Microwave heating temperature control method and system based on self-adaptive whale optimization algorithm

Abstract

The invention discloses a microwave heating temperature control method and system based on a self-adaptive whale optimization algorithm. The method comprises the following steps: S1, constructing a multi-objective optimization problem of microwave heating temperature control; s2, based on the feasible region of the control variable, randomly generating an initial whale population containing a plurality of individuals; s3, performing simulation evaluation on each individual in the initial whale population; controller parameters corresponding to the individuals are input into the microwave heating system simulation model, temperature response data of the system are obtained, and the value of a comprehensive fitness function J is calculated according to the temperature response data; s4, executing self-adaptive whale optimization algorithm iteration, and updating the whale population; and S5, when an iteration termination condition is satisfied, outputting a global optimal individual, and applying a controller parameter corresponding to the global optimal individual to an actual microwave heating control system. The method has the advantages of adaptively improving temperature uniformity, response speed, control precision and the like.

Description

Microwave Heating Temperature Control Method and System Based on Adaptive Whale Optimization Algorithm Technical Field

[0001] This invention relates to the field of microwave heating technology, specifically to a microwave heating temperature control method and system based on an adaptive whale optimization algorithm. Background Technology

[0002] Microwave heating technology is currently used in kilns, offering significant advantages over traditional heating methods, including shorter cycles, lower sintering temperatures, improved product performance, and energy savings. However, it also presents several challenges: nonlinearity (the material's dielectric properties, or ability to absorb microwaves), spatiotemporal coupling (the interaction between the microwave field and the material creates uneven "hot spots" and "cold spots," difficult to measure with a single sensor), model uncertainty (establishing an accurate physical model of microwave heating, involving electromagnetic fields, heat conduction, and material changes), and multiple inputs and outputs (control variables may include microwave power, frequency (if adjustable), stirrer speed, and tray rotation, while the controlled variable is the temperature at multiple points on the material). Traditional temperature control methods, such as PID control, often fall short in handling such complex conditions, struggling to simultaneously guarantee speed, stability, and uniformity.

[0003] The existing main technical solutions include fuzzy logic control, model predictive control, neural network control, genetic algorithm, and particle swarm optimization algorithm. These are all improved control methods based on traditional control methods. These algorithms can achieve better control effects to varying degrees in different aspects.

[0004] The shortcomings of existing technologies are as follows: Switching control suffers from the worst control quality, continuous temperature fluctuations, frequent start-stop cycles that negatively impact magnetron lifespan, and high energy consumption. PID control exhibits poor adaptability; fixed-parameter PID controllers cannot adapt to changes in dielectric properties and load, and performance deteriorates sharply when facing nonlinear and time-varying conditions, easily leading to overshoot and oscillations; tuning is difficult, and even well-tuned parameters may fail with different materials or loads. Fuzzy control is highly subjective in design, with control performance heavily reliant on expert experience and the completeness of the rule base; it lacks systematic and analytical design methods, making it difficult to achieve optimal control; and with a large rule base, logical conflicts may arise, making adjustment difficult. Model predictive control (MPC) is highly model-dependent, its performance heavily dependent on the accuracy of the predictive model, and establishing an accurate microwave-thermal-material coupling model is extremely difficult and computationally expensive; simplifying the model leads to decreased control performance, heavy computational burden, and high hardware requirements. Multi-source / phase control is extremely complex and expensive, requiring multiple independent microwave sources, phase detection, and control systems; the algorithms are complex, implementation is difficult, and costs increase by orders of magnitude, currently limiting it mainly to laboratory and high-end applications. Summary of the Invention

[0005] To address the technical problems existing in the prior art, this invention provides a microwave heating temperature control method and system based on an adaptive whale optimization algorithm that adaptively improves temperature uniformity, response speed, and control accuracy.

[0006] To solve the above-mentioned technical problems, the technical solution proposed in this invention is: a microwave heating temperature control method based on an adaptive whale optimization algorithm, comprising the following steps: S1. Constructing a multi-objective optimization problem for microwave heating temperature control; defining performance indicators, and constructing a comprehensive fitness function J based on weight coefficients; wherein the performance indicators include the integral ITAE of time multiplied by absolute error and the standard deviation of temperature distribution σ. T Average power P avg S1. The maximum overshoot OS; and the determination of control variables, including microwave power P and heating time t; S2. Based on the feasible region of the control variables, an initial whale population containing multiple individuals is randomly generated; wherein the position vector of each individual corresponds to a set of controller parameters to be optimized; S3. Simulation evaluation is performed on each individual in the initial whale population; the controller parameters corresponding to the individual are input into the microwave heating system simulation model to obtain the temperature response data of the system, and the value of the comprehensive fitness function J defined in S1 is calculated based on the temperature response data; S4. The adaptive whale optimization algorithm is iterated to update the whale population; wherein during the iteration process, the probability threshold p used to select the encirclement mechanism or the spiral update mechanism is dynamically adjusted according to the standard deviation of the temperature distribution; S5. When the iteration termination condition is met, the globally optimal individual is output, and its corresponding controller parameters are applied to the actual microwave heating control system.

[0007] Preferably, in step S4, the specific process of executing the adaptive whale optimization algorithm iteration and updating the whale population is as follows: First, the whales engage in encirclement hunting, conducting a global exploration of the search space to find potential prey; the whale population will then move towards the optimal individual according to the following formula:

[0008] in, Indicates the first The position of the first whale at time t+1 in the next generation. To indicate the first The position of the first whale at time t. Let t represent the optimal position of the whale, and t be the current iteration number; where A is the random search coefficient and C is the random perturbation coefficient; then, a bubble net attack is performed. After prey is found, the bubble net hunting behavior of a humpback whale is simulated; the shrinking encirclement mechanism or the spiral update position is selected according to the random probability p; when p < 0.5, the encirclement phase is entered; when p ≥ 0.5, the spiral hunting phase is entered, and the update expression is as follows:

[0009] Where b is the helical shape coefficient; Given a random number uniformly distributed within the interval [-1, 1]; finally, perform a random search, when... When the value is greater than 1, the global exploration phase begins. A random whale individual is selected as a reference for global exploration, and the update expression is as follows:

[0010] In the formula, The location of an individual randomly selected in the t-th generation whale population.

[0011] Preferably, in step S4, the probability threshold used to select the encirclement mechanism or the spiral update mechanism is dynamically adjusted based on the standard deviation of the temperature distribution. The specific formula is as follows:

[0012] Where k is the current iteration number; The basic probability; where This is a uniformity-driven adjustment term; To optimize the phase-driven adjustment items.

[0013] Preferably, wherein As a uniformity-driven adjustment term, it specifically responds to the non-uniformity of the temperature field. The higher the non-uniformity, the more it tends to select the spiral renewal mechanism that promotes local equilibrium, i.e., it increases... The optimized formula adopts an S-shaped response function and introduces a threshold and saturation mechanism:

[0014] in -0.5 maps the output range to [-0.5, 0.5]. The uniformity threshold; For scale parameters; This is the maximum adjustment range coefficient.

[0015] Preferably, The calculation formula is:

[0016] In the formula, The strength coefficient is adjusted in stages; This represents the maximum number of iterations.

[0017] Preferably, in step S1, the formula for the comprehensive fitness function J is:

[0018] Among them, w1, w2, w3, and w4 are adjustable weight coefficients.

[0019] Preferably, the controller parameter in step S2 is the proportional coefficient k of the PID controller. p Integral coefficient k i and the wind coefficient k d .

[0020] Preferably, in step S5, the controller parameters are applied to the actual microwave heating control system, using an incremental PID control algorithm. The formula for calculating the control quantity u(k) is: u(k) = u(k-1) + k p [e(k) e(k-1)]+k i e(k)+k d [e(k)-2e(k-1)+e(k-2)] where e(k) is the temperature difference at the current moment; k p k i k d These are the optimal PID parameters that have been tuned.

[0021] Preferably, in step S1, the control variables further include the phase angle φ and frequency f of multiple microwave sources.

[0022] The present invention also discloses a microwave heating temperature control system based on an adaptive whale optimization algorithm, comprising a memory and a processor connected to each other, wherein the memory stores a computer program, and the computer program executes the steps of the method described above when run by the processor.

[0023] Compared with existing technologies, the advantages of this invention are as follows: This invention possesses powerful global optimization capabilities: WOA can effectively escape local optima and find superior PID parameters or control sequences that are difficult to discover using traditional methods, making it particularly suitable for nonlinear systems such as microwave heating; it is independent of mathematical models: unlike traditional model predictive control, this method does not require high model accuracy. It evaluates parameter quality through input and output data and can adapt to the slow drift of system parameters (such as the dielectric constant of materials changing with temperature); when system characteristics change, WOA can be restarted for parameter tuning, or online rolling optimization can naturally adapt to such changes; flexibility: the fitness function can be flexibly designed to simultaneously optimize multiple objectives, such as speed, stability, uniformity, and energy consumption, achieving multi-objective optimization. Attached Figure Description

[0024] Figure 1 is a flowchart of the microwave heating temperature control method of the present invention in an embodiment.

[0025] Figure 2 is an embodiment of the microwave heating temperature control method of the present invention in a specific application. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0027] As shown in Figure 1, the microwave heating temperature control method based on the adaptive whale optimization algorithm provided in this embodiment of the invention transforms the microwave heating temperature control problem into an optimization problem. Utilizing the powerful global search capability of the whale optimization algorithm, it finds the optimal control strategy or parameters to solve problems such as nonlinearity, time-varying nature, and spatial inhomogeneity in microwave heating. The specific steps are as follows: S1. Construct a multi-objective optimization problem for microwave heating temperature control; Define the control objective: Through microwave heating, enable the actual temperature of the material to quickly, stably, and accurately track the preset process temperature curve, and minimize spatial temperature differences; The controlled object is the microwave heating system (including the magnetron, cavity, and heated material); The control variables are microwave power P and heating time t (in more complex systems, this may also include the phase and frequency (if adjustable) of multiple microwave sources); Based on the integral ITAE (the integral of time multiplied by the absolute error, penalizing persistent errors), the maximum overshoot OS, and the standard deviation σ of the temperature distribution... T (Measures spatial uniformity), average power P avg A comprehensive performance index, including weighting coefficients w, is defined as the fitness function J of WOA, specifically:

[0028] Where w1, w2, w3, and w4 are the adjustable weight coefficients corresponding to each item, which can be dynamically adjusted according to process requirements; S2. Encode the three parameters of the PID controller into the position vector of an individual "whale"; then initialize it, and within a reasonable range of parameters, randomly generate a group of "whales" (i.e., multiple sets of PID parameters) to form an initial whale population; S3. Evaluate the initial whale population, and for each individual in the initial whale population (i.e., each set of PID parameters), substitute it into the microwave heating control system simulation model (usually, a verified mathematical model is used for simulation first to save costs and avoid risks), run the simulation, obtain the temperature response curve of the system, and calculate the value of its fitness function J based on the temperature response curve; where the smaller the J value, the better the performance of the set of parameters.

[0029] S4. Execute the Whale Adaptive Optimization (WOA) algorithm iteration. WOA simulates the cruising foraging (global exploration) and attacking predation (local exploitation) behavior of whales. It updates the positions of all squids based on their fitness values, thus generating new parameter combinations. This is an iterative process that continuously eliminates poor-performing parameter combinations and searches for regions with better performance.

[0030] Specifically, the proportional coefficient k in the PID controllerp Integral coefficient k i and the wind coefficient k d The iteration process mainly consists of three stages: encirclement and predation, bubble net attack, and search and foraging. The first stage is encirclement and predation, where the whale conducts a global search of the search space to find potential prey (the optimal solution area).

[0031] Whale populations will converge toward the optimal individual according to the following formula:

[0032] in, Indicates the first The position of the first whale at time t+1 in the next generation. To indicate the first The position of the first whale at time t. Let A represent the optimal position of the whale, and t be the current iteration number; where A is the random search coefficient and C is the random perturbation coefficient.

[0033]

[0034]

[0035] Where r1 and r2 are random numbers between [0,1]; a is a convergence factor that decreases linearly from 2 to 0; and Max_I represents the maximum number of iterations.

[0036] Following this, a bubble-net attack is initiated. Upon spotting prey, the bubble-net hunting behavior of a humpback whale is simulated. The whale algorithm selects either a shrinking encirclement mechanism or a spiral update position based on a random probability p (a random number within [0,1]). When p < 0.5, the encirclement phase begins; when p ≥ 0.5, the spiral hunting phase begins. The update expression is as follows:

[0037] Where b is the helical shape coefficient; Given a random number uniformly distributed within the interval [-1, 1]; finally, perform a random search, when... When the value is greater than 1, the global exploration phase begins, randomly selecting one whale individual as a reference for global exploration. The update expression is as follows:

[0038] In the formula, The location of an individual randomly selected in the t-th generation whale population.

[0039] Where the standard deviation σ of the temperature distribution is... TThe random probability p of spiral renewal and predation encirclement is dynamically adjusted; when temperature non-uniformity is high, the spiral renewal probability is increased to enhance the ability to achieve local temperature equilibrium. Specifically, the probability... The formula is:

[0040] Where k is the current iteration number; Based on the basic probability, such as ;in As a uniformity-driven adjustment term, it specifically responds to the non-uniformity of the temperature field. The higher the non-uniformity, the more it tends to select the spiral renewal mechanism that promotes local equilibrium, i.e., it increases... The optimized formula adopts an S-shaped response function and introduces a threshold and saturation mechanism:

[0041] in -0.5 maps the output range to [-0.5, 0.5]. The uniformity threshold; For scale parameters; This is the maximum adjustment range coefficient; where To optimize the phase-driven adjustment items, the strategy bias is adjusted according to the optimization progress, specifically as follows:

[0042] In the formula, The intensity coefficient is adjusted for each stage; in the initial iteration, For larger positive values, increasing p tends to favor spiral updates (spiral updates have a certain local development capability while exploring, making them suitable for finding promising regions in a large area in the early stages); in the later stages of iteration, When p becomes negative, it decreases and tends to shrink the confluence; this facilitates a finer search near the already discovered optimal solution, thus accelerating convergence.

[0043] S5. When the maximum number of iterations is reached or the fitness value meets the requirements, stop the search, output the globally optimal individual (PID parameter combination), that is, terminate the output, and apply the tuned optimal PID parameters to the actual microwave heating control system.

[0044] As shown in Figure 2, the PID controller uses an incremental PID algorithm. Based on the deviation e(k) between the target value r(k) and the actual output value y(k), i.e., e(k) = r(k) - y(k), the output control quantity u(k) at the current time k is adjusted to: u(k) = u(k-1) + k p [e(k) e(k-1)]+k i e(k)+k d[e(k)-2e(k-1)+e(k-2)] where: k p k i k d These are the optimal PID parameters that have been tuned above; k represents the sampling time.

[0045] This invention addresses several inherent problems of traditional microwave heating methods for kilns, including low thermal efficiency, difficulty in exhaust gas emission and treatment, difficulty in controlling temperature uniformity, system complexity, and potential safety hazards. Specifically, it designs a microwave heating temperature control method based on the Whale Optimization Algorithm (WOA), representing a technical path that deeply integrates nature-inspired intelligent optimization with advanced process control. By transforming complex control problems into intelligent search problems, it provides a novel and effective solution for overcoming core challenges in microwave heating (such as nonlinearity, thermal runaway, and non-uniformity), achieving the following technical advantages: superior global search capability: The WOA's bubble net mechanism (spiral update) effectively coordinates global exploration and local development, avoiding premature convergence and increasing the likelihood of finding globally optimal or suboptimal controller parameters / control sequences.

[0046] Strong robustness: It has excellent adaptability to the nonlinear and time-varying changes in the dielectric properties of materials with temperature during microwave heating. When process conditions change, WOA can be restarted for parameter tuning, or online rolling optimization can naturally compensate for such changes.

[0047] Avoid model dependence: Unlike traditional MPC, which requires an accurate model, the WOA-PID scheme is based entirely on input and output data. WOA-MPC also has relatively relaxed requirements for the accuracy of the prediction model and focuses more on compensating for model errors through optimization.

[0048] Multi-objective optimization potential: By cleverly designing the fitness function, multiple objectives such as dynamic performance (e.g., rise time, overshoot), steady-state performance (e.g., accuracy), economy (e.g., energy consumption) and spatial uniformity can be optimized simultaneously.

[0049] This invention possesses powerful global optimization capabilities: WOA can effectively escape local optima and find superior PID parameters or control sequences that are difficult to discover using traditional methods, making it particularly suitable for nonlinear systems such as microwave heating; it is independent of mathematical models: unlike traditional model predictive control, this method does not require high model accuracy. It evaluates parameter quality through input and output data and can adapt to the slow drift of system parameters (such as the dielectric constant of materials changing with temperature); when system characteristics change, WOA can be restarted for parameter tuning, or online rolling optimization can naturally adapt to such changes; it is flexible: the fitness function can be flexibly designed to simultaneously optimize multiple objectives, such as speed, stability, uniformity, and energy consumption, achieving multi-objective optimization.

[0050] This invention also discloses a microwave heating temperature control system based on an adaptive whale optimization algorithm, comprising an interconnected memory and a processor. The memory stores a computer program, which, when run by the processor, executes the steps of the method described above. The control system of this invention corresponds to the control method described above and also possesses the advantages described therein.

[0051] The present invention can implement all or part of the processes in the methods of the above embodiments, or it can be implemented by hardware related to computer program instructions. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above method embodiments. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable storage medium includes: any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. The memory is used to store computer programs and / or modules. The processor implements various functions by running or executing the computer programs and / or modules stored in the memory, and by calling data stored in the memory. The memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0052] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A microwave heating temperature control method based on an adaptive whale optimization algorithm, characterized in that, The steps include: S1. Constructing a multi-objective optimization problem for microwave heating temperature control; defining performance indices and constructing a comprehensive fitness function J based on weighting coefficients; wherein the performance indices include the integral ITAE of time multiplied by absolute error and the standard deviation of temperature distribution σ. T Average power P avg and maximum overshoot OS; And determine the control variables, including microwave power P and heating time t; S2. Based on the feasible domain of the control variables, an initial whale population containing multiple individuals is randomly generated; wherein the position vector of each individual corresponds to a set of controller parameters to be optimized; S3. Simulation evaluation is performed on each individual in the initial whale population; the controller parameters corresponding to the individual are input into the microwave heating system simulation model to obtain the temperature response data of the system, and the value of the comprehensive fitness function J defined in S1 is calculated based on the temperature response data; S4. Execute the adaptive whale optimization algorithm iteration to update the whale population; During the iteration process, the probability threshold p used to select the encirclement mechanism or the spiral update mechanism is dynamically adjusted according to the standard deviation of the temperature distribution; S5. When the iteration termination condition is met, the global optimal individual is output, and its corresponding controller parameters are applied to the actual microwave heating control system.

2. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to claim 1, characterized in that, In step S4, the adaptive whale optimization algorithm is iterated, and the specific process of updating the whale population is as follows: First, the whales engage in encirclement hunting, conducting a global search of the search space to find potential prey; the whale population will then move towards the optimal individual according to the following formula: in, Indicates the first The position of the first whale in the next generation at t+1. To indicate the first The position of the first whale at time t. Let t represent the optimal position of the whale, and t be the current iteration number; where A is the random search coefficient and C is the random perturbation coefficient; then, a bubble net attack is performed. After prey is found, the bubble net hunting behavior of a humpback whale is simulated; the shrinking encirclement mechanism or the spiral update position is selected according to the random probability p; when p < 0.5, the encirclement phase is entered; when p ≥ 0.5, the spiral hunting phase is entered, and the update expression is as follows: Where b is the helical shape coefficient; Given a random number uniformly distributed within the interval [-1, 1]; finally, perform a random search, when... When the value is greater than 1, the global exploration phase begins. A random whale individual is selected as a reference for global exploration, and the update expression is as follows: In the formula, The location of an individual randomly selected in the t-th generation whale population.

3. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to claim 2, characterized in that, In step S4, the probability threshold used to select the encirclement mechanism or the spiral update mechanism is dynamically adjusted based on the standard deviation of the temperature distribution. The specific formula is as follows: Where k is the current iteration number; Basic probability; in This is a uniformity-driven adjustment term; To optimize the phase-driven adjustment items.

4. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to claim 3, characterized in that, in As a uniformity-driven adjustment term, it specifically responds to the non-uniformity of the temperature field. The higher the non-uniformity, the more it tends to select the spiral renewal mechanism that promotes local equilibrium, i.e., it increases... The optimized formula adopts an S-shaped response function and introduces a threshold and saturation mechanism: in -0.5 maps the output range to [-0.5, 0.5]. The uniformity threshold; For scale parameters; This is the maximum adjustment range coefficient.

5. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to claim 3, characterized in that, The calculation formula is: In the formula, The strength coefficient is adjusted in stages; This represents the maximum number of iterations.

6. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to any one of claims 1-5, characterized in that, In step S1, the formula for the comprehensive fitness function J is: Among them, w1, w2, w3, and w4 are adjustable weight coefficients.

7. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to any one of claims 1-5, characterized in that, The controller parameter in step S2 is the proportional coefficient k of the PID controller. p Integral coefficient k i and the wind coefficient k d .

8. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to any one of claims 1-5, characterized in that, In step S5, the controller parameters are applied to the actual microwave heating control system, using an incremental PID control algorithm. The formula for calculating the control quantity u(k) is: u(k) = u(k-1) + k p [e(k) e(k-1)]+k i e(k)+k d [e(k)-2e(k-1)+e(k-2)] where e(k) is the temperature difference at the current moment; k p k i k d These are the optimal PID parameters that have been tuned.

9. The microwave heating temperature control method based on the adaptive whale optimization algorithm according to any one of claims 1-5, characterized in that, In step S1, the control variables also include the phase angle φ and frequency f of multiple microwave sources.

10. A microwave heating temperature control system based on an adaptive whale optimization algorithm, comprising an interconnected memory and a processor, wherein the memory stores a computer program, characterized in that, The computer program, when run by a processor, performs the steps of the method as described in any one of claims 1-9.

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