Metal induction heating minimum energy consumption calculation method and system based on optimization model

Abstract

The application discloses a metal induction heating minimum energy consumption calculation method and system based on an optimization model, generates a sample data set according to a mapping relationship of metal heating characteristics and metal heating timing, heating power and metal rod rotating speed; performs a pretreatment operation on the sample data set; takes the metal heating characteristics as input variables, takes the metal heating timing, heating power and metal rod rotating speed as output variables, and establishes a BP neural network; adopts an improved Guan-Hogu optimization algorithm to optimize initial weights and thresholds of the BP neural network, and assigns the initial weights and thresholds to the BP neural network; trains the BP neural network after the assignment, and obtains a prediction model; takes the output of the prediction model as input of a multi-objective improved particle swarm optimization algorithm, and realizes accurate prediction of metal heating characteristic parameters and effective connection of minimum energy consumption. The method realizes accurate calculation of metal induction heating minimum energy consumption in a manner of prediction first and then calculation, and further improves calculation precision and accuracy of metal induction heating.

Description

Technical Field

[0001] This invention relates to the field of heat treatment technology, and more specifically to a method and system for calculating the minimum energy consumption of metal induction heating based on an optimization model. Background Technology

[0002] Heat treatment, as a fundamental metal processing technique, is an indispensable part of sheet metal production. The core of the heat treatment process is the metal's temperature; controlling the metal's temperature at different times directly determines the metal's properties. In actual heat treatment, mastering the maximum heating time at the metal's rated temperature can guide the heat treatment process and ensure metal quality.

[0003] The current approach involves manually analyzing and calculating the characteristic parameters of metals during the heating process to achieve accurate prediction and minimize energy consumption. However, the prediction process for these characteristic parameters is complex and time-consuming, requiring the analysis of large amounts of data. To address this issue, various gradient-based artificial neural network methods are employed to predict the characteristic parameters of non-ferrous metal surfaces. These neural networks offer high speed and accuracy and are considered one of the most suitable techniques for predicting characteristic parameters of metals during heating.

[0004] However, when dealing with complex problems involving multiple factors, traditional neural network methods can significantly increase the convergence time of the network due to the gradient learning approach, thus failing to achieve a good balance between the convenience, sensitivity, and cost of monitoring.

[0005] Based on this, the present invention proposes a method and system for calculating the minimum energy consumption of metal induction heating based on an optimization model. This method achieves accurate calculation of the minimum energy consumption of metal induction heating through a prediction-then-calculation approach, further improving the calculation accuracy and precision of metal induction heating. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for calculating the minimum energy consumption of metal induction heating based on an optimization model, so as to solve the problems in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the minimum energy consumption of metal induction heating based on an optimization model, the calculation method comprising the following steps: A sample dataset is generated based on the mapping relationship between metal heating characteristics and metal heating timing, heating power, and metal rod rotation speed; Perform preprocessing operations on the sample dataset; A BP neural network is established by taking the metal heating characteristics as input variables and the metal heating time, heating power, and metal rod rotation speed as output variables. By incorporating the elite guidance strategy, the cosine dynamic population adjustment strategy, and the dynamic reverse somersault mutation strategy into the Crowned hog optimization algorithm, an improved Crowned hog optimization algorithm is obtained. An improved porcupine optimization algorithm was used to optimize the initial weights and thresholds of the BP neural network, obtain the optimal initial weights and thresholds, and assign them to the BP neural network. The preprocessed sample dataset is used to train the assigned BP neural network to obtain the prediction model. The actual metal heating characteristic data are input into the prediction model, and the output of the prediction model is used as the input of the multi-objective improved particle swarm algorithm. The particles are evaluated and updated according to multiple objective functions to find the Pareto optimal solution set that satisfies multiple objectives. Finally, the result of the minimum energy consumption calculation for induction heating is obtained.

[0008] Preferably, in the first defense strategy of the Crowned Porcupine optimization algorithm, the elite guidance strategy introduces a weighted elite guidance strategy to update the individual position when executing the first defense strategy, with the following formula: , In the formula, For the first During the nth iteration The position of each individual For random numbers that follow a normal distribution, for Random numbers between, The position of an individual randomly selected from the elite set. For the first The optimal solution in the next iteration.

[0009] Preferably, the cosine dynamic population adjustment strategy dynamically adjusts the population size using a cosine function, as shown in the formula: , In the formula, N is the population size in the current iteration; N min The minimum population size; A(t) is the time-varying amplitude function; t is the current iteration number; % is the modulo operation; T is the cycle period; N' is the initial population size; T max This represents the maximum number of iterations.

[0010] Preferably, the dynamic reverse somersault mutation strategy is an improved strategy that combines the dynamic reverse learning strategy with the somersault strategy. In each iteration, all individuals are sorted by fitness, the first 50% are updated using somersault, and the remaining individuals are updated using dynamic reverse learning. Then, the newly generated individuals are merged with the parent generation, and the top N individuals are selected from the best to the worst fitness to enter the next generation. The expression for the dynamic reverse learning strategy is: , In the formula, X DOBL Represents the reverse initial population, X initial This represents the population generated by randomly initializing the population; r1 and r2 are both random numbers between [0, 1], Lb is the lower bound of the search space, and Ub is the upper bound of the search space; The somersault strategy uses the current global optimal solution as a fulcrum, mapping individuals to their mirror image with respect to the optimal solution. The position update formula is: , In the formula, For the first The updated position of each individual For the first The position of each individual The current global optimal individual position is represented by r1 and r2, which are both random numbers between [0, 1].

[0011] Preferably, the BP neural network includes an input layer, a hidden layer, and an output layer; During the data forward propagation phase, the input signal is first transmitted from the input layer to the hidden layer, and the output of the hidden layer... Represented as: , In the formula, The output value of the hidden layer of the neural network. The activation function of the hidden layer. The weights from the input layer to the hidden layer. For input features, The hidden layer threshold is n, and the number of input layer nodes is n. The data stream is then transmitted from the hidden layer to the output layer, and the output layer outputs the results. Represented as: , In the formula, Let g be the output value of the output layer of the neural network, and g be the activation function of the output layer. The weights from the hidden layer to the output layer. The threshold value for the output layer. This represents the number of hidden layer nodes. After the BP neural network completes its first forward propagation, due to the output value of the BP neural network... Compared with the true value There is a deviation between them, and the resulting error E is expressed as: , In the formula, m is the number of output layer nodes. The actual value; Error propagates along the reverse path. The BP neural network uses gradient descent to optimize and adjust the weight parameters. The weight update formula is: , In the formula, This represents the learning rate parameter; This represents the error of the k-th sample. The updated weights from the input layer to the hidden layer. The updated weights from the hidden layer to the output layer; The error parameters are continuously adjusted through an iterative optimization process. When the algorithm reaches the convergence condition, the training is terminated, and the optimized final result is output.

[0012] Preferably, the multi-objective improved particle swarm optimization algorithm takes the output of the prediction model as input, and the optimization objective is to minimize the energy consumption of metal heating. The objective function formula is: , In the formula, For the output of the prediction model, Energy is consumed for heating metals. This represents the energy consumption of induction heating. , This refers to the energy consumption of induction heating. .

[0013] Preferably, the improved multi-objective particle swarm optimization algorithm is obtained by introducing a linear differential decreasing strategy, a time-varying acceleration coefficient, and a mutation strategy to improve the multi-objective particle swarm optimization algorithm MOPSO. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm continuously updates the position and velocity of particles based on the interaction of information from the global optimum and the individual historical optimum. The update process is represented as follows: , In the formula, X i (t) and V i (t) represent the position and velocity of the i-th particle at the t-th iteration, respectively. i (t+1) and V i (t+1) represent the position and velocity of the i-th particle at the (t+1)-th iteration, respectively. i (t) and Gbest i (t) represents the historical optimal position and the global optimal position of the i-th particle in the t-th iteration, respectively, w is the inertia weight factor, c1 and c2 are acceleration factors greater than zero, and γ1, γ2∈[0,1].

[0014] Preferably, the expression for the linear differential decreasing strategy is as follows: , , , In the formula, This represents the value of the inertia weight factor in the t-th iteration. Indicates the maximum number of iterations. , This indicates the upper and lower limits of the inertia weighting factor.

[0015] Preferably, in the multi-objective improved particle swarm optimization algorithm, time-varying acceleration coefficients c1 and c2 are introduced, with the following expressions: , , In the formula, and Let c1 and c2 represent the values ​​of c1 and c2 in the t-th iteration, respectively, where t is the current iteration number. This indicates the maximum number of iterations.

[0016] Preferably, the expression for the mutation strategy is as follows: , In the formula, Δ represents the mutation factor, and rand represents a random number between (0, 1), which satisfies the mutation condition. Mutation occurs according to probability p; , In the formula, p max p min These represent the upper and lower limits of the variation rate, respectively.

[0017] This application also provides a calculation system for minimum energy consumption of metal induction heating based on an optimization model, including: Generation module: used to generate sample datasets based on the mapping relationship between metal heating characteristics and metal heating timing, heating power and metal rod rotation speed; Preprocessing module: Used to perform preprocessing operations on the sample dataset; Establishment Module: Used to establish a BP neural network by taking the metal heating characteristics as input variables and the metal heating time, heating power, and metal rod rotation speed as output variables; Improved module: This module incorporates the elite guidance strategy, cosine dynamic population adjustment strategy, and dynamic reverse somersault mutation strategy into the Crowned Porcupine optimization algorithm to obtain the improved Crowned Porcupine optimization algorithm. Optimization module: Used to optimize the initial weights and thresholds of the BP neural network using the improved crown porcupine optimization algorithm, obtain the optimal initial weights and thresholds, and assign them to the BP neural network; Training module: Used to train the assigned BP neural network on the sample dataset after preprocessing to obtain the prediction model; The solution module is used to input actual metal heating characteristic data into the prediction model, and use the output of the prediction model as the input of the multi-objective improved particle swarm optimization algorithm. It evaluates and updates the particles according to multiple objective functions, finds the Pareto optimal solution set that satisfies multiple objectives, and finally obtains the result of the minimum energy consumption calculation for induction heating.

[0018] The technical effects and advantages provided by the present invention in the above technical solution are as follows: This application employs elite guidance, cosine dynamic population adjustment, and dynamic reverse somersaulting to improve the global optimization capability of the Crowned Porcupine Optimization Algorithm (CPO algorithm), resulting in the Multi-Strategy Improved Crowned Porcupine Optimization Algorithm (MSECPO algorithm). This enhances the generalization ability of the prediction model. The improved MSECPO algorithm is used to optimize the hyperparameters of the BP neural network, improving the accuracy of BP neural network predictions. After optimizing the hyperparameters in the BP neural network using MSECPO, the optimized BP neural network is trained to obtain the prediction model. The output of the prediction model is used as one of the inputs in the Multi-Objective Improved Particle Swarm Optimization Algorithm (MOIPSO algorithm), achieving an effective connection between accurate prediction of metal heating characteristic parameters and minimum energy consumption. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0020] Figure 1 The flowchart for the optimized model of this invention is shown below.

[0021] Figure 2 This is a comparison diagram of the Pareto frontier of the present invention.

[0022] Figure 3 This is a schematic diagram of superconducting DC induction heating. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] High-temperature superconducting DC induction heating utilizes a superconducting coil to generate a strong DC magnetic field. A metal rod is placed within this field, its axis perpendicular to the magnetic field direction, and rotated under the influence of an external electric motor. This generates a motional electromotive force (EMF) within the metal rod. Under the influence of this EMF, a current flows through the metal rod, producing Joule heating, thus heating the metal rod. Figure 3 As shown. This technology can improve the overall heating efficiency to over 80%, offering a significant advantage in improving quality and efficiency. Electromagnetic induction heating is widely used in the processing of non-ferrous metal materials. Due to its very low heating frequency, it has superior temperature uniformity and heating quality. Furthermore, the equipment is safe to operate, grid-friendly, and can achieve efficient and uniform preheating treatment of metals during the rolling and forming process.

[0025] Example: This example establishes an optimized model (MSECPO-BP-MOIPSO) for calculating the minimum energy consumption of induction heating in high-temperature superconducting metals, such as... Figure 1 As shown, the construction of the MSECPO-BP-MOIPSO model includes the following steps: To improve the optimization performance and convergence efficiency of the CPO algorithm (Corrugated Porcupine Optimization Algorithm), an elite-guided strategy, a cosine dynamic population adjustment strategy, and a dynamic reverse somersault mutation strategy are introduced to improve it, resulting in the improved CPO algorithm (MSECPO algorithm). Using the initial weights and thresholds of the BP neural network as the core optimization objective, the MSECPO algorithm leverages its stronger global search capability and local optimization accuracy to efficiently optimize network parameters, laying the foundation for accurate model training and performance improvement. Then, the hyperparameters optimized by the MSECPO algorithm are assigned to the BP neural network, initiating the network training process. This approach effectively avoids the local optimum trap caused by traditional random initialization, accelerates convergence, and enhances the model's fitting ability and generalization stability in complex data scenarios, comprehensively improving the overall performance of the BP neural network. This method generates a sample dataset by mapping the metal heating characteristics (rated metal temperature, metal length, initial temperature) to the metal heating time, heating power, and metal rod rotation speed. The dataset undergoes preprocessing, including data normalization. A post-processed backpropagation (BP) neural network is trained using this preprocessed dataset to obtain a prediction model. Finally, the output of the prediction model (metal heating time, heating power, and metal rod rotation speed) is used as one of the inputs to a multi-objective improved particle swarm optimization (MOIPSO) algorithm. The particles are evaluated and updated according to multiple objective functions. By continuously optimizing the particle positions, the state of the high-temperature superconducting induction heating characteristic parameters is determined, thus obtaining the result of the minimum energy consumption calculation during the metal heating process. This method is characterized by its wide applicability and high computational accuracy.

[0026] The Cronbach's Optimization (CPO) algorithm is based on the assumption that a hierarchy and role distinction exist among individuals in a pig herd, similar to human society. In the algorithm, a King is defined, representing the current optimal solution, and other ordinary pigs (Pigs) represent potential candidate solutions. Each pig in the herd improves its physical capabilities (i.e., the quality of the solution) through simulated competition and cooperation. One of the core strategies is information sharing: ordinary pigs adjust their actions and behavioral strategies by observing the King's state, gradually approaching the optimal solution. Furthermore, the algorithm introduces an "exploration-exploitation" mechanism, allowing pigs in the herd to dynamically balance exploring new territory with utilizing known information.

[0027] The CPO algorithm proposes a cyclic population reduction (CPR) technique to maintain population diversity while accelerating convergence. This strategy simulates that not all crested porcupines activate defense mechanisms, but only those that are threatened. During optimization, this method removes some crested porcupines from the population to speed up convergence and then reintroduces them to improve diversity and avoid getting trapped in local minima. The calculation method is as follows: , In the formula, N is the population size in the current iteration; N min N' is the minimum population size; N' is the initial population size; t is the current iteration number; % is the modulo operation; T is the loop period; T max This represents the maximum number of iterations.

[0028] In the CPO algorithm, individuals in the population decide which exploration strategy to adopt based on their relative distance from the predator. and It is the distance threshold parameter, where Indicates the safe distance threshold. Indicates the warning distance threshold. When < When the actual distance between an individual and a predator is less than a warning threshold, a global exploration is initiated, which mainly includes a first defense strategy and a second defense strategy. Firstly, during the global exploration phase, random values ​​are generated using a normal distribution. and This reflects the randomness of decision-making in nature.

[0029] when < At this point, the first defense strategy (exploration phase) is implemented. When the crested porcupine becomes aware of the predator, it begins to raise and fan its quills. The predator then has two options: move towards it or move away. In the first option, the distance between the predator and the crested porcupine decreases as the predator moves towards it. This option encourages exploration of the area between the predator and the crested porcupine to accelerate convergence. Conversely, in the second option, the distance between the predator and the crested porcupine is maximized because the predator chooses to leave. This option encourages exploration of distant areas to identify unvisited regions, which may be involved in the desired solution. Random values ​​are generated using a normal distribution to mathematically model these options. If these random values ​​are less than 1 or greater than 1... If the predator is attracted to the crested porcupine, it will be encouraged to approach. Otherwise, the predator will stay away from the crested porcupine. This behavior is typically mathematically simulated as follows: , in, For the first During the nth iteration The position of each individual For the first The optimal solution in the next iteration. It is in the A vector generated between an individual and an individual randomly selected from the population, used to represent the predator in the [number]th [phase]. Position at the next iteration These are random numbers based on a normal distribution. It is a random value within the interval [0,1]. Generating... The mathematical formula is shown below: , where r is a random number between [1, N].

[0030] when ≥ During this phase, the second defense strategy (exploration phase) is implemented. In this strategy, the crested porcupine uses sound to create noise and threaten predators. The porcupine's calls become louder when a predator approaches. Its expression is: , Where U1 is a vector randomly generated between [0, 1]; y is the predator strategy vector; and Let r1 and r2 be two randomly selected individual position vectors, where r1 and r2 are two random integers between [1, N]. It is a random value generated between 0 and 1.

[0031] when ≥ This refers to localized defense strategies employed when predators do not enter the warning range, primarily including third and fourth defense strategies. This is achieved by comparing random numbers. and the trade-off parameter T f The size of the parameter T determines the defense strategy. In this embodiment, the trade-off parameter T is used. f The value is set to 0.8.

[0032] when When the value is less than 0.8, the third defense strategy (development phase) is implemented. In this strategy, the crested porcupine secretes a foul odor, which spreads throughout its surrounding area to prevent predators from approaching. Its expression is: ,

[0033] Where r3 is a random number between [1, N], and δ is a parameter used to control the search direction. For randomly selected individual position vectors, It is a defensive factor. It is a random value within the interval [0,1]. It is an odor diffusion factor.

[0034] , , , in, Indicates the first The objective function value of the i-th individual in the nth iteration. Indicates the first The objective function value of the k-th individual in the k-th iteration, ε is a small value to avoid division by zero, and rand is a random number generated randomly between 0 and 1.

[0035] The U1 vector is used to simulate three possible scenarios in this strategy: 1) When U1 equals 0, the hooded porcupine will stop spreading its scent because the predator will stop moving out of fear of the hooded porcupine, so the distance between the predator and the hooded porcupine remains constant; 2) When U1 equals 1, the hooded porcupine will significantly release its scent because the predator is nearby; 3) When U1 is a combination of 0 and 1, the predator maintains a safe distance from the hooded porcupine, so there is no need for it to release its scent widely.

[0036] when When the coefficient of performance (COP) is ≥0.8, the fourth defense strategy (development phase) is implemented, which is physical attack. When a predator gets close and attacks with short, thick feathers, the crested porcupine will resort to physical attack. During the physical attack, the two objects strongly merge, representing a one-dimensional inelastic collision. Its physical attack behavior is expressed as: , Among them, It is the first The optimal solution at the nth iteration represents the predator at that position, and α is the convergence rate factor. and It is a random value within the interval [0,1]. It is the inelastic collision force generated when an individual attacks the i-th predator with its body.

[0037] It is defined by the inelastic collision law: , in, It is a random value within the interval [0,1]. It is the first The quality of the i-th individual (predator) in the next iteration. Is the i-th individual in the i-th... The final speed at the next iteration Is the i-th individual in the i-th... The initial velocity at the next iteration.

[0038] (1) Elite Guidance Strategy

[0039] During the global exploration phase, when < When implementing a defense strategy, a weighted elite guidance strategy is introduced. This strategy, by fusing the current individual's position with elite individual information, constructs an update formula with targeted search characteristics, as shown below: , in, For the first During the nth iteration The position of each individual For random numbers that follow a normal distribution, for Random numbers between, The position of an individual randomly selected from the elite set. For the first The optimal solution at the next iteration. In the position update process of the MSECPO algorithm, not only are the random perturbation and global optimal guidance mechanisms of the CPO algorithm retained, but a weighted elite guidance strategy is also innovatively introduced. Through the current solution... With random elite solutions The arithmetic mean of the points is used to generate local search center points, retain the high-quality features of elite individuals, and inherit them into the next position update process. This allows the algorithm to improve local optimization efficiency while maintaining global exploration, achieving a synergistic improvement in convergence speed and solution quality.

[0040] (2) Cosine dynamic population adjustment strategy

[0041] The improved dynamic population adjustment strategy uses a cosine function to dynamically adjust the population size, allowing the population size to change smoothly during iteration. Its expression is shown below: ,

[0042] Where N is the population size in the current iteration; N min The minimum population size; A(t) is the time-varying amplitude function; t is the current iteration number; % is the modulo operation; T is the cycle period; N' is the initial population size; T max This represents the maximum number of iterations. Let N be the maximum number of iterations. min =30, N'=100, T max =200.

[0043] (3) Dynamic reverse somersault variation strategy

[0044] Inverse learning (OBL) is an improved strategy for swarm intelligence optimization algorithms. During the optimization process, an inverse solution is generated based on the current solution. The objective function values ​​of the current solution and the inverse solution are compared, and the better solution is selected for the next iteration. However, since the distance between the inverse solution generated by OBL and the current solution is fixed, it lacks randomness and cannot effectively enhance the diversity of the population within the search space. To enhance the randomness of the inverse solution and thus improve the algorithm's optimization ability, this invention adopts a dynamic inverse learning strategy, expressed as follows: , Among them, X DOBL Represents the reverse initial population, X initial This represents the population generated by randomly initializing the population; r1 and r2 are both random numbers between [0, 1], Lb is the lower bound of the search space, and Ub is the upper bound of the search space.

[0045] The somersault strategy is a position update operator in manta ray foraging optimization: using the current global optimum as a fulcrum, it maps an individual to its mirror image with respect to the optimum, achieving a fast leap-like search, defined as: , in, For the first The updated position of each individual For the first The position of each individual The current global optimal individual position is represented by r1 and r2, which are both random numbers between [0, 1].

[0046] This invention proposes an improved strategy that combines dynamic backward learning with somersault updates. In each iteration, all individuals are first sorted by fitness, with the top 50% updated using somersault updates and the remaining individuals updated using dynamic backward learning. Subsequently, the newly generated individuals are merged with their parents, and the top N individuals are selected from best to worst fitness to enter the next generation.

[0047] As a typical feedforward deep learning architecture, the BP neural network's computational topology comprises three key stages: forward signal propagation, loss calculation, and backward gradient update. In the feedforward stage, input features are abstracted layer by layer through multiple nonlinear transformations (typically using the Sigmoid or ReLU activation functions). When the output layer's prediction error exceeds a preset threshold, the system initiates the backpropagation mechanism, using the chain rule to distribute the error gradient backward along the computational graph to each hidden layer node. The standard computational steps of a BP neural network are shown below:

[0048] During the data forward propagation phase, the input signal is first transmitted from the input layer to the hidden layer, at which point the output of the hidden layer is determined. Represented as: , In the formula, The output value of the hidden layer of the neural network. The activation function of the hidden layer. The weights from the input layer to the hidden layer. For input features, The hidden layer threshold is n, and the number of input layer nodes is n.

[0049] The data stream is then transmitted from the hidden layer to the output layer, and the output layer outputs the results. Represented as: , In the formula, Let g be the output value of the output layer of the neural network, and g be the activation function of the output layer. The weights from the hidden layer to the output layer. The threshold value for the output layer. This represents the number of hidden layer nodes.

[0050] After the neural network completes its first forward propagation, due to the output value of the neural network... Compared with the true value There is a deviation between them, and the resulting error E can be expressed as: , Where m is the number of output layer nodes; y k This is the actual value.

[0051] Error propagates along the reverse path. The BP neural network uses gradient descent to optimize and adjust the weight parameters. The weight update formula is shown below: , In the formula, This represents the learning rate parameter; This represents the error of the k-th sample. The updated weights from the input layer to the hidden layer. This refers to the updated weights from the hidden layer to the output layer.

[0052] The error parameters are continuously adjusted through an iterative optimization process. When the algorithm reaches the convergence condition, the training is terminated, and the optimized final result is output.

[0053] The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm simulates the foraging behavior of birds in nature, analogizing the location of food to the optimal solution set of an optimization problem, and the flight direction and position of birds to the velocity and position of particles. Based on the interaction of information from the global optimum (Gbest) and the individual historical optimum (Pbest), the position and velocity of particles are continuously updated, improving search efficiency and effectively guiding the population to convergence. However, this also leads to the possibility of getting trapped in local optima. The specific update process is as follows: ,

[0054] Among them, X i (t) and V i (t) represent the position and velocity of the i-th particle at the t-th iteration, respectively. i (t+1) and V i (t+1) represent the position and velocity of the i-th particle at the (t+1)-th iteration, respectively. i (t) and Gbest i (t) represents the historical optimal position and the global optimal position of the i-th particle in the t-th iteration, respectively, w is the inertia weight factor, c1 and c2 are acceleration factors greater than zero, and γ1, γ2∈[0,1].

[0055] The essential difference between multi-objective optimization problems and single-objective optimization problems is that the solutions obtained in multi-objective optimization problems are not unique, but rather consist of a set of non-dominant Pareto solutions. Since the global optimum cannot be directly selected, appropriate strategies are needed to obtain it. For the problem of selecting a local optimum (Pbest) in MOPSO, when precise comparison is not possible, one solution is randomly selected as the historical optimum. Regarding how to select the global optimum (Gbest) in MOPSO, MOPSO selects a leader from the set of optimal solutions (archives) based on crowding levels, aiming for a uniformly distributed particle distribution. An adaptive grid method is applied when selecting the leader and updating the archive. Taking bi-objective optimization as an example, the specific steps are as follows:

[0056] (1) Divide the space of the objective function into spaces of equal size. In this invention, f1 and f2 are used as objective functions, and the boundaries of f1 and f2 (min f1(t), max f1(t)) and (min f2(t), max f2(t)) are calculated at the t-th iteration.

[0057] (2) Divide the target space into M×M grids, with the grid modulus being: ,

[0058] (3) Record the grid numbers of all particles in the external archive;

[0059] (4) Calculate the density of particles in the grid. If the number of particles in a single grid exceeds 1, then the particles in that grid will be randomly deleted.

[0060] Selecting the global optimum based on particle density: The higher the particle density in the grid, the closer the objective function values ​​are, which makes the algorithm more prone to local convergence. Therefore, particles with lower grid density have a higher probability of being selected.

[0061] This invention improves the multi-objective particle swarm optimization algorithm (MOPSO algorithm) by introducing a linear differential decreasing strategy, a time-varying acceleration coefficient, and a mutation strategy, resulting in a multi-objective improved particle swarm optimization algorithm (MOIPSO algorithm).

[0062] In the MOIPSO algorithm, the multi-objective optimization mathematical model is as follows: , in, For the output of the prediction model, Energy is consumed for heating metals. This represents the energy consumption for induction heating (the product of the metal rod's rotational speed and the heating time). This represents the energy consumption of induction heating (the product of heating power and heating time).

[0063] In the linear decreasing strategy, because the slope remains constant, the rate of change of the inertia factor remains constant. If a good point is not generated in the initial iteration, the algorithm is likely to get trapped in a local optimum as iterations accumulate and the speed rapidly decreases. Therefore, this invention proposes a linear differential decreasing strategy to improve the MOPSO algorithm, the specific expression of which is as follows: , , ,

[0064] In the formula, This represents the value of the inertia weight factor in the t-th iteration. Indicates the maximum number of iterations. , This indicates the upper and lower limits of the inertia weighting factor.

[0065] In particle swarm optimization (PSO), keeping the acceleration coefficients c1 and c2 constant has become a common practice. To further improve the performance of the MOPSO algorithm, this invention introduces time-varying acceleration coefficients c1 and c2. This enhances the global search capability in the early stages and allows for focused searching in later iterations, thereby improving the algorithm's optimization accuracy. The expression is as follows: , ,

[0066] In the formula, and Let c1 and c2 represent the values ​​of c1 and c2 in the t-th iteration, respectively, where t is the current iteration number. This indicates the maximum number of iterations.

[0067] Furthermore, since the population search space continuously shrinks during the iteration process, in order to maintain particle diversity, this invention introduces a mutation mechanism from genetic algorithms based on the above improvements. This mechanism involves reinitializing certain variables with a certain probability, specifically in the form of the following expression: ,

[0068] In the formula, Δ represents the mutation factor, and rand represents a random number between (0, 1), which satisfies the mutation condition. Mutation occurs according to probability p; ,

[0069] In the formula, p max p min and represent the upper and lower limits of the mutation rate, respectively. As the number of iterations t increases, the mutation rate p decreases exponentially.

[0070] The mutation strategy can expand the search range of particles, allowing them to jump out of the position of the previous iterative optimal solution, increasing the possibility of discovering new Pbest and Gbest, expanding the search space while maintaining species diversity, and increasing the probability of the algorithm finding the optimal solution.

[0071] This embodiment evaluates the effectiveness of the MSECPO-BP-MOIPSO model using various evaluation metrics, thereby verifying the superiority of the model proposed in this invention in calculating the minimum energy consumption of high-temperature superconducting induction heating.

[0072] To objectively evaluate the overall performance of each model method in predicting metal heating time, the errors between predicted and measured values ​​are introduced, including the maximum absolute percentage error (MAXAPE), mean absolute percentage error (MAPE), mean absolute error (MAE), and coefficient of determination (R²). 2 The four indicators are calculated as follows: ; ; ; ;

[0073] in, This is the actual value. For predicted values, Let M be the mean and M be the sample size.

[0074] The smaller the values ​​of MAXAPE, MAPE, and MAE, the closer the predicted values ​​of the model method are to the actual values, and the higher the prediction accuracy; R 2 The closer the value is to 1, the higher the goodness of fit between the model's predicted value and the actual value, and the better the prediction (calculation) effect.

[0075] To demonstrate that the MSECPO-BP-MOIPSO model has better computational efficiency and generalization performance in calculating the minimum energy consumption for metal heating, a comparative study of several similar algorithms is conducted. This invention will perform simulation experiments on the BP network, GPR network, and MSECPO-BP network to predict metal heating characteristic parameters, and then compare the results. Furthermore, this invention uses the same training and test sets throughout the simulation experiments. The input samples are metal heating characteristic parameter data, including three metal heating characteristics: rated metal temperature, metal length, and initial temperature; the output samples are data on metal heating timing, heating power, and metal rod rotation speed. A total of 39,430 sets of sample data from 2024 were selected, with 29,430 sets used as the training set and 10,000 sets as the test set. The proposed MSECPO-BP network is used to train the minimum energy consumption model for metal heating, and the results are compared with the BP network and GPR network algorithms. Table 1 below shows the comparison of evaluation metrics for different algorithm models in the test set.

[0076] Table 1 Comparison of Evaluation Metrics for Different Algorithm Models

[0077] The results in Table 1 clearly show that MSECPO-BP significantly outperforms the traditional BP and GPR algorithms in all metrics. Specifically, MSECPO-BP is lower than the other two models in MAXAPE, MAPE, and MAE (values ​​are 8.543%, 1.311%, and 14.989s, respectively). 2 The metric closest to 1 indicates that MSECPO-BP has the best overall performance, demonstrating that the MSECPO algorithm can optimize the hyperparameters of the BP network. It also confirms that the MSECPO-BP algorithm outperforms both the BP and GPR algorithms. Therefore, compared to traditional methods, the MSECPO-BP algorithm model has smaller errors and higher reliability, making it more suitable for predicting / calculating characteristic parameters of metal heating.

[0078] The MSECPO-BP neural network is trained on the training set samples, and then the algorithm model is applied to the prediction of metal heating characteristic parameters. This invention uses test samples to verify the prediction accuracy of the MSECPO-BP algorithm. The trained neural network is then used as one of the inputs to MOIPSO to realize the MSECPO-BP-MOIPSO algorithm calculation model. Since the factory preheats a wide variety of metal types, each with significant differences in length and batch size, even for the same type of product, the initial temperature and other data vary due to production time and environmental factors. Therefore, three metal heating characteristics—actual (rated) temperature, metal length, and initial temperature—are selected as influencing factors in actual operation. A set of heating parameters (300 samples) is selected as the test set, using the metal heating characteristics as input samples and the actual heating time, heating power, and metal rod rotation speed as output samples. To further verify the prediction effect of the MSECPO-BP network, this invention selects any four sets of metal heating characteristic parameters for temperature prediction. The prediction results for the three sets of metal heating characteristic parameters and their heating time, heating power, and metal rod rotation speed are shown in Table 3 below.

[0079] Table 2. Actual results of four randomly set high-temperature superconducting induction heating metal heating parameters.

[0080] Table 3. Prediction results of heating parameters for four randomly selected high-temperature superconducting induction heating metals (MSECPO-BP)

[0081] The trained MSECPO-BP network was used to test four sets of data, with the actual (rated) temperature of the metal, the metal length, and the initial temperature parameters as test inputs. The optimized model results were compared with the actual heating data (power consumption). As shown in Table 3, the optimized values ​​were approximately 6 kW lower than the actual values, and the minimum energy consumption was approximately 1 kW. This indicates that the established MSECPO-BP prediction model has a superior network structure and is feasible for optimizing the minimum energy consumption of high-temperature superconducting induction heating metals.

[0082] Overall, the experimental results show that the MSECPO-BP network has a superior network structure for optimizing the minimum energy consumption of heated metals. It can accurately calculate the minimum energy consumption of heated metals, thereby effectively monitoring the temperature operation status during the high-temperature superconducting induction heating of metals.

[0083] First, a proxy model is encapsulated using MSECPO-BP to represent the dependent variables (actual heating time, heating power, and metal rod rotation speed) and independent variables (metal rated temperature, metal length, and initial temperature). Then, MOIPSO is used to find the extreme values ​​(actual heating time, heating power, and metal rod rotation speed), and the corresponding Pareto solutions for induction heating kinetic energy consumption (the product of metal rod rotation speed and heating time, heating efficiency) and induction heating electrical energy consumption (the product of heating power and heating time) are provided. First, the MSECPO-BP neural network is trained on the training set samples. Then, the algorithm model is applied to the optimization of minimum energy consumption in metal heating, using the neural network trained by MSECPO-BP as input to MOIPSO. Finally, the MSECPO-BP-MOIPSO algorithm computation model is implemented. This optimization algorithm achieves the following Pareto front for minimum energy consumption optimization in metal heating: Figure 2 As shown, the Pareto front of the MSECPO-BP-MOIPSO algorithm completely dominates the MOPSO and BP-MOPSO algorithms in the range of power consumption of 80-100kWh, heating efficiency of 80-95%, and temperature control error of 0-2℃, demonstrating its significant advantage in multi-objective optimization.

[0084] This embodiment also provides a minimum energy consumption calculation system for metal induction heating based on an optimization model, including:

[0085] Generation module: used to generate sample datasets based on the mapping relationship between metal heating characteristics and metal heating timing, heating power and metal rod rotation speed;

[0086] Preprocessing module: Used to perform preprocessing operations on the sample dataset;

[0087] Establishment Module: Used to establish a BP neural network by taking the metal heating characteristics as input variables and the metal heating time, heating power, and metal rod rotation speed as output variables;

[0088] Improved module: This module incorporates the elite guidance strategy, cosine dynamic population adjustment strategy, and dynamic reverse somersault mutation strategy into the Crowned Porcupine optimization algorithm to obtain the improved Crowned Porcupine optimization algorithm.

[0089] Optimization module: Used to optimize the initial weights and thresholds of the BP neural network using the improved crown porcupine optimization algorithm, obtain the optimal initial weights and thresholds, and assign them to the BP neural network;

[0090] Training module: Used to train the assigned BP neural network on the sample dataset after preprocessing to obtain the prediction model;

[0091] The solution module is used to input actual metal heating characteristic data into the prediction model, and use the output of the prediction model as the input of the multi-objective improved particle swarm optimization algorithm. It evaluates and updates the particles according to multiple objective functions, finds the Pareto optimal solution set that satisfies multiple objectives, and finally obtains the result of the minimum energy consumption calculation for induction heating.

[0092] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0093] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to specific implementations. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for calculating the minimum energy consumption of metal induction heating based on an optimization model, characterized in that: The calculation method includes the following steps: A sample dataset is generated based on the mapping relationship between metal heating characteristics and metal heating timing, heating power, and metal rod rotation speed; Perform preprocessing operations on the sample dataset; A BP neural network is established by taking the metal heating characteristics as input variables and the metal heating time, heating power, and metal rod rotation speed as output variables. By incorporating the elite guidance strategy, the cosine dynamic population adjustment strategy, and the dynamic reverse somersault mutation strategy into the Crowned hog optimization algorithm, an improved Crowned hog optimization algorithm is obtained. An improved porcupine optimization algorithm was used to optimize the initial weights and thresholds of the BP neural network, obtain the optimal initial weights and thresholds, and assign them to the BP neural network. The preprocessed sample dataset is used to train the assigned BP neural network to obtain the prediction model. The actual metal heating characteristic data are input into the prediction model, and the output of the prediction model is used as the input of the multi-objective improved particle swarm algorithm. The particles are evaluated and updated according to multiple objective functions to find the Pareto optimal solution set that satisfies multiple objectives. Finally, the result of the minimum energy consumption calculation for induction heating is obtained.

2. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 1, characterized in that: In the first defense strategy of the Crown Porcupine optimization algorithm, the elite guidance strategy is introduced to update the individual position when executing the first defense strategy. The formula is as follows: ， In the formula, For the first During the nth iteration The location of each individual For random numbers that follow a normal distribution, for Random numbers between, The position of an individual randomly selected from the elite set. For the first The optimal solution in the next iteration.

3. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 2, characterized in that: The cosine dynamic population adjustment strategy dynamically adjusts the population size using a cosine function, with the following formula: ， In the formula, N is the population size in the current iteration; N min The minimum population size; A(t) is the time-varying amplitude function; t is the current iteration number; % is the modulo operation; T is the cycle period; N' is the initial population size; T max This represents the maximum number of iterations.

4. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 3, characterized in that: The dynamic reverse somersault mutation strategy is an improved strategy that combines the dynamic reverse learning strategy with the somersault strategy. In each iteration, all individuals are sorted by fitness, the top 50% are updated using somersault, and the remaining individuals are updated using dynamic reverse learning. Then, the newly generated individuals are merged with the parent generation, and the top N individuals are selected from the best to the worst fitness to enter the next generation. The expression for the dynamic reverse learning strategy is: ， In the formula, X DOBL Represents the reverse initial population, X initial This represents the population generated by randomly initializing the population; r1 and r2 are both random numbers between [0, 1], Lb is the lower bound of the search space, and Ub is the upper bound of the search space; The somersault strategy uses the current global optimal solution as a fulcrum, mapping individuals to their mirror image with respect to the optimal solution. The position update formula is: ， In the formula, For the first The updated position of each individual For the first The location of each individual The current global optimal individual position is represented by r1 and r2, which are both random numbers between [0, 1].

5. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 1, characterized in that: The BP neural network includes an input layer, hidden layers, and an output layer; During the data forward propagation phase, the input signal is first transmitted from the input layer to the hidden layer, and the output of the hidden layer... Represented as: ， In the formula, The output value of the hidden layer of the neural network. The activation function of the hidden layer. The weights from the input layer to the hidden layer. As input features, The hidden layer threshold is n, and the number of input layer nodes is n. The data stream is then transmitted from the hidden layer to the output layer, and the output layer outputs the results. Represented as: ， In the formula, Let g be the output value of the output layer of the neural network, and g be the activation function of the output layer. The weights from the hidden layer to the output layer. The threshold value for the output layer. This represents the number of hidden layer nodes. After the BP neural network completes its first forward propagation, due to the output value of the BP neural network... Compared with the true value There is a deviation between them, and the resulting error E is expressed as: ， In the formula, m is the number of output layer nodes. The actual value; Error propagates along the reverse path. The BP neural network uses gradient descent to optimize and adjust the weight parameters. The weight update formula is: ， In the formula, This represents the learning rate parameter; This represents the error of the k-th sample. The updated weights from the input layer to the hidden layer. The updated weights from the hidden layer to the output layer; The error parameters are continuously adjusted through an iterative optimization process. When the algorithm reaches the convergence condition, the training is terminated, and the optimized final result is output.

6. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 1, characterized in that: The multi-objective improved particle swarm optimization algorithm takes the output of the prediction model as input and aims to minimize the energy consumption of metal heating. The objective function is as follows: ， In the formula, For the output of the prediction model, Energy is consumed for heating metals. This represents the energy consumption for induction heating. , This refers to the energy consumption of induction heating. .

7. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 6, characterized in that: The improved multi-objective particle swarm optimization algorithm is obtained by introducing a linear differential decreasing strategy, a time-varying acceleration coefficient, and a mutation strategy to improve the multi-objective particle swarm optimization algorithm MOPSO. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm continuously updates the position and velocity of particles based on the interaction of information from the global optimum and the individual historical optimum. The update process is represented as follows: ， In the formula, X i (t) and V i (t) represent the position and velocity of the i-th particle at the t-th iteration, respectively. i (t+1) and V i (t+1) represent the position and velocity of the i-th particle at the (t+1)-th iteration, respectively. i (t) and Gbest i (t) represents the historical optimal position and the global optimal position of the i-th particle in the t-th iteration, respectively, w is the inertia weight factor, c1 and c2 are acceleration factors greater than zero, and γ1, γ2∈[0,1]; The expression for the linear differential decreasing strategy is as follows: ， ， ， In the formula, This represents the value of the inertia weight factor in the t-th iteration. Indicates the maximum number of iterations. , This indicates the upper and lower limits of the inertia weighting factor.

8. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 7, characterized in that: In the improved multi-objective particle swarm optimization algorithm, time-varying acceleration coefficients c1 and c2 are introduced, and their expressions are as follows: ， ， In the formula, and Let c1 and c2 represent the values ​​of c1 and c2 in the t-th iteration, respectively, where t is the current iteration number. This indicates the maximum number of iterations.

9. The method for calculating the minimum energy consumption of metal induction heating based on an optimization model according to claim 8, characterized in that: The expression for the mutation strategy is as follows: ， In the formula, Δ represents the mutation factor, and rand represents a random number between (0, 1), which satisfies the mutation condition. Mutation occurs according to probability p; ， In the formula, p max p min These represent the upper and lower limits of the variation rate, respectively.

10. A minimum energy consumption calculation system for metal induction heating based on an optimization model, used to implement the calculation method described in any one of claims 1-9, characterized in that: include: Generation module: used to generate sample datasets based on the mapping relationship between metal heating characteristics and metal heating timing, heating power and metal rod rotation speed; Preprocessing module: Used to perform preprocessing operations on the sample dataset; Establishment Module: Used to establish a BP neural network by taking the metal heating characteristics as input variables and the metal heating time, heating power, and metal rod rotation speed as output variables; Improved module: This module incorporates the elite guidance strategy, cosine dynamic population adjustment strategy, and dynamic reverse somersault mutation strategy into the Crowned Porcupine optimization algorithm to obtain the improved Crowned Porcupine optimization algorithm. Optimization module: Used to optimize the initial weights and thresholds of the BP neural network using the improved crown porcupine optimization algorithm, obtain the optimal initial weights and thresholds, and assign them to the BP neural network; Training module: Used to train the assigned BP neural network on the sample dataset after preprocessing to obtain the prediction model; The solution module is used to input actual metal heating characteristic data into the prediction model, and use the output of the prediction model as the input of the multi-objective improved particle swarm optimization algorithm. It evaluates and updates the particles according to multiple objective functions, finds the Pareto optimal solution set that satisfies multiple objectives, and finally obtains the result of the minimum energy consumption calculation for induction heating.

Images