A method for predicting icebreaking capability of high-pressure water jet based on BKA-BP neural network

Abstract

The present invention discloses a method for predicting the icebreaking ability of a high-pressure water jet based on a BKA-BP neural network, which includes conducting a high-pressure water jet icebreaking test, analyzing the test data to find independent variable parameters closely related to the icebreaking volume; constructing a neural network prediction model composed of a BP neural network BKA algorithm, and training and testing the neural network prediction model using a training set and a test set composed of test data; and using the neural network prediction model that has passed the test to predict the icebreaking ability of the high-pressure water jet. The present invention uses a BP neural network model optimized by the Black Kite algorithm to predict the icebreaking ability of the high-pressure water jet, which effectively addresses the problems of many influencing factors and complex laws in the high-pressure water jet icebreaking process. The method of the present invention provides an efficient and reliable high-pressure water jet icebreaking ability prediction model, which has engineering optimization significance.

Description

Technical Field

[0001] The present invention relates to the technical field of high-pressure water jet application, and in particular to a method for predicting the ice-breaking capability of a high-pressure water jet. Background Art

[0002] High-pressure water jet technology utilizes a high-pressure pump to pressurize water to extremely high pressures. This high-pressure water is then converted into a high-speed, high-energy-density water jet through a specialized nozzle, which then acts on the target. Due to its high efficiency, environmental friendliness, and low cost, it has broad application prospects in icebreaking applications such as polar resource development and ship navigation. Unlike conventional applications of high-pressure water jets, such as coal seam permeability enhancement and ore mining, the mechanism and capabilities of high-pressure water jet icebreaking are still unclear, and related research is still in the experimental stage. Predicting icebreaking capabilities using extensive test data is crucial for understanding actual operating conditions and optimizing on-site operation parameters.

[0003] Icebreaking with high-pressure water jets is a complex process involving multiple fields. Accurately predicting icebreaking capabilities requires considering multiple factors, multiple variables, and the complex relationships between them, including jet pressure, jet target distance, ice strength, etc. It is difficult to comprehensively describe the nonlinear dynamic relationship between the jet and the ice body based on theoretical derivation or experimental data regression analysis. Therefore, a more efficient and accurate method is needed to deal with complex actual situations. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a high-pressure water jet icebreaking ability prediction method based on BKA-BP neural network to solve the technical problem of accurately predicting the high-pressure water jet icebreaking ability under the influence of multiple factors.

[0005] The method for predicting the icebreaking ability of a high-pressure water jet based on a BKA-BP neural network of the present invention comprises the following steps:

[0006] (1) Conducting a high-pressure water jet icebreaking test and collecting test data, wherein the test data includes independent variable parameters of the high-pressure water jet icebreaking operation and the icebreaking volume corresponding to the independent variable parameters.

[0007] (2) Perform a correlation analysis on the independent variable parameters and the icebreaking volume, and find out that the independent variable parameters closely related to the icebreaking volume are: jet pressure, nozzle diameter, jet target distance and impact time.

[0008] (3) A neural network prediction model for predicting the icebreaking ability of high-pressure water jets is constructed. The neural network prediction model consists of a BP neural network and a BKA algorithm module for optimizing the BP neural network. The number of neurons in the output layer of the BP neural network is determined to be four, and the jet pressure, nozzle diameter, jet target distance and impact time are used as the inputs of the four output layer neurons respectively; the number of neurons in the output layer of the BP neural network is determined to be one, and the output of the output layer neurons is the predicted value of the icebreaking volume.

[0009] (4) The jet pressure, nozzle diameter, jet target distance, impact time and ice breaking volume obtained from the experiment were normalized and processed for outliers, and then the training set and test set of the neural network prediction model were constructed using the data after the above processing.

[0010] (5) The data in the training set is input into the neural network prediction model to train it. During the training process, the weights and thresholds generated by the BP neural network are input into the BKA algorithm module, the weights and thresholds are optimized by the BKA algorithm module, and the optimized weights and thresholds are returned to the BP neural network.

[0011] (6) The trained neural network prediction model is tested using the test data in the test set, and the ability of high-pressure water jet to break ice is predicted using the neural network prediction model that has passed the test.

[0012] Beneficial effects of the present invention:

[0013] This method, based on a BKA-BP neural network, predicts the icebreaking capacity of high-pressure water jets. This method uses a BP neural network model optimized by the Black Kite algorithm to predict the icebreaking capacity of high-pressure water jets. This method effectively addresses the numerous factors influencing the icebreaking process and the complex patterns involved. This method provides an efficient and reliable model for predicting the icebreaking capacity of high-pressure water jets, which has significant implications for engineering optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the process of using BKA algorithm to optimize BP neural network prediction.

[0015] Figure 2 Schematic diagram of the BP neural network structure for predicting the icebreaking ability of high-pressure water jets. DETAILED DESCRIPTION

[0016] The present invention will be further described below with reference to the accompanying drawings and examples.

[0017] As shown in the figure, the method for predicting the icebreaking capability of high-pressure water jets based on the BKA-BP neural network in this embodiment includes the following steps:

[0018] (1) Conducting a high-pressure water jet icebreaking test and collecting test data, wherein the test data includes independent variable parameters of the high-pressure water jet icebreaking operation and the icebreaking volume corresponding to the independent variable parameters.

[0019] (2) Perform correlation analysis on the independent variable parameters and icebreaking volume to find out the independent variable parameters that are closely related to the icebreaking volume.

[0020] When conducting a high-pressure water jet icebreaking test, there are many independent variables that affect the high-pressure water jet's icebreaking ability, including jet pressure, nozzle diameter, jet target distance, impact time, jet angle, ice strength, ice temperature, etc. Each independent variable parameter is analyzed for correlation with the icebreaking volume index and ranked. The purpose of the correlation analysis is to filter out important and relevant feature vectors from all possible variables to remove redundant features as much as possible, reduce computational complexity, and improve the model's interpretability and predictive performance. In this embodiment, the correlation between the independent variable and the icebreaking volume is analyzed by comparing the size of the Pearson correlation coefficient, and its calculation formula is:

[0021]

[0022] Among them, x i ,y i are the two variable values ​​of the i-th sample data point, and are the sample means of the two variables, and n is the number of sample data points.

[0023] After screening and verification, it was determined that the jet pressure P, jet target distance D, impact time T, and nozzle diameter d are closely related to the icebreaking ability of high-pressure water jets. Therefore, these four parameters were determined as the input data for predicting the icebreaking ability, and the icebreaking volume was used as the predicted output value.

[0024] (3) A neural network prediction model for predicting the icebreaking capability of high-pressure water jets was constructed. The neural network prediction model consisted of a BP neural network and a BKA algorithm module for optimizing the BP neural network. The number of neurons in the output layer of the BP neural network was determined to be four, and the jet pressure, nozzle diameter, jet target distance, and impact time were used as the inputs of the four output layer neurons. The number of neurons in the output layer of the BP neural network was determined to be one, and the output of the output layer neurons was the predicted value of the icebreaking volume. The number of neurons in the hidden layer of the BP neural network was determined according to the empirical formula hiddennum=sqrt(m+n)+a, where m and n are the number of neurons in the input layer and output layer, respectively, and a is an integer between 1 and 10. Therefore, the number of neurons in the hidden layer was initially determined to be an integer between 3 and 12. After running, it was found that the performance was best when the number of neurons was 9.

[0025] (4) The jet pressure, nozzle diameter, jet target distance, impact time and ice breaking volume obtained from the experiment were normalized and processed for outliers, and then the training set and test set of the neural network prediction model were constructed using the data after the above processing.

[0026] The purpose of normalization is to simplify calculations and ensure that the comparison and weighting between features are treated fairly. This embodiment uses the minimum / maximum normalization method to perform dimensionless conversion of data. The normalization formula is as follows:

[0027]

[0028] Where X' is the normalized data, X is the original data, min(X) is the minimum value in the data set, and max(X) is the maximum value in the data set.

[0029] (5) Input the data in the training set into the BP neural network for training. Set the parameters of the BP neural network, including setting the learning rate to 0.01, setting the number of training times to 1000, setting the training target minimum error to 0.0001, setting the momentum factor to 0.01, and setting the minimum performance gradient to 1e-6; randomly initialize the weights and thresholds of the BP neural network. In order to avoid the symmetry of the neural network, which causes the neurons to be unable to distinguish during training updates, a randomization strategy is used to initialize the weights and thresholds. In this example, the weight matrix W1 from the input layer to the hidden layer contains 4*9=36 parameters, and the weight matrix W2 from the hidden layer to the output layer contains 9*1=9 parameters. The threshold vector b1 of the hidden layer contains 9 parameters, and the threshold scalar b2 of the output layer contains 1 parameter, so the total number of parameters is 55, that is, a 55-dimensional vector [W1, b1, W2, b2]. Set the initial range of the weights and thresholds to [-1, 1].

[0030] During the training process, the weights and thresholds generated by the BP neural network are input into the BKA algorithm (Black Kite Algorithm) module, the weights and thresholds are optimized by the BKA algorithm module, and the optimized weights and thresholds are returned to the BP neural network.

[0031] The Black Kite Algorithm is inspired by the migration and predation behavior of the black kite in nature. It is a typical meta-heuristic optimization algorithm that converts the biological behavioral characteristics of the black kite into a mathematical model, combines the capabilities of global search and local development, and aims to solve optimization problems.

[0032] The process of the Black Kite algorithm is as follows:

[0033] ① Initialization: Random initialization, evenly assign the position of each black kite as the solution:

[0034] X i =BKlb +rand(BK ub -BK lb )

[0035] Where i is an integer between 1 and pop, pop is the number of potential solutions, BKlb and BKub are the lower and upper bounds of the i-th black kite in the j-th dimension, and rand represents a random value in the interval [0, 1]. During initialization, the algorithm selects the individual with the best fitness value as the leader XL in the initial population, which can be considered the optimal position of the black kite.

[0036] Randomly initialize the population: According to the empirical formula, in this example, the number of individuals in the population is pop = 37. For each individual in the population, a parameter vector (55 dimensions) is randomly generated. Each parameter value is between the upper and lower bounds. The fitness values ​​of all individuals are calculated, and the individual with the smallest fitness value is selected as the initial global optimal solution. In this embodiment, the fitness function of the Black Kite algorithm is defined as follows:

[0037]

[0038] Among them, X i represents the BP neural network parameters of the i-th individual, y j represents the true value of the jth sample, Indicates that the BP network uses parameter X i The predicted output. The fitness function is used to measure the quality of a candidate solution (i.e., weight and threshold parameters) for the problem. The smaller the fitness function value, the better the corresponding solution. The mean square error can well guide model adjustment and is a smooth function suitable for solving problems.

[0039] ② Attack Behavior: The black kite is a carnivorous bird that adjusts the angle of its wings and tail based on wind speed, hovers in mid-air to observe, and then dives at extremely high speed to attack its prey. The different attack behaviors included in this strategy are used for global search and exploration in the algorithm. The following is a mathematical model of the black kite's attack behavior:

[0040]

[0041] in, and represents the position of the i-th black kite in the j-th dimension in the t-th and (t+1)-th iterations, respectively. r is a random number ranging from (0 to 1). p is a constant with a value of 0.9. t is the number of completed iterations. T is the total number of iterations. In this embodiment, T is set to 500.

[0042] Using a mathematical model of the black kite's attack behavior, the position of each individual is updated and the fitness values ​​of all individuals are recalculated. Aggressive behavior randomly perturbs existing solutions (weights and thresholds) to explore a larger solution space and search for potentially better solutions. Random numbers r and p are used to control different update strategies, enabling both large-scale random searches (exploring new areas) and local adjustments. The dynamic step size n is large in the early stages, helping the algorithm quickly explore the solution space; it gradually decreases in the later stages to enhance the stability of the solution. Sine functions and random perturbations provide diversity in updates, preventing solutions from converging prematurely in local areas. Aggressive behavior updates the weights and threshold vectors of the neural network, generating new candidate solutions. Fitness is recalculated after each update, and individuals with better fitness are selected for the next iteration.

[0043] ③ Migration behavior: Black kite migration is an instinctive survival response to follow the natural environment. Migration behavior is usually led by a leader. Therefore, based on this behavior, the algorithm proposes a hypothesis: compare fitness values. If the fitness value of the current population is less than that of the random population, then the leader will give up leadership and join the population, indicating that it is not suitable to lead the population. On the contrary, if the fitness value of the current population is greater than that of the random population, the leader will lead the population to the destination. This strategy can dynamically select excellent leaders to ensure the success of migration. The following is a mathematical model of black kite migration behavior:

[0044]

[0045] in, is the leader of the black kites in dimension j in the t-th iteration so far, i.e., the current optimal solution. and are the positions of the i-th black-winged kite in the j-th dimension in the t-th and (t+1)-th iterations, respectively. C(0,1) represents the Cauchy mutation, the probability density function of the standard one-dimensional Cauchy distribution:

[0046]

[0047] The mathematical model of migration behavior enhances local search capabilities by directing individuals toward the current global optimal solution. Cauchy-distributed random variables are introduced to add randomness to the solution, preventing it from being trapped in a local optimum. A dynamic step size adjusted by a sinusoidal function improves solution flexibility. Assuming L is the current optimal weight and threshold, migration behavior gradually brings the weights and thresholds of other individuals closer to L. After each migration, the fitness value is recalculated to update the global optimal solution.

[0048] Therefore, the Black Kite algorithm uses the synergistic effects of attack and migration behavior to continuously optimize the parameters of the BP neural network, making its predicted output y as close to the true value as possible. This ensures that the algorithm has extensive search capabilities in the solution space, guides the population to gather in the optimal area, improves convergence accuracy, and strikes a balance between global search and local development.

[0049] (6) The trained neural network prediction model is tested using the test data in the test set, and the ability of high-pressure water jet to break ice is predicted using the neural network prediction model that has passed the test.

[0050] The generalization ability and prediction accuracy of the neural network prediction model are verified by the test set to ensure its reliability in practical applications. The test set is 20% of the experimental data set. After the training set is qualified, the test set data is imported and the output results are denormalized. The mean absolute error MAE, mean square error MSE, root mean square error RMSE, mean absolute percentage error MAPE, and determination coefficient R 2 The neural network model was used to evaluate the icebreaking ability prediction effect. 2 When the value is greater than 0.9, MAE is less than 0.1, and MAPE is less than 0.1%, it is considered that a good icebreaking capability prediction model is obtained. The specific calculation formulas for MAE are as follows:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] Among them, n is the amount of prediction data, y pi is the predicted value of the i-th data, y ti is the true value of the i-th data.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the weight requirements of the present invention.

Claims

1. A method for predicting the icebreaking capability of high-pressure water jets based on a BKA-BP neural network, characterized by: Including steps: (1) conducting a high-pressure water jet icebreaking test and collecting test data, wherein the test data includes independent variable parameters of the high-pressure water jet icebreaking operation and the icebreaking volume corresponding to the independent variable parameters; (2) Carry out correlation analysis on the independent variable parameters and ice breaking volume, and find out that the independent variable parameters closely related to ice breaking volume are: jet pressure, nozzle diameter, jet target distance and impact time; (3) Construct a neural network prediction model for predicting the icebreaking capability of high-pressure water jets. The neural network prediction model consists of a BP neural network and a BKA algorithm module for optimizing the BP neural network. The number of neurons in the output layer of the BP neural network is determined to be four, and the jet pressure, nozzle diameter, jet target distance, and impact time are used as inputs of the four output layer neurons respectively. The number of neurons in the output layer of the BP neural network is determined to be one, and the output of the output layer neurons is the predicted value of the icebreaking volume. (4) The jet pressure, nozzle diameter, jet target distance, impact time, and ice breaking volume obtained from the experiment were normalized and processed for outliers, and then the training set and test set of the neural network prediction model were constructed using the processed data. (5) Inputting the data in the training set into the BP neural network for training, inputting the weights and thresholds generated by the BP neural network into the BKA algorithm module during the training process, optimizing the weights and thresholds through the BKA algorithm module, and returning the optimized weights and thresholds to the BP neural network; (6) The trained neural network prediction model is tested using the test data in the test set, and the ability of high-pressure water jet to break ice is predicted using the neural network prediction model that has passed the test.

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