A method for optimizing the placement of sensors in remote sensing satellite high-stability structures based on compressed sensing

Abstract

A method for optimizing the placement of sensors for high-stability structures of remote sensing satellites based on compressed sensing belongs to the field of structural health monitoring of on-orbit spacecraft. The method includes the following steps: 1) obtaining the maximum strain values ​​of all unit nodes of the high-stability structure through dynamic simulation analysis to obtain an original data set; 2) performing peak-to-valley transformation and sorting to obtain a reconstructed data set, and then determining the number of sensor points through frequency domain conversion; 3) constructing all measurement matrices based on the number of points and the number of unit nodes of the finite element model; 4) solving the L1 norm problem of data reconstruction using the basis pursuit algorithm, and repeatedly calculating the reconstruction curves corresponding to all measurement matrices; 5) evaluating the optimization effect of the points and determining the point placement scheme. This method can not only achieve a reasonable arrangement of the number of sensors and the location of measurement points, but also achieve the inversion of the extreme strain values ​​of all measurement points, providing a data basis for improving the imaging quality of the camera and effectively saving the economic cost of remote sensing satellite structural monitoring.

Description

Technical Field

[0001] The present invention belongs to the field of structural health monitoring of on-orbit spacecraft, and in particular relates to a method for optimizing the arrangement of high-stability structural sensors of remote sensing satellites based on compressed sensing. Background Art

[0002] Remote sensing satellites are artificial satellites used as remote sensing platforms in outer space. Their applications in surveying, mapping, remote sensing, navigation, and other fields are becoming increasingly important. Their imaging accuracy and stability are crucial for obtaining ground information. High-stability structures, as one of the primary structures of remote sensing satellites, carry cameras and star sensors. Their dynamic response directly impacts imaging quality and satellite lifespan. As remote sensing satellites develop towards larger and more multifunctional features, they may carry more star sensors and camera functional structures. High-stability support structures are becoming larger and more complex, leading to inconsistencies in the micro-vibration behavior of the various camera and star sensor support components under the vibration behavior of the high-stability structures.

[0003] In order to ensure higher imaging quality, it is necessary to know the deformation of the supporting structure in a timely manner. The typical method is to obtain the attitude and displacement information of key positions by installing sensors on it. However, the layout and number of sensors are crucial to the monitoring effect, and are limited by factors such as structural complexity and signal interference. Remote sensing satellites are far away from the ground when in orbit, and the bandwidth for ground data transmission is very limited. Due to the complex structure and numerous rods of the high-stability structure itself, high-precision and high-stability satellites cannot be equipped with too many sensors, and the number of deployment points is limited. As the main structure for carrying cameras, the high-stability structure cannot directly measure the response of key positions by arranging sensors, and the deployment point location is also limited.

[0004] Traditional sensor placement optimization methods often suffer from unstable placement, excessive number of placement points, and poor optimization results. Therefore, optimal sensor placement has become a key step in structural health monitoring, and how to achieve both monitoring effectiveness and cost-effectiveness with a limited number of sensors is a research hotspot in the field of sensor optimization. Summary of the Invention

[0005] In order to overcome the problems existing in the above-mentioned prior art, the present invention provides a method for optimizing the layout of high-stability structural sensors of remote sensing satellites based on compressed sensing, so as to achieve the goals of efficient monitoring and optimized resource utilization, and provide necessary technical support for relevant engineering personnel.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for optimizing the placement of sensors for a remote sensing satellite high-stability structure based on compressed sensing, characterized in that the method comprises the following steps:

[0008] Step S1: acquiring dynamic data of a remote sensing satellite high-stability structure, obtaining the maximum strain of all unit nodes of the high-stability structure through dynamic simulation analysis, and merging the data by node number to obtain an original data set;

[0009] Furthermore, the step S1 specifically includes:

[0010] S11. Construct a finite element model of the remote sensing satellite's high-stability structure;

[0011] S12. Perform dynamic simulation analysis to obtain strain time history data of all unit nodes;

[0012] S13. Preprocess and merge the strain data to obtain the original data set.

[0013] Step S2: Determine the number of sensor points. Perform peak-to-valley transformation on the original data set to obtain a reconstructed data set. Obtain sparse coefficients of the four working conditions through frequency domain transformation to determine the number of sensor points.

[0014] Furthermore, the step S2 specifically includes:

[0015] S21, performing peak-to-valley transformation sorting on the original data set to obtain a reconstructed data set;

[0016] The data of all unit nodes are processed in ascending order, the strain data of odd-numbered nodes are extracted and processed in descending order, and the strain data of even-numbered nodes are extracted and recombined to obtain the peak-to-valley transformed signal; the original data set is sorted by peak-to-valley transformation, and the corresponding relationship between the numbers of the original data set and the reconstructed data set is recorded to obtain the reconstructed data set;

[0017] S22, performing Fourier transform on the reconstructed data set and drawing a frequency domain graph;

[0018] Using the Fourier transform formula Perform a frequency domain conversion, where x(n) is the signal in the reconstructed dataset, X(k) is the frequency domain signal, N is the length of the signal, and j is the imaginary unit. Given a Fourier transform basis B, convert the reconstructed dataset to the frequency domain and plot the frequency domain graph.

[0019] S23, determining the number of sensor points according to the amplitude information of the frequency domain graph;

[0020] According to the formula m=klog(n), the number of main peaks in the frequency domain diagram is taken as k, the number of unit nodes is taken as n, and the number of distribution points is determined.

[0021] Step S3: Construction of the measurement matrix, combining the number of points and the number of unit nodes of the finite element model,

[0022] Construct all measurement matrices corresponding to the point distribution scheme through permutations and combinations;

[0023] Furthermore, the step S3 specifically includes:

[0024] S31. Design the measurement matrix based on the number of points and the number of unit nodes of the finite element model;

[0025] After the finite element mesh is divided into high-stability structures, all grid cells and node positions are obtained. The unit node position is selected as the measurement point n where the sensor is placed. n is the number of columns in the measurement matrix, and the number of points is determined as the number of rows in the matrix m. The measurement matrix L consists of elements with values ​​of '0' and '1', which respectively indicate the absence or presence of a sensor at the unit node position.

[0026] S32, matching all candidate layout schemes with the measurement matrix to construct all measurement matrices;

[0027] For n possible placement locations, m sensors need to be placed, and the corresponding number of placement solutions is The choice of measurement matrix L is Construct all measurement matrices corresponding to the alternative layout schemes.

[0028] Step S4: Design a perception reconstruction algorithm, use the basis pursuit algorithm to solve the L1 norm problem of data reconstruction, and repeatedly calculate the reconstruction curves corresponding to all measurement matrices;

[0029] Furthermore, the step S4 specifically includes:

[0030] S41. Design a perceptual reconstruction algorithm to minimize the L1 norm;

[0031] The design variable is the measurement matrix L, the constraint condition is B, and the perception matrix A is introduced by the formula A=LB. Under the condition that the underdetermined problem A*x=y is satisfied, the measurement value y of the known signal is known, and the goal is to minimize the L1 norm of the signal x;

[0032] S42. Substitute all measurement matrices and repeatedly calculate the corresponding reconstructed curves.

[0033] Step S5: evaluate the optimization effect of the point distribution and determine the point distribution plan. Calculate the reconstruction of all measurement matrices and the curve fitting rate of the original data, evaluate the rationality of the point distribution plan, and obtain the optimal measurement matrix, that is, the corresponding point distribution plan.

[0034] Furthermore, the step S5 specifically includes:

[0035] S51, matching the reconstructed curve with the original data set number to obtain the reconstructed curve of the original data set;

[0036] S52, calculating the curve fitting rate between the reconstructed curves of all measurement matrices and the original data set;

[0037] Select R 2 The coefficient of determination is a measure of the degree of fit between the reconstructed curve and the original curve, and its calculation formula is: where y i is the original signal value, is the reconstructed signal value, n is the signal length, is the average value of the original signal; the optimal measurement matrix under four working conditions is calculated to obtain the four working condition point positions, optimal measurement matrix and curve fitting rate R 2 ;

[0038] S53, comparing the curve fitting rates and determining the optimal measurement matrix, i.e., the corresponding point distribution scheme;

[0039] The curve fitting rate of the reconstructed curve and the original curve reaches the maximum, R 2 The measurement matrix L corresponding to the global maximum value is the optimal location of the sensor.

[0040] The beneficial effects of the present invention are:

[0041] Compressed sensing is a new signal processing technology that can reconstruct signals using a small amount of sampled data. It has significant advantages such as efficient transmission, low cost, high fidelity and robustness, and can process large-scale signal data efficiently and quickly. Compressed sensing breaks through the limitations of the Nyquist sampling theorem, completes data compression during the sampling process, and can accurately reconstruct the global structural signal using a small amount of sampled data, providing new ideas and methods for solving the problem of optimal sensor layout in remote sensing satellite structural health monitoring.

[0042] This method not only enables the rational placement of sensor measurement points but also inverts strain extremes at all measurement points, providing a data foundation for improving camera imaging quality and effectively reducing the economic costs of remote sensing satellite structural monitoring. This method not only considers the rationality of sensor placement and location, but also considers the correlation between partial measurement point reconstruction and the original global node strain extremes. It can be applied to the optimal placement of sensors on actual in-orbit satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flowchart of a method for optimizing the arrangement of high-stability structural sensors on an on-orbit satellite based on compressed sensing in an embodiment of the present invention.

[0044] Figure 2 It is a finite element model of a remote sensing satellite high stability structure in an embodiment of the present invention.

[0045] Figure 3 It is the original data set of global unit node strain under four working conditions in the embodiment of the present invention.

[0046] Figure 4 This is the peak-valley transformation sorting process in the embodiment of the present invention.

[0047] Figure 5 It is a global unit node strain reconstruction data set under four working conditions in the embodiment of the present invention.

[0048] Figure 6 is a frequency domain diagram of the reconstructed data set in an embodiment of the present invention.

[0049] Figure 7 This is the process of using the CVX toolbox in the embodiment of the present invention to solve the strain data reconstruction problem.

[0050] Figure 8 3 is a comparison diagram of the reconstructed strain and original strain curves after sorting in an embodiment of the present invention.

[0051] Figure 9 3 is a comparison diagram of the reconstructed strain and original strain curves before sorting in an embodiment of the present invention.

[0052] Figure 10 This is the final layout plan for the high-stability structure in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0054] In order to illustrate the technical solution of the present invention, specific embodiments are provided below.

[0055] like Figure 1 As shown, the method for optimizing the arrangement of sensors for a remote sensing satellite high-stability structure based on compressed sensing provided in this embodiment includes the following steps:

[0056] Step S1: Acquisition of dynamic data of a remote sensing satellite high-stability structure. The maximum strain values ​​of all unit nodes of the high-stability structure are obtained through dynamic simulation analysis. The data are then merged according to the node numbers to obtain the original data set.

[0057] This step completes the construction of the finite element model of the satellite's high-stability structure and the acquisition and preprocessing of dynamic data. The specific implementation process is as follows:

[0058] S11. Construct a finite element model of the high-stability structure of the remote sensing satellite.

[0059] According to the actual model parameters of the remote sensing satellite high stability structure, the finite element model of the remote sensing satellite high stability structure is established using the finite element analysis software ABAQUS, and the finite element mesh is divided to obtain the satellite's dynamic test data, such as Figure 2 It should be noted that the satellite dynamics test software is not limited to ABAQUS, but can also be other finite element model building and analysis software.

[0060] S12. Perform dynamic simulation analysis to obtain the strain time history data of all unit nodes.

[0061] Using the Dynamic Implicit analysis step in the finite element simulation software ABAQUS, transient loads under four different operating conditions were applied to the satellite's high-stability structure to obtain the strain time-history response of each unit node of the satellite's high-stability structure. It is important to note that the dynamic analysis loads here should be customized according to the actual structural characteristics of the satellite.

[0062] S13. Preprocess and merge the strain data to obtain the original data set.

[0063] The maximum value of the strain time history of each unit node is extracted as the ordinate, the unit node number is the abscissa, and the curve is drawn to obtain the original data set of global unit node strain under four working conditions, such as Figure 3 shown.

[0064] Step S2: Determine the number of sensor points. Perform peak-to-valley transformation on the original data set to obtain a reconstructed data set. Obtain sparse coefficients of the four working conditions through frequency domain transformation to determine the number of sensor points.

[0065] This step includes the following steps:

[0066] S21. Perform peak-to-valley transformation sorting on the original data set to obtain a reconstructed data set.

[0067] Process the data of all unit nodes in ascending order, extract the strain data of odd-numbered nodes and process them in descending order, extract the strain data of even-numbered nodes, and recombine the two to obtain the signal after peak-valley transformation. The process is as follows: Figure 4 The original data set is sorted by peak-to-valley transformation, and the corresponding relationship between the original data set and the reconstructed data set is recorded. The result of the reconstructed data set is as follows Figure 5 As shown;

[0068] S22. Perform Fourier transform on the reconstructed data set and draw a frequency domain graph.

[0069] Using the Fourier transform formula Perform frequency domain conversion, where x(n) is the signal in the reconstructed data set, X(k) is the frequency domain signal, N is the length of the signal, and j is the imaginary unit. Given the Fourier transform basis B, convert the reconstructed data set to the frequency domain and draw the frequency domain graph, such as Figure 6 shown.

[0070] S23. Determine the number of sensor points according to the amplitude information of the frequency domain graph.

[0071] According to the formula m=klog(n), the number of main peaks in the frequency domain diagram is taken as k, the number of unit nodes is taken as n, and the number of points is determined; in this example, under the four working conditions, m=1log(211)≈3.

[0072] Step S3: Construction of the measurement matrix. Combining the number of points and the number of unit nodes of the finite element model, all measurement matrices corresponding to the point distribution scheme are constructed through permutations and combinations.

[0073] This step includes the following steps:

[0074] S31. Design the measurement matrix based on the number of points and the number of unit nodes of the finite element model.

[0075] After the finite element mesh is generated, all grid cells and node locations are obtained. The cell node locations are selected as the measurement points n where sensors are placed. n is the number of columns in the measurement matrix, and the number of points is determined by the number of rows m in the matrix. The measurement matrix L typically consists of elements with values ​​of '0' and '1', indicating the presence or absence of a sensor at the cell node location, respectively.

[0076] S32. Match all alternative layout schemes with the measurement matrix and construct all measurement matrices.

[0077] For n possible placement locations, if m sensors need to be placed, then the corresponding placement plan is The possible choices for the measurement matrix L are Construct all measurement matrices corresponding to the alternative point distribution schemes in this example.

[0078] Step S4: Design a perception reconstruction algorithm, use the basis pursuit algorithm to solve the L1 norm problem of data reconstruction, and repeatedly calculate the reconstruction curves corresponding to all measurement matrices.

[0079] This step includes the following steps:

[0080] S41. Design a perceptual reconstruction algorithm to minimize the L1 norm.

[0081] The CVX toolbox of the numerical analysis software MATLAB is used to solve the basis pursuit problem, that is, the L1 norm minimization problem. The design variable is the measurement matrix L, the constraint condition is B, and the perception matrix A is introduced by the formula A=LB. Under the condition that the underdetermined problem A*x=y is satisfied, the measurement value y of the known signal is known, and the goal is to minimize the L1 norm of the signal x. The solution process is as follows Figure 7 shown.

[0082] S42. Substitute all measurement matrices and repeatedly calculate the corresponding reconstructed curves.

[0083] The strain curves after sorting the four working conditions are substituted into the point distribution optimization algorithm for calculation, and the measurement matrix L with the highest curve fitting rate is selected. The corresponding sorted reconstructed strain is compared with the original strain curve, as shown in the following example: Figure 8 shown.

[0084] Step S5: evaluate the optimization effect of the point distribution and determine the point distribution plan. Calculate the reconstruction of all measurement matrices and the curve fitting rate of the original data, evaluate the rationality of the point distribution plan, and obtain the optimal measurement matrix, that is, the corresponding point distribution plan.

[0085] This step includes the following steps:

[0086] S51 , matching the reconstructed curve with the original data set number to obtain the reconstructed curve of the original data set.

[0087] According to the data number of the original strain curve, the reconstructed strain and original strain curves after sorting are matched with the reconstructed strain and original strain curves before sorting, and the comparison of the reconstructed strain and original strain curves before sorting under the four working conditions of the high-stability bracket is obtained, as shown in Figure 2. Figure 9 shown.

[0088] S52. Calculate the curve fitting rates of all measurement matrix reconstructed curves and the original data set.

[0089] Select R 2 The (R-Square) coefficient of determination is used as a measure of the degree of fit between the reconstructed curve and the original curve. Its calculation formula is: where y i is the original signal value, is the reconstructed signal value, n is the signal length, y i is the average value of the original signal. The optimal measurement matrix under four working conditions is calculated to obtain the four working condition point positions, optimal measurement matrix and curve fitting rate R 2 , as shown in Table 1.

[0090] Table 1. Layout locations, optimal measurement matrix, and curve fitting rate R for four working conditions 2

[0091]

[0092] S53. Compare the curve fitting rates and determine the optimal measurement matrix, i.e., the corresponding point distribution scheme.

[0093] The problem of sensor placement optimization is defined as a method to select an optimal measurement matrix L from a set of alternative measurement matrices such that R 2 Reaching the maximum, that is, the curve fitting rate of the reconstructed curve and the original curve reaches the maximum, R 2 The measurement matrix L corresponding to the global maximum value is the optimal placement position of the sensor, corresponding to the placement scheme, summarizing the placement positions under multiple working conditions, and the final placement scheme is as follows Figure 10 shown.

[0094] In summary, this invention uses the maximum strain at the measurement points of a remote sensing satellite's highly stable structure as the objective function. By using a sparse representation of the data to determine the number of measurement points, constructing a complete measurement matrix, and integrating this matrix into the perception reconstruction algorithm, the optimal measurement point layout is obtained. The final solution significantly reduces the number of measurement points for the highly stable structure and enables the inversion of global measurement point strain data, providing a data foundation for improving camera imaging quality and effectively reducing the economic costs of remote sensing satellite structural monitoring.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the placement of high-stability structure sensors on remote sensing satellites based on compressed sensing, characterized in that: The method comprises the following steps: Step S1: acquiring dynamic data of a remote sensing satellite high-stability structure, obtaining the maximum strain of all unit nodes of the high-stability structure through dynamic simulation analysis, and merging the data by node number to obtain an original data set; Step S2: Determine the number of sensor points. Perform peak-to-valley transformation on the original data set to obtain a reconstructed data set. Obtain sparse coefficients of the four working conditions through frequency domain transformation to determine the number of sensor points. S21, performing peak-to-valley transformation sorting on the original data set to obtain a reconstructed data set; Process the data of all unit nodes in ascending order, extract the strain data of odd-numbered nodes and process them in descending order, extract the strain data of even-numbered nodes, and recombine the two to obtain the signal after peak-valley transformation; Perform peak-to-valley transformation sorting on the original data set, and record the number correspondence between the original data set and the reconstructed data set to obtain the reconstructed data set; S22, performing Fourier transform on the reconstructed data set and drawing a frequency domain graph; Using the Fourier transform formula Perform frequency domain conversion, where x(n) is the signal in the reconstructed dataset, X(k) is the frequency domain signal, N is the length of the signal, and j is the imaginary unit; given the Fourier transform basis B, convert the reconstructed dataset to the frequency domain and plot the frequency domain graph; S23, determining the number of sensor points according to the amplitude information of the frequency domain graph; According to the formula m=klog(n), take the number of main peaks in the frequency domain diagram as k and the number of unit nodes as n to determine the number of points; Step S3: constructing a measurement matrix, combining the number of points and the number of unit nodes of the finite element model, and constructing all measurement matrices corresponding to the point layout scheme through permutations and combinations; S31. Design the measurement matrix based on the number of points and the number of unit nodes of the finite element model; After the finite element mesh is divided into high-stability structures, all grid cells and node positions are obtained. The unit node position is selected as the measurement point n where the sensor is placed. n is the number of columns in the measurement matrix, and the number of points is determined as the number of rows in the matrix m. The measurement matrix L consists of elements with values ​​of '0' and '1', which respectively indicate the absence or presence of a sensor at the unit node position. S32, matching all candidate layout schemes with the measurement matrix to construct all measurement matrices; For n possible placement locations, m sensors need to be placed, and the corresponding number of placement solutions is The choice of measurement matrix L is Construct all measurement matrices corresponding to the alternative point distribution schemes; Step S4: Design a perception reconstruction algorithm, use the basis pursuit algorithm to solve the L1 norm problem of data reconstruction, and repeatedly calculate the reconstruction curves corresponding to all measurement matrices; Step S5: evaluate the optimization effect of the point distribution and determine the point distribution plan. Calculate the reconstruction of all measurement matrices and the curve fitting rate of the original data, evaluate the rationality of the point distribution plan, and obtain the optimal measurement matrix, that is, the corresponding point distribution plan.

2. The method for optimizing the placement of sensors for a remote sensing satellite high-stability structure based on compressed sensing according to claim 1, characterized in that: The step S1 specifically includes: S11. Construct a finite element model of the remote sensing satellite's high-stability structure; S12. Perform dynamic simulation analysis to obtain strain time history data of all unit nodes; S13. Preprocess and merge the strain data to obtain the original data set.

3. The method for optimizing the placement of sensors for a remote sensing satellite high-stability structure based on compressed sensing according to claim 1, characterized in that: The step S4 specifically includes: S41. Design a perceptual reconstruction algorithm to minimize the L1 norm; The design variable is the measurement matrix L, the constraint condition is B, and the perception matrix A is introduced by the formula A=LB. Under the condition that the underdetermined problem A*x=y is satisfied, the measurement value y of the known signal is known, and the goal is to minimize the L1 norm of the signal x; S42. Substitute all measurement matrices and repeatedly calculate the corresponding reconstructed curves.

4. The method for optimizing the placement of sensors for a remote sensing satellite high-stability structure based on compressed sensing according to claim 1, characterized in that: The step S5 specifically includes: S51, matching the reconstructed curve with the original data set number to obtain the reconstructed curve of the original data set; S52, calculating the curve fitting rate between the reconstructed curves of all measurement matrices and the original data set; Select R 2 The coefficient of determination is a measure of the degree of fit between the reconstructed curve and the original curve, and its calculation formula is: where y i is the original signal value, is the reconstructed signal value, n is the signal length, ӯ i is the average value of the original signal; The optimal measurement matrix under four working conditions is calculated to obtain the four working condition point positions, optimal measurement matrix and curve fitting rate R 2 ; S53, compare the curve fitting rate, determine the optimal measurement matrix, that is, the corresponding point distribution scheme; the curve fitting rate of the reconstructed curve and the original curve reaches the maximum, R 2 The measurement matrix L corresponding to the global maximum value is the optimal location of the sensor.

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