A metamaterial wireless passive temperature sensor high q value design optimization method and system

Abstract

The application discloses a metamaterial wireless passive temperature sensor high-q value design optimization method and system, and belongs to the technical field of sensor design, which determines the outer ring length, ring width, ring opening width and interval between two rings of a square double-loop structure as key geometric parameters, and takes the resonant frequency and quality factor as performance indexes; a metamaterial structure-performance dataset is constructed through full-wave electromagnetic simulation; a resonant frequency Kriging surrogate model and a quality factor Kriging surrogate model are trained based on the dataset; a multi-objective genetic algorithm is adopted to obtain a Pareto optimal solution set with the optimization objectives of resonant frequency maximization and quality factor maximization; and the best scheme is determined through an information entropy weight method combined with an ideal solution approximation sorting technology. The application can realize fast prediction of the structure performance of a metamaterial sensor, multi-objective collaborative optimization and automatic selection of a design scheme.

Description

Technical Field

[0001] This invention belongs to the field of sensor design technology, specifically relating to a high q-value design optimization method and system for a metamaterial wireless passive temperature sensor. Background Technology

[0002] In aerospace, gas turbine, and energy equipment industries, engine hot-end components, combustion chambers, turbine blades, and high-temperature structural parts are subjected to prolonged exposure to high temperatures, strong vibrations, strong electromagnetic interference, and confined spaces. Their temperature status directly impacts equipment operational safety, thermal protection design, and lifespan assessment. Traditional wired temperature sensors require lead wires and power or signal transmission channels. In high-temperature rotating parts, enclosed cavities, or deeply embedded structures, they are easily limited by wiring space, insulation reliability, lead wire fatigue, and maintenance difficulty, making it difficult to meet the requirements for long-term stable monitoring under complex operating conditions. Therefore, wireless passive temperature sensors, which do not require built-in power supplies and signal lines, are gradually becoming an important technological direction for temperature sensing in high-temperature environments.

[0003] Existing wireless passive temperature sensors mainly include near-field coupled LC sensors, surface acoustic wave (SAW) sensors, and microwave scattering wireless passive temperature sensors. Near-field coupled LC sensors have a simple structure, but their readout distance is relatively short, their quality factor is low, and they are easily affected by eddy current losses when attached to or near metal surfaces, leading to a broadening of the resonance peak, signal attenuation, and decreased recognition accuracy. SAW sensors can achieve passive wireless measurement, but they typically have high requirements for piezoelectric substrate materials and packaging processes. At relatively low operating frequencies, the interrogation antenna size is large, which is not conducive to integrated applications in compact spaces such as aerospace. In contrast, microwave scattering wireless passive temperature sensors utilize the electromagnetic interaction between incident microwaves and the sensor's metal structure to generate a temperature-sensitive resonant response (such as frequency shift), and transmit temperature information through backscattered signals. They have advantages such as better penetration, stronger resistance to environmental interference, and suitability for long-distance readout.

[0004] In microwave scattering-type wireless passive temperature sensors, the metallic structure serves as both a resonator (its size determines its inherent resonant frequency) and a scattering antenna. Its geometry and dimensions directly determine the sensor's resonant frequency, quality factor, and temperature recognition capability. Metamaterial structures, especially square double-open-loop structures, can generate strong electromagnetic field localization effects in the openings, edges, and inter-loop regions, which is beneficial for forming a sharper resonant response and improving the recognizability of temperature-induced frequency shifts. Therefore, using a square double-open-loop structure as the metallic resonant structure in a wireless passive temperature sensor is an important way to improve the sensor's sensitivity and resolution.

[0005] However, the structural design of existing metamaterial wireless passive temperature sensors still mainly relies on empirical selection, parameter scanning, or a limited number of orthogonal experiments. For square double-open-loop structures, there is a strong coupling relationship between key geometric parameters such as the outer ring length, ring width, ring opening width, and the spacing between the two rings. Changes in any parameter may simultaneously affect the resonant frequency, quality factor, and resonant peak morphology. In particular, high quality factor design usually requires reducing losses or changing the equivalent electromagnetic dimensions, but this adjustment may cause a decrease in resonant frequency or a shift in the operating frequency band, resulting in a performance trade-off between resonant frequency and quality factor that is difficult to reconcile.

[0006] Furthermore, a clear high-dimensional, nonlinear mapping relationship exists between metamaterial structural parameters and sensor electromagnetic response; even minute changes in structural parameters can lead to significant fluctuations in the resonant response. Directly relying on full-wave electromagnetic simulation for point-by-point searching is not only computationally expensive but also difficult to cover the continuous design space. If discrete sampling methods such as orthogonal experiments are used, optimal combinations can usually only be selected from a limited number of sampling points, making it difficult to obtain global optimization results and even more difficult to conduct objective and quantitative comprehensive evaluations among multiple performance indicators.

[0007] Therefore, existing methods lack a systematic design approach that can simultaneously achieve rapid structure-performance prediction, multi-objective collaborative optimization, and automatic selection of the optimal solution, which limits the design efficiency and engineering application reliability of high-Q structure for metamaterial wireless passive temperature sensors. Summary of the Invention

[0008] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a high q-value design optimization method and system for metamaterial wireless passive temperature sensors. This method addresses the problem that existing metamaterial wireless passive temperature sensors have strong coupling and nonlinear mapping between their square double open-loop structure parameters, resonant frequency, and quality factor. Relying on empirical trial and error, parameter scanning, or discrete experiments makes it difficult to simultaneously consider resonant frequency and quality factor within a continuous design space, and it is also difficult to automatically select the optimal engineering-available solution.

[0009] The present invention adopts the following technical solution: A high-q value design optimization method for a metamaterial wireless passive temperature sensor includes the following steps: S1. Determine the key geometric parameters and performance indicators of the square double open-ring structure. The key geometric parameters include the outer ring length, ring width, ring opening width, and the interval between the two rings. The performance indicators include the resonant frequency and the quality factor. Generate multiple sets of structural parameter combinations within the preset value range of each key geometric parameter, and obtain the resonant frequency and quality factor corresponding to each structural parameter combination through full-wave electromagnetic simulation to construct a metamaterial structure-performance dataset. S2. Based on the metamaterial structure-performance dataset, train the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model respectively. S3. Using the key geometric parameters as variables to be optimized, with the optimization objectives of maximizing the resonant frequency and maximizing the quality factor, the resonant frequency is predicted by calling the Kriging surrogate model, the quality factor is predicted by calling the Kriging surrogate model, and a multi-objective genetic algorithm is used to obtain the Pareto optimal solution set. S4. By combining the information entropy weight method with the approximation ideal solution sorting technique, the candidate structure schemes in the Pareto optimal solution set are sorted, and the candidate structure scheme with the best sorting result is determined as the best scheme.

[0010] Furthermore, in step S1, the outer ring length ranges from 11mm to 19mm, and the ring width, ring opening width, and the interval between the two rings all range from 0.1mm to 1.5mm.

[0011] Furthermore, in step S1, the multiple sets of structural parameter combinations are generated through simple random sampling, orthogonal experimental design, or Latin hypercube sampling.

[0012] Furthermore, in step S1, the full-wave electromagnetic simulation is a full-wave electromagnetic simulation based on the finite element method, and the core performance indicators of the sensor corresponding to each combination of structural parameters are obtained through the full-wave electromagnetic simulation.

[0013] Furthermore, in step S2, before training the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model, the structural parameters and performance response data in the metamaterial structure-performance dataset are normalized respectively, and the normalized metamaterial structure-performance dataset is divided into a training set and a test set.

[0014] Furthermore, in step S2, both the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model include zero-mean Gaussian processes of polynomial basis functions, regression coefficients, and covariance functions, and the Kriging model is established using a Gaussian correlation function.

[0015] Furthermore, the maximum likelihood estimation method is used to evaluate the hyperparameters in the Gaussian correlation function, and the predicted mean and variance of the test sample are calculated based on the evaluated hyperparameters.

[0016] Further, in step S3, the multi-objective genetic algorithm is the NSGA-II algorithm, which includes: determining the upper and lower bounds of the variable to be optimized and generating a random initial population; calling the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model to predict the resonant frequency and quality factor of individuals in the population; performing selection, crossover, and mutation operations on the population to generate offspring; merging the parent and offspring to form a new population; calculating the objective function value and crowding degree corresponding to the new population, and using fast non-dominated sorting to divide individuals into Pareto front layers of different priorities; selecting a new generation of population based on the distance between the non-dominated level and the crowding degree, until the preset maximum number of generations is reached, and then outputting the first non-dominated layer as the Pareto optimal solution set.

[0017] Further, in step S4, the Pareto optimal solution set is used to construct an original decision matrix, and the original decision matrix is ​​standardized; the information entropy weighting method is used to determine the weight coefficients of the resonant frequency and the quality factor; a weighted standardized decision matrix is ​​constructed based on the weight coefficients, and the positive ideal solution and the negative ideal solution are determined; the distance between each candidate structural scheme and the positive ideal solution and the negative ideal solution is calculated, and the relative proximity coefficient of each candidate structural scheme is calculated based on the distance, and the candidate structural schemes are ranked by the relative proximity coefficient.

[0018] Secondly, embodiments of the present invention provide a high-q value design optimization system for a metamaterial wireless passive temperature sensor, comprising: The metamaterial structure-performance dataset construction module is used to determine the key geometric parameters and performance indicators of a square double-open-ring structure. The key geometric parameters include the outer ring length, ring width, ring opening width, and the spacing between the two rings. The performance indicators include the resonant frequency and the quality factor. It is also used to generate multiple sets of structural parameter combinations within the preset value range of each key geometric parameter, and obtain the resonant frequency and quality factor corresponding to each structural parameter combination through full-wave electromagnetic simulation, thereby constructing the metamaterial structure-performance dataset. The structure-performance parameter mapping relationship construction module is used to train the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model respectively based on the metamaterial structure-performance dataset. The sensor structure adaptive global optimization module is used to take the key geometric parameters as the variables to be optimized, with the optimization objectives of maximizing the resonant frequency and maximizing the quality factor. It calls the Kriging surrogate model of the resonant frequency to predict the resonant frequency, calls the Kriging surrogate model of the quality factor to predict the quality factor, and uses a multi-objective genetic algorithm to obtain the Pareto optimal solution set. The global optimization performance evaluation module is used to sort the candidate structural schemes in the Pareto optimal solution set by combining the information entropy weight method with the approximation ideal solution sorting technique, and to determine the candidate structural scheme with the best sorting result as the best scheme.

[0019] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described high-q value design optimization method for a metamaterial wireless passive temperature sensor.

[0020] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described high-q value design optimization method for a metamaterial wireless passive temperature sensor.

[0021] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described high-q value design optimization method for a metamaterial wireless passive temperature sensor.

[0022] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described high q-value design optimization method for a metamaterial wireless passive temperature sensor.

[0023] Compared with the prior art, the present invention has at least the following beneficial effects: A high-q-value design optimization method for metamaterial wireless passive temperature sensors is proposed. This method involves a complete process: constructing a metamaterial structure-performance dataset, using a Kriging surrogate model, employing a multi-objective genetic algorithm, and combining an information entropy weighting method to approximate the ideal solution ranking technique. This forms a design strategy and performance-optimization collaborative analysis framework for microwave scattering wireless passive metallic metamaterial structures. Using the outer ring length, ring width, ring opening width, and spacing between the two rings of a square double-open-ring structure as structural parameters, and resonant frequency and quality factor as performance indicators, a closed-loop design approach consisting of data-driven, model-predictive, intelligent optimization, and scheme evaluation is realized. This approach can replace traditional empirical trial and error and discrete parameter screening, improving the systematicity, efficiency, and quantifiability of high-q-value structure design for metamaterial wireless passive temperature sensors.

[0024] Furthermore, the outer ring length, ring width, ring opening width, and spacing between the two rings directly affect the equivalent inductance, equivalent capacitance, resonant frequency, and loss characteristics of the square double open-ring structure. By limiting the range of values ​​for these parameters, the optimization search is constrained within a structural space that conforms to the actual operating frequency band and fabrication feasibility, avoiding the generation of invalid solutions with abnormal dimensions or difficult fabrication by the optimization algorithm. This improves the engineering applicability of the sensor structure obtained from subsequent proxy modeling and intelligent optimization.

[0025] Furthermore, employing simple random sampling, orthogonal experimental design, or Latin hypercube sampling to generate structural parameter combinations can cover different parameter regions with limited samples, providing a better spatial distribution foundation for metamaterial structure-performance datasets. Due to the complex coupling relationships between the parameters of the square double open-loop structure, it helps the Kriging surrogate model learn the variation patterns between different structural combinations and resonant frequencies and quality factors, improving the reliability of subsequent structural parameter-to-sensor performance index prediction models.

[0026] Furthermore, full-wave electromagnetic simulation based on the finite element method can simulate the electromagnetic response of a square double-open-loop structure under microwave excitation, reflecting the localized electromagnetic field effects in the opening, edges, and regions between the two rings, and thereby extracting the resonant frequency and quality factor. This ensures that the structure-performance dataset is derived from high-fidelity electromagnetic simulation, rather than simple equivalent circuits or empirical estimations, thus providing a physically reliable data foundation for accurate predictions and global optimization using the Kriging model.

[0027] Furthermore, normalizing the structural parameters and performance response data can eliminate dimensional and numerical scale differences between different parameters and performance indicators, reducing computational bias during model training. Dividing the dataset into training and test sets allows verification of the Kriging surrogate model's predictive ability for unknown combinations of structural parameters. This facilitates statistical mapping and rapid evaluation of performance within the design space, reducing the risk of the surrogate model overfitting existing simulation samples.

[0028] Furthermore, the Kriging model describes the overall trend through multinomial basis functions and the spatial correlation between samples through a zero-mean Gaussian process of the covariance function, making it suitable for handling high-dimensional, nonlinear mapping relationships between metamaterial structural parameters and electromagnetic responses. Establishing Kriging surrogate models for resonant frequency and quality factor separately can improve the specificity of predictions for different performance indicators, enabling accurate prediction, statistical mapping, and rapid evaluation from structural parameters to sensor performance indicators.

[0029] Furthermore, the maximum likelihood estimation method is used to evaluate the hyperparameters in the Gaussian correlation function. This allows for the automatic determination of the sample correlation scale based on existing structure-performance data, reducing subjective errors caused by manually setting parameters. Further calculation of the predicted mean and variance of the test samples not only yields the predicted performance values ​​corresponding to unknown structural parameter combinations but also reflects prediction uncertainty, providing a reliable basis for the rapid evaluation of a large number of candidate structures during the optimization process of multi-objective genetic algorithms.

[0030] Furthermore, the NSGA-II algorithm is employed for multi-objective collaborative optimization, simultaneously maximizing the resonant frequency and the quality factor. This avoids the resonant frequency deviating from the target operating region due to simply pursuing a high q value, or reducing the sharpness of the resonant peak due to simply pursuing the resonant frequency. Through fast non-dominated sorting and crowding distance filtering, the Pareto optimal front after global optimization can be obtained, enabling different structural schemes to form comparable performance trade-offs between resonant frequency and quality factor, and providing a set of candidate schemes for intelligent optimization of sensor structures.

[0031] Furthermore, multiple candidate structural schemes in the Pareto optimal front exhibit different performance trade-offs, making it difficult to determine the final structure solely based on human experience. By combining the information entropy weighting method with the approximation ideal solution ranking technique, the weights of the resonant frequency and quality factor can be objectively determined according to the information entropy weighting method. The candidate structural schemes are then ranked using positive ideal solutions, negative ideal solutions, and relative proximity coefficients, thereby automatically selecting the optimal scheme suitable for actual sensor manufacturing and testing. This provides a scientific evaluation method and quantitative reference for the engineering application of sensor design schemes.

[0032] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0033] In summary, this invention establishes a closed-loop optimization process for the structural design of metamaterial wireless passive temperature sensors by employing full-wave electromagnetic simulation, Kriging proxy model, multi-objective genetic algorithm, and an approximation ideal solution sorting technique combined with information entropy weighting. This process can quickly predict the resonant frequency and quality factor of different square double open-loop structures, obtain the Pareto optimal frontier that balances operating frequency band and high Q value, and automatically select the best solution suitable for manufacturing and testing, thereby improving design efficiency and engineering applicability.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0035] Figure 1 This is a diagram illustrating the overall technical framework of the present invention; Figure 2 This is a schematic diagram of the temperature sensor structure of the present invention; Figure 3 This is a schematic diagram showing the boundary condition settings for the temperature sensor simulation modeling of the present invention; Figure 4 The overall process of a multi-objective intelligent optimization method with embedded agent model; Figure 5The prediction results of the surrogate model are as follows: (a) resonant frequency prediction results on the training set, (b) resonant frequency prediction results on the test set, (c) quality factor prediction results on the training set, and (d) quality factor prediction results on the test set. Figure 6 The results of adaptive global optimization of sensor structure based on intelligent algorithms and the evaluation results of global optimization performance; Figure 7 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 8 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0036] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0037] 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, not all, of the embodiments of the present invention. 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.

[0038] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0039] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0040] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B indicates three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0041] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0042] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0043] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0044] This invention provides a high-q value design optimization method for metamaterial wireless passive temperature sensors. It constructs a data-driven intelligent optimization framework with the simultaneous maximization of the resonant frequency and quality factor of the metamaterial sensor's structural parameters as the multi-objective optimization goal. This framework embeds a high-precision Kriging surrogate model into the fitness evaluation loop of the NSGA-II algorithm, thereby replacing time-consuming full-wave electromagnetic simulation with instantaneous model prediction, achieving a leap in optimization efficiency. Specifically, through the construction of a square double open-loop structure and full-wave electromagnetic simulation, the response values ​​of each sample point are determined, and the influence of structural parameters is initially obtained. Then, using randomly sampled structures and performance parameters obtained from simulation, a training set containing finite structures and corresponding performance parameters is constructed. A high-performance Kriging surrogate model is trained based on the training set to establish a precise mapping relationship between structural parameters and sensor performance. Finally, the trained Kriging surrogate model is used as a fast predictor to evaluate the performance of arbitrary structural parameters during the optimization process, and a set of Pareto front solutions is generated through the NSGA-II global optimization algorithm, providing a strong basis for the sensor's structural design. Furthermore, by employing an approximation ideal solution ranking technique combined with the information entropy weighting method, the optimal solution suitable for practical sensor manufacturing and testing is automatically selected from multiple frontier solutions, providing a quantitative reference for the final sensor structure selection. This invention establishes a new paradigm of "data-driven - model prediction - intelligent optimization" for the design of microwave scattering wireless passive temperature sensors, deepening the understanding of the mechanism of the complex relationship between metamaterial structures and sensor performance, and providing a reliable tool for its high-performance design.

[0045] Please see Figure 1 This invention discloses a high-q value design optimization method for a metamaterial wireless passive temperature sensor, comprising the following steps: S1, Construction of the metamaterial structure-performance dataset; First, the key geometric parameters and performance indicators of the metamaterials were determined. Then, an initial set of metamaterial structures was generated using typical sampling methods. Subsequently, high-fidelity simulations of each set of parameters were performed using full-wave electromagnetic simulation software based on the finite element method to obtain the corresponding core sensor performance indicators. Finally, a metamaterial structure-performance dataset was constructed based on the above simulation data.

[0046] S101. Determine the key geometric parameters and performance indicators of metamaterials; Based on the working mechanism of the wireless passive temperature sensor and the basic geometry of the metamaterial structure, the key geometric parameters are determined, and the key performance indicators are determined through the sensor's working principle and practical application requirements.

[0047] Please see Figure 2The wireless passive temperature sensor operates based on the microwave scattering mechanism, and its core sensing unit adopts a square double-open-ring resonator structure. The square double-open-ring structure is made of platinum metal and is determined by four key geometric parameters: the outer ring length l, the ring width t, the opening width s, and the inter-ring spacing g. The resonant frequency is inherently sensitive to disturbances in its electromagnetic environment and geometric structure.

[0048] The resonant frequency of a sensor is a key indicator of its performance. The sensor's temperature-sensitive function is achieved through the thermal response characteristics of the substrate material, which is alumina ceramic with a circular structure. The alumina substrate has a positive temperature coefficient of dielectric constant; its dielectric constant increases with temperature, thus enhancing the structure's equivalent capacitance and causing the resonant frequency to drift towards lower frequencies with increasing temperature. The quality factor (Q factor) of the sensor's resonance is another key indicator of its performance. It is defined as the ratio of stored energy at resonance to energy lost per cycle. A high Q value indicates low loss, manifested as a sharp and narrow resonance peak. From a sensing perspective, a high Q value directly improves detection accuracy and resolution. The sharp resonance peak allows for the clear identification of minute frequency shifts caused by temperature changes, thereby improving the signal-to-noise ratio and overall sensitivity of the wireless measurement system. Therefore, resonant frequency and quality factor are chosen as performance indicators.

[0049] S102. Generate an initial set of metamaterial structures using typical sampling methods; First, considering the operating frequency band of the actual sensor and the constraints of the fabrication process, the value ranges of each parameter are set to ensure the practicality and manufacturability of the design space. Then, an initial set of metamaterial structures is generated through typical sampling methods such as simple random sampling, orthogonal experimental design, and Latin hypercube sampling. The definitions and value ranges of each structural parameter are shown in Table 1: Table 1 Dimensional parameters of metamaterial temperature sensors

[0050] S103. Simulation is performed using full-wave electromagnetic simulation software based on the finite element method. For the initial set of metamaterial structures, a simulation finite element model is constructed using full-wave electromagnetic simulation software based on the finite element method, and the performance indicators corresponding to each metamaterial structure are calculated.

[0051] For the initial set of metamaterial structures, high-fidelity simulations of each set of parameters were performed using COMSOL Multiphysics, a full-wave electromagnetic simulation software based on the finite element method, to obtain the corresponding core sensor performance indicators: resonant frequency and quality factor. Numerical simulations were performed using the FEM tool in COMSOL Multiphysics 6.3, and the constructed simulation finite element model is shown below. Figure 3 As shown.

[0052] To analyze the transmission and resonance characteristics of a planar helical electromagnetic component, a rectangular simulation cavity model based on a PEC / PMC hybrid boundary was constructed. The upper and lower surfaces of the cavity were designed as ideal electrical conductors (PEC) to simulate the metallic shielding effect; the remaining four sidewalls were designed as ideal magnetic conductors (PMC) to constrain the electromagnetic field modes and simplify calculations. Signal excitation and response measurement were achieved through two orthogonally placed lumped ports: port 1 was fed along the x-direction, and port 2 acquired the signal along the y-direction, thus fully characterizing the electromagnetic coupling and scattering characteristics of the device in a two-dimensional plane. A physical field-controlled mesh was used in the simulation. The number of mesh points was 663,864. The simulation model accurately constructed the electromagnetic response environment of the sensor in the microwave frequency band, ensuring the physical accuracy of the data generation.

[0053] S104, Training Dataset Construction and Preprocessing.

[0054] The structural parameters and performance metrics are mapped one-to-one to form a complete dataset, which is then normalized to eliminate the influence of units. The dataset is further divided into training and testing sets.

[0055] Based on the characteristics of the square double-open-ring structure of the metamaterial unit, four parameters—outer ring length, ring width, ring opening width, and the spacing between the two rings—are selected to describe the square double-open-ring structure. COMSOL simulations are used to obtain the dimensional values ​​of the square double-open-ring structure parameters, along with the sensor's resonant frequency and quality factor data.

[0056] Based on the simulation results, a dataset was constructed. To ensure the stability and efficiency of the surrogate model training, the input structural parameters and output performance response data were normalized and preprocessed before being input into the Kriging model, mapping them to the interval [-1, 1]. This step aims to eliminate computational biases that may be caused by differences in the units and numerical ranges of different parameters, thereby improving the convergence speed and prediction accuracy of the model. Finally, a complete dataset with 71 sets of "structure-performance" pairs constitutes the training dataset for the Kriging surrogate model, providing a reliable data foundation for subsequent structural optimization.

[0057] In addition, when training the Kriging agent model, the dataset was divided into two parts: 80% for training and 20% for validation, to further verify the model's generalization performance on unknown data.

[0058] S2. Construction of structure-performance parameter mapping relationship based on agent model; High-performance surrogate models are constructed to model the complex, high-dimensional, nonlinear mapping relationship between structural parameters and electromagnetic responses, providing a large number of new structural performance features for intelligent optimization algorithms.

[0059] Kriging models are employed as high-performance surrogate models. Kriging models possess excellent global approximation capabilities, considering the spatial location and correlation of known sample data to provide linear and unbiased estimations of the samples to be tested. This is crucial for guiding optimization searches with limited samples. Through forced interpolation characteristics and a probabilistic framework based on spatial correlation, Kriging models achieve high-precision fitting and rapid prediction of sensor performance in high-dimensional design spaces using only 71 sets of high-fidelity simulation samples, significantly reducing dependence on simulation data while maintaining accuracy. This characteristic makes Kriging models particularly suitable for the optimization tasks of metamaterial structures with multi-parameter coupling and complex response surfaces in this invention, laying a reliable and efficient surrogate foundation for subsequent multi-objective collaborative optimization based on intelligent algorithms. The specific implementation process is as follows: Let the input vector be... Then the corresponding random response Represented as: (1) in, These are polynomial basis functions. These are the corresponding regression coefficients. Indicates the trend of the Gaussian process; It is a zero-mean Gaussian process with a covariance function, expressed as: (2) in, Indicates the variance of a Gaussian process; It is a related function A set of hyperparameters. This invention uses the commonly used Gaussian correlation function to establish the Kriging model, defined as: (3) in, n It is the number of input variables. Indicates the corresponding to the first k The relevant parameters of each variable, and They are points and The k The coordinates are then used. The maximum likelihood estimation method is then used to evaluate the hyperparameters. Then the regression coefficients and variance are... The calculation is as follows: (4) (5) in, It is a matrix, where , It is a matrix, where .

[0060] Then, the predicted mean at a new point and variance The estimate is as follows: (6) (7) (8) in, It is a matrix, and its elements are defined as follows: .

[0061] Due to the complex and inconsistent coupling relationships and sensitivity characteristics between multiple performance parameters and the structure, independent surrogate models are constructed for different performance indicators to obtain a more targeted mapping relationship between structural parameters and sensor electromagnetic responses. The models are then trained and optimized based on the constructed training sets.

[0062] During the experiment, a high-performance Kriging surrogate model was established using MATLAB. Due to the complex and inconsistent coupling relationships and sensitivity characteristics between multiple performance parameters and the structure, this invention addresses the resonant frequency separately. With quality factor Q An independent Kriging surrogate model was constructed to obtain a more targeted mapping relationship between structural parameters and sensor electromagnetic response. The model was trained based on 71 sets of high-fidelity training samples obtained through full-wave electromagnetic simulation. After experiments with different hyperparameter selections, the final parameters of the Kriging model are shown in Table 2, and a high-performance trained Kriging model was obtained.

[0063] Table 2 Kriging model parameters

[0064] The Kriging model was used to establish a framework for predicting the sensor resonant frequency and quality factor of a square double open-loop structure under fixed size constraints, thereby enabling efficient prediction of the sensor resonant frequency and quality factor under different combinations of structural parameters.

[0065] S3. Sensor structure adaptive global optimization based on intelligent algorithms; Based on the mapping relationship between structural parameters and electromagnetic response of the trained high-performance surrogate model, a multi-objective collaborative optimization is performed using an intelligent optimization algorithm to obtain a set of Pareto optimal frontier solutions representing the best performance.

[0066] Please see Figure 4The NSGA-II algorithm is used to achieve multi-objective collaborative optimization. First, the upper and lower bounds of the variables to be optimized are determined, and a random initial population is generated. Then, a trained surrogate model is used as a fast predictor to evaluate the performance of arbitrary structural parameters during the optimization process, expressed as: (9) (10) in, To design variable vectors, the algorithm does not perform time-consuming and labor-intensive real simulations in each generation of optimization. Instead, it directly calls the surrogate model to predict the values ​​of all individuals in the population. and value.

[0067] Subsequently, appropriate optimization objectives are designed based on actual needs. Maximizing both the resonant frequency and the quality factor are set as the two optimization objectives. The algorithm performs genetic operations such as selection, crossover, and mutation on the population to generate offspring, and merges the parents and offspring to form a new population. The objective function value and crowding degree corresponding to the new population are calculated, and individuals are divided into Pareto front layers of different priorities using fast non-dominated sorting. Simultaneously, the crowding distance of individuals within the same non-dominated layer in the objective space is calculated to assess their distribution diversity. Based on the criteria of non-dominated level and crowding distance, the algorithm selects a new generation of population, thereby guiding the population to converge to the optimal front while maintaining a good solution set distribution breadth. This iterative process continues until the preset maximum number of generations is reached, finally outputting the first non-dominated layer, which is the Pareto optimal solution set that satisfies both maximizing the resonant frequency and maximizing the quality factor. Subsequent final decisions are made based on specific applications. Furthermore, structures with the maximum quality factor in different frequency bands can be selected based on the Pareto optimal solution set to meet the needs of different scenarios, demonstrating broad adaptability and convenience.

[0068] S4. Global optimization performance evaluation; The intelligent optimization algorithm outputs a Pareto optimal front containing multiple non-dominated solutions, each of which achieves a different trade-off between maximizing the resonant frequency and the quality factor. Based on adaptive sorting technology, it automatically selects the best solution suitable for actual sensor manufacturing and testing, scientifically and transparently screening out the single implementation scheme with the most comprehensive advantages from multiple equally excellent non-dominated solutions, thus perfecting the final link from automated design to engineering application.

[0069] This invention employs an approximation-ideal-solution ranking technique combined with information entropy weighting. This method ranks candidate solutions from best to worst. The optimal design should simultaneously be "closest" to the positive ideal solution composed of the optimal values ​​of each indicator in the multi-objective space, and "farthest" from the negative ideal solution composed of the worst values ​​of each indicator. This entropy-weighted TOPSIS decision-making process combines the automatically generated Pareto solution set with objective data-driven weights, effectively and accurately evaluating each Pareto solution. It scientifically and transparently selects the unique implementation scheme with the most comprehensive advantages from multiple non-dominated solutions, facilitating implementation from automated design to engineering applications.

[0070] Specifically, the Pareto solution set generated by the NSGA-II algorithm is used to construct the original decision matrix as follows: (11) in, Indicates the first i The first scheme j The value of each evaluation indicator m and n These refer to the number of design schemes and performance indicators, respectively.

[0071] First, the matrix is ​​standardized to eliminate the influence of dimensions: (12) To objectively reflect the relative importance of each indicator in decision-making and avoid bias from subjective weighting, this study uses the information entropy weighting method to automatically determine the weights. Information entropy measures the dispersion of the indicator data; the smaller the value, the greater the difference between different options and the more information it provides, thus warranting a higher weight in decision-making. Weight calculation is based on standardized data, ensuring the objectivity of weight allocation and data-driven characteristics. Therefore, the entropy method is used to determine the weight coefficients of each evaluation indicator. Information Entropy The calculation formula is: (13) in, For adjustment coefficients; Yes The result of standardization.

[0072] The weighting coefficients of each performance index are calculated using the entropy weighting method. The calculation formula is as follows: (14) Taking into account the weighting coefficients of each performance metric, the regularization results are weighted as follows: (15) in, It is the weight factor of the j-th indicator.

[0073] Obtaining the weights of each indicator Then, a weighted standardized decision matrix is ​​constructed. Subsequently, the positive ideal solution, composed of the optimal values ​​of each indicator, is determined. and the negative ideal solution composed of the worst values ​​of each index Ideal solutions and negative ideal solutions can be defined as follows: (16) For the two evaluation indices of resonant frequency and quality factor in this invention, the positive ideal solution is composed of the maximum value of each index, and the negative ideal solution is composed of the minimum value of each index. This is expressed as: (17) Subsequently, the Euclidean distance between each Pareto solution and the positive and negative ideal solutions was calculated. and The calculation is as follows: (18) in, and These represent the distances between the alternative solution and the ideal solution and the negative ideal solution, respectively.

[0074] Relative proximity coefficient of each scheme Defined as its relative proximity to the negative ideal solution, i.e.: (19) pass Rank the various options. The range of is [0, 1]. The larger the value, the closer the scheme is to the positive ideal solution and the farther it is from the negative ideal solution, and the better its overall performance. Therefore, it has the maximum The optimal compromise design point is determined by the chosen solution. The structural parameters corresponding to this point (outer ring length, ring width, opening width, and ring spacing) achieve a balanced design that maximizes the relative quality factor while satisfying the frequency constraint, providing a clear basis for subsequent sensor fabrication and experimental verification.

[0075] This entropy-weighted TOPSIS decision-making process combines the Pareto solution set automatically generated by the algorithm with objective data-driven weights, scientifically and transparently selecting the unique implementation scheme with the most comprehensive advantages from multiple equally excellent non-dominated solutions, thus perfecting the final link from automated design to engineering application.

[0076] In another embodiment of the present invention, a high q-value design optimization system for a metamaterial wireless passive temperature sensor is provided. This system can be used to implement the above-mentioned high q-value design optimization method for a metamaterial wireless passive temperature sensor. Specifically, the high q-value design optimization system for a metamaterial wireless passive temperature sensor includes a metamaterial structure-performance dataset construction module, a structure-performance parameter mapping relationship construction module, a sensor structure adaptive global optimization module, and a global optimization performance evaluation module.

[0077] The metamaterial structure-performance dataset construction module is used to determine the key geometric parameters and performance indicators of the square double open-ring structure. The key geometric parameters include the outer ring length, ring width, ring opening width, and the interval between the two rings. The performance indicators include the resonant frequency and the quality factor. It is also used to generate multiple sets of structural parameter combinations within the preset value range of each key geometric parameter, and obtain the resonant frequency and quality factor corresponding to each structural parameter combination through full-wave electromagnetic simulation to construct the metamaterial structure-performance dataset. The structure-performance parameter mapping relationship construction module is used to train the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model respectively based on the metamaterial structure-performance dataset. The sensor structure adaptive global optimization module is used to take the key geometric parameters as the variables to be optimized, with the optimization objectives of maximizing the resonant frequency and maximizing the quality factor. It calls the Kriging surrogate model of the resonant frequency to predict the resonant frequency, calls the Kriging surrogate model of the quality factor to predict the quality factor, and uses a multi-objective genetic algorithm to obtain the Pareto optimal solution set. The global optimization performance evaluation module is used to sort the candidate structural schemes in the Pareto optimal solution set by combining the information entropy weight method with the approximation ideal solution sorting technique, and to determine the candidate structural scheme with the best sorting result as the best scheme.

[0078] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used in the operation of a high-q value design optimization method for metamaterial wireless passive temperature sensors, including: The key geometric parameters and performance indicators of a square double-open-ring structure are determined. The key geometric parameters include the outer ring length, ring width, ring opening width, and the spacing between the two rings. The performance indicators include the resonant frequency and the quality factor. Multiple sets of structural parameter combinations are generated within preset value ranges for each key geometric parameter. The resonant frequency and quality factor corresponding to each structural parameter combination are obtained through full-wave electromagnetic simulation, constructing a metamaterial structure-performance dataset. Based on the metamaterial structure-performance dataset, a resonant frequency Kriging surrogate model and a quality factor Kriging surrogate model are trained respectively. Using the key geometric parameters as the variables to be optimized, and maximizing the resonant frequency and quality factor as the optimization objectives, the resonant frequency Kriging surrogate model is used to predict the resonant frequency, and the quality factor Kriging surrogate model is used to predict the quality factor. A multi-objective genetic algorithm is used to obtain the Pareto optimal solution set. By combining the information entropy weight method with the approximation ideal solution ranking technique, the candidate structural schemes in the Pareto optimal solution set are ranked, and the candidate structural scheme with the best ranking result is determined as the optimal scheme.

[0079] Please see Figure 7The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the high-q-value design optimization method for the metamaterial wireless passive temperature sensor in this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the high-q-value design optimization system for the metamaterial wireless passive temperature sensor in this embodiment. To avoid repetition, details are omitted here.

[0080] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 7 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0081] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0082] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0083] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0084] Please see Figure 8 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0085] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

[0086] Storage unit 620 may include readable media in the form of volatile storage units, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include read-only memory (ROM) 6203.

[0087] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0088] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0089] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0090] This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0091] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0092] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0093] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the high-q value design optimization method for metamaterial wireless passive temperature sensors in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps: The key geometric parameters and performance indicators of a square double-open-ring structure are determined. The key geometric parameters include the outer ring length, ring width, ring opening width, and the spacing between the two rings. The performance indicators include the resonant frequency and the quality factor. Multiple sets of structural parameter combinations are generated within preset value ranges for each key geometric parameter. The resonant frequency and quality factor corresponding to each structural parameter combination are obtained through full-wave electromagnetic simulation, constructing a metamaterial structure-performance dataset. Based on the metamaterial structure-performance dataset, a resonant frequency Kriging surrogate model and a quality factor Kriging surrogate model are trained respectively. Using the key geometric parameters as the variables to be optimized, and maximizing the resonant frequency and quality factor as the optimization objectives, the resonant frequency Kriging surrogate model is used to predict the resonant frequency, and the quality factor Kriging surrogate model is used to predict the quality factor. A multi-objective genetic algorithm is used to obtain the Pareto optimal solution set. By combining the information entropy weight method with the approximation ideal solution ranking technique, the candidate structural schemes in the Pareto optimal solution set are ranked, and the candidate structural scheme with the best ranking result is determined as the optimal scheme.

[0094] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0095] 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0096] Through hyperparameter tuning, model training, and testing, the constructed Kriging surrogate model achieved satisfactory fit results on both evaluation metrics. Figure 5 As shown, for the two indices, the results predicted by the Kriging model are in high agreement with the actual simulation results. On the training set, the R-values ​​of the two indices are... 2 With all values ​​being 1, the intrinsic relationship between structural parameters and performance can be learned excellently with limited training data. On the test set, the resonant frequency... R 2 The quality factor reached 0.9294. Q R 2 A score of 0.7483 is achieved, meeting the accuracy requirements of the conceptual design phase. In the following sections, the trained model will be combined with an evolutionary algorithm to provide performance parameters for various structures of the evolutionary model in a very short time.

[0097] Please see Figure 6 Through the study of existing simulation points, it can be found that there is a conflicting relationship between the two optimization objectives; the improvement of one objective comes at the expense of the performance of the other. Therefore, the NSGA-II genetic algorithm is used for optimization, aiming to simultaneously maximize the resonant frequency. and quality factor Q To achieve the objective, a global search is performed in the design space. The algorithm achieves a uniformly distributed Pareto front in the solution space through non-dominated sorting and crowding distance sorting, effectively handling conflicts between objectives. Using a grid search strategy, the population size of the NSGA-II algorithm is ultimately set to 100, the maximum number of generations to 30, the crossover rate to 0.95, and the mutation rate to 0.15. After multiple rounds of iterative calculations, the Pareto optimal solution is finally determined. Figure 6The Pareto optimal front obtained after iterative search using the NSGA-II algorithm is shown. It can be seen that the overall performance of the structure optimized by the NSGA-II algorithm is located to the right and top of the simulation results, indicating that the optimized result has superior overall performance. Based on this, we obtained multiple sets of structures that meet specific frequency band requirements and have high quality factors in the frequency band of interest (5.4-5.7). We automatically obtained the optimal structure using a global optimization performance evaluation method based on a sorting technique for approximating ideal solutions combined with information entropy weighting, and this method can be extended to the design requirements of other frequency bands for the same structure. It is worth noting that our Kriging model is a general model, providing a powerful tool for the design of similar structures and broadening the horizons for the design of more complex metamaterial structures.

[0098] Furthermore, in terms of computational efficiency, performance fitting based on the Kriging model plays a crucial role in the multi-objective joint optimization process. The NSGA-II algorithm generates 100 new generation structures per round, resulting in 3000 structures over 30 iterations. Each structure requires over an hour of simulation time, a computational burden that is unacceptable in temperature sensor structure optimization. In contrast, the proposed method can complete 30 iterations within 2 minutes, obtaining a high-performance sensor structure with minimal computational cost.

[0099] After obtaining the Pareto front, we selected the optimal points within the frequency band of interest for structural simulation and experimental verification. Additionally, several points were randomly selected for simulation testing to fully verify the accuracy of the model's fitting performance. Using the structural parameters of these optimized points, the performance response of the structure was obtained using COMSOL Multiphysics software and then compared with the predicted objective function value.

[0100] Table 3 Comparison of optimized values ​​and actual results within the target frequency band

[0101] Table 3 shows the comparison between the optimized predicted values ​​and the simulated values, demonstrating good consistency and proving the reliability and superiority of the proposed structural optimization method.

[0102] The optimization results show that, compared with the traditional simulation optimization method, the proposed method can improve the quality factor by 8%-28% while obtaining similar characteristic frequencies, effectively improving the transmission performance of the wireless passive temperature sensor.

[0103] Table 4. Final sensor structure parameters adopted

[0104] Finally, the optimal scheme of adaptive calculation using the approximation ideal solution sorting technique is used as the structure of our sensor, and its structural parameters and corresponding performance are shown in Table 4.

[0105] In summary, this invention presents a high-q-value design optimization method and system for a metamaterial wireless passive temperature sensor. It establishes a data-driven mapping relationship between structural parameters and sensor performance by using the outer ring length, ring width, ring opening width, and spacing between the two rings of a square double-open-ring structure as key geometric parameters, and resonant frequency and quality factor as performance indicators. High-fidelity structure-performance data is obtained through full-wave electromagnetic simulation, ensuring the physical reliability of the surrogate model training data. A Kriging surrogate model replaces numerous repetitive simulations, enabling rapid prediction and statistical evaluation of performance within the design space. A multi-objective genetic algorithm simultaneously optimizes the resonant frequency and quality factor, obtaining a Pareto optimal front that balances the operating frequency band and high Q-value. Finally, by combining the information entropy weight method with an approximation-ideal solution ranking technique, the optimal solution with the best overall performance is automatically selected from multiple non-dominated structural schemes. Therefore, this invention reduces the uncertainty caused by empirical trial and error and discrete parameter selection, improving the structural design efficiency, optimization accuracy, and engineering application adaptability of the metamaterial wireless passive temperature sensor.

[0106] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0107] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0108] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0109] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0110] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0111] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0112] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A high-q value design optimization method for a metamaterial wireless passive temperature sensor, characterized in that, Includes the following steps: S1. Determine the key geometric parameters and performance indicators of the square double open-ring structure. The key geometric parameters include the outer ring length, ring width, ring opening width, and the interval between the two rings. The performance indicators include the resonant frequency and the quality factor. Generate multiple sets of structural parameter combinations within the preset value range of each key geometric parameter, and obtain the resonant frequency and quality factor corresponding to each structural parameter combination through full-wave electromagnetic simulation to construct a metamaterial structure-performance dataset. S2. Based on the metamaterial structure-performance dataset, train the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model respectively. S3. Using the key geometric parameters as variables to be optimized, with the optimization objectives of maximizing the resonant frequency and maximizing the quality factor, the resonant frequency is predicted by calling the Kriging surrogate model, the quality factor is predicted by calling the Kriging surrogate model, and a multi-objective genetic algorithm is used to obtain the Pareto optimal solution set. S4. By combining the information entropy weight method with the approximation ideal solution sorting technique, the candidate structure schemes in the Pareto optimal solution set are sorted, and the candidate structure scheme with the best sorting result is determined as the best scheme.

2. The high q-value design optimization method for metamaterial wireless passive temperature sensors according to claim 1, characterized in that, In step S1, the length of the outer ring ranges from 11mm to 19mm, and the width of the ring, the width of the ring opening, and the interval between the two rings all range from 0.1mm to 1.5mm.

3. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S1, the multiple sets of structural parameter combinations are generated through simple random sampling, orthogonal experimental design, or Latin hypercube sampling.

4. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S1, the full-wave electromagnetic simulation is a full-wave electromagnetic simulation based on the finite element method, and the core performance indicators of the sensor corresponding to each combination of structural parameters are obtained through the full-wave electromagnetic simulation.

5. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S2, before training the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model, the structural parameters and performance response data in the metamaterial structure-performance dataset are normalized respectively, and the normalized metamaterial structure-performance dataset is divided into a training set and a test set.

6. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S2, both the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model include zero-mean Gaussian processes of polynomial basis functions, regression coefficients, and covariance functions, and the Kriging model is established using the Gaussian correlation function.

7. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 6, characterized in that, The hyperparameters in the Gaussian correlation function are evaluated using the maximum likelihood estimation method, and the predicted mean and variance of the test sample are calculated based on the evaluated hyperparameters.

8. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S3, the multi-objective genetic algorithm is the NSGA-II algorithm. The NSGA-II algorithm includes: determining the upper and lower bounds of the variable to be optimized and generating a random initial population; calling the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model to predict the resonant frequency and quality factor of individuals in the population; performing selection, crossover, and mutation operations on the population to generate offspring; merging the parent and offspring to form a new population; calculating the objective function value and crowding degree corresponding to the new population, and using fast non-dominated sorting to divide individuals into Pareto front layers of different priorities; selecting a new generation of population based on the distance between the non-dominated level and the crowding degree, until the preset maximum number of generations is reached, and then outputting the first non-dominated layer as the Pareto optimal solution set.

9. The high q-value design optimization method for a metamaterial wireless passive temperature sensor according to claim 1, characterized in that, In step S4, the Pareto optimal solution set is used to form an original decision matrix, and the original decision matrix is ​​standardized; the information entropy weighting method is used to determine the weight coefficients of the resonant frequency and the quality factor; a weighted standardized decision matrix is ​​constructed based on the weight coefficients, and the positive ideal solution and the negative ideal solution are determined. Calculate the distance between each candidate structural scheme and the positive ideal solution and the negative ideal solution, and calculate the relative proximity coefficient of each candidate structural scheme based on the distance. Then, rank the candidate structural schemes based on the relative proximity coefficient.

10. A high-q value design optimization system for a metamaterial wireless passive temperature sensor, characterized in that, include: The metamaterial structure-performance dataset construction module is used to determine the key geometric parameters and performance indicators of a square double-open-ring structure. The key geometric parameters include the outer ring length, ring width, ring opening width, and the spacing between the two rings. The performance indicators include the resonant frequency and the quality factor. It is also used to generate multiple sets of structural parameter combinations within the preset value range of each key geometric parameter, and obtain the resonant frequency and quality factor corresponding to each structural parameter combination through full-wave electromagnetic simulation, thereby constructing the metamaterial structure-performance dataset. The structure-performance parameter mapping relationship construction module is used to train the resonant frequency Kriging surrogate model and the quality factor Kriging surrogate model respectively based on the metamaterial structure-performance dataset. The sensor structure adaptive global optimization module is used to take the key geometric parameters as the variables to be optimized, with the optimization objectives of maximizing the resonant frequency and maximizing the quality factor. It calls the Kriging surrogate model of the resonant frequency to predict the resonant frequency, calls the Kriging surrogate model of the quality factor to predict the quality factor, and uses a multi-objective genetic algorithm to obtain the Pareto optimal solution set. The global optimization performance evaluation module is used to sort the candidate structural schemes in the Pareto optimal solution set by combining the information entropy weight method with the approximation ideal solution sorting technique, and to determine the candidate structural scheme with the best sorting result as the best scheme.

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