Impeller temperature field monitoring sensor layout optimization method based on physical driving

Abstract

The invention discloses an impeller temperature field monitoring sensor layout optimization method based on physical driving, and belongs to the technical field of hot charging processes. Comprising the steps that a control equation and a geometric constraint domain are determined according to physical characteristics of a target object, and the target object is used for indicating a to-be-monitored impeller entity; constructing a system matrix based on the control equation; according to the mapping relation between the sensor layout position and the system matrix, an objective function is constructed, and the objective function is used for evaluating the inversion stability of the physical field; and based on the geometric constraint domain, solving the objective function through an optimization algorithm, and determining an optimal sensor layout coordinate. According to the method, the system matrix and the objective function are constructed through physical driving, the optimal layout is solved under geometric constraints, the problems of low prediction precision and easy interference caused by dependence on experience in the prior art are solved, and the accuracy of impeller temperature field monitoring and the process stability are effectively improved.

Description

Technical Field

[0001] This application relates to the field of thermal charging technology, and in particular to a method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive. Background Technology

[0002] In the manufacturing of large compressor rotors, the hot-fitting process is a critical step. This process involves heating the impeller to expand its inner bore, then fitting it onto the main shaft, and finally cooling it to form an interference fit. To ensure assembly quality, the temperature field of the impeller must be monitored in real time, especially the temperature of the mating surface between its inner ring and the main shaft. As a typical process, the quality of interference fit directly affects the rotor's performance during service. Therefore, real-time perception and control of quality risks during assembly are essential. The temperature distribution at the impeller-main shaft contact surface is a core factor determining assembly quality. However, this contact temperature distribution is difficult to measure directly in real time during assembly, posing a significant challenge to real-time control of assembly quality.

[0003] Currently, a feasible solution is to place temperature sensors on the impeller surface and use an artificial intelligence proxy model built based on high-fidelity finite element simulation to achieve real-time prediction of the contact temperature distribution. However, the arrangement of the temperature sensors directly affects the accuracy of the physical field prediction.

[0004] Existing deployment methods rely heavily on experience, lacking scientific basis and systematic optimization guidance, leading to easily susceptible prediction results and insufficient process stability. Specifically, current technologies typically employ an experience-based point placement scheme, where process engineers randomly or uniformly arrange several thermocouples or infrared temperature measurement points on the outer surface of the impeller based on historical experience. After collecting temperature data from these external measurement points, the average value of the external measurement points is directly used to represent the overall temperature, assuming a uniform temperature distribution on the impeller; or, based on a simple one-dimensional heat conduction formula, the inner hole temperature is roughly estimated using the outer surface temperature. This method lacks scientific basis, cannot accurately reflect the complex temperature field distribution, resulting in low prediction accuracy and susceptibility to noise interference. Summary of the Invention

[0005] This application provides a physics-driven method for optimizing the layout of impeller temperature field monitoring sensors, which at least solves the problems in the prior art where sensor layout schemes rely on experience, lack scientific basis and systematic optimization guidance, resulting in low temperature field prediction accuracy, susceptibility to noise interference and insufficient process stability.

[0006] In a first aspect, this application provides a method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive, the method comprising: Based on the physical characteristics of the target object, the governing equations and geometric constraint domains are determined. The target object is used to indicate the impeller entity to be monitored. The physical characteristics include the geometric model, thermal property parameters, and structural features. Based on the governing equations, a system matrix is ​​constructed, which is used to characterize the thermophysical properties of the target object. Based on the mapping relationship between sensor layout and system matrix, an objective function is constructed. The sensor layout represents the candidate spatial coordinates of the sensor in the geometric constraint domain. The objective function is used to evaluate the stability of physical field inversion. Based on the geometric constraint domain, the objective function is solved through an optimization algorithm to determine the optimal sensor layout coordinates.

[0007] The above technical solution constructs a system matrix by combining the physical characteristics of the target object, establishes a mapping relationship between the sensor layout position and the system matrix to construct an objective function for evaluating the stability of the physical field inversion, and uses an optimization algorithm to solve it in the geometric constraint domain. This achieves a scientific and systematic design of the sensor layout scheme, effectively solving the problems of low prediction accuracy, susceptibility to noise interference, and lack of theoretical guidance caused by the reliance on experience in existing technologies. It significantly improves the accuracy of impeller temperature field reconstruction and the stability of the assembly process.

[0008] Secondly, this application provides a physics-driven impeller temperature field monitoring sensor layout optimization system, the system comprising: The first determining module is used to determine the governing equations and geometric constraint domains based on the physical characteristics of the target object, wherein the target object is used to indicate the impeller entity to be monitored, and the physical characteristics include geometric model, thermophysical parameters and structural features.

[0009] A construction module is used to construct a system matrix based on the control equations, the system matrix being used to characterize the thermophysical properties of the target object.

[0010] The second construction module is used to construct an objective function based on the mapping relationship between the sensor layout position and the system matrix. The sensor layout position represents the candidate spatial coordinates of the sensor in the geometric constraint domain. The objective function is used to evaluate the stability of the physical field inversion.

[0011] The second determining module is used to determine the optimal sensor layout coordinates by solving the objective function based on the geometric constraint domain and through an optimization algorithm.

[0012] Thirdly, this application also provides a computer-readable storage medium storing at least one piece of program code, which is loaded and executed by a processor to implement the operations performed by the physical-driven impeller temperature field monitoring sensor layout optimization method.

[0013] Fourthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described physical-driven impeller temperature field monitoring sensor layout optimization method or the steps of the above-described physical-driven impeller temperature field monitoring sensor layout optimization method. Attached Figure Description

[0014] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0015] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0016] Figure 1 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 1 ; Figure 2 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 2 ; Figure 3 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 3 ; Figure 4 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 4 ; Figure 5 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 5 ; Figure 6 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 6 ; Figure 7 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 7 ; Figure 8 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 8 ; Figure 9A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 9 ; Figure 10 A flowchart illustrating the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment. Figure 10 ; Figure 11 This application provides a schematic diagram of the hardware connection topology for a physics-driven impeller temperature field monitoring sensor layout optimization system. Figure 1 ; Figure 12 This application provides a schematic diagram of the hardware connection topology for a physics-driven impeller temperature field monitoring sensor layout optimization system. Figure 2 . Detailed Implementation

[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of this application.

[0018] It should be noted that, in the description of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. The terms "first," "second," etc., in this application are used to distinguish similar objects and are not used to describe a specific order or sequence.

[0019] In related technologies, the heat-fitting process of large compressor rotors typically employs an empirically-based point-of-sampling scheme. Process engineers often rely on historical experience to randomly or evenly place several thermocouples or infrared temperature measurement points on the outer surface of the impeller, assuming a uniform temperature distribution on the impeller or calculating the inner bore temperature based on a simple one-dimensional heat conduction formula. However, this method lacks scientific basis and cannot accurately reflect the complex temperature field distribution. In particular, the temperature of the mating surface between the impeller inner bore and the main shaft is difficult to measure directly. If the external measuring point layout is unreasonable, the inversion of the internal temperature field using measurement data is easily affected by measurement noise, resulting in low prediction accuracy, insufficient process stability, and an inability to meet the real-time monitoring requirements for high-quality assembly.

[0020] To address the aforementioned technical issues, this application provides a physics-driven method for optimizing the layout of impeller temperature field monitoring sensors. This method introduces a physical model-driven approach, constructs a system matrix reflecting thermophysical characteristics, establishes a quantitative mapping relationship between sensor layout and physical field inversion performance, and utilizes Fisher information matrix to construct an objective function. An optimization algorithm is then used to search for the optimal sensor placement location, thereby achieving scientific optimization of the sensor layout while considering measurement noise, significantly improving the accuracy and stability of temperature field reconstruction.

[0021] After introducing the application scenarios of the embodiments of this application, the technical solutions provided by the embodiments of this application will be described below. (See also...) Figure 1 The method includes the following steps.

[0022] Step S101: Determine the governing equations and geometric constraint domain based on the physical characteristics of the target object.

[0023] The target object refers to the impeller entity to be monitored, whose physical characteristics include geometric model, thermophysical parameters, and structural features. Specifically, the heat transfer mechanism of the impeller's thermal mounting process is analyzed, including convective heat transfer between the high-temperature impeller and the surrounding air, and contact thermal resistance heat transfer between the impeller's inner bore and the main shaft contact surface. Based on heat transfer theory, a heat conduction differential equation describing the transient temperature field change of the impeller is established, and the governing equations are determined by combining initial and boundary conditions. Simultaneously, based on the three-dimensional structural model of the impeller, structural avoidance areas such as bolt holes and blade roots where sensors cannot be installed are identified. These infeasible regions are eliminated, and the remaining outer surface area constitutes the geometric constraint domain of the sensor.

[0024] Step S102: Construct the system matrix based on the control equations.

[0025] The system matrix characterizes the thermophysical properties of the target object. Specifically, the governing equations are spatially discretized using the finite element method. The impeller's geometric model is divided into a finite number of discrete elements, and the heat conduction and heat capacity matrices of each element are obtained through integration. Based on the node topology, all element matrices are assembled into the overall heat conduction and heat capacity matrices, and boundary conditions are introduced for correction, ultimately constructing the system matrix characterizing the overall thermophysical properties of the impeller. This system matrix describes the intrinsic laws governing the change of node temperature over time and heat transfer.

[0026] Step S103: Construct the objective function based on the mapping relationship between the sensor layout positions and the system matrix.

[0027] In this framework, the sensor placement represents the candidate spatial coordinates of the sensor within the geometrically constrained domain, and the objective function is used to evaluate the stability of the physical field inversion. Specifically, the sensor placement corresponds to a specific finite element node within the geometrically constrained domain. An observation matrix is ​​introduced to characterize the one-to-one correspondence between sensor measurement points and system nodes. The sensitivity matrix is ​​derived using the system matrix to characterize the sensitivity of the temperature response to changes in the heat source. Based on the observation and sensitivity matrices, the transfer relationship between the measured data and the parameters to be inverted is derived, thereby constructing the Fisher information matrix. This matrix contains the effective information from the measured data used to reconstruct the temperature field. The objective function is constructed by maximizing this information or minimizing the matrix condition number, thereby evaluating the stability of the physical field inversion under different placement schemes.

[0028] Step S104: Based on the geometric constraint domain, solve the objective function through an optimization algorithm to determine the optimal sensor layout coordinates.

[0029] Specifically, within the feasible solution space defined by the geometric constraint domain, optimization algorithms (such as genetic algorithms and particle swarm optimization) are used to find the optimal solution. The optimization algorithm randomly generates an initial layout population, calculates the fitness value (i.e., the objective function value) of each individual, and continuously eliminates inferior solutions and retains superior solutions through iterative updates, eventually converging to the individual with the highest fitness. The coordinates corresponding to this individual are then output as the optimal sensor layout coordinates.

[0030] This embodiment establishes a quantitative mapping relationship between sensor layout and physical field inversion stability by constructing control equations and finite element system matrices based on heat transfer mechanisms. It also constructs an objective function using Fisher information matrix and optimizes the sensor layout under geometric constraints using optimization algorithms. This transforms the sensor layout scheme from experience-dependent to physics-driven, effectively solving the problems of low temperature field reconstruction accuracy and poor anti-interference ability caused by unreasonable placement in existing technologies. It significantly improves the reliability of impeller hot-assembly process monitoring and the level of assembly quality control.

[0031] It should be noted that the above steps S101-S104 are a simplified description of the embodiments provided in this application.

[0032] The steps provided in the embodiments of this application will be described in more detail below with some examples. See also: Figure 2 Following step S104, the physical-driven impeller temperature field monitoring sensor layout optimization method provided in this application embodiment further includes the following steps: Step S105: Construct a temperature field reconstruction model based on the optimal sensor layout coordinates.

[0033] Specifically, after outputting the optimal sensor layout coordinates through the optimization algorithm, this embodiment constructs a temperature field reconstruction verification model to verify the effectiveness of the layout scheme in actual physical field inversion. Based on the optimized coordinate positions, temperature response data is extracted at the corresponding nodes of the impeller's finite element model to simulate the actual measurement signal of the sensor. To approximate real-world operating conditions, Gaussian white noise with a specific signal-to-noise ratio can be added to the simulated measurement data to simulate random sensor errors. Subsequently, using the constructed temperature field reconstruction model (such as a regularized inversion algorithm or a pre-trained artificial intelligence proxy model), the simulated measurement data is used as input to invert and calculate the temperature field distribution inside the impeller, especially in the key mating surface area.

[0034] Step S106: Based on the temperature field reconstruction model, determine the error norm between the reconstructed temperature field and the theoretical temperature field.

[0035] Specifically, the temperature field obtained from high-fidelity finite element simulation is used as the reference true value, i.e., the theoretical temperature field. The reconstructed temperature field obtained from the inversion calculation in step S105 is compared with this theoretical temperature field. Key monitoring areas (such as the mating surface between the impeller inner hole and the main shaft) or discrete nodes across the entire domain are selected to calculate the error norm between the two. This error norm can be expressed as root mean square error (RMSE), maximum absolute error, or L2 norm, etc., and is used to quantitatively evaluate the reconstruction accuracy of the current layout scheme under the presence of measurement noise interference.

[0036] Step S107: If the error norm is less than the preset threshold, then the optimal sensor layout coordinates are confirmed to be valid.

[0037] Specifically, the calculated error norm is compared with a preset engineering allowable threshold. This preset threshold is set based on the specific requirements of the thermal charging process for temperature monitoring accuracy. If the error norm is less than the preset threshold, it indicates that the measurement data under this layout scheme contains sufficient information to ensure that the accuracy of the inversion results meets the engineering control requirements, thus confirming the validity of the optimal sensor layout coordinates. If the error norm exceeds the threshold, it indicates that the optimization parameters need to be readjusted or the model constraints need to be checked until the accuracy requirements are met.

[0038] This embodiment constructs a temperature field reconstruction model and introduces an error norm verification mechanism. It uses the theoretical temperature field as a benchmark to quantitatively evaluate the actual inversion effect of the optimized layout. This ensures that the final determined sensor layout coordinates not only meet the theoretical optimal index, but also meet the strict requirements for temperature field reconstruction accuracy in actual engineering. It effectively avoids layout failure caused by the deviation between the theoretical model and the actual working conditions, and significantly improves the engineering practicality and reliability of the method.

[0039] The methods provided in this application embodiment will be described in detail in conjunction with specific application scenarios. It should be noted that in actual engineering applications, the key technical features such as "constructing a system matrix" and "constructing an objective function" in the aforementioned steps can be implemented through various specific technical paths, depending on the specific monitoring object and process constraints. To more clearly and completely demonstrate the specific application methods and technical details of the technical solution of this application in actual complex scenarios, the following will take the typical engineering scenario of "compressor rotor hot mounting" as an example, and elaborate on the methods provided in this application embodiment in detail, combining specific physical modeling methods (such as meshless discretization) and numerical calculation strategies. It should be understood that the following specific implementation methods are further concretization and engineering implementation of the technical features in steps S101 to S107 above, and the two are consistent in technical principles.

[0040] The method provided in this application is applied to temperature monitoring in the hot-fitting process of a large compressor rotor. The specific implementation process of steps S101 to S107 in actual engineering applications is detailed below. This specific implementation process mainly includes the following steps: Step S1: Construct a rotor thermophysical model.

[0041] Specifically, by importing the three-dimensional CAD geometric model of the compressor rotor impeller and its material thermal properties (thermal conductivity, density, specific heat capacity), a three-dimensional transient heat conduction partial differential equation describing the heat loading process is established:

[0042] in, Let be the temperature field distribution to be determined, and let be the spatial coordinates. and time The function, in Kelvin . This is a time variable, representing the process time of hot charging. It is the density of the impeller material, in units of... It is the specific heat capacity of the material, in units of... . This term represents the rate of increase of the system's internal energy (thermal energy) over time (heat storage term). The thermal conductivity of the material, in units of It characterizes the material's ability to conduct heat. This term represents the net heat flux flowing into the control volume through heat conduction (diffusion term). For internal heat source items, units The overall meaning of the formula is that the energy required for the impeller temperature to rise is equal to the energy flowing in through heat conduction plus the heat generated inside. It is used to predict the temperature field distribution in the invisible area inside the impeller and constitutes the specific form of the control equation described in step S101.

[0043] Step S2: Geometric constraint domain partitioning.

[0044] Read the rotor inner diameter Set the sensor installation avoidance distance Delineate prohibited areas. Defined as The space. This region corresponds to the mating surface, and the software algorithm will forcibly remove coordinates falling into this region during subsequent optimization. Candidate Region Defined as The rotor body surface area. This is the effective search space where the sensor can be installed, constituting the specific definition of the geometric constraint domain described in step S101.

[0045] Step S3: Meshless physical discretization.

[0046] Due to the complex rotor geometry, the radial basis function-finite difference (RBF-FD) technique is used to transform the aforementioned partial differential equations into a system of algebraic equations. This step does not require historical data and is based solely on the geometric point cloud. A discrete set of nodes is generated in the rotor region. For each node... The global physical stiffness matrix is ​​constructed using the RBF basis function approximation differential operator. The resulting system of linear equations is in the form of: .in It contains the physical mechanism of heat conduction, which is a specific implementation of the system matrix described in step S102.

[0047] Step S4: Construct optimization criteria based on condition number.

[0048] Observation matrix A sparse matrix representing the sensor placement location. Constructing the augmented system matrix. physical matrix With observation matrix Stacking, for Calculate the fitness function, i.e., the matrix. Condition number (ConditionNumber, ):

[0049] condition number The smaller the value, the more stable the inversion system and the stronger its ability to resist measurement noise. The goal of the optimization algorithm is to find the optimal matrix. (i.e., sensor position), making The minimum condition number function is a specific mathematical expression of the objective function described in step S103, used to quantitatively evaluate the stability of the physical field inversion.

[0050] Step S5: Optimization using a genetic algorithm with a geometric filter.

[0051] Initialize a randomly generated population, i.e., multiple sets of sensor coordinates. Through geometric constraint filtering, examine the coordinates of each individual in each generation of evolution. Calculate radial distance Determine whether it has fallen into the inner ring restricted area. If so, a forced correction is performed. The point is then projected radially onto the boundary. Alternatively, generate new random individuals until the conditions are met. Calculate the condition number of the corrected individuals. The process involves selection, crossover, and mutation, repeatedly checking the coordinates of each individual and calculating the condition number until convergence. Finally, a set of sensor coordinates is output that satisfies both physical optimality (minimum condition number) and engineering feasibility (avoiding the inner loop), thus achieving the process of determining the optimal sensor layout coordinates in step S104.

[0052] Step S6: Temperature field reconstruction verification and error assessment.

[0053] Specifically, based on the optimal sensor layout coordinates output in step S5, temperature response data is extracted at the corresponding nodes of the impeller's finite element model to simulate the actual measurement signal of the sensor. To approximate real-world operating conditions, Gaussian white noise with a specific signal-to-noise ratio is added to the simulated measurement data to simulate random sensor errors. Subsequently, using the constructed temperature field reconstruction model (such as a regularized inversion algorithm), the simulated measurement data is used as input to invert and calculate the temperature field distribution inside the impeller, especially in the key mating surface area, thereby realizing the process of constructing the temperature field reconstruction model in step S105.

[0054] The temperature field obtained by high-fidelity finite element simulation is used as the reference true value (i.e., the theoretical temperature field). The reconstructed temperature field is compared with the theoretical temperature field, and the error norm (such as root mean square error RMSE) between the two is calculated. This is used to quantitatively evaluate the reconstruction accuracy of the current layout scheme under the presence of measurement noise interference. This achieves the process of determining the error norm between the reconstructed temperature field and the theoretical temperature field in step S106.

[0055] Step S7: Online reconstruction and monitoring of hardware.

[0056] The error norm calculated in step S6 is compared with a preset engineering allowable threshold. If the error norm is less than the preset threshold, it indicates that the measurement data under this layout scheme contains sufficient information to ensure that the accuracy of the inversion results meets the engineering control requirements, thus confirming the validity of the optimal sensor layout coordinates. After confirmation, the sensor is installed at the coordinate position output in step S5 to collect real-time temperature data. Server receives Combined with physical matrix The inverse problem equations are solved to calculate the overall temperature distribution, including the inner ring region. This achieves the verification of the optimal sensor layout coordinates in step S107. This step enables real-time monitoring of the compressor rotor's hot-fitting process and verifies the effectiveness of the optimal layout coordinates in practical engineering.

[0057] In some embodiments, see Figure 3 Based on the governing equations, a system matrix is ​​constructed, including: Step S301: Determine the finite element discretization scheme based on the governing equations.

[0058] Specifically, for the impeller heat conduction governing equations (partial differential equations), this embodiment employs the Galerkin weighted residual method for spatial domain discretization. The continuous geometric model of the impeller is divided into several discrete finite element elements (such as tetrahedral or hexahedral elements), and an appropriate interpolation function (shape function) is selected within each element to approximate the temperature field distribution. By performing weak form processing and discretization derivation on the governing equations, an algebraic relationship between element node temperature and heat flux density is established, which is the finite element discretization scheme.

[0059] Step S302: Based on the finite element discretization scheme, determine the element heat conduction matrix and element heat capacity matrix.

[0060] Specifically, based on the discrete scheme, numerical integration is performed on each element by combining the thermophysical parameters of the impeller material (thermal conductivity, density, specific heat capacity). For the element heat conduction matrix, its elements are determined by the integral of the gradient of the shape function and the thermal conductivity, reflecting the thermal resistance characteristics and heat diffusion capacity inside the element; for the element heat capacity matrix, its elements are determined by the integral of the shape function and the density and specific heat capacity, reflecting the thermal inertia and temperature change rate characteristics of the element.

[0061] Step S303: Construct the system matrix based on the unit heat conduction matrix and the unit heat capacity matrix.

[0062] Specifically, based on the topological connections of the finite element mesh, the heat conduction and heat capacity matrices of all elements are superimposed and assembled according to node numbers to form the overall heat conduction and heat capacity matrices characterizing the thermal properties of the entire impeller structure. Subsequently, boundary conditions from actual thermal assembly processes (such as convective heat transfer boundary conditions on the impeller surface) are introduced to modify the overall matrix, ultimately constructing a system matrix describing the dynamic characteristics of the system's temperature response. This system matrix will serve as the foundational data for subsequent sensitivity analysis and objective function construction.

[0063] This embodiment transforms complex partial differential control equations into a solvable set of algebraic equations using finite element discretization technology. By assembling the element matrix and introducing boundary conditions, a system matrix that can accurately characterize the impeller's geometric features and thermal properties is constructed. This provides a solid mathematical and physical model foundation for subsequent calculation of the sensitivity matrix and optimization of sensor layout, effectively ensuring that the optimization process truly reflects the physical mechanism.

[0064] In some embodiments, see Figure 4 Based on the mapping relationship between sensor placement and the system matrix, an objective function is constructed, including: Step S401: Determine the observation matrix based on the sensor layout.

[0065] The observation matrix indicates the correspondence between sensor measurement points and discrete nodes in the system; specifically, it establishes the correspondence between sensor measurement signals and the temperatures of discrete nodes in the system. In the finite element model, it is assumed that the system has a total of... N If a discrete node is selected from the current layout scheme, then... M If sensors are placed at each node location, a dimension of is constructed. M×N The observation matrix H. Each row of this matrix corresponds to a sensor measurement point. If the first row is the first row, then the second row is the first row. i The sensors are arranged in the... k At the nth node, the nth node in the observation matrix i Line number k The column contains only 1s, and all other elements in the row are 0s. Using the observation matrix, local temperature information at the sensor measurement location can be extracted from the system's full-dimensional temperature vector.

[0066] Step S402: Determine the sensitivity matrix based on the system matrix.

[0067] The sensitivity matrix indicates how sensitive the temperature response of each node in the system is to changes in the heat source; specifically, it reflects the sensitivity of the system's temperature field to changes in the parameters to be inverted (such as unknown heat sources or boundary heat flows). Based on the system matrix constructed in the preceding steps, the sensitivity equation is solved using the direct differentiation method or the adjoint method. In the heat conduction problem, the elements in the sensitivity matrix S represent the...i The temperature of the node affects the first j The partial derivatives of each heat source parameter, i.e. This sensitivity matrix quantitatively describes how minute perturbations in the physical field parameters are transmitted through the network and cause changes in the temperature response of each node, revealing the physical coupling strength between the measurement location and the region to be inverted.

[0068] Step S403: Determine the mapping relationship based on the observation matrix and the sensitivity matrix.

[0069] The mapping relationship is used to represent the mathematical association between sensor measurement data and the physical field parameters to be inverted. Specifically, the observation matrix H and the sensitivity matrix S are combined to construct a direct mathematical association between the sensor measurement data and the physical field parameters to be inverted. The parameter identification transfer matrix P = SP = H × S is obtained using matrix multiplication. This matrix represents the mapping path from the space of the heat source parameters to be inverted to the space of sensor measurement data. Through this mapping relationship, internally unmeasurable physical parameters can be transformed into observable external temperature signal changes, thus providing a crucial mathematical model foundation for subsequent information assessment and inversion calculations.

[0070] Step S404: Determine the Fisher information matrix based on the mapping relationship.

[0071] The Fisher information matrix indicates the amount of effective information contained in the measurement data for reconstructing the temperature field. Specifically, the Fisher information matrix is ​​constructed using the parameter identification transfer matrix P, thereby quantifying the amount of effective information contained in the measurement data for parameter estimation. Assuming that the measurement noise follows a Gaussian distribution, the Fisher information matrix J can be expressed as J=P. T WP, where W is the weight matrix (related to the noise covariance matrix). The inverse of the Fisher information matrix is ​​often used as a lower bound for the parameter estimation error covariance matrix. Therefore, the eigenvalues ​​of this matrix directly reflect the ability of the sensor layout scheme to suppress the uncertainty of physical field parameter inversion. The larger the matrix information content, the higher the inversion accuracy.

[0072] Step S405: Construct the objective function based on the Fisher information matrix.

[0073] Specifically, to find the optimal layout through optimization algorithms, the Fisher information matrix needs to be transformed into a comparable scalar index as the objective function. This embodiment selects the determinant of the Fisher information matrix (corresponding to the D-optimality criterion) or the condition number as the optimization index. A larger determinant indicates a smaller confidence ellipsoid volume for parameter estimation and higher inversion accuracy; a smaller condition number indicates a lower ill-conditioned nature of the inversion problem and better numerical stability. Based on the selected index, an objective function is constructed, such as maximizing det(J) or minimizing cond(J), thereby transforming the sensor layout optimization problem into a mathematical programming problem of finding the extremum of the objective function within the geometric constraint domain.

[0074] This embodiment constructs a complete mapping path from the parameters to be inverted to the measurement data by sequentially determining the observation matrix and the sensitivity matrix. The information transmission efficiency and noise resistance of the mapping path are quantitatively evaluated using the Fisher information matrix. Finally, an objective function with clear physical meaning is constructed, realizing a scientific quantitative evaluation of the stability and accuracy of the sensor layout scheme inversion, and providing a solid mathematical basis for finding the optimal solution in the future.

[0075] In some embodiments, see Figure 5 Based on the geometrically constrained domain, the objective function is solved using an optimization algorithm to determine the optimal sensor layout coordinates, including: Step S501: Within the feasible region of the geometric constraint domain, randomly generate an initial sensor layout population.

[0076] Specifically, the geometric constraint domain of the impeller's outer surface is discretized into a finite set of candidate nodes from which sensors can be placed. During the initial optimization algorithm phase, a random encoding method is used to randomly select several node coordinates from this candidate node set as an individual, representing a sensor layout scheme. This process is repeated to generate multiple individuals, forming the initial sensor layout population. The number of sensors in each individual is preset according to actual monitoring requirements and must satisfy geometric avoidance constraints to ensure that the initial solutions are distributed within the feasible solution space, providing a diversity basis for the global search.

[0077] Step S502: Based on the objective function, determine the fitness value of individuals in the initial sensor layout population.

[0078] Specifically, for each individual in the initial population, its sensor coordinate information is analyzed to construct a corresponding observation matrix. Using the sensitivity matrix derived in the preceding steps, the Fisher information matrix under this layout scheme is calculated, and numerical operations are performed according to the constructed objective function (such as calculating the determinant of the matrix or the reciprocal of the condition number) to obtain the fitness value of that individual. This fitness value quantifies the contribution of the current layout scheme to the stability of the physics field inversion; a higher fitness indicates that the layout scheme has a greater advantage in suppressing measurement noise and improving reconstruction accuracy.

[0079] Step S503: Use the optimization algorithm to iteratively update the sensor layout position until the preset convergence condition is met, and output the coordinates of the individual with the highest fitness value as the optimal sensor layout coordinates.

[0080] Specifically, intelligent optimization strategies such as genetic algorithms and particle swarm optimization are employed to iteratively evolve the population. High-fitness individuals are retained through selection operations, and new layout schemes are generated through crossover and mutation operations to explore a better solution space. In each generation of evolution, the fitness value of the new individuals is recalculated, and the global optimal solution is updated. The iteration process terminates when the number of iterations reaches a preset maximum value or the change in fitness value is less than a preset threshold (i.e., the convergence condition is met). At this point, the node coordinates carried by the individual with the highest fitness value in the population are output as the optimal placement position of the sensor on the impeller surface.

[0081] This embodiment generates an initial population within the geometric constraint domain and uses an optimization algorithm for iterative optimization, thereby achieving a global intelligent search for sensor layout schemes. This effectively overcomes the shortcomings of traditional empirical methods that are prone to getting trapped in local optima, ensuring that the final layout scheme can maximize the information gain of temperature field reconstruction under complex engineering constraints.

[0082] In some embodiments, see Figure 6 Based on the physical characteristics of the target object, the governing equations and geometric constraint domains are determined, including: Step S601: Determine the heat transfer mechanism and structural avoidance area based on the physical characteristics of the target object.

[0083] Specifically, the physical processes of the impeller hot-fitting process are analyzed in depth. During the heating stage, the impeller is placed in a heating furnace and absorbs heat primarily through radiation and convection. During the transfer and assembly stages, the impeller surface undergoes convective heat transfer with the air, while the inner bore contacts the main shaft, resulting in contact thermal resistance heat transfer. Based on this, the heat transfer mechanism of the impeller is determined to include the coupling effects of heat conduction, convection, and radiation heat transfer. Simultaneously, based on the impeller's geometric model, areas where sensor placement is prohibited are identified, such as the impeller blade edges (due to excessive curvature making installation difficult), the area around bolt holes (requiring wrench space), and chamfered areas with structural interference risks. These areas are marked as structural avoidance zones.

[0084] Step S602: Based on the heat transfer mechanism and the structural avoidance region, determine the heat conduction differential equation and the sensor infeasibility region.

[0085] Specifically, based on the law of conservation of energy and Fourier's law of heat conduction, a three-dimensional unsteady-state heat conduction differential equation describing the temperature field distribution inside the impeller is established, which is expressed in the following form:

[0086] in ρ For density, c For specific heat capacity, k Thermal conductivity, Q It serves as an internal heat source. Simultaneously, the structural avoidance area determined in step S601 is mapped onto the surface of the impeller's three-dimensional geometric model, and this surface area is defined as the sensor infeasible region, i.e., the set of regions where generating sensor coordinates is prohibited during the optimization process.

[0087] Step S603: Determine the governing equations based on the heat conduction differential equation and boundary conditions.

[0088] Specifically, to ensure that the heat conduction differential equation has a definite solution, initial conditions and boundary conditions must be introduced. The initial condition is set as the ambient temperature or preheating temperature before heating; the boundary conditions include the convective heat transfer coefficient of the impeller surface, the comprehensive heat transfer coefficient (considering radiation), and the contact thermal resistance boundary conditions of the inner hole and the main shaft contact surface. Combining the heat conduction differential equation with the above definite solution conditions constitutes a complete mathematical physics definite solution problem, which is the governing equation described in this embodiment, used to describe the temperature field evolution law of the impeller throughout the entire heat assembly process.

[0089] Step S604: Determine the geometric constraint domain based on the sensor infeasibility domain.

[0090] Specifically, the non-feasible region for sensors is removed from the outer surface area of ​​the impeller's overall structure, and the remaining continuous or discrete surface area constitutes the geometric constraint domain. This geometric constraint domain represents the feasible solution space for sensor placement. In subsequent optimization algorithms, the coordinates of all candidate sensor layouts must fall within this geometric constraint domain to ensure that the optimization results conform to both the physical laws of heat transfer and the structural and technological requirements for on-site installation.

[0091] This embodiment analyzes the heat transfer mechanism and structural characteristics of the impeller hot-fitting process in depth, transforms physical laws into mathematical control equations, and transforms engineering installation constraints into geometric constraint domains. This achieves an organic combination of physical model and engineering constraints, ensuring that the subsequent optimization model not only has a solid physical foundation, but also that the optimization results are engineering-feasible.

[0092] In some embodiments, see Figure 7 Based on the element heat conduction matrix and element heat capacity matrix, a system matrix is ​​constructed, including: Step S701: Assemble based on the unit heat conduction matrix and unit heat capacity matrix to determine the overall heat conduction matrix and overall heat capacity matrix.

[0093] Specifically, in finite element analysis, the overall impeller structure is discretized into a finite number of elements. First, all elements are traversed, and based on the mapping relationship between element node numbers and overall node numbers, the contributions of the heat conduction and heat capacity matrices of each element are accumulated and added to the corresponding positions in the overall matrix. This process is called overall assembly, ultimately yielding the overall heat conduction matrix (denoted as K) characterizing the thermal resistance of the entire impeller structure and the overall heat capacity matrix (denoted as M) characterizing its thermal inertia. The dimensions of these two matrices are the same as the total number of nodes in the finite element model, reflecting the overall geometric structure and material property distribution of the impeller.

[0094] Step S702: Based on the overall heat conduction matrix and the overall heat capacity matrix, introduce boundary conditions to determine the system matrix.

[0095] Specifically, after assembly, the overall matrix needs to be corrected to reflect the actual physical environment. Based on the actual operating conditions during the impeller hot-mounting process, a third type of boundary condition (such as convective heat transfer between the impeller surface and the surrounding air) is introduced and superimposed as an additional heat transfer term into the overall heat transfer matrix. Simultaneously, for nodes with known temperatures, the matrix equations are corrected using either the set-to-1 method or the multiplication method. The matrix equations after boundary condition processing are the system matrix described in this embodiment, and their form is: ,in, C The total heat capacity matrix, Let be the vector of the derivative of the nodal temperature with respect to time. KThe overall heat conduction matrix, where T is the nodal temperature array and F is the nodal thermal load vector, describes the transient thermophysical behavior of the impeller under specific conditions.

[0096] This embodiment constructs a complete finite element system matrix through matrix assembly and the introduction of boundary conditions, realizing the mapping from local element characteristics to the overall structural physical model, and providing an accurate mathematical and physical model foundation for subsequent solution of the sensitivity matrix and temperature field inversion.

[0097] In some embodiments, see Figure 8 Based on the observation matrix and sensitivity matrix, the mapping relationship is determined, including: Step S801: Determine the observation equation based on the observation matrix.

[0098] Specifically, the observation matrix H is a sparse matrix where the number of rows represents the number of sensors and the number of columns represents the total number of nodes in the finite element model. The system state vector is then multiplied by this matrix on the left. T (Nodal temperature array), construct the observation equation ,in Y For sensor measurement data vectors, This equation is used to measure the noise vector. It establishes a direct link between finite measurement point data and the overall temperature state, describing "what was measured".

[0099] Step S802: Determine the state response equation based on the sensitivity matrix.

[0100] Specifically, the sensitivity matrix S reflects the degree to which the temperature field is sensitive to changes in the parameters to be inverted (such as the heat flux density of the internal pores). Based on the linearization assumption, the state-response equation T=S is constructed. Q ,in Q Let be the vector of physical field parameters to be inverted, and T be the system node temperature response. This equation describes how changes in physical field parameters drive the evolution of the temperature field, i.e., "how the state changes".

[0101] Step S803: Determine the parameter identification transfer matrix based on the observation equation and the state response equation.

[0102] Specifically, the state response equation is substituted into the observation equation to eliminate the intermediate variable, the system state vector. T ,get ,in Y Let H be the sensor measurement data vector, S be the observation matrix, S be the sensitivity matrix, and Q be the physical field parameter vector to be inverted. Let P be the measurement noise vector. Define P = HS as the parameter identification transfer matrix. This parameter identification transfer matrix P establishes a linear mapping bridge between the sensor measurement data and the physical field parameters to be inverted, quantifying the response of the measured values ​​to parameter changes.

[0103] Step S804: Determine the mapping relationship based on the parameter identification transfer matrix.

[0104] Specifically, the parameter identification transfer matrix P is defined as the core mapping relationship between the sensor layout and the parameters to be inverted. The rank of this parameter identification transfer matrix P determines the parameter identifiability of the inversion problem, and the singular values ​​of the parameter identification transfer matrix P determine the numerical stability and noise resistance of the inversion problem, forming the key mathematical basis for subsequently constructing the optimization objective function.

[0105] This embodiment derives the parameter identification transfer matrix by simultaneously solving the observation equation and the state response equation, thereby establishing a direct mapping relationship from the measurement space to the parameter space, and providing mathematical logic for quantitatively evaluating the impact of sensor layout on inversion performance.

[0106] In some embodiments, see Figure 9 Based on the mapping relationship, the Fisher information matrix is ​​determined, including: Step S901: Determine the measurement noise covariance matrix based on the mapping relationship.

[0107] The measurement noise covariance matrix is ​​used to indicate the statistical characteristics of random errors in sensor measurement data. Specifically, based on sensor selection and the industrial environment, a statistical model for measurement noise is determined. It is assumed that the measurement noise at each measuring point is independent and follows a zero-mean Gaussian distribution, with its standard deviation determined by the sensor's accuracy specifications. A measurement noise covariance matrix R is constructed; this is a diagonal matrix, with diagonal elements representing the variance of the corresponding sensor noise, reflecting the reliability of the measurement data.

[0108] Step S902: Determine the analytical expression of the Fisher information matrix based on the measurement noise covariance matrix.

[0109] Specifically, based on the Cramer-Rao lower bound theorem in statistics, and assuming that the measurement noise follows a Gaussian distribution, the analytical expression of the Fisher information matrix is ​​derived as follows: Where P is the parameter recognition transfer matrix, and R... 1 This is the inverse of the noise covariance matrix. This expression shows that the amount of information depends not only on the sensitivity of the layout location (transfer matrix) but also on the measurement noise level.

[0110] Step S903: Determine the Fisher information matrix based on the analytical expression of the Fisher information matrix.

[0111] Specifically, the transfer matrix P and noise covariance matrix R determined in the preceding steps are substituted into the analytical expression, and matrix operations are performed to calculate the specific Fisher information matrix value. This matrix contains all the effective information about the parameters to be inverted from the measurement data, and its inverse matrix is ​​the lower bound of the parameter estimation error covariance matrix.

[0112] This embodiment introduces the statistical characteristics of measurement noise and derives the analytical expression of the Fisher information matrix, realizing the probabilistic statistical modeling of the sensor layout scheme information acquisition capability. This enables the optimization process to take into account both sensitivity and noise resistance, and improves the robustness of the optimization results.

[0113] In some embodiments, see Figure 10 Based on the Fisher information matrix, construct the objective function, including: Step S1001: Determine the matrix determinant or condition number based on the Fisher information matrix.

[0114] Specifically, scalar indices are extracted from the Fisher information matrix to meet different optimization requirements. If the goal is to improve the overall accuracy of parameter estimation (minimize the volume of the uncertain ellipsoid), the determinant det(J) of the matrix is ​​calculated; if the goal is to improve the numerical stability of the inversion problem (avoid ill-conditioned equations), the condition number cond(J) of the matrix is ​​calculated.

[0115] Step S1002: Determine the mathematical expression of the optimization objective based on the matrix determinant or condition number.

[0116] Specifically, the aforementioned scalar indicators are transformed into an optimization objective function. If the determinant is used as the indicator, a maximization objective function is constructed. (D-optimal criterion); if the condition number is used as the indicator, construct a minimization objective function. Furthermore, the two can be weighted and combined according to actual needs to form a multi-objective optimization expression.

[0117] Step S1003: Construct the objective function based on the mathematical expression of the optimization objective.

[0118] Specifically, the final constructed objective function f(x) Define a set of layout coordinates, calculate the Fisher information matrix corresponding to the layout, and then calculate the objective function value, which serves as the basis for evaluating the merits of the layout scheme.

[0119] This embodiment transforms the sensor layout optimization problem into a solvable mathematical programming problem by converting the multidimensional Fisher information matrix into a scalarized objective function, ensuring that the optimization algorithm can find the optimal solution that meets the requirements of high precision and high stability.

[0120] Figure 11This is a schematic diagram of the physical-driven impeller temperature field monitoring sensor layout optimization system 11 provided in this application embodiment. See also... Figure 11 The system includes: a first determining module 1101, a first constructing module 1102, a second constructing module 1103, and a second determining module 1104; the specific configuration is as follows: The first determining module 1101 is used to determine the control equations and geometric constraint domains based on the physical characteristics of the target object. The target object is used to indicate the impeller entity to be monitored. The physical characteristics include geometric model, thermal property parameters and structural features. The first construction module 1102 is used to construct a system matrix based on the control equation, wherein the system matrix is ​​used to characterize the thermophysical properties of the target object; The second construction module 1103 is used to construct an objective function based on the mapping relationship between the sensor layout position and the system matrix. The sensor layout position represents the candidate spatial coordinates of the sensor in the geometric constraint domain. The objective function is used to evaluate the stability of the physical field inversion. The second determining module 1104 is used to determine the optimal sensor layout coordinates by solving the objective function through an optimization algorithm based on the geometric constraint domain.

[0121] Optionally, see Figure 12 The physical-driven impeller temperature field monitoring sensor layout optimization system 11 also includes: The third construction module 1105 is used to construct a temperature field reconstruction model based on the optimal sensor layout coordinates.

[0122] The third determining module 1106 is used to determine the error norm between the reconstructed temperature field and the theoretical temperature field based on the temperature field reconstruction model.

[0123] The confirmation module 1107 is used to confirm that the optimal sensor layout coordinates are valid if the error norm is less than a preset threshold.

[0124] Optionally, the first construction module 1102 includes: Discrete elements are used to determine the finite element discretization scheme based on the governing equations.

[0125] The first determining unit is used to determine the element thermal conduction matrix and the element thermal capacity matrix based on the finite element discretization scheme.

[0126] The first building unit is used to build a system matrix based on the unit thermal conduction matrix and the unit thermal capacity matrix.

[0127] Optionally, the second building module 1103 includes: The second determining unit is used to determine the observation matrix based on the sensor layout position. The observation matrix is ​​used to indicate the correspondence between the sensor measurement point position and the discrete nodes of the system.

[0128] The third determining unit is used to determine a sensitivity matrix based on the system matrix, wherein the sensitivity matrix is ​​used to indicate the sensitivity of the temperature response of each node in the system to changes in the heat source.

[0129] The fourth determining unit is used to determine a mapping relationship based on the observation matrix and the sensitivity matrix, wherein the mapping relationship is used to represent the mathematical association between the sensor measurement data and the physical field parameters to be inverted.

[0130] The fifth determining unit is used to determine the Fisher information matrix based on the mapping relationship. The Fisher information matrix is ​​used to indicate the amount of effective information contained in the measurement data for reconstructing the temperature field.

[0131] The second construction unit is used to construct the objective function based on the Fisher information matrix.

[0132] Optionally, the second determining module 1104 includes: The generation unit is used to randomly generate an initial sensor layout population within the feasible region of the geometric constraint domain.

[0133] The sixth determining unit is used to determine the fitness value of individuals in the initial sensor layout population based on the objective function.

[0134] The output unit is used to iteratively update the sensor layout position using an optimization algorithm until a preset convergence condition is met, and outputs the coordinates of the individual with the highest fitness value as the optimal sensor layout coordinates.

[0135] Optionally, the first determining module 1101 includes: The seventh determining unit is used to determine the heat transfer mechanism and structural avoidance area based on the physical characteristics of the target object.

[0136] The eighth determining unit is used to determine the heat conduction differential equation and the sensor infeasibility region based on the heat transfer mechanism and the structural avoidance region.

[0137] The ninth determining unit is used to determine the governing equations based on the heat conduction differential equation and boundary conditions.

[0138] The tenth determining unit is used to determine the geometric constraint domain based on the infeasible domain of the sensor.

[0139] Optionally, the first building unit includes: Assemble sub-units for assembling based on the unit heat conduction matrix and unit heat capacity matrix, and determine the overall heat conduction matrix and overall heat capacity matrix.

[0140] Sub-units are introduced to determine the system matrix by introducing boundary conditions based on the overall thermal conduction matrix and the overall thermal capacity matrix.

[0141] Optionally, the fourth determining unit includes: The first determining subunit is used to determine the observation equation based on the observation matrix.

[0142] The second determining subunit is used to determine the state response equation based on the sensitivity matrix.

[0143] The third determining subunit is used to determine the parameter identification transfer matrix based on the observation equation and the state response equation.

[0144] The fourth determining subunit is used to identify the transfer matrix based on the parameters and determine the mapping relationship.

[0145] Optionally, the fifth determining unit includes: The fifth determining subunit is used to determine the measurement noise covariance matrix based on the mapping relationship. The measurement noise covariance matrix is ​​used to indicate the statistical characteristics of random errors in the sensor measurement data. The sixth determining subunit is used to determine the analytical expression of the Fisher information matrix based on the measurement noise covariance matrix.

[0146] The seventh determining subunit is used to determine the Fisher information matrix based on the analytical expression of the Fisher information matrix.

[0147] Optionally, the second building unit includes: The eighth determining subunit is used to determine the matrix determinant or condition number based on the Fisher information matrix.

[0148] The ninth determining subunit is used to determine the mathematical expression of the optimization objective based on the matrix determinant or condition number.

[0149] Construct sub-units to build objective functions based on the mathematical expression of the optimization objective.

[0150] It should be noted that the physical-driven impeller temperature field monitoring sensor layout optimization system provided in the above embodiments is only an example of the division of the above functional modules when optimizing the layout of the impeller temperature field monitoring sensor. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the computer device can be divided into different functional modules to complete all or part of the functions described above. In addition, the vehicle control device provided in the above embodiments and the physical-driven impeller temperature field monitoring sensor layout optimization method embodiments belong to the same concept, and the specific implementation process is detailed in the method embodiments, which will not be repeated here.

[0151] This embodiment also provides a computer-readable storage medium storing computer program code. When the computer program code is run on a computer, the computer executes the above-described related method steps to implement the physical-driven impeller temperature field monitoring sensor layout optimization method provided in the above embodiment.

[0152] This embodiment also provides a computer program product that, when run on a computer, causes the computer to perform the aforementioned related steps to implement the physical-driven impeller temperature field monitoring sensor layout optimization method provided in the above embodiment.

[0153] In this embodiment, the device, computer-readable storage medium, computer program product, or chip are all used to execute the corresponding methods provided above. Therefore, the beneficial effects they can achieve can be referred to the beneficial effects in the corresponding methods provided above, and will not be repeated here.

[0154] Through the above description of the embodiments, those skilled in the art will understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0155] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus 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 apparatus, 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 apparatuses or units may be electrical, mechanical, or other forms.

[0156] The above description is only a specific implementation of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application.

Claims

1. A method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive, characterized in that, The method includes: Based on the physical characteristics of the target object, the governing equations and geometric constraint domains are determined. The target object is used to indicate the impeller entity to be monitored. The physical characteristics include geometric model, thermophysical parameters, and structural features. Based on the governing equations, a system matrix is ​​constructed, which is used to characterize the thermophysical properties of the target object; Based on the mapping relationship between the sensor layout positions and the system matrix, an objective function is constructed, where the sensor layout positions represent the candidate spatial coordinates of the sensors within the geometrically constrained domain. The objective function is used to evaluate the stability of the physical field inversion. Specifically, based on the sensor layout positions, an observation matrix is ​​determined, which indicates the correspondence between the sensor measurement point positions and the discrete nodes of the system. Based on the system matrix, a sensitivity matrix is ​​determined, which indicates the sensitivity of each node's temperature response to changes in the heat source. Based on the observation matrix and the sensitivity matrix, a mapping relationship is determined, which represents the mathematical association between the sensor measurement data and the physical field parameters to be inverted. Based on the geometric constraint domain, the objective function is solved using an optimization algorithm to determine the optimal sensor layout coordinates.

2. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 1, characterized in that, The construction of the system matrix based on the control equations includes: Based on the aforementioned governing equations, the finite element discretization scheme is determined; Based on the aforementioned finite element discretization scheme, the element heat conduction matrix and element heat capacity matrix are determined; Based on the unit heat conduction matrix and the unit heat capacity matrix, a system matrix is ​​constructed.

3. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 1, characterized in that, The step of constructing the objective function based on the mapping relationship between the sensor layout positions and the system matrix includes: Based on the mapping relationship, a Fisher information matrix is ​​determined, which is used to indicate the amount of effective information contained in the measurement data for reconstructing the temperature field. Based on the Fisher information matrix, construct the objective function.

4. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 1, characterized in that, The step of determining the optimal sensor layout coordinates by solving the objective function through an optimization algorithm based on the geometric constraint domain includes: Within the feasible region of the geometric constraint domain, an initial sensor layout population is randomly generated; Based on the objective function, determine the fitness value of individuals in the initial sensor layout population; The sensor layout is iteratively updated using an optimization algorithm until a preset convergence condition is met. The coordinates of the individual with the highest fitness value are then output as the optimal sensor layout coordinates.

5. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 1, characterized in that, The step of determining the governing equations and geometric constraint domain based on the physical characteristics of the target object includes: Based on the physical characteristics of the target object, determine the heat transfer mechanism and structural avoidance area; Based on the heat transfer mechanism and the structural avoidance region, the heat conduction differential equation and the sensor infeasibility region are determined. Based on the aforementioned heat conduction differential equation and boundary conditions, the governing equations are determined; Based on the infeasibility region of the sensor, the geometric constraint region is determined.

6. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 2, characterized in that, The construction of the system matrix based on the unit heat conduction matrix and the unit heat capacity matrix includes: Based on the unit heat conduction matrix and unit heat capacity matrix, the overall heat conduction matrix and overall heat capacity matrix are determined by assembly. Based on the overall heat conduction matrix and overall heat capacity matrix, boundary conditions are introduced to determine the system matrix.

7. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 3, characterized in that, Determining the mapping relationship based on the observation matrix and the sensitivity matrix includes: Based on the observation matrix, determine the observation equation; Based on the sensitivity matrix, determine the state response equation; Based on the observation equation and the state response equation, determine the parameter identification transfer matrix; Based on the parameters, the transfer matrix is ​​identified, and the mapping relationship is determined.

8. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 3, characterized in that, The determination of the Fisher information matrix based on the mapping relationship includes: Based on the mapping relationship, the measurement noise covariance matrix is ​​determined, which is used to indicate the statistical characteristics of random errors in sensor measurement data; Based on the measurement noise covariance matrix, determine the analytical expression for the Fisher information matrix; The Fisher information matrix is ​​determined based on the analytical expression of the Fisher information matrix.

9. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 3, characterized in that, The step of constructing the objective function based on the Fisher information matrix includes: Based on the Fisher information matrix, determine the matrix determinant or condition number; Based on the matrix determinant or condition number, determine the mathematical expression of the optimization objective; Based on the mathematical expression of the optimization objective, an objective function is constructed.

10. The method for optimizing the layout of impeller temperature field monitoring sensors based on physical drive according to claim 1, characterized in that, After determining the optimal sensor layout coordinates, the method further includes: Based on the optimal sensor layout coordinates, a temperature field reconstruction model is constructed. Based on the temperature field reconstruction model, the error norm between the reconstructed temperature field and the theoretical temperature field is determined. If the error norm is less than a preset threshold, the optimal sensor layout coordinates are confirmed to be valid.

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