An inductive conductivity sensor probe parameter intelligent optimization method

Abstract

The application discloses an intelligent optimization method for parameters of an inductive conductivity sensor probe, and belongs to the technical field of fiber grating sensing, which is used for optimizing probe parameters and comprises the following steps: an initial simulation sample library is generated by constructing a probe parameterized simulation model, and a comprehensive objective function containing linearity, output voltage, loss and volume is established; a Gaussian process regression proxy model is trained by using the sample library, and a predicted mean value and a standard deviation are output; a confidence upper bound acquisition function is constructed, the function is maximized in a feasible parameter space to actively recommend a next set of simulation parameter combinations; after high-fidelity simulation verification, the sample library is updated and iteratively optimized until the optimal parameters are output. The application realizes global optimization under a limited number of simulations, effectively balances exploration and development, significantly reduces the calculation cost, simultaneously meets multi-objective engineering constraints, and is suitable for efficient and accurate design of inductive conductivity sensor probes.

Description

Technical Field

[0001] This invention relates to the field of fiber optic grating sensing technology, and more particularly to the field of fiber optic grating signal processing technology, specifically to an intelligent optimization method for the probe parameters of an inductive conductivity sensor. Background Technology

[0002] Electrical conductivity is an important physical quantity characterizing the ability of a medium to conduct electricity, and it is widely used in seawater salinity measurement, industrial water quality monitoring, environmental monitoring, and deep-sea exploration. Traditional electrode-type conductivity sensors achieve measurement by direct contact between the electrodes and the measured medium, offering high sensitivity, but are susceptible to factors such as electrode polarization, corrosion, biofouling, and contaminant deposition.

[0003] Inductive conductivity sensors utilize the electromagnetic induction relationship between an alternating magnetic field and a conductive medium for non-contact measurement. They offer advantages such as corrosion resistance, contamination resistance, and suitability for long-term in-situ monitoring; however, their measurement performance is highly dependent on probe parameters. Existing probe parameter optimization schemes include:

[0004] (1) Experience-based trial and error and physical prototype verification scheme;

[0005] First, the initial frequency, core size, and number of coil turns of the probe are determined based on experience. Then, a prototype is fabricated and the relationship between output voltage and conductivity is measured through standard solution experiments. Subsequently, the probe structure and probe parameters are modified based on the experimental results. This approach relies on manual experience, has a long development cycle, and high processing and testing costs. It is difficult to fully grasp the coupling relationship between parameters such as excitation frequency, core size, number of coil turns, and current channel size before the probe is manufactured.

[0006] (2) Parameter scanning scheme based on multiphysics simulation;

[0007] A probe model of an inductive conductivity sensor is established using multiphysics simulation software. Parameters such as excitation frequency, magnetic ring size, and coil turns are parametrically scanned to obtain results including output voltage, linearity, loss distribution, and magnetic field distribution. Designers then select appropriate parameters based on the simulation curves. While this approach relies solely on multiphysics simulation or full-parameter scanning to reduce physical trial and error, it still requires a large number of simulations in high-dimensional parameter spaces. Furthermore, simulation results typically depend on manual comprehensive consideration, making it difficult to simultaneously address multiple constraints such as linearity, sensitivity, energy loss, and miniaturization, and hindering the formation of a repeatable and scalable intelligent optimization loop.

[0008] (3) Parameter determination scheme based on geometric and frequency comprehensive factor and thermomagnetic balance factor;

[0009] Chinese invention patent CN120781575B discloses a method for rapidly determining the parameters of an inductive conductivity sensor probe. This method is based on the electromagnetic induction principle and skin effect characteristics of the inductive conductivity sensor, introducing a probe geometry-frequency comprehensive factor and a thermomagnetic balance factor to establish a quantitative correlation between parameters. It also combines multiphysics simulation to achieve rapid optimization of probe parameters, enabling coordinated matching of parameters such as excitation frequency, magnetic ring size, spacing, and number of turns, and verifying the rationality of the parameters before actual fabrication. While this scheme can quickly determine a set of feasible probe parameters, it lacks predictive ability for unsimulated regions in the parameter space and lacks an intelligent optimization mechanism that actively selects the next set of simulation parameters based on model uncertainty, easily leading to local optima or redundant simulations.

[0010] Therefore, there is an urgent need to develop a method that can predict the performance of unknown regions with a limited multiphysics simulation budget, perform global optimization in a higher-dimensional parameter space with fewer high-fidelity simulations, and actively recommend the next set of parameters with the greatest optimization potential through Bayesian optimization. This would form a closed-loop optimization method of simulation, learning, recommendation, verification, and updating, thereby improving the efficiency and accuracy of probe parameter determination and meeting the actual needs of rapid development of high-performance probes under complex engineering constraints. Summary of the Invention

[0011] The purpose of this invention is to provide an intelligent optimization method for the probe parameters of an inductive conductivity sensor, in order to solve the technical problems in the prior art, such as low optimization efficiency of probe parameters and difficulty in achieving global optimization under limited budget, due to the high cost of multiphysics simulation calculation and the difficulty in covering high-dimensional parameter space.

[0012] To address the above objectives, this invention provides a method for intelligent optimization of probe parameters in an inductive conductivity sensor, comprising: S1. Determine the design variables and parameter range for probe parameter optimization, construct a probe parameter simulation model, set the design variables as automatically updatable global parameters, generate multiple sets of candidate parameter combinations within the parameter range, input the probe parameter vectors of each candidate parameter combination into the probe parameter simulation model to run the simulation, and obtain the performance data of each candidate parameter combination. S2. Construct a comprehensive objective function. Based on the performance data obtained in S1, calculate the comprehensive objective function value of each candidate parameter combination and construct a simulation sample library. S3. Using the probe parameter vectors of various parameter combinations in the simulation sample library as input and the comprehensive objective function value of the probe parameter vectors as output, construct and train the GPR surrogate model. S4. After training, construct an optimized acquisition function based on the predicted mean and predicted standard deviation output by the GPR proxy model, calculate the optimization value of each candidate parameter combination, and output the recommended parameter combination. S5. Input the probe parameter vector of the recommended parameter combination into the probe parameter simulation model to run the simulation, obtain the performance data of the recommended parameter combination, calculate the comprehensive objective function value of the recommended parameter combination and update the simulation sample library; S6. Based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination, the GPR surrogate model is iteratively converged and verified, and the optimal probe parameter combination is output.

[0013] In S1, the probe parameter vector is: ; In the formula, Represents the probe parameter vector. Indicates the excitation frequency. Indicates the number of turns of the excitation coil. To detect the number of coil turns, Indicates the inner radius of the magnetic ring. Indicates the outer radius of the magnetic ring. Indicates the coil spacing. Indicates the length of the magnetic core; Within the parameter range, multiple sets of candidate parameter combinations are generated using Latin hypercube sampling, orthogonal experimental design, uniform design, Sobol sequence sampling, or a hybrid sampling method combining engineering experience. The performance data for each candidate parameter combination includes output voltage data, electromagnetic field distribution data, and loss distribution data under different simulation medium conditions.

[0014] In S2, the comprehensive objective function is: ; ; ; In the formula, express The comprehensive objective function value, , express Intermediate calculation parameters, Indicates after normalization linearity, Indicates after normalization The output voltage, Indicates after normalization Core loss, Indicates after normalization Coil copper loss, Indicates after normalization The probe volume, , , , , They represent , , , , The weighting coefficients.

[0015] The core loss is: ; ; In the formula, express The core loss per unit volume, express The volume of the magnetic core, , , These are the Steinmetz coefficients. express excitation frequency, express The maximum magnetic flux density of the magnetic core; The coil copper loss is: ; In the formula, Indicates the coil current. express The square of, express The DC resistance of the coil, Indicates the skin effect coefficient; The probe volume is: ; In the formula, express The outer radius of the magnetic ring, express The length of the magnetic core, express The coil spacing.

[0016] In S6, the GPR surrogate model is iteratively converged and verified based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination. When the training process of the GPR surrogate model does not meet the iterative convergence condition, the process returns to step S3 until the training process of the GPR surrogate model meets the iterative convergence condition. Then, the recommended parameter combination output in the last iteration is taken as the optimal probe parameter combination, and the probe parameters of the optimal probe parameter combination and the performance data of the optimal parameter combination are output.

[0017] The simulation sample library is as follows: ; In the formula, Indicates the iteration count index. Indicates the first Simulation sample library during round iteration, express The number of simulation samples in the middle, Indicates the simulation sample index. Indicates the first One simulation sample, Indicates the first The probe parameter vector of a simulated sample, express The comprehensive objective function value.

[0018] The optimized acquisition function is as follows: ; In the formula, Indicates the first Optimize the acquisition function value through round-by-round iteration. Indicates the first The predicted mean of each iteration, Indicates the first The standard deviation of the prediction in each iteration. Indicates the exploration coefficient; Within the set of valid parameters, a maximum search is performed on the optimal acquisition function value to output a recommended parameter combination: ; In the formula, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. The effective parameter set consists of combinations of candidate parameters that satisfy the engineering optimization constraints. To maximize the search function.

[0019] Engineering optimization constraints include: ; ; ; In the formula, Indicates minimum linearity. Indicates the maximum allowable power consumption. This indicates the maximum permissible probe volume.

[0020] The iterative convergence condition for iterative convergence verification of the GPR surrogate model is: ; In the formula, express The comprehensive objective function value, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. This indicates the number of iterations for consecutive comparisons. This represents the convergence threshold.

[0021] The GPR surrogate model characterizes the comprehensive objective function through a Gaussian process. By building an approximate model on simulation samples, it outputs the comprehensive objective function value of parameter combinations that have not yet participated in the simulation. After the GPR surrogate model is trained, for any parameter combination input to the GPR surrogate model, the GPR surrogate model outputs the predicted mean and predicted standard deviation of the parameter combination.

[0022] Compared with the prior art, the present invention has the following beneficial effects: This invention requires only initial samples and several rounds of Bayesian optimization to obtain optimal solutions, which significantly reduces the number of high-fidelity simulations compared to full-parameter scanning and improves computational efficiency. In addition, each Bayesian optimization recommendation is verified by high-fidelity simulation and fed back to the sample library. The surrogate model is gradually refined with iteration, making the optimization process adaptive and convergent, and finally outputting a parameter combination that simultaneously satisfies engineering constraints and has the best overall performance. This invention provides prediction uncertainty through the GPR model and constructs a data acquisition function to balance exploration and development, avoiding local convergence caused by simply relying on the current optimal value, and is able to find the globally optimal parameter combination with a higher probability. This invention incorporates linearity, output voltage, core loss, copper loss, and volume into a unified weighted objective function, and the weights can be flexibly adjusted to adapt to different application scenarios such as deep-sea low power consumption, high-precision measurement, or miniaturized design, overcoming the subjectivity and inconsistency of manual multi-index trade-offs. The proxy model provided by this invention does not depend on specific simulation software and can also use neural networks, random forests, etc. to replace simulation software; the acquisition function can be selected in various forms such as expectation improvement and probability improvement, and has good portability and adaptability. Attached Figure Description

[0023] Figure 1 The overall flowchart of the intelligent optimization method for probe parameters provided by the present invention; Figure 2 This invention provides an architecture diagram of the intelligent probe parameter optimization system. Figure 3 The Bayesian-optimized line graph provided by this invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] Figure 1 The overall flowchart of the intelligent optimization method for the probe parameters of an inductive conductivity sensor provided by the present invention is as follows: Figure 1 As shown, the design variables and parameter ranges of the probe are first determined, a COMSOL parametric simulation model is established, and initial samples are generated for simulation. Performance indicators and comprehensive objective functions are calculated to construct a simulation sample library. Subsequently, a GPR surrogate model is trained using the sample library data. Based on the predicted mean and standard deviation of the model output, a Bayesian optimization acquisition function is constructed to obtain candidate parameter combinations. Then, COMSOL high-fidelity simulation is used to verify and update the simulation sample library. It is determined whether the iterative convergence condition has been met. If the convergence condition is not met, the process returns to retraining the GPR surrogate model to carry out iterative optimization. When the convergence condition is met, the optimal probe parameter combination and its performance data are output, realizing the intelligent optimization design of multiple parameters of the inductive conductivity sensor probe.

[0026] Figure 2 The system module architecture diagram for intelligent optimization of inductive conductivity sensor probe parameters is as follows: Figure 2 As shown, the system consists of multiple functional modules. The parameter range setting module inputs parameter boundary conditions to the parameterized simulation model module and the initial sample generation module, respectively. The initial sample generation module outputs initial samples to the simulation sample library module. The data from the simulation sample library module is input to the performance evaluation module to calculate performance indicators and the comprehensive objective function. The calculation results are sent to the GPR surrogate model module to train the Gaussian process regression surrogate model. After training, the Bayesian optimization module calculates candidate parameter combinations. The candidate parameter combinations are input to the simulation verification module, which calls the parameterized simulation model module to conduct high-fidelity simulations. The simulation results are sent to the sample library update module to expand the simulation sample library. Subsequently, the results are sent to the convergence judgment unit. If convergence fails, the updated sample library is re-input to the performance evaluation module, and the iterative process of surrogate model training, Bayesian optimization, and simulation verification is repeated. If convergence is achieved, the optimal probe parameters are output. The candidate parameter combinations are fed back to the simulation verification module, forming a closed-loop iterative optimization system.

[0027] Figure 3Record the performance index corresponding to the current optimal parameter combination after each round of Bayesian optimization iteration. The horizontal axis represents the Bayesian optimization round, the left vertical axis represents the comprehensive objective function value, and the right vertical axis represents the output voltage (mV). The two curves in the figure respectively represent the changing trends of the comprehensive objective function value and output voltage of the optimal parameter combination with the optimization round during the iteration process. Figure 3 As shown, with the increase of Bayesian optimization iterations, both the overall objective function value and the output voltage show an upward trend. The performance indicators improve significantly in the early stages of optimization. However, in the later stages of iteration, the growth of the two curves gradually slows down and becomes stable, indicating that the algorithm continuously searches for better probe parameter combinations. The overall performance of the probe and the output voltage gradually improve. In the later stages of iteration, the optimization results tend to converge, resulting in a probe parameter scheme with better performance.

[0028] Example 1 A method for intelligent optimization of probe parameters of an inductive conductivity sensor includes: S1. Initial sampling and simulation; Determine the design variables and parameter ranges for probe parameter optimization, construct a probe parameter simulation model, set the design variables as automatically updatable global parameters, generate multiple sets of candidate parameter combinations within the parameter range, input the probe parameter vectors of each candidate parameter combination into the probe parameter simulation model to run the simulation, and obtain the performance data of each candidate parameter combination; S2. Construct a comprehensive objective function and simulation sample library; Based on the performance data obtained from S1, the comprehensive objective function value of each candidate parameter combination is calculated, and a simulation sample library is constructed. S3. Train the GPR agent model; Using the probe parameter vectors of various parameter combinations in the simulation sample library as input and the comprehensive objective function value of the probe parameter vectors as output, a Gaussian process regression (GPR) surrogate model is trained. S4, Bayesian optimization recommendation; After training, an optimized acquisition function is constructed based on the predicted mean and predicted standard deviation output by the GPR surrogate model, the optimization value of each candidate parameter combination is calculated, and the recommended parameter combination is output. S5. Simulation verification and sample library update; Input the probe parameter vector of the recommended parameter combination into the probe parameter simulation model to run the simulation, obtain the performance data of the recommended parameter combination, calculate the comprehensive objective function value of the recommended parameter combination and update the simulation sample library; S6. Iterative convergence verification and optimal parameter output; The GPR surrogate model is iteratively converged and verified based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination, and the optimal probe parameter combination is output. Specifically, the GPR surrogate model is iteratively converged and verified. If the iterative convergence condition is not met, the process returns to step S3 until the convergence condition is met. Then, the recommended parameter combination output in the last iteration is taken as the optimal probe parameter combination, and the probe parameters and performance data of the optimal probe parameter combination are output.

[0029] In S1, the probe parameter vector is: ; In the formula, Represents the probe parameter vector. Indicates the excitation frequency. Indicates the number of turns of the excitation coil. To detect the number of coil turns, Indicates the inner radius of the magnetic ring. Indicates the outer radius of the magnetic ring. Indicates the coil spacing. Indicates the length of the magnetic core; Within the parameter range, multiple sets of candidate parameter combinations are generated using Latin hypercube sampling, orthogonal experimental design, uniform design, Sobol sequence sampling, or a hybrid sampling method combining engineering experience. The performance data for each candidate parameter combination includes output voltage data, electromagnetic field distribution data, and loss distribution data under different simulation medium conditions.

[0030] In S2, the comprehensive objective function is: ; ; ; In the formula, express The comprehensive objective function value, , express Intermediate calculation parameters, Indicates after normalization linearity, Indicates after normalization The output voltage, Indicates after normalization Core loss, Indicates after normalization Coil copper loss, Indicates after normalization The probe volume, , , , , They represent , , , , The weighting coefficients.

[0031] linearity The coefficients of determination, obtained by linearly fitting the output voltage of the probe under at least five standard conductivity solutions with uniform coverage of the measurement range, are used to characterize the linear response quality of the probe's output voltage to conductivity. The amplitude of the induced voltage output under the conductivity condition at the midpoint of the measurement range is used to characterize the signal strength of the probe. The core loss is: ; ; In the formula, express The core loss per unit volume, express The volume of the magnetic core, , , The Steinmetz coefficient is determined by the selected core material. express excitation frequency, express The maximum magnetic flux density of the magnetic core; The volume of the magnetic core is determined by the geometric dimensions of the magnetic rings. In this embodiment, the probe adopts a dual-magnetic-ring structure (one excitation magnetic ring and one detection magnetic ring, with identical geometric dimensions). The formula for calculating its total volume is as follows: ; In the formula, express The outer radius of the magnetic ring, express The inner radius of the magnetic ring, express The length of the magnetic core; The coil copper loss is: ; In the formula, This represents the coil current, which is automatically calculated by simulation software based on the set excitation voltage amplitude and the actual coil impedance. express The square of, express The DC resistance of the coil, The skin effect coefficient represents the proportion by which the effective resistance of a conductor increases due to the skin effect under alternating current. It is determined by the ratio of the conductor diameter to the skin depth. In this embodiment, the conductor diameter is fixed at 0.2 mm. In actual engineering, the conductor diameter is determined according to the actual winding process and the area of ​​the magnetic ring window. The probe volume is: ; In the formula, express The outer radius of the magnetic ring, express The length of the magnetic core, express The coil spacing.

[0032] In S6, the GPR surrogate model is iteratively converged and verified based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination. When the training process of the GPR surrogate model does not meet the iterative convergence condition, the process returns to step S3 until the training process of the GPR surrogate model meets the iterative convergence condition. Then, the recommended parameter combination output in the last iteration is taken as the optimal probe parameter combination, and the probe parameters of the optimal probe parameter combination and the performance data of the optimal parameter combination are output.

[0033] The simulation sample library is as follows: ; In the formula, Indicates the iteration count index. Indicates the first Simulation sample library during round iteration, express The number of simulation samples in the middle, Indicates the simulation sample index. Indicates the first One simulation sample, Indicates the first The probe parameter vector of a simulated sample, express The comprehensive objective function value.

[0034] The optimized acquisition function is as follows: ; In the formula, Indicates the first Optimize the acquisition function value through round-by-round iteration. Indicates the first The predicted mean of each iteration, Indicates the first The standard deviation of the prediction in each iteration. Indicates the exploration coefficient; Within the set of valid parameters, a maximum search is performed on the optimal acquisition function value to output a recommended parameter combination: ; In the formula, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. The effective parameter set consists of combinations of candidate parameters that satisfy the engineering optimization constraints. To maximize the search function.

[0035] Engineering optimization constraints include: ; ; ; In the formula, Indicates minimum linearity. Indicates the maximum allowable power consumption. This indicates the maximum permissible probe volume.

[0036] The iterative convergence condition for iterative convergence verification of the GPR surrogate model is: ; In the formula, express The comprehensive objective function value, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. This indicates the number of iterations for consecutive comparisons. Indicates the convergence threshold, preferred , This indicates that the change in the optimal comprehensive objective value over five consecutive rounds is less than 0.1%. In practical applications, this can be adjusted as needed. If a higher precision optimal solution is required, it can be tightened to... If computing resources are limited and results are required quickly, the time limit can be relaxed to [percentage missing]. .

[0037] The GPR surrogate model characterizes the comprehensive objective function through a Gaussian process. By building an approximate model on simulation samples, it outputs the comprehensive objective function value of parameter combinations that have not yet participated in the simulation. After the GPR surrogate model is trained, for any parameter combination input to the GPR surrogate model, the GPR surrogate model outputs the predicted mean and predicted standard deviation of the parameter combination.

[0038] An inductive conductivity sensor probe consists of an excitation coil, a detection coil, a magnetic core, a current-carrying channel, and a housing. The measurement performance of an inductive conductivity sensor is highly dependent on the probe parameters. If the excitation frequency is too low, the output signal amplitude will be insufficient; if the frequency is too high, core loss, copper loss, parasitic coupling, and nonlinear errors may increase. Increasing the number of coil turns can improve magnetic coupling strength, but it may also lead to increased coil resistance, volume, and heat generation. The inner diameter, outer diameter, height, and spacing of the magnetic ring affect the magnetic reluctance, magnetic flux distribution, and current-carrying channel dimensions.

[0039] Inductive conductivity sensor probes have many designable and adjustable parameters, including operating conditions, geometric structure, and electromagnetic structure parameters, such as excitation frequency, number of turns in the transmitting coil, number of turns in the receiving coil, coil radius, coil spacing, core length, core radius, shielding structure dimensions, and probe outer diameter. In S1, the probe parameters are represented as a parameter vector. The variables (design variables) and the value ranges (parameter ranges) of each variable are determined to construct the probe parameter vector. Design variables include, but are not limited to, excitation frequency, number of turns in the excitation coil, number of turns in the receiving coil, inner diameter of the magnetic ring (including inner radius and inner diameter of the core), outer diameter of the magnetic ring, core height, spacing between the two magnetic rings, radius of the current guiding channel, and excitation voltage. The parameter range can be determined based on the sensor installation space, material parameters, target range, power consumption constraints, and manufacturing constraints. Each set of probe parameters is equivalent to determining a probe design scheme. The probe parameter vector corresponding to the probe design scheme is obtained and input into the parametric simulation model. The model calculates the response, electromagnetic loss, and structural volume of the probe structure under different conductivity conditions based on the probe parameter vector.

[0040] In engineering applications, the radius of the current guiding channel and the excitation voltage are usually fixed in advance by the range requirements and the front-end power supply specifications, and are usually not used as optimization variables. However, the coil wire diameter is constrained by the winding process and the magnetic ring window area, and its impact on the optimization results is relatively independent. Therefore, in the probe parameter vector, seven parameters are selected as probe parameter optimization variables: excitation frequency, number of turns of excitation coil, number of turns of detection coil, inner radius of magnetic ring, outer radius of magnetic ring, coil spacing, and magnetic core length. The meaning and value range of each parameter are shown in Table 1.

[0041] Table 1 Probe parameters; .

[0042] As shown in Table 1, the probe optimization parameter vector covers multiple dimensions, including excitation frequency, coil turns, and key geometric dimensions of the magnetic ring. Twenty initial candidate parameter combinations were generated within the parameter range of Table 1 using the Latin hypercube sampling (LHS) method. A parameterized frequency domain electromagnetic simulation model of the probe was established using simulation software (preferably COMSOL Multiphysics, but can be replaced by ANSYS Maxwell, CST, or other electromagnetic simulation tools). The design variables were set as global parameters. The model included the excitation coil, detection coil, magnetic core, conductive medium domain, and external air domain, and the material permeability, conductivity, boundary conditions, and frequency domain solver were set. The 20 parameter combinations were sequentially input into the model, and the output voltage of each combination was calculated under multiple conductivity standard solutions. Electromagnetic field distribution and loss distribution data were extracted.

[0043] The combination of parameters determines the probe structure and operating state. COMSOL simulation provides the performance indicators of this structure, and subsequent optimization algorithms use these performance indicators to determine whether the set of parameters is worth retaining or further exploration. There are coupling relationships between the various parameters of the probe; optimizing a single parameter alone is unlikely to achieve the overall optimal effect. Therefore, for each set of parameters, it is not sufficient to consider only one indicator; multiple performance indicators need to be examined simultaneously.

[0044] In S2, multiple performance metrics are combined into a single comprehensive score, and a comprehensive objective function is constructed based on the normalized performance metrics. The comprehensive objective function is then used to compare the overall advantages and disadvantages of different parameter combinations.

[0045] For each set of simulation results, performance indicators include, but are not limited to, linearity, output voltage, core loss, coil copper loss, and probe volume. Linearity is obtained from the coefficient of determination of the fit between output voltage and conductivity, with the output voltage taken as the amplitude of the induced voltage at the midpoint of the range or at a specific conductivity. For core loss, the maximum magnetic flux density of the core is extracted from the simulated magnetic field distribution, and the Steinmetz coefficient is determined by the core material. For coil copper loss, the DC resistance of the coil is calculated from the coil geometry and resistivity. All indicators are normalized to... The interval is defined, and non-negative weights are assigned. ,in, It can be set according to design preferences; for example, when more measurement accuracy is emphasized, it can be increased. and When more emphasis is placed on low power consumption and miniaturization, it can improve , and Taking a focus on accuracy and signal strength as an example, weights are set. , , , , Among the various performance indicators, higher linearity and output voltage indicate better probe performance, while smaller core loss, coil copper loss, and probe size also contribute to better probe performance. Furthermore, after obtaining the initial 20 sets of simulation samples, the weights of each indicator can be automatically calculated based on its actual dispersion (coefficient of variation). Indicators with greater dispersion have higher weights, representing a greater contribution to distinguishing the merits of different schemes.

[0046] S3 takes the parameter vectors from the sample library as input and the corresponding comprehensive objective function value as output to train a Gaussian process regression model. A squared exponential kernel function is selected, and the kernel function hyperparameters (signal variance, length scale, etc.) are optimized through maximum likelihood estimation. After training, the GPR model can output the predicted mean and predicted standard deviation for any unsimulated candidate parameters.

[0047] In practical engineering, parameters cannot be arbitrarily chosen. Even if a set of parameters appears good in the overall score, basic engineering constraints must still be met. These constraints include linearity not falling below the required level, power consumption not exceeding the allowable upper limit, and probe size not exceeding the installation space limit. In this embodiment, the engineering constraint is set as minimum linearity. Maximum allowable power consumption Watt, maximum probe volume Square centimeters.

[0048] In S4, based on engineering constraints, a confidence upper bound acquisition function (optimized acquisition function) is constructed, and the coefficients are explored. Typically, the value is taken between 1.0 and 2.0, with the exploration coefficient being preferred. Within the effective parameter set, multi-starting-point gradient optimization or genetic algorithm is used to maximize the acquisition function to obtain recommended parameter combinations. The effective parameter set is a set of parameter combinations that simultaneously satisfy the above constraints and variable upper and lower limits. After obtaining the recommended parameter combinations, the simulation sample library is updated, and the GPR model is retrained using the updated simulation sample library. Then, the process returns to step S4 for the next round of recommendation. Each round records the current optimal comprehensive target value and the corresponding performance index. Convergence conditions are set: 5 consecutive rounds (…). The improvement in the optimal value of the overall objective function is less than the convergence threshold. If the condition is met, the iteration stops; otherwise, it continues. Additionally, on the initial sample set, the exploration coefficients can be set to 0.5, 1.0, 1.5, 2.0, and 2.5 respectively. Leave-one-out cross-validation can be used to compare the simulation improvement of the recommended parameters, and the optimal value of the exploration coefficient can be selected.

[0049] A method for intelligent optimization of probe parameters in an inductive conductivity sensor is proposed. This method uses the COMSOL multiphysics simulation model as a high-fidelity evaluator to construct a parameterized simulation model. An initial simulation sample library is used as training data, a Gaussian Process Regression (GPR) model is used as a surrogate model, and a Bayesian optimization algorithm is used as the parameter recommendation strategy, forming a closed loop of "parameterized modeling, sample generation, surrogate learning, active recommendation, simulation verification, sample updating, and convergence output." The COMSOL parameterized simulation model is not only used for one-time parameter scanning but also serves as a high-fidelity simulation platform that can be repeatedly used by the optimization algorithm. The GPR surrogate model is used to learn the nonlinear mapping relationship between probe parameters and performance indicators. Bayesian optimization selects the next most promising parameter combination based on the predicted mean and prediction uncertainty of the surrogate model, thereby reducing the number of invalid simulations and improving the global optimization capability.

[0050] This embodiment involves 20 rounds of Bayesian iterations, with a total of 40 high-fidelity simulations (20 initial sample iterations plus 20 Bayesian recommendation iterations). The current optimal integrated objective function value and performance data after each stage of optimization are shown in Table 2.

[0051] Table 2 records the optimal performance index at the current stage during the Bayesian optimization iteration process; .

[0052] Table 3 Comparison of key performance indicators of the probe before and after optimization; .

[0053] Record the current optimal parameter combination and its performance index after each round of Bayesian optimization, and generate a line graph, as shown in the figure. Figure 3 As shown in Table 4, round 0 represents the optimal feasible solution in the initial sample library, and rounds 1 to 20 represent the current optimal result after each acquisition function recommendation, COMSOL high-fidelity verification, and sample library update. The changes in the current output voltage and the optimal value of the comprehensive objective function in each round of Bayesian optimization are shown in Table 4.

[0054] Table 4. Bayesian optimization results; .

[0055] As shown in Tables 2 and 4, with the advancement of Bayesian optimization rounds, the current optimal comprehensive objective function value and the current optimal output voltage exhibit a clear monotonically increasing trend. In the early stages of Bayesian optimization (rounds 0 to 10), the comprehensive objective function value rapidly increased from 0.684 to 0.782, an increase of 14.3%, indicating that the surrogate model actively explored unknown high-value parameter regions through high prediction standard deviations in the early stages of optimization, achieving global search gains. In the later stages of optimization (rounds 10 to 20), the comprehensive objective function value gradually increased from 0.782 to 0.821, with the increase narrowing to 5.0%, and the output voltage also steadily increased from 98mV to 105mV, with the curve becoming flatter. The changing patterns in Table 2 clearly show that the GPR surrogate model balanced model development and exploration through the acquisition function (confidence upper bound), enabling the search process to automatically transition from global coarse screening to local fine optimization. This trend closely matches the iterative convergence condition set in step S6 (the improvement of the comprehensive target is less than the threshold for multiple consecutive rounds), proving the rationality and practicality of the convergence criterion. As shown in Table 3, under a limited computational budget of only 40 high-fidelity simulations (20 initial samples plus 20 rounds of Bayesian recommendation), the linearity improved from 0.9912 to 0.9963, enhancing the measurement consistency of the sensor across the entire range. In terms of signal strength, the induced voltage increased from 82mV to 105mV, a relative improvement of 28.0%, which directly benefits the improvement of the signal-to-noise ratio and reduces the amplification burden of subsequent signal conditioning circuits. In terms of power characteristics, the total loss (the sum of core loss and coil copper loss) decreased from 1.86W to 1.29W, a reduction of 30.6%, effectively suppressing the risk of permeability degradation and zero drift caused by temperature rise. In terms of structural compactness, the probe volume decreased from 18.5... Reduced to 15.5 This reduced the efficiency by 16.2%, improving its adaptability to installation in confined spaces (such as deep-sea exploration cabins or pipeline walls). Ultimately, the comprehensive objective function value J increased from 0.684 to 0.821, representing an overall relative improvement of 20.0%, fully demonstrating the effectiveness of this method in efficiently finding the optimal solution under multi-objective constraints.

[0056] Example 2 An intelligent optimization system for the parameters of an inductive conductivity sensor probe includes a parameter range setting module, a parameterized simulation model module, an initial sample generation module, a simulation sample library module, a performance evaluation module, a GPR surrogate model module, a Bayesian optimization module, a simulation verification and update module, and an optimal parameter output module.

[0057] The parameter range setting module is used to determine the probe design variables to be optimized and their value ranges. Design variables include, but are not limited to, excitation frequency, number of turns in the excitation coil, number of turns in the receiving coil, inner radius of the magnetic ring, outer radius of the magnetic ring, magnetic core height, distance between the two magnetic rings, radius of the current guiding channel, and excitation voltage. The value range of each design variable can be determined based on sensor installation space, material parameters, target measurement range, power consumption constraints, and manufacturing constraints.

[0058] The parametric simulation model module is used to implement the electromagnetic induction principle of inductive conductivity sensors, establishing a simulation model of the probe parameters for the inductive conductivity sensor probe. The probe parameter simulation model includes the excitation coil, detection coil, magnetic core, conductive medium domain, and external air domain, and sets the material permeability, conductivity, coil excitation method, boundary conditions, and frequency domain solver. The parameter range setting module determines the probe design variables to be optimized. This module can automatically update the geometric dimensions, coil turns, and excitation frequency based on the input parameter combinations, and output corresponding performance index data such as electromagnetic field distribution data, output voltage data, and loss distribution data. The probe parameter simulation model is a COMSOL parametric simulation model.

[0059] The initial sample generation module is used to generate initial samples within a preset parameter range (equivalent to generating candidate parameters within the parameter range). Initial samples can be generated using Latin hypercube sampling, orthogonal experiments, uniform design, random sampling, or a hybrid sampling method combining engineering experience. The number of initial samples should meet the initial training needs of the GPR surrogate model, while avoiding excessive high-fidelity simulations that would waste computational resources.

[0060] The simulation sample library module stores each parameter combination and its corresponding simulation results. A sample record in the library must include at least the parameter vector, output voltage, linearity, sensitivity, core loss, copper loss, probe volume, overall objective function value, and simulation status. The sample library can be stored in the form of a table, database, or structured file.

[0061] The performance evaluation module calculates various performance metrics based on COMSOL simulation results. These metrics include, but are not limited to, conductivity-output voltage fitting determination coefficient, sensitivity, output signal amplitude, core loss, coil copper loss, temperature rise risk, probe size, and manufacturability. The module also normalizes multiple metrics and forms a comprehensive objective function.

[0062] The GPR surrogate model module takes a parameter vector as input and outputs either a comprehensive objective function value or multiple performance indicators to train a Gaussian process regression model, resulting in a GPR surrogate model capable of predicting the performance and uncertainty of unsimulated parameter combinations. The trained GPR surrogate model can output the predicted mean and predicted standard deviation for any unsimulated candidate parameter combination. The predicted mean represents the model's estimate of the performance of that parameter combination, equivalent to the comprehensive objective function value that the GPR surrogate model believes that the parameter combination may achieve, while the predicted standard deviation represents the model's uncertainty regarding the prediction result.

[0063] The Bayesian optimization module constructs a data acquisition function based on the predicted mean and standard deviation output by the GPR surrogate model, selecting the next set or batch of parameter combinations most worthy of high-fidelity simulation. The data acquisition function can employ expected improvement, confidence upper bound, improvement probability, or variations thereof. Bayesian optimization considers both performance improvement potential and model uncertainty, thus achieving a balance between local exploitation and global exploration.

[0064] The simulation verification and update module inputs the candidate parameter combinations recommended by Bayesian optimization into COMSOL for high-fidelity simulation to obtain realistic simulation metrics, and adds the new samples to the simulation sample library. The updated sample library is used to retrain or incrementally update the GPR surrogate model.

[0065] The optimal parameter output module is used to output the optimal probe parameter combination and its prediction performance and simulation verification performance after the convergence conditions are met. The convergence conditions can be reaching the maximum number of iterations, the improvement of the comprehensive target in multiple consecutive rounds being less than a preset threshold, the prediction error of the surrogate model being lower than a preset threshold, or meeting engineering constraints such as linearity, output voltage, loss, and volume.

[0066] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for intelligent optimization of probe parameters of an inductive conductivity sensor, characterized in that, include: S1. Determine the design variables and parameter range for probe parameter optimization, construct a probe parameter simulation model, set the design variables as automatically updatable global parameters, generate multiple sets of candidate parameter combinations within the parameter range, input the probe parameter vectors of each candidate parameter combination into the probe parameter simulation model to run the simulation, and obtain the performance data of each candidate parameter combination. S2. Construct a comprehensive objective function. Based on the performance data obtained in S1, calculate the comprehensive objective function value of each candidate parameter combination and construct a simulation sample library. S3. Using the probe parameter vectors of various parameter combinations in the simulation sample library as input and the comprehensive objective function value of the probe parameter vectors as output, construct and train the GPR surrogate model. S4. After training, construct an optimized acquisition function based on the predicted mean and predicted standard deviation output by the GPR proxy model, calculate the optimization value of each candidate parameter combination, and output the recommended parameter combination. S5. Input the probe parameter vector of the recommended parameter combination into the probe parameter simulation model to run the simulation, obtain the performance data of the recommended parameter combination, calculate the comprehensive objective function value of the recommended parameter combination and update the simulation sample library; S6. Based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination, the GPR surrogate model is iteratively converged and verified, and the optimal probe parameter combination is output.

2. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 1, characterized in that, In S1, the probe parameter vector is: ； In the formula, This represents the probe parameter vector. Indicates the excitation frequency. Indicates the number of turns of the excitation coil. To detect the number of coil turns, Indicates the inner radius of the magnetic ring. Indicates the outer radius of the magnetic ring. Indicates the coil spacing. Indicates the length of the magnetic core; Within the parameter range, multiple sets of candidate parameter combinations are generated using Latin hypercube sampling, orthogonal experimental design, uniform design, Sobol sequence sampling, or a hybrid sampling method combining engineering experience. The performance data for each candidate parameter combination includes output voltage data, electromagnetic field distribution data, and loss distribution data under different simulation medium conditions.

3. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 2, characterized in that, In S2, the comprehensive objective function is: ； ； ； In the formula, express The comprehensive objective function value, , express Intermediate calculation parameters, Indicates after normalization linearity, Indicates after normalization The output voltage, Indicates after normalization Core loss, Indicates after normalization Coil copper loss, Indicates after normalization The probe volume, , , , , They represent , , , , The weighting coefficients.

4. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 3, characterized in that, The core loss is: ； ； In the formula, express The core loss per unit volume, express The volume of the magnetic core, , , These are the Steinmetz coefficients. express excitation frequency, express The maximum magnetic flux density of the magnetic core; The coil copper loss is: ； In the formula, Indicates the coil current. express The square of, express The DC resistance of the coil, Indicates the skin effect coefficient; The probe volume is: ； In the formula, express The outer radius of the magnetic ring, express The length of the magnetic core, express The coil spacing.

5. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 4, characterized in that, In S6, the GPR surrogate model is iteratively converged and verified based on the recommended parameter combination and the comprehensive objective function value of the recommended parameter combination. When the training process of the GPR surrogate model does not meet the iterative convergence condition, the process returns to step S3 until the training process of the GPR surrogate model meets the iterative convergence condition. Then, the recommended parameter combination output in the last iteration is taken as the optimal probe parameter combination, and the probe parameters of the optimal probe parameter combination and the performance data of the optimal parameter combination are output.

6. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 5, characterized in that, The simulation sample library is as follows: ； In the formula, Indicates the iteration count index. Indicates the first Simulation sample library during round iteration, express The number of simulation samples in the middle, Indicates the simulation sample index. Indicates the first One simulation sample, Indicates the first The probe parameter vector of a simulated sample, express The comprehensive objective function value.

7. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 6, characterized in that, The optimized acquisition function is as follows: ； In the formula, Indicates the first Optimize the acquisition function value through round-by-round iteration. Indicates the first The predicted mean of each iteration, Indicates the first The standard deviation of the prediction in each iteration. Indicates the exploration coefficient; Within the set of valid parameters, a maximum search is performed on the optimal acquisition function value to output a recommended parameter combination: ； In the formula, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. The effective parameter set consists of combinations of candidate parameters that satisfy the engineering optimization constraints. To maximize the search function.

8. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 7, characterized in that, Engineering optimization constraints include: ； ； ； In the formula, Indicates minimum linearity. Indicates the maximum allowable power consumption. This indicates the maximum permissible probe volume.

9. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 8, characterized in that, The iterative convergence condition for iterative convergence verification of the GPR surrogate model is: ； In the formula, express The comprehensive objective function value, Indicates the first The probe parameter vector representing the recommended parameter combinations output by round iteration. This indicates the number of iterations for consecutive comparisons. This represents the convergence threshold.

10. The intelligent optimization method for the parameters of an inductive conductivity sensor probe according to claim 9, characterized in that, The GPR surrogate model characterizes the comprehensive objective function through a Gaussian process. By building an approximate model on simulation samples, it outputs the comprehensive objective function value of parameter combinations that have not yet participated in the simulation. After the GPR surrogate model is trained, for any parameter combination input to the GPR surrogate model, the GPR surrogate model outputs the predicted mean and predicted standard deviation of the parameter combination.

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