A method for optimizing the layout of internal flow field measurement sensors based on numerical data mining

Abstract

This invention belongs to the field of aero-engine measurement technology and relates to a method for optimizing the layout of sensors for internal flow field measurement based on numerical data mining. The method involves four steps: acquiring numerical data of the interface under multiple operating conditions, extracting feature points based on Gaussian process regression, establishing a single-condition sensor layout based on mutual information criteria, and determining the optimal sensor layout based on k-means clustering algorithm. This method aims to capture as much spatial distribution information of flow field physical quantities as possible with a limited number of sensors, guiding the sensor arrangement in geometrically constrained internal flow field experiments. The goal is to minimize experimental costs while ensuring the capture of key flow field features. The optimized sensor layout obtained by this invention improves the accuracy of spatial mean measurements and has significant advantages in capturing key flow field features.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine measurement technology and relates to a method for optimizing the layout of internal flow field measurement sensors based on numerical data mining. Background Technology

[0002] When using sensors to experimentally measure the internal flow field of aero-engines, limitations imposed by geometric constraints, structural strength, and interference with the flow field restrict not only the spatial placement of sensors but also their number and measurement locations. In traditional internal flow field measurements (such as compressor tip clearance static pressure, engine inlet Mach number, blade surface static pressure, and engine inlet distortion), sensors are typically uniformly distributed or, based on experience, installed at specific locations for single-point measurements. In recent years, with increasing demands for aircraft maneuverability, higher requirements have been placed on the aerodynamic performance of aero-engines under harsh operating conditions and inlet distortion environments, prompting researchers to focus on capturing details of non-uniform flow fields such as inlet distortion, large separation, and shock waves. However, traditional uniform sensor layout schemes and single-point measurements are insufficient to meet these requirements. To resolve this contradiction, obtaining as much flow field information as possible with as few sensors as possible becomes crucial; therefore, optimizing the internal flow field sensor layout has become one of the urgent technical problems to be solved.

[0003] Sensor placement optimization has garnered significant attention in fields such as indoor environmental monitoring, structural health monitoring, agricultural environmental monitoring, robotic sensing, spacecraft attitude control, and biomedical engineering. From the perspective of optimization objectives, it can be categorized into two types: One type aims to obtain more reliable signals by optimizing sensor placement. For example, in rocket attitude control research, a dual-rate gyroscope sensor placement optimization method is used to suppress elastic vibration interference and improve measurement accuracy. In aero-engine vibration research, optimization criteria are proposed based on the vibration amplitude and vibration components in each direction at the measurement point, ensuring that sensors are placed in locations sensitive to the excitation response of each bearing position, thus improving the accuracy of vibration measurements. The other type aims to obtain as much information as possible with as few sensors as possible by optimizing sensor placement. For example, in the field of autonomous driving, particle swarm optimization and genetic algorithms are used to solve the sensor placement optimization problem, rationally arranging sensors to expand the coverage area. In forest fire detection, the Conditional Value at Risk mutual information placement model and the Submodular Online Greedy algorithm are used to optimize the placement of wireless sensors, achieving comprehensive monitoring of the entire area. In the field of structural health monitoring, deep neural networks are used to solve the sensor placement optimization problem, enabling scientific and rational assessment of structures.

[0004] The purpose of this invention is similar to the latter; however, the difference lies in the fact that the above is essentially a coverage problem. In other words, ensuring that the overlap of the areas detected / collected by the sensors is minimized ensures that a limited number of sensors can collect as much information as possible. In contrast, the amount of information in the field described in this invention (experimental measurement of the spatial distribution of physical quantities in the flow field within an aero-engine) depends on the richness of the capture of complex physical phenomena such as flow separation, shock waves, and wakes. Therefore, it is necessary to develop sensor layout optimization methods suitable for experimental measurement of the spatial distribution of physical quantities in the flow field within an aero-engine, based on specific requirements.

[0005] The optimization calculation method based on Gaussian process regression provides a reference for the selection of sensor placement locations. This involves using existing experimental measurement data as input, fitting the spatial distribution of the physical field through Gaussian process regression, and then employing a greedy algorithm to solve for a set of optimal sensor locations, as described in patent 201410223460.0. However, three challenges remain in the field of aero-engine measurement: first, the availability of abundant experimental data as input; second, how to quantitatively assess the amount of information carried by the sensor measurement points; and third, given the high sensitivity of the internal flow field of aero-engines to changes in incoming flow conditions, how to ensure the robustness of sensor placement schemes obtained through data mining. Summary of the Invention

[0006] The technical solution adopted by this invention to solve the technical problem is: a method for optimizing the layout of internal flow field measurement sensors based on numerical data mining, comprising the following steps:

[0007] Step S1: Obtain numerical data of the test section under multiple operating conditions. Use numerical simulation to simulate the flow field under d different incoming flow conditions (i.e., operating conditions), and extract the geometric coordinates and corresponding physical quantities of the center point of the grid of the test section. For operating condition i, the set of coordinates of the center point of the grid of the test section i∈[1,d] and the set of physical quantities are respectively represented by Q. i and F(Q) i ) represents the number of grid center points, i.e., Q. i The number of elements in the middle is denoted by q, i.e., |Q i |=q i ;

[0008] Step S2: Feature point extraction based on Gaussian process regression. The numerical simulation data of the cross-section to be measured in Step S1 is used as input data to address the problem of insufficient experimental data. Feature point extraction involves selecting a subspace location set C from Q using a greedy algorithm as the feature point spatial set. The number of feature points is m, i.e., |C| = m. A Gaussian process regression model is established based on C and the corresponding physical quantity set F(C), reducing the area-weighted root mean square error (RMSE) of the model's prediction of physical quantities at q spatial points to within ε0. The definition of RMSE is as follows:

[0009]

[0010] In formula (1):

[0011] W j F represents the area of ​​the grid at the center point j. j and These represent the numerical calculation result and the prediction result at the grid center point j, respectively; the choice of ε0 is flexibly determined according to the desired accuracy.

[0012] Step S3: Single-condition sensor layout based on mutual information criterion; Based on the geometric constraints on sensor placement under the influence of multiple walls and structural strength in internal flow field measurement, the obtained feature point spatial set C is decomposed into a spatial set P where sensors can be placed and a spatial set N where sensors cannot be placed, i.e., C = P∪N; Select a set Y from P such that I(F Y ;F C\Y The maximum value is reached, as shown in equation (8):

[0013]

[0014] I(F) Y ;F C\Y The simplified expression is MI(Y). A greedy algorithm is used to solve this problem, selecting sensor positions one by one to maximize the increase in mutual information. The position A of the next sensor should satisfy:

[0015] A = argmax A∈P\Y [MI(Y∪A)-MI(Y)] (9)

[0016] According to information theory, the objective function in equation (9) is calculated from equation (10); where H(F A |F Y )and Representing the given F Y and Under the premise F A Conditional entropy; M represents M\(Y∪A);

[0017]

[0018] Using Gaussian process regression, a regression model is established based on the physical quantities at the sensor location, and the physical quantities at locations where no sensor is placed are obtained through prediction; the optimization problem of equation (9) is expressed as:

[0019]

[0020]

[0021] Step S4: Optimal sensor layout based on k-means clustering algorithm; The optimal sensor layout with high robustness is obtained from the sensor positions obtained from multiple operating conditions using a clustering algorithm.

[0022] Preferably, the numerical simulation method in step S1 includes, but is not limited to, the Reynolds-averaged method (RANS), the large eddy simulation method (LES), and the hybrid RANS-LES method.

[0023] Preferably, in step S2, the selection range of ε0 is between 1% and 5%.

[0024] Preferably, step S2 includes the following specific steps:

[0025] Step S2-1: Initialize Set C: Select the locations corresponding to the maximum and minimum values ​​of physical quantities in the numerical data of the cross-section to be measured as the initial feature location set, that is:

[0026]

[0027] Step S2-2: Establish a Gaussian process regression model based on the spatial location set C and its corresponding physical quantity F(C); the Gaussian process regression model is uniquely determined by the mean function M(·) and the kernel function K(·,·), that is:

[0028]

[0029] In equation (3), c j ∈C, j∈[1,2,…,m], simplifying the notation, equation (3) is simplified to equation (4), that is, for a set of spatial locations C, its average vector is represented by μ c This is represented by M(·), where each element is determined by M(·), and the covariance matrix is ​​represented by Σ. CC This means that each element is calculated using K(·,·):

[0030] F(C)~GP(μ C ,Σ CC (4)

[0031] Step S2-3: Prediction of flow field physical quantities based on Gaussian process regression model:

[0032] Based on the Gaussian process model established above, the physical quantities at q grid center points on the surface to be measured can be predicted, that is, the mean μ of the conditional probability distribution predicted for any spatial location A in set Q. A|C Covariance

[0033]

[0034]

[0035] The RMSE error of the prediction of physical quantities at q spatial locations on the cross section to be measured under the current number of feature points is calculated according to equation (1).

[0036] Step S2-4: Select the spatial location A of the next feature point:

[0037] Choose the covariance in equation (6). The location A where the maximum value is located is taken as the next feature point spatial location and added to the feature point spatial location set C:

[0038]

[0039] Step S2-5: Determine whether RMSE≤ε0 is satisfied. If it is satisfied, then the number of elements m in C is the optimal number of feature points, and the corresponding position set C is the final feature point set; otherwise, repeat steps S2-2 to S2-4.

[0040] Preferably, step S3 includes the following specific steps:

[0041] Step S3-1: Processing geometric constraints: Extract the set of alternative spatial locations P from the set of spatial locations of feature points C based on geometric constraints;

[0042] Step S3-2: Initial sensor spatial location set Y and preset number of sensors: Based on the numerical data, select the spatial location corresponding to the maximum or minimum value of the physical quantity in set P as the initial sensor spatial location set Y, that is: Given a preset number of sensors n0, which is given based on the maximum possible sensor placement location in the experiment, and n0≤|P|;

[0043] Step S3-3: The next spatial location A for placing the sensor: For all A∈P\Y, the intermediate variable δ is calculated according to equation (12). A According to equation (11), choose the one that makes δ AThe spatial location where the maximum value is reached is taken as the next spatial location A for placing the sensor, and this spatial location is added to the set Y;

[0044] Step S3-4: Loop: Calculate the RMSE error of the physical quantity of the cross section to be measured based on the measurement results of the sensors in the current set Y according to equation (1); repeat steps S3-2 to S3-3 until the number of elements in set Y reaches n0, i.e., |Y|=n0;

[0045] Step S3-5: Determining the sensor location and the optimal number of sensors: When the RMSE error remains basically unchanged with the increase of the sensor measurement point location, the corresponding optimal number of sensors is n, and the corresponding set of sensor locations is the set of sensor locations Y selected under the current working condition.

[0046] Preferably, in step S4, considering the results of d operating conditions, the optimal number of sensors for each operating condition is n. i , where i∈[1,d]; the set of positions obtained for d working conditions in The k-means clustering algorithm is used to divide the location set of the above d working conditions into k clusters, denoted as S = {S1, S2, ..., S...} k}, the set of the center points of the k-cluster is D = {D1, D2, ..., D} k This refers to the optimal sensor layout considering multiple operating conditions.

[0047] More preferably, in step S4, the formula In this context, these N spatial locations are divided into k clusters, denoted as S = {S1, S2, ..., S...}. k}, which minimizes the sum of squares within the cluster; that is:

[0048]

[0049] Where D i In cluster S i The center point, that is:

[0050]

[0051] |S i | represents S i The number of elements in the middle.

[0052] The beneficial effects of this invention are:

[0053] 1. This invention establishes an internal flow field sensor layout optimization method based on numerical data mining, which uses a limited number of sensors to capture as much spatial distribution information of flow field physical quantities as possible. This information is used to guide the arrangement of sensors in geometrically constrained internal flow field experimental measurements, achieving the goal of minimizing experimental costs while ensuring that the main features of the flow field are captured. Compared with the traditional uniform sensor layout, the sensor optimization layout obtained by the method proposed in this invention can improve the accuracy of spatial mean measurement.

[0054] 2. The sensor optimization layout measurement results of the present invention can not only capture the two low total pressure regions near the upper and lower end walls, as well as the high total pressure region of the area, but also capture the trend of the low total pressure region near the upper wall shrinking and the low total pressure region near the lower end wall increasing as the incoming Mach number increases. Traditional uniform layout schemes are difficult to capture the above features. Therefore, the sensor optimization layout method of the present invention has significant advantages in capturing the main features of the flow field. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for optimizing the layout of internal flow field measurement sensors based on numerical data mining;

[0056] Figure 2 This is a flowchart of feature point extraction based on Gaussian process regression;

[0057] Figure 3 This is a flowchart of the optimal sensor layout for a single operating condition based on the mutual information criterion.

[0058] Figure 4 It is a geometric model of a compressor blade cascade with tip clearance and a cross-sectional view to be measured;

[0059] Figure 5 It is a grid distribution diagram of the section to be measured;

[0060] Figure 6 The diagram shows the dimensionless total pressure distribution of the cross section under three operating conditions (with inflow Mach numbers of 0.4, 0.5, and 0.6, respectively).

[0061] Figure 7 This is a graph showing the relationship between the RMSE error of the physical quantity of the measured cross section predicted by the Gaussian process regression model based on feature points and the number of feature points.

[0062] Figure 8 The distribution of physical quantities of the cross section under test is obtained based on feature point prediction under three operating conditions (flow Mach numbers of 0.4, 0.5 and 0.6 respectively);

[0063] Figure 9 This is a graph showing the relationship between the RMSE error of the physical quantity of the measured cross section predicted by the Gaussian process regression model based on sensor measurement results and the number of sensor measurement points.

[0064] Figure 10 This is the optimal layout diagram of the sensors;

[0065] Figure 11 It is a distribution map of physical quantities of the cross section to be measured, obtained by predicting the optimal layout of sensors under multiple working conditions based on the k-means clustering algorithm.

[0066] Figure 12 It is a distribution map of physical quantities of the cross section to be measured after linear interpolation of the measurement results of 12 uniformly placed sensors. Detailed Implementation

[0067] The related technologies of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0068] refer to Figures 1-12 This invention provides a method for optimizing the layout of internal flow field sensors based on numerical data mining, in order to solve the technical problem that the uniformly distributed sensor layout in current aero-engine internal flow field measurement is difficult to capture flow field details.

[0069] The flowchart of the optimal sensor placement method for internal flow field based on numerical data mining is as follows: Figure 1 As shown, the process mainly includes four steps: acquiring numerical data of the interface under multiple working conditions, feature point extraction based on Gaussian process regression, sensor layout under a single working condition based on mutual information criterion, and optimal sensor layout based on k-means clustering algorithm.

[0070] The following will introduce them one by one:

[0071] Step 1: Obtain numerical data of the cross-section under d working conditions:

[0072] Numerical simulation was used to simulate the flow field under d different incoming flow conditions, and the geometric coordinates and corresponding physical quantities of the center points of the grid at the test section were extracted. For operating condition i, the set of coordinates of the center points of the grid at the test section i∈[1,d] and the set of physical quantities are respectively represented by Q. i and F(Q) i The number of grid center points (Q) is represented by ). i The number of elements in the middle is represented by q, i.e., |Q| i |=q i To simplify the description, the subscripts indicating the operating conditions will be omitted below without causing ambiguity.

[0073] The numerical simulation methods discussed here include, but are not limited to, the Reynolds-averaged method (RANS), the large eddy simulation method (LES), and the hybrid RANS-LES method. The choice of specific numerical simulation method requires a trade-off between the required numerical accuracy and the acceptable computational load. For highly separated, high Reynolds-number flow fields, the hybrid RANS-LES method is recommended; for highly separated, low Reynolds-number flow fields, the LES method can be chosen; and for flow fields with relatively small separation, the RANS method is sufficient.

[0074] Step 2: Feature point extraction based on Gaussian process regression

[0075] Numerical simulation data of the cross-section under test is used as input data to address the problem of limited experimental data availability. However, even for a single cross-section under test, the amount of numerical data is typically very large (10). 3 ~10 5 Using this data as input for sensor layout optimization is not only time-consuming but also prone to overfitting. This problem is particularly pronounced in some high-fidelity numerical methods, such as LES and hybrid RANS-LES. Therefore, before optimizing sensor layout, feature extraction should be used to reduce the amount of numerical data.

[0076] The principle of feature point extraction is to use a greedy algorithm to select a subspace location set C from Q as the feature point space set, with the number of feature points being m (i.e., |C|=m). A Gaussian process regression model is established based on C and the corresponding physical quantity set F(C), which reduces the area-weighted root mean square error (RMSE) of the model's prediction of physical quantities at q spatial points to within ε0. The definition of RMSE is as follows:

[0077]

[0078] Among them W j F represents the area of ​​the grid at the center point j. j and These represent the numerical calculation result and the prediction result at the grid center point j, respectively. The choice of ε0 should be flexibly determined according to the desired accuracy, and it is recommended to choose between 1% and 5%.

[0079] The specific process is as follows: Figure 2 As shown:

[0080] S2-1: Initialize Set C: Select the locations corresponding to the maximum and minimum values ​​of physical quantities in the numerical data of the cross-section to be measured as the initial feature location set, i.e.:

[0081]

[0082] S2-2: Establishing a Gaussian process regression model based on the spatial location set C and its corresponding physical quantity F(C): The Gaussian process regression model can be uniquely determined by the mean function M(·) and the kernel function K(·,·), that is:

[0083]

[0084] In equation (3), c j ∈C, j∈[1,2,…,m], where the mean function value is the physical quantity at the corresponding location. The key to this model lies in determining the kernel function. Currently, the most commonly used kernel function in Gaussian process regression is the radial basis function. In addition, there are linear kernel functions, polynomial kernel functions, periodic kernel functions, etc. The choice of kernel function needs to be based on the flow field characteristics to select the one that maximizes the model's generalization ability. In the method of this invention, the choice of kernel function is not specifically defined.

[0085] To simplify the notation, equation (3) is simplified to equation (4), that is, for a set of spatial locations C, its average vector is represented by μ. C This is represented by M(·), where each element is determined by M(·), and the covariance matrix is ​​represented by Σ. CC This means that each element is calculated using K(·,·).

[0086] F(C)~GP(μ C ,Σ CC (4)

[0087] S2-3: Prediction of flow field physical quantities based on Gaussian process regression model:

[0088] Based on the Gaussian process model established above, the physical quantities at q grid center points on the surface to be measured can be predicted, that is, the mean μ of the conditional probability distribution predicted for any spatial location A in set Q. A|C Covariance

[0089]

[0090]

[0091] The RMSE error of the prediction of physical quantities at spatial positions on the cross section to be measured is calculated according to the current number of feature points.

[0092] S2-4: Select the spatial location of the next feature point A:

[0093] σ in equation (6) A|C To reflect the uncertainty of the prediction results, covariance is chosen. The location A where the maximum value is located is taken as the next feature point spatial location and added to the feature point spatial location set C:

[0094]

[0095] S2-5: Determine whether RMSE≤ε0 is satisfied. If it is satisfied, then the number of elements m in C is the optimal number of feature points, and the corresponding position set C is the final feature point set; otherwise, repeat steps S2-2 to S2-4.

[0096] Step 3: Optimal sensor layout for a single operating condition based on mutual information criterion

[0097] In internal flow field measurements, the placement of sensors is typically constrained by geometric factors such as multiple walls and structural strength. Based on this constraint, the spatial set C of feature points obtained above is decomposed into a set P of possible sensor placement locations and a set N of locations where sensors cannot be placed, i.e., C = P∪N. The goal of the "sensor placement selection based on mutual information criterion" step is to select a set Y of n spatial locations in P that contains the maximum amount of information.

[0098] Here, "information content" is quantified by the mutual information between the spatial set Y and the set of all other spatial points C besides Y (denoted as C\Y). Therefore, the goal of this step is to select a set Y from P such that I(F Y ;F C\Y The maximum value is reached, as shown in equation (8).

[0099]

[0100] To simplify the expression, I(F) Y ;F C\Y Let MI(Y) be the denoted MI(Y). Since equation (8) is an NP-hard nondeterministic polynomial problem, a greedy algorithm is used to solve it, that is, to select the sensor positions one by one to maximize the increase in mutual information. In other words, the position A of the next sensor should satisfy:

[0101] A = argmax A∈P\Y [MI(Y∪A)-MI(Y)] (9)

[0102] According to information theory, the objective function in equation (9) can be calculated from equation (10). Where H(F) A |F Y )and Representing the given F Y and Under the premise F A The conditional entropy. Here... This represents M\(Y∪A).

[0103]

[0104] To determine the conditional entropy in equation (10), we need not only the physical quantities at the sensor's location but also the physical quantities at locations where no sensor is placed. Here, Gaussian process regression is used to establish a regression model based on the physical quantities at the sensor's location, and the physical quantities at locations where no sensor is placed are predicted. Combining equations (5), (6), and (10), the optimization problem in equation (9) can be expressed as:

[0105]

[0106]

[0107] The specific process is as follows: Figure 3 As shown:

[0108] S3-1: Handling geometric constraints: Extract the set of alternative spatial locations P from the set of spatial locations of feature points C based on geometric constraints.

[0109] S3-2: Initial sensor spatial location set Y and preset number of sensors: Based on the numerical data, the spatial location corresponding to the maximum or minimum value of the physical quantity in set P is selected as the initial sensor spatial location set Y, that is: Given a preset number of sensors n0, which is given based on the maximum possible sensor placement location in the experiment, and n0≤|P|; the final optimal number of sensor locations n can be obtained according to process S3-4, usually n<n0; if the number of sensors is a fixed value in the experiment, then n0 here is the final number of sensors n, that is, there is no need to optimize the number of sensors.

[0110] S3-3: The next spatial location for placing the sensor A: For all A∈P\Y, the intermediate variable δ is calculated according to equation (12). A According to equation (11), choose the one that makes δ A The spatial location where the maximum value is reached is taken as the next spatial location A for placing the sensor, and this spatial location is added to the set Y.

[0111] S3-4: Loop: Calculate the RMSE error of the predicted physical quantity of the cross section based on the measurement results of the sensors in the current set Y according to equation (1). Repeat S3-2 to S3-3 until the number of elements in set Y reaches n0, i.e., |Y|=n0.

[0112] S3-5: Determination of sensor location and optimal number of sensors: When the RMSE error remains basically unchanged when the sensor measurement point location is increased, the corresponding optimal number of sensors is n, and the corresponding set of sensor locations is the set of sensor locations Y selected under the current working condition.

[0113] Step 4: Optimal sensor layout considering operating conditions based on k-means clustering algorithm

[0114] The distribution of physical quantities in the internal flow field is sensitive to changes in the incoming flow conditions. When the incoming flow conditions change, the distribution of physical quantities in the flow field also changes, and the sensor placement positions obtained based on the numerical flow field data also change. This invention uses a clustering algorithm to obtain a robust optimal sensor layout from sensor positions obtained under multiple conditions.

[0115] Considering the results of d operating conditions, the optimal number of sensors for each condition is n. i Where i∈[1,d]. The set of positions obtained for d working conditions. in The goal is to divide these N spatial locations into k clusters such that the sum of squares within each cluster is minimized. In other words, the objective is to divide the N spatial locations into k clusters, denoted as S = {S1, S2, ..., S...}. k}, so that:

[0116]

[0117] Where D i In cluster S i The center point, that is:

[0118]

[0119] |S i | represents S i The number of elements in the cluster, and the set of the center points of the k-cluster D = {D1, D2, ..., D...} k This refers to the optimal sensor layout that takes into account multiple operating conditions.

[0120] Example

[0121] This embodiment uses the dimensionless total pressure measurement of the outlet flow field section of a compressor cascade with tip clearance as an example to illustrate the technical solution of the present invention. The geometric model of the compressor cascade is as follows: Figure 4 As shown. The section to be measured is located at the channel exit, with a height equal to the distance between the upper and lower end walls and a length equal to the grid spacing. The mesh distribution for the numerical simulation of the section to be measured is as follows. Figure 5 As shown, the set of geometric coordinates of the grid center points is Q. In this example, the number of grid center points for the section to be measured is 8211, i.e., q = 8211.

[0122] Step 1: Obtain the dimensionless total pressure Cp2 at the center point of the grid of the test section under different working conditions through numerical simulation. In this example, three working conditions with different incoming Mach numbers are selected for the study, i.e., d = 3. The incoming Mach numbers Ma are 0.4, 0.5, and 0.6, respectively. The numerical simulation results in this example are calculated using the Reynolds-averaged (RANS) numerical method. In practical applications, methods include, but are not limited to, RANS, Large Eddy Simulation (LES), and hybrid RANS-LES. The distribution of the dimensionless static pressure Cp2 of the test section under the three working conditions is shown below. Figure 6 As shown, the physical quantity to be measured, F, in this example is the total pressure. It should be noted that Cp2 here has been normalized to improve the accuracy of the Gaussian process regression model. Dimensionlessness and normalization do not affect the spatial distribution characteristics of the total pressure; therefore, without ambiguity, the physical quantity to be measured, F, in the following text represents the normalized dimensionless total pressure.

[0123] Step 2: Spatial feature point extraction based on Gaussian process regression.

[0124] (S2-1) Initialization of the spatial location set of feature points and preset of the number of feature points. For working condition d1( Figure 6 (a)), select the spatial locations C where Cp2 reaches its maximum and minimum values. max =argmaxX Q C min =argminX Q As the initial set of spatial locations of feature points, i.e., C = C max ∪C min .

[0125] (S2-2) According to equation (3), based on the spatial location set C and its corresponding physical quantity X C Establish a Gaussian process regression model.

[0126] (S2-3) Based on equations (5) and (6), calculate the mean μ at all spatial locations A∈Q. A|C Covariance At the same time, the RMSE error of the prediction of the physical quantities of q spatial positions on the cross section to be measured under the current number of feature points is calculated according to Equation (1).

[0127] (S2-4) Choosing covariance The location A where the maximum value is located is taken as the next feature point spatial location and added to the feature point spatial location set C.

[0128] (S2-5) In this example, ε0 is set to 5%. We check if RMSE ≤ ε0. If it does, the optimal number of feature points m is the number of elements in the current spatial location set C, and the corresponding location set C is used as the final feature points. Otherwise, we repeat (S2-2) to (S2-4). The relationship between RMSE and the increase in the number of feature points in this example is as follows: Figure 7 As shown, when the number of feature points reaches 80, the RMSE steadily decreases to below 5%, therefore m = 80. The distribution of physical quantities of the measured cross section predicted based on m feature points is as follows. Figure 8 As shown in (a).

[0129] Step 3: Sensor location selection based on mutual information criterion

[0130] (S3-1) Handling geometric constraints: Considering that the radius of the sensor is 1mm, the sensor position can only be placed within the range of x2∈[0.001,0.099]. Extract the points in the feature point spatial position set C that satisfy x2∈[0.001,0.099] as the candidate spatial position set P for placing the sensor.

[0131] (S3-2) Initial Sensor Spatial Positions: For the numerical data of operating condition d1, the spatial position corresponding to the minimum physical quantity in set P is selected as the initial set of sensor spatial positions, i.e. In this example, considering the cost of data acquisition, the number of sensor locations is preset to 30 based on experience, i.e., n0 = 30.

[0132] (S3-3) The next spatial location A for placing the sensor: For all A∈P\Y, the intermediate variable δ is calculated according to equation (12). A According to equation (11), choose the one that makes δ A The spatial location where the maximum value is reached is taken as the next spatial location A for placing the sensor, and this spatial location is added to the set Y.

[0133] (S3-4) Loop: Calculate the RMSE error of the predicted physical quantity of the cross section based on the measurement results of the sensors in the current set Y according to equation (1). Repeat (3.3) until the number of elements in set Y reaches n0, i.e., |Y|=n0.

[0134] (S3-5) Determination of the optimal layout and number of sensors for a single operating condition: The relationship between the number of sensor measuring points and the RMSE error of the physical quantity of the measured cross section predicted by the Gaussian process regression model based on the sensor measuring point results is as follows: Figure 9 As shown, the RMSE error remains essentially unchanged when the number of sensor measurement points reaches 12. Therefore, the minimum number of sensor measurement points is 12, and the corresponding spatial location set is the optimal sensor layout under condition d1. Figure 10The square dots represent the Chinese Communist Party.

[0135] Step 4: Optimal sensor layout based on k-means clustering algorithm

[0136] (S4-1) Based on the numerical data of operating conditions d2 and d3, repeat steps 2 and 3 respectively to obtain the optimal sensor layout under operating conditions d2 and d3, as shown below. Figure 10 As shown in the circles and triangles, the number of sensors is 12, i.e., n1 = n2 = n3 = 12. At this time, the total number of spatial positions obtained from the three working conditions is N = 36.

[0137] (S4-2) Divide these 36 spatial locations into 12 clusters, i.e., k = 12. The set of spatial locations D obtained based on equations (12) and (13) is as follows: Figure 10 As shown in the star shape, D represents the optimal sensor layout considering multiple operating conditions. A Gaussian process regression model is established based on this location set.

[0138] Advantages of this embodiment:

[0139] This section compares the results obtained using the traditional uniform sensor layout method with the results obtained after sensor layout optimization to analyze the advantages of this embodiment. The traditional sensor layout method is a uniform layout, where 12 sensors are arranged at 12 positions consisting of x1 = [0.125t, 0.375t, 0.625t, 0.875t] and x2 = [0.1h, 0.5h, 0.9h].

[0140] From a quantitative perspective, the spatial average value of the physical quantity of the cross section to be measured is predicted based on the sensor measurement results, as shown in Table 1.

[0141]

[0142] Table 1 Comparison of the mean dimensionless total pressure space values ​​of the measured cross section obtained by optimized and uniform sensor layouts.

[0143] Based on numerical data results, it can be seen that the measurement errors of the spatial average value of cross-sectional physical quantities under three working conditions based on the optimal sensor layout are 7.3%, 7.8%, and 6.9%, respectively, while the measurement errors of the traditional uniform layout are 11.5%, 11.5%, and 10.8%, respectively. It can be seen that, compared with the traditional uniform sensor layout, the optimized sensor layout obtained by the method proposed in this invention can improve the accuracy of spatial average value measurement.

[0144] From a qualitative perspective, based on the measurement results of the optimal layout of 12 sensors, the distribution of physical quantities on the measured cross-section using a Gaussian process regression model is as follows: Figure 11As shown, the distribution of physical quantities of the cross-section under test is obtained by predicting the optimal sensor layout considering multiple operating conditions based on the k-means clustering algorithm (Gaussian process regression is used for prediction). The distribution of physical quantities of the cross-section under test after linear interpolation of the measurement results of 12 uniformly placed sensors is as follows. Figure 12 As shown. Compared with baseline data. Figure 6 The comparison shows that the sensor optimization layout measurement results can not only capture the two low total pressure regions near the upper wall (x2∈[0.08,0.1] and the lower wall (x2∈[0,0.02]), as well as the high total pressure region in the x2∈[0.04,0.08] region, but also capture the trend that the low total pressure region near the upper wall shrinks and the low total pressure region near the lower wall increases with the increase of the incoming Mach number. However, the traditional uniform layout scheme is difficult to capture the above characteristics. This demonstrates the advantages of the sensor optimization layout method proposed in this invention in capturing the main features of the flow field.

[0145] In summary, this invention establishes an internal flow field sensor layout optimization method based on numerical data mining. This method uses a limited number of sensors to capture as much spatial distribution information of flow field physical quantities as possible, which is then used to guide the sensor arrangement in geometrically constrained internal flow field experiments. This achieves the goal of minimizing experimental costs while ensuring that the main flow field features are captured. The optimized sensor layout obtained by this invention can improve the accuracy of spatial mean measurements, and the method has significant advantages in capturing the main flow field features. Therefore, this invention has broad application prospects.

[0146] It should be emphasized that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A numerical data mining based internal flow field measurement sensor layout optimization method, characterized in that, The method comprises the following steps: Step S1: Obtain numerical data of the cross-section under multiple working conditions: Use numerical simulation methods to... Numerical simulations were performed on the flow field under different incoming flow conditions, and the geometric coordinates and corresponding physical quantities of the center point of the grid at the test section were extracted. The set of coordinates of the center point of the grid of the section to be measured and the set of physical quantities are respectively used as and It means that among them The number of grid center points, i.e. The number of elements in the middle, using It means, that is ; Step S2: Feature point extraction based on Gaussian process regression: from Subspace position set is selected by greedy algorithm As a feature point space set, the number of feature points is That is , the Gaussian process regression model is established based on and corresponding physical quantity set , so that the area weighted root mean square error of the model for predicting the physical quantity of space points is reduced to within ; The definition is as follows: （1） In formula (1): denotes the grid area at the grid center point denotes the grid area at the grid center point and denotes the grid area at the grid center point denotes the numerical result and the prediction result at the grid center point denotes the error upper limit, which is flexibly determined according to the accuracy to be achieved Step S3: Single operating condition sensor layout based on mutual information criterion: From the set of spatial locations where sensors can be placed extracted from the set of characteristic points space ; the set of sensor location spaces is selected from using a greedy algorithm , the location of the sensor selected at each step should satisfy: (11) (12) wherein denotes ; the variance and covariance matrix , and through the set of spatial positions and corresponding physical quantities established by Gaussian process regression model calculation; similarly, the variance and covariance matrix , and through the set of spatial positions and corresponding physical quantities without placing sensors established by Gaussian process regression model calculation; Step S4: Based on Optimal sensor layout using mean clustering algorithm; using clustering algorithm to get a more robust optimal sensor layout from multiple working conditions In the step S2, the specific steps are as follows: Step S2-1: initialization Set: select the positions corresponding to the maximum and minimum values of the physical quantity in the numerical data on the section to be measured as the initial feature position set, that is, （2） Step S2-2: Based on the set of spatial positions and its corresponding physical quantity Establishing a Gaussian process regression model: The Gaussian process regression model uses a mean function and a kernel function Uniquely determined, for a set of spatial positions The mean vector is represented by where each element is determined by The covariance matrix is represented by Each element is calculated by ​ （4） Step S2-3: flow field physical quantity prediction based on a Gaussian process regression model: Based on the Gaussian process model established above, predictions can be made on the surface to be tested. The physical quantity of each grid center point, that is, for the set any spatial location The mean of the conditional probability distribution of the prediction Covariance : （5） (6) According to formula (1), the error of the prediction of the physical quantity of the spatial position on the to-be-tested section under the current number of feature points is calculated as ​​ Step S2-4: Selecting the spatial position of the next feature point : Selecting the covariance in formula (6) The position of the maximum as the next feature point spatial position and added to the set of feature point spatial positions in: (7) Step S2-5: Determine if the condition is met. If the condition is met, then at this time... Number of elements in That is, the optimal number of feature points, and the corresponding set of locations. This serves as the final set of feature points; otherwise, repeat steps S2-2 to S2-4. In the step S3, the specific steps are as follows: Step S3-1 : Processing geometric constraints: extracting a set of alternative spatial positions where a sensor can be placed from the set of feature point spatial positions according to geometric constraints ;​ Step S3-2: initial sensor spatial position set and preset sensor number: according to numerical data, select the spatial position corresponding to the maximum or minimum value of the physical quantity in the set as the initial sensor spatial position set , that is: , given the preset sensor number , the value is given according to the maximum value of the sensor position that can be placed in the experiment, and ; Step S3-3: Next spatial location for placing the sensor For all The intermediate variables are calculated according to equation (12). According to equation (11), choose the one that makes The spatial location where the maximum value is reached will be used as the next spatial location for placing the sensor. And add that spatial location to the set. middle; Step S3-4: Loop: Calculate the prediction of the physical quantity of the section to be measured based on the measurement results of the sensors in the current set according to formula (1) Error; repeat steps S3-2-S3-3 until the number of elements in the set reaches , i.e. ; Step S3-5: determination of sensor position and optimal sensor number: when the sensor measurement point position increases The optimal sensor number corresponding to the error that does not change substantially is The corresponding sensor position set is the sensor position set selected under the current working condition .

2. The numerical data mining based internal flow field measurement sensor layout optimization method according to claim 1, characterized in that, The numerical simulation method in the step S1 includes but is not limited to a Reynolds average method RANS, a large eddy simulation method LES and a hybrid RANS-LES method.

3. The numerical data mining based internal flow field measurement sensor layout optimization method according to claim 1, characterized in that, The selection range of the step S2, is between 1% and 5%.

4. The numerical data mining based internal flow field measurement sensor layout optimization method of claim 1, wherein, In the step S4, considering the results of the M working conditions, the optimal sensor number in each working condition is , wherein ; for the M working conditions, the position set is obtained , wherein ; the position set of the M working conditions is divided into K clusters by using the mean clustering algorithm , wherein ; the K cluster center point position set is represented as , , The optimal sensor layout considering the multiple working conditions is obtained.​​ 5. The numerical data mining based internal flow field measurement sensor layout optimization method according to claim 4, characterized in that, In the step S4, the spatial positions are divided into clusters, denoted as , such that the sum of squares within the clusters is minimized; i.e.: ​​​ (13) wherein represents the center point of the cluster i.e.: (14) denotes the number of elements in the set.

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