Optimized arrangement method and system for airfoil flow field sensors

Abstract

The invention provides an airfoil flow field sensor optimization arrangement method and system, and the method comprises the steps: obtaining the surface flow field parameter data of an airfoil under different working conditions, and constructing a data matrix; complementing the data matrix by using the matrix complementing model; and searching and optimizing the arrangement position of the sensor by taking the completion error of the matrix completion model as an optimization target to obtain an optimal sensor arrangement scheme. The method further comprises the steps that the reconstructed complete pressure distribution is compared with actual measurement data or historical simulation data of the partial redundant sensors, and if errors exceed a preset threshold value, re-optimization of the optimal sensor arrangement scheme is triggered. According to the method, the data detected by the sensor is recovered and extracted by using the matrix completion algorithm, so as to obtain information as much as possible; the genetic algorithm is used for optimizing the configuration position of the sensor so as to maximize the information carried by the sensor detection data; the problems of sensor efficient configuration and data reconstruction in flow field detection are solved.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic data detection technology for aircraft, and in particular to a method and system for optimizing the arrangement of airfoil flow field sensors. Background Technology

[0002] From active flow control to intelligent control of future deformable aircraft, the detection of aerodynamic parameters of the flow field plays a crucial role in aircraft operation. In these flow field detection scenarios, the number of sensors can be strictly limited due to constraints such as space and cost. This raises two questions: how to rationally arrange the sensor positions to maximize the information carried by the sensor detection data, and how to extract as much information as possible from the limited sensor detection data.

[0003] Existing methods primarily address these two problems based on proper orthogonal decomposition (POD). A typical example is the use of a greedy algorithm combined with the Gappy POD method to configure sensor placement, and its application in unsteady flow within cylindrical wakes. Furthermore, applications include using heuristic algorithms for efficient sensor placement in cylindrical wake flows, and using POD methods combined with self-organizing maps to predict complete data from limited probe data. These POD-based methods have a potential limitation, making them difficult to apply to complex scenarios. This is because the original POD method is a linear model, making it difficult to handle nonlinear data. Even in transonic flow fields, performance degradation occurs. Improvements to address this issue typically require modeling the specific original physics problem, which limits the applicability of these improved methods. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for optimizing the arrangement of airfoil flow field sensors, aiming to solve the above-mentioned problems in the prior art.

[0005] This invention provides a method for optimizing the arrangement of airfoil flow field sensors, including: Acquire surface flow field parameter data of the airfoil under different operating conditions to form a data matrix containing multiple operating condition samples and multiple potential sensor measurement locations; A matrix completion model is established based on the low-rank characteristic of the data matrix, and the data matrix is ​​completed using the matrix completion model. The completion error of the matrix completion model is used as the optimization target to search and optimize the sensor placement to obtain the optimal sensor placement scheme.

[0006] This invention provides an airfoil flow field sensor optimization arrangement system, comprising: The data module is used to acquire surface flow field parameter data of the airfoil under different operating conditions, forming a data matrix containing multiple operating condition samples and multiple potential sensor measurement locations; The completion module is used to establish a matrix completion model based on the low-rank characteristics of the data matrix, and to complete the data matrix using the matrix completion model; The optimization module is used to search and optimize the sensor placement by taking the completion error of the matrix completion model as the optimization target, so as to obtain the optimal sensor placement scheme.

[0007] This invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the above-described airfoil flow field sensor optimization arrangement method.

[0008] This invention also provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-described airfoil flow field sensor optimization arrangement method.

[0009] The following beneficial effects can be achieved by adopting the embodiments of the present invention: The embodiments of the present invention propose an airfoil sensor arrangement scheme based on matrix completion algorithm combined with genetic algorithm. The scheme uses matrix completion algorithm to recover and extract the data detected by the sensor in order to obtain as much information as possible; the genetic algorithm is used to optimize the configuration position of the sensor in order to maximize the information carried by the sensor detection data; so as to solve the problem of efficient sensor configuration and data reconstruction in flow field detection. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart of the airfoil flow field sensor optimization arrangement method according to an embodiment of the present invention; Figure 2 This is an overall flowchart of the airfoil flow field sensor optimization arrangement method based on matrix completion and genetic algorithm according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the optimal sensor arrangement scheme according to an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the arrangement scheme of the present invention with random and uniform arrangement schemes; Figure 5 This is a schematic diagram of the optimized arrangement system of airfoil flow field sensors according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the optimized arrangement system of flow field sensors according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the aircraft wall pressure real-time monitoring and reconstruction system according to an embodiment of the present invention. Detailed Implementation

[0012] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0013] Method Implementation Examples According to an embodiment of the present invention, a method for optimizing the arrangement of airfoil flow field sensors is provided. Figure 1 This is a flowchart of the airfoil flow field sensor optimization arrangement method according to an embodiment of the present invention, as follows: Figure 1 As shown, the airfoil flow field sensor optimization arrangement method according to an embodiment of the present invention specifically includes: Step S101: Obtain surface flow field parameter data of the airfoil under different working conditions, and form a data matrix containing multiple working condition samples and multiple potential sensor measurement positions; The surface flow field parameter data are the pressure coefficients of the airfoil surface; The potential sensor measurement locations correspond to the computational grid points on the airfoil surface; The data matrix was obtained through computational fluid dynamics numerical simulation.

[0014] Step S102: Establish a matrix completion model based on the low-rank characteristic of the data matrix, and use the matrix completion model to complete the data matrix; The matrix completion model is a low-rank matrix completion model constructed based on the minimization of the nuclear norm, and is solved by an iterative soft-threshold singular value decomposition algorithm to recover complete data from sparse observation data.

[0015] Step S103 involves using the completion error of the matrix completion model as the optimization objective to search for and optimize the sensor placement, thereby obtaining the optimal sensor placement scheme. Specifically, this includes: Using the completion error of the matrix completion model as the optimization objective, a genetic algorithm is employed to search and optimize the sensor placement, resulting in the optimal sensor placement scheme that minimizes the completion error. Specifically, this includes: A binary encoding method is used to represent whether the sensor is placed at each potential location, and the root mean square error of the matrix completion model is used as the fitness function to construct an optimization problem. An initial population is generated, and selection, crossover, and mutation operations are performed iteratively to optimize the population; When the preset termination condition is met, output the sensor layout scheme corresponding to the individual with the smallest fitness function value; The initial population includes elite individuals generated by selecting measurement locations where the gradient of flow field parameter changes exceeds a preset threshold, and random individuals generated by random sampling without replacement.

[0016] The method further includes: The complete pressure distribution reconstructed by the optimal sensor arrangement scheme is compared with the measured data of some redundant sensors or historical simulation data. If the error exceeds a preset threshold, the optimal sensor arrangement scheme is re-optimized.

[0017] The following describes in detail the above-mentioned technical solution of the present invention with reference to the specific details of the airfoil flow field sensor optimization arrangement method in the embodiments of the present invention.

[0018] This invention provides a method for optimizing the arrangement of airfoil flow field sensors, such as... Figure 2 As shown, it includes the following steps: S1. Constructing the flow field data matrix: Based on historical or simulation data, form a data matrix containing airfoil surface parameters under multiple operating conditions. Where m is the number of samples and n is the number of potential sensor locations; The airfoil surface parameters are pressure coefficients, and a complete dataset is obtained through CFD simulation at different angles of attack, Mach numbers, and flight altitudes. The potential sensor locations correspond to mesh points on the airfoil surface, and the number of these points is related to the number of object surface meshes in the CFD calculation mesh.

[0019] S2. Matrix Completion Processing: Missing parts in the data matrix are restored using a low-rank matrix completion algorithm. This algorithm is based on a nuclear norm minimization model and satisfies the following optimization problem: ; Where X represents the complete matrix (target recovery matrix) containing airfoil surface pressure coefficient data under all operating conditions. The nuclear norm of matrix X is the sum of all its singular values, used to measure the low rank of the matrix; M represents the observation matrix, i.e., the original data matrix with known partial data. This represents the known observation at position (i, j). The constraint is that at a known location, i.e., under the i-th operating condition, the value of the recovery matrix at the j-th sensor must be consistent with the observed value.

[0020] The matrix completion algorithm specifically employs the Iterative Soft Threshold Singular Value Decomposition (IST-SVD) algorithm to solve the nuclear norm minimization problem.

[0021] S3. Sensor Position Optimization: Using the root mean square error of matrix completion as the fitness function, a genetic algorithm iteratively searches for the optimal combination of sensor positions to minimize the fitness function. Specifically, this includes: S31. Define the feasible region space Ω and the optimization problem: ; In the formula, x∈Ω is a feasible solution in the feasible region, representing a possible sensor arrangement scheme; matrix X is consistent with the above definition; N represents the total number of missing matrix elements; This represents the true observations where the matrix elements have missing values, while This represents the predicted value for these missing elements; S32. Generate an initial population and calculate the fitness value of each individual in the population according to the above formula; S33. Use the selection operator to generate the offspring population from the previous generation population, and then use the crossover operator and mutation operator to operate on the offspring population in sequence to achieve the purpose of evolution. S34. Repeat the operation process of the three genetic operators until the population converges to obtain the final optimal sensor layout scheme.

[0022] Specifically, the technical solution of this invention can be divided into three core steps, with each step forming a closed-loop synergy. The detailed steps are as follows: Step 1: Construction of airfoil flow field sample dataset (offline stage) The core objective of this step is to generate a high-quality sample dataset to provide data support for subsequent algorithms. Specific operations include: First, airfoil modeling and mesh generation were performed, and CFD numerical simulation parameters were set. The three-dimensional Reynolds-averaged Navier-Stokes equations were solved using the finite volume method, and the SST k- turbulence model was selected. Model (balancing subsonic viscous flow and transonic shock wave capture accuracy); Boundary condition settings: inlet boundary is pressure far field, outlet boundary is pressure outlet, airfoil surface is no-slip adiabatic wall. Secondly, the working condition sample design and data collection were carried out. The Latin hypercube sampling (LHS) method was used to design the working condition combination to avoid sample redundancy and cover the entire working condition range.

[0023] Data storage format: The airfoil surface pressure coefficient data for each working condition is stored as a 1×n vector (n is the number of potential sensors, corresponding to the number of grid points on the CFD calculation surface). All samples are combined to form an m×n dimensional data matrix X, where the rows of the matrix represent working condition samples and the columns represent the pressure coefficient values ​​at the locations of potential sensors.

[0024] Step 2: Sensor position optimization based on genetic algorithm This step utilizes the global search capability of a genetic algorithm to find the sensor placement location that minimizes the matrix completion MSE, thereby maximizing the amount of information in the detected data. The specific steps are as follows: 1. First, define the optimization problem: Decision variables: Let the number of sensors be k, and the decision variables be binary vectors. , =1 indicates that the sensor is placed at the j-th potential location. =0 indicates no arrangement, and ; Objective function: ; That is, the root mean square error of matrix completion under the corresponding layout scheme; 2. Genetic Algorithm Parameter Design: A. Population encoding: Binary encoding is used, with each individual corresponding to a binary vector of length n (n=160 or 320), and the number of "1"s in the vector is k.

[0025] B. Initial population generation: A combined strategy of "elite initialization + random generation" is adopted; Elite individuals: Prioritize the selection of the k positions with the largest standard deviation of the pressure coefficient from potential positions (i.e., the regions with the highest information entropy, such as the leading edge of the airfoil and the middle section of the upper surface) to generate an initial population of 10%. Random individuals: The remaining 90% of the initial population is generated through random sampling without replacement to ensure population diversity; Population size: set to 50 (subsonic) - 80 (transonic) to balance search efficiency and diversity.

[0026] C. Genetic operators: Selection operator: Tournament selection is adopted. Five individuals are randomly selected each time, and the two with the smallest MSE are selected to enter the offspring population. The operation is repeated until the size of the offspring population is the same as that of the parent population. Crossover operator: Single-point crossover is used. For the selected parent individuals, a crossover point is randomly selected, and the gene segments after the crossover point are exchanged. To ensure that the number of "1"s in the crossover individuals is still k, individuals with an incorrect number of "1"s after crossover are adjusted by random replacement (e.g., if there are too many "1"s, they are replaced with "0", and if there are too few, "1"s are added). The crossover probability is set to 0.8. Mutation operator: A bit-flipping mutation is used, flipping each gene bit in each offspring individual with a probability of 0.05 (0 < ... 1 or 1 0); similarly, it is necessary to ensure that the number of "1"s after mutation is k; the mutation probability is set to 0.05.

[0027] D. Termination condition: Iteration stops when the maximum number of generations is 200 (subsonic) - 300 (transonic), or when the change in MSE of the best individual in the population is <1e-7 for 20 consecutive generations.

[0028] E. Output and Verification of Optimal Layout Scheme like Figure 3 As shown, after the iteration is complete, the sensor location corresponding to the individual with the smallest MSE in the population is output.

[0029] Step 3: Actual flow field detection and data reconstruction (online stage) This step applies the optimal layout scheme output from step 2 to a real-world engineering scenario, enabling real-time reconstruction from sparse observations to complete flow field data. The specific steps are as follows: 1. Data preprocessing: Filter the collected raw data to obtain the online observation matrix Y; 2. Real-time data reconstruction: The matrix completion algorithm from step 2 is called to complete the online observation matrix Y; 3. Reconstruction Result Evaluation and Feedback (Real-time Evaluation): Calculate the MSE of the reconstructed data and the observations of a small number of redundant sensors (placed in non-critical areas for verification). If the MSE > preset threshold (e.g., subsonic 2e-03, transonic 3e-03), trigger re-optimization (return to step 2 to adjust the number or location of sensors). 4. Output of results: The reconstructed complete surface pressure coefficient data is converted into visual curves (such as pressure coefficient distribution curves and isobaric plots) and transmitted to the aircraft control system to provide support for flow control decisions.

[0030] The following are two specific implementation examples generated based on experimental data of the subsonic NACA0012 airfoil and the transonic RAE2822 airfoil, which are used to further support the technical solutions proposed in the embodiments of the present invention.

[0031] Example 1: Optimized Arrangement of Subsonic NACA0012 Airfoil Sensor 1. Data Matrix Construction Complete surface pressure coefficient data for 510 different working conditions were obtained through CFD numerical simulation, and a data matrix was constructed. ; Each row of the matrix corresponds to the pressure coefficient value at 160 locations for a given operating condition.

[0032] 2. Matrix completion verification Low-rank verification: Data shows that the pressure coefficient curves are similar in shape under different working conditions, and the singular values ​​of the matrix decay rapidly, satisfying the low-rank hypothesis (the first 12 singular values ​​contribute more than 99.7% cumulatively). Missing data threshold test: When the missing data rate is ≤70%, the root mean square error (MSE) of matrix completion is less than 1.0× When the missing rate is >70%, the error increases sharply.

[0033] 3. Genetic Algorithm Optimization The sensor configuration scheme was optimized using a genetic algorithm, and compared with uniform and random sensor placement schemes. Different conditions were set, with the number of sensors ranging from 6 to 20, corresponding to missing rates ranging from 87% to 96%, and the sensor placement scheme under these conditions was optimized using a genetic algorithm. Parameter settings: Population size 100, crossover probability 0.8, mutation probability 0.02, maximum iterations 200 generations; Optimization results: 6-sensor configuration: Optimal positions are concentrated on the upper surface of the airfoil's leading edge (high-pressure gradient region) and the lower surface of the trailing edge (separation region). Reconstruction accuracy: MSE reduced to 1.084× Significantly superior to uniform arrangement (error exceeding 5×) ).

[0034] 4. Technical Effects Reconstruction comparison: such as Figure 4 As shown, the reconstructed curves of the six optimized sensors almost perfectly match the true values, with minimal error, especially in the rapidly changing leading-edge region. Efficiency improvement: Only six sensors are needed to replace the traditional uniformly arranged 20 sensors, reducing costs by 70%.

[0035] Example 2: Optimized Arrangement of Transonic RAE2822 Airfoil Sensor This embodiment demonstrates the effectiveness of the present invention in nonlinear effects and variable boundaries in transonic flow field data. This example simulates a surface pressure coefficient detection scenario for a deformable airfoil based on the RAE2822 supercritical airfoil under transonic conditions. For simplicity, the RAE2822 airfoil was parameterized using a 16-parameter shape function / class function (CST) parameterization method. Surface pressure coefficient data from a total of 184 sample points were obtained by changing the shape control parameter A and performing CFD numerical simulation. Specific implementation steps include: 1. Data generation and parameterization: The 16-parameter CST (class function / shape function) parameterization method was used to generate 184 deformable airfoil samples. CFD simulation was used to obtain 320 surface pressure coefficient points for each sample (160 points on the upper and lower surfaces).

[0036] 2. Optimization results of genetic algorithm Number of sensors: 16-32 (corresponding to a missing rate of 90%-95%).

[0037] Optimal placement pattern: As the genetic algorithm evolves, the root mean square error of the best individual in the population decreases significantly, which is consistent with the results of the subsonic embodiment. This indicates that the genetic algorithm effectively reduces the test error of the matrix completion algorithm, thereby effectively obtaining the optimal sensor placement scheme. The effectiveness of the obtained optimal configuration scheme is further verified on the validation sample set.

[0038] System Implementation Examples According to an embodiment of the present invention, an optimized arrangement system for airfoil flow field sensors is provided. Figure 5 This is a schematic diagram of an airfoil flow field sensor optimization arrangement system according to an embodiment of the present invention, as shown below. Figure 5 As shown, the airfoil flow field sensor optimization arrangement system according to an embodiment of the present invention specifically includes: Data module 50 is used to acquire surface flow field parameter data of airfoil under different working conditions, forming a data matrix containing multiple working condition samples and multiple potential sensor measurement positions; The completion module 52 is used to establish a matrix completion model based on the low-rank characteristics of the data matrix, and to complete the data matrix using the matrix completion model; The optimization module 54 is used to search and optimize the sensor placement by taking the completion error of the matrix completion model as the optimization target, so as to obtain the optimal sensor placement scheme. The system further includes: The verification module is used to compare the complete pressure distribution reconstructed by the optimal sensor arrangement scheme with the measured data of some redundant sensors or historical simulation data. If the error exceeds a preset threshold, the optimal sensor arrangement scheme is re-optimized.

[0039] The following describes in detail the above-mentioned technical solutions of the present invention with reference to the specific details of the airfoil flow field sensor optimization arrangement system of the present invention.

[0040] This invention also provides an airfoil flow field sensor optimization arrangement system, such as... Figure 6 As shown, it includes: Data acquisition module: used to acquire flow field data of airfoil surface under multiple operating conditions; Matrix completion calculation module: Configured to execute low-rank matrix completion algorithm to restore missing data; Genetic Algorithm Optimization Module: Used to optimize sensor placement and output the optimal configuration scheme.

[0041] The data acquisition module supports the fusion input of offline complete data and online sparse data, ensuring that each column in the matrix has at least one observation.

[0042] Preferably, this embodiment of the invention also provides a real-time monitoring and reconstruction system for airfoil surface pressure. It uses the sensor arrangement scheme described in the method embodiment to collect sparse data and reconstructs the pressure distribution across the entire airfoil surface in real time using a matrix completion algorithm. Specifically, it includes four parts: an offline database, an online pressure sensing module, a matrix completion calculation module, and an online pressure reconstruction module. Figure 7 As shown; The offline database contains pre-calculated full wall pressure data, forming a data matrix; The online pressure sensing module collects sparse pressure data in real time from sensors with optimized configuration locations; The matrix completion calculation module takes the full offline database and the coefficient pressure data collected by the sensors as input, and uses the matrix completion method to solve the problem, thereby restoring the complete wall pressure distribution from the sparse sensor data. The online pressure reconstruction module uses the calculation results of the matrix completion calculation module as the wall pressure reconstruction result to realize the pressure reconstruction function.

[0043] The embodiments of the present invention are system embodiments corresponding to the above method embodiments. The specific operation of each module can be understood by referring to the description of the method embodiments, and will not be repeated here.

[0044] In summary, this invention proposes a method and system for optimizing the arrangement of airfoil flow field sensors based on matrix completion and genetic algorithms. The method first constructs a multi-condition airfoil surface flow field data matrix and then uses a low-rank matrix completion algorithm (such as a kernel norm minimization model) to accurately recover missing data. Secondly, using the root mean square error of the matrix completion as the fitness function, a genetic algorithm is used to globally search for the optimal sensor placement, achieving the reconstruction of complete flow field data with the fewest possible sensors. This invention solves the performance degradation problem of traditional linear methods in nonlinear flow fields, is applicable to subsonic and transonic scenarios, and requires only six sensors to accurately reconstruct the airfoil surface pressure distribution, significantly improving detection efficiency and reducing costs. The specific beneficial effects of this invention include: 1. Strong nonlinear adaptability: It breaks through the linear limitation of traditional POD-type methods and directly processes nonlinear data of transonic flow fields through low-rank matrix completion. The MSE of shock wave region reconstruction is ≤2.13e-03, which is more than 50% lower than that of DPOD method. 2. High sensor efficiency: Only 6 sensors are needed to achieve complete data reconstruction in subsonic conditions (missing rate 96.25%), and 16 sensors are needed to meet the accuracy requirements in transonic conditions (missing rate 95%), reducing the number of sensors by 60%-70% compared to a uniform arrangement scheme; 3. Good versatility and robustness: No need to customize models for specific airfoils or working conditions, it can be directly applied to different airfoils such as the NACA series and RAE series, and maintains stable accuracy when the missing rate is ≤70%; 4. High engineering practicality: Online reconstruction time ≤ 0.05s, meeting the requirements of real-time detection; optimized sensor layout can effectively reduce the number of sensors required.

[0045] Device Example 1 This invention provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it performs the steps described in the method embodiment.

[0046] Device Example 2 This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, performs the steps described in the method embodiment.

[0047] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; 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; and these 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 optimizing the arrangement of airfoil flow field sensors, characterized in that, include: Acquire surface flow field parameter data of the airfoil under different operating conditions to form a data matrix containing multiple operating condition samples and multiple potential sensor measurement locations; A matrix completion model is established based on the low-rank characteristic of the data matrix, and the data matrix is ​​completed using the matrix completion model. The completion error of the matrix completion model is used as the optimization target to search and optimize the sensor placement to obtain the optimal sensor placement scheme.

2. The method according to claim 1, characterized in that, The method further includes: The complete pressure distribution reconstructed by the optimal sensor arrangement scheme is compared with the measured data of some redundant sensors or historical simulation data. If the error exceeds a preset threshold, the optimal sensor arrangement scheme is re-optimized.

3. The method according to claim 1, characterized in that, The surface flow field parameter data are the pressure coefficients of the airfoil surface; The potential sensor measurement locations correspond to the computational grid points on the airfoil surface; The data matrix was obtained through computational fluid dynamics numerical simulation.

4. The method according to claim 1, characterized in that, The matrix completion model is a low-rank matrix completion model constructed based on the minimization of the nuclear norm, and is solved by an iterative soft-threshold singular value decomposition algorithm to recover complete data from sparse observation data.

5. The method according to claim 1, characterized in that, Using the completion error of the matrix completion model as the optimization objective, the sensor placement is searched and optimized to obtain the optimal sensor placement scheme, which specifically includes: Using the completion error of the matrix completion model as the optimization objective, a genetic algorithm is used to search and optimize the sensor placement to obtain the optimal sensor placement scheme that minimizes the completion error.

6. The method according to claim 5, characterized in that, The use of genetic algorithms to search for and optimize the placement of sensors specifically includes: A binary encoding method is used to represent whether the sensor is placed at each potential location, and the root mean square error of the matrix completion model is used as the fitness function to construct an optimization problem. An initial population is generated, and selection, crossover, and mutation operations are performed iteratively to optimize the population; When the preset termination condition is met, output the sensor layout scheme corresponding to the individual with the smallest fitness function value; The initial population includes elite individuals generated by selecting measurement locations where the gradient of flow field parameter changes exceeds a preset threshold, and random individuals generated by random sampling without replacement.

7. An optimized arrangement system for airfoil flow field sensors, characterized in that, include: The data module is used to acquire surface flow field parameter data of the airfoil under different operating conditions, forming a data matrix containing multiple operating condition samples and multiple potential sensor measurement locations; The completion module is used to establish a matrix completion model based on the low-rank characteristics of the data matrix, and to complete the data matrix using the matrix completion model; The optimization module is used to search and optimize the sensor placement by taking the completion error of the matrix completion model as the optimization target, so as to obtain the optimal sensor placement scheme.

8. The system according to claim 7, characterized in that, The system further includes: The verification module is used to compare the complete pressure distribution reconstructed by the optimal sensor arrangement scheme with the measured data of some redundant sensors or historical simulation data. If the error exceeds a preset threshold, the optimal sensor arrangement scheme is re-optimized.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the airfoil flow field sensor optimization arrangement method as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the airfoil flow field sensor optimization arrangement method as described in any one of claims 1-6.

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