the improved WOA algorithm as described in any one of claims 1-4.

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