A Multi-Structure Dynamic Compressed Sensing Mechanical Vibration Signal Reconstruction Method Based on Edge Computation

Abstract

This invention belongs to the field of data compression and reconstruction in wireless sensor networks for mechanical vibration, specifically relating to a method for reconstructing multi-structure dynamic compressed sensing mechanical vibration signals based on edge computing. The method includes: acquiring the original mechanical vibration signal through edge computing nodes; obtaining a sparse mechanical vibration signal using a sparse decomposition algorithm; obtaining the compressed mechanical vibration signal observation value based on a dual-structure measurement matrix corresponding to an initial compression ratio; obtaining the reconstructed mechanical vibration signal using a greedy algorithm; determining whether the error between the reconstructed and original mechanical vibration signals meets a set threshold requirement, and then dynamically adjusting the compression ratio; obtaining the optimal mechanical vibration signal observation value based on the dual-structure measurement matrix corresponding to the dynamic compression ratio; and reconstructing the optimal mechanical vibration signal observation value using a greedy algorithm through a central server to obtain the final reconstructed mechanical vibration signal. This invention utilizes edge computing technology to preprocess the mechanical vibration signal, improving the flexibility and efficiency of state monitoring; effective data compression measurement at the edge computing nodes optimizes subsequent reconstruction accuracy, significantly improves signal recovery quality, and also reduces the computational burden on the central server.

Description

Technical Field

[0001] This invention belongs to the field of data compression and reconstruction of wireless sensor networks for mechanical vibration, and specifically relates to a method for reconstructing mechanical vibration signals based on edge computing and dynamic compression sensing of multiple structures. Background Technology

[0002] As machine complexity continues to increase, the number of signals that need to be captured and processed is growing explosively, posing enormous challenges and pressures to data center servers in wireless sensor networks. Traditional data processing methods struggle to effectively handle such massive data flows, limiting the efficiency of data transmission, storage, and analysis, and potentially causing data loss or delays.

[0003] In wireless sensor networks (WSNs), the significant energy consumption associated with data communication over channels has become a key issue restricting their development in the field of mechanical vibration. Especially in environments with increasing machine complexity and increasingly demanding signal acquisition requirements, effectively utilizing the correlation between sensor signals to compress and acquire large amounts of distributed sensing data has become a crucial research problem.

[0004] Introducing compressed sensing as a novel data acquisition and compression theory into WSNs provides an innovative solution to the challenges faced by WSN data acquisition. By applying compressed sensing technology during the sensing data acquisition process, and fully utilizing the prior information of correlation between sensing data, edge computing nodes can perform compressed sampling simultaneously with data acquisition. This shifts the computational tasks of data compression and acquisition to powerful aggregation nodes, thereby reducing the complexity of compression coding. For example, Chinese patent CN117412260A discloses a data collection method for wireless sensor networks based on compressed sensing. This method considers the impact of compressed sensing on energy consumption, redefines the energy consumption model, and reduces the amount of data transmitted. Finally, the base station reconstructs the original data from the received data using a compressed sensing recovery algorithm.

[0005] However, the structures of observation matrices in current compressed sensing technologies are relatively simple, mainly divided into two categories: random measurement matrices and deterministic measurement matrices. Random measurement matrices offer better reconstruction performance, but their computation is extremely complex, making them difficult to implement in hardware systems and increasing hardware design complexity and cost. While deterministic measurement matrices are easier to implement in hardware systems, their reconstruction performance is inferior to the former. Furthermore, current measurement matrix design techniques do not consider dynamically adapting to the characteristics of the acquired signal. Therefore, existing technologies cannot yet guarantee signal reconstruction accuracy while reducing computational complexity based on the characteristics of the current signal. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a multi-structure dynamic compressed sensing mechanical vibration signal reconstruction method based on edge computing. The method is applied to edge computing nodes and a central server, and includes:

[0007] 101. Acquire raw mechanical vibration signals through edge computing nodes;

[0008] 102. At the edge computing node, the original mechanical vibration signal is processed by a sparse decomposition algorithm to obtain a sparse mechanical vibration signal; the sparse mechanical vibration signal is composed of the product of the sparse basis matrix and the sparse coefficients.

[0009] 103. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the initial compression ratio to obtain the compressed mechanical vibration signal observation value; the compressed mechanical vibration signal observation value is composed of the product of the sensing matrix and the sparse coefficients; the sensing matrix is ​​composed of the product of the dual-structure measurement matrix and the sparse basis matrix;

[0010] 104. At the edge computing node, the compressed mechanical vibration signal observations are reconstructed using a greedy algorithm to obtain the reconstructed mechanical vibration signal;

[0011] 105. At the edge computing node, determine whether the error between the reconstructed mechanical vibration signal and the original mechanical vibration signal meets the set threshold requirement, and then dynamically adjust the compression ratio;

[0012] 106. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the dynamic compression ratio until the optimal mechanical vibration signal observation value is obtained.

[0013] 107. At the central server, the optimal mechanical vibration signal observation value is reconstructed using a greedy algorithm to obtain the final reconstructed mechanical vibration signal.

[0014] The beneficial effects of this invention include:

[0015] This invention addresses the problem of excessive data transmission volume in mechanical vibration monitoring using wireless sensor networks by introducing compressed sensing technology. Starting with the measurement matrix, it delves into the linear measurement process of the signal, combining the advantages of random and deterministic measurement matrices to design a multi-structure measurement matrix that reduces computational complexity while ensuring signal reconstruction accuracy. Simultaneously, an adaptive dynamic measurement matrix is ​​designed using error feedback. By adjusting the observation values, it solves the problem that a fixed observation matrix cannot reconstruct optimal results from compressed observation values ​​for different signals, ensuring good final signal reconstruction accuracy. This invention utilizes edge computing technology for preprocessing mechanical vibration signals, improving the flexibility and efficiency of condition monitoring. Effective data compression measurement at edge computing nodes effectively optimizes subsequent reconstruction accuracy, significantly improving signal recovery quality while reducing the computational burden on the central server. Attached Figure Description

[0016] Figure 1 This is a flowchart of the multi-structure dynamic compression sensing vibration signal reconstruction method in this invention;

[0017] Figure 2 This is a schematic diagram of the original data sampling in this invention;

[0018] Figure 3 This is a schematic diagram of the multi-structure dynamic compression sensing vibration signal reconstruction algorithm in this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This invention proposes a multi-structure dynamic compressed sensing mechanical vibration signal reconstruction method based on edge computing. The method is applied to edge computing nodes and a central server. The edge computing nodes are located at the network edge, close to the computing resources of data sources or user terminals, and are distributed near IoT devices, industrial equipment, mobile terminals, etc. The edge computing nodes can be edge gateways, edge servers, routers, IoT terminal devices, or other fixed or mobile devices with computing capabilities. The central server is a large server located in a data center or cloud computing platform. The edge computing nodes connect to the central server and other edge computing nodes via wired or wireless communication networks. The edge computing nodes can also connect to each other via gateway devices or the Internet. The central server can communicate with the edge computing nodes via a high-speed network to acquire and process data from the edge computing nodes, such as the optimal mechanical vibration signal observations obtained by the edge computing nodes. The central server can also connect to other data centers and cloud computing platforms via the Internet to achieve broader resource sharing and collaboration.

[0021] First see Figure 1 and Figure 3 ,like Figure 1 This invention proposes a multi-structure dynamic compressed sensing mechanical vibration signal reconstruction method based on edge computing, the method comprising the following:

[0022] 101. Acquire raw mechanical vibration signals through edge computing nodes;

[0023] In this embodiment of the invention, the original mechanical vibration signal can be obtained from the experimental data of the power transmission system diagnostic simulator (DDS). Eight different fault state experimental data are collected through edge computing nodes, and the sample length of each sampling is 2048.

[0024] In this embodiment of the invention, the original mechanical vibration signal can also be obtained from a real sensor device, such as... Figure 2 As shown, for example, an inertial accelerometer is installed on mechanical equipment to measure vibration acceleration data from multiple directions. Ensure the sensor is securely fixed to the equipment to accurately capture vibration characteristics. Establish correct physical and electrical connections between the inertial accelerometer, the data acquisition system, and the computer to ensure interference-free and stable signal transmission. Set the total sampling duration to T seconds and select a suitable sampling frequency fs Hz. Based on these settings, calculate the corresponding number of sampling points N, i.e., N = fs × T. Through multiple samplings, the sample length can also be set to 2048, thus obtaining a time-domain vibration acceleration signal matrix X.

[0025] In this embodiment of the invention, the acquisition of the original mechanical vibration signal is performed at the edge computing node, which can reduce the amount of data transmission, has strong real-time performance, reduces the load on the central server, and protects data security and privacy.

[0026] 102. At the edge computing node, the original mechanical vibration signal is processed by a sparse decomposition algorithm to obtain a sparse mechanical vibration signal; the sparse mechanical vibration signal is composed of the product of the sparse basis matrix and the sparse coefficients.

[0027] In this embodiment of the invention, the original mechanical vibration signal is processed using a sparse decomposition algorithm to obtain a sparsed mechanical vibration signal, including:

[0028] Select an initial dictionary; the size of the initial dictionary is greater than the dimension of the original mechanical vibration signal;

[0029] The sparse coding method is used to find the sparse coefficients in the dictionary for each original mechanical vibration signal sample;

[0030] The dictionary is updated based on the obtained sparse coefficients and the original mechanical vibration signal;

[0031] Through iterative processes of sparse coding and dictionary updates, the sparsed mechanical vibration signal is obtained when the convergence condition is met.

[0032] In some embodiments of the present invention, the K-SVD algorithm can also be used to update the algorithm by alternating between sparse representation and constrained singular value decomposition, resulting in an adaptive redundant dictionary D, the objective function of which can be expressed as:

[0033]

[0034] in, Let D ∈ R be the target signal. N×K (K << N) is a sparse representation dictionary; For sparse representation coefficients; ||·|| F The Frobenius norm error is used; ||·|0 is the l0 norm, i.e., the number of non-zero elements; K is the maximum number of non-zero elements in the sparse coefficients.

[0035] In some embodiments of the present invention, the SAMP algorithm is used in the sparse coding part of the K-SVD algorithm. The SAMP algorithm estimates the true sparsity of the signal by progressively selecting dictionary atoms with the highest correlation. The sparse coding process is further refined by first fixing the dictionary D and then optimizing the sparse matrix X. The following sparse representation model is adopted:

[0036] S test =DΨ test +Ek

[0037] Where D is the dictionary obtained through the K-SVD algorithm dictionary learning, and E k The error matrix is ​​represented by Ψ. By minimizing the residual matrix, the dictionary D and the sparse matrix Ψ are progressively improved, thereby increasing the accuracy of the sparse representation and obtaining a better sparsed mechanical vibration signal.

[0038] 103. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the initial compression ratio to obtain the compressed mechanical vibration signal observation value; the compressed mechanical vibration signal observation value is composed of the product of the sensing matrix and the sparse coefficients; the sensing matrix is ​​composed of the product of the dual-structure measurement matrix and the sparse basis matrix;

[0039] In this embodiment of the invention, a new dual-structure measurement matrix can be designed based on the initial compression ratio (CR). The dual-structure measurement matrix is ​​formed by merging an M-dimensional identity matrix and an M×(NM) random Bernoulli matrix, and the specific size can be determined according to the actual needs of the application scenario.

[0040] In some embodiments of the present invention, the initial compression ratio CR is set to 0.6, the number of original signal samples and the signal length are (200, 512), i.e., N = 512, and the formula for calculating the number of rows of the dual-structure measurement matrix is:

[0041] M = N - CR × N

[0042] Where CR represents the current compression ratio and N represents the length of the original mechanical vibration signal. Therefore, the number of rows M of the resulting measurement matrix is ​​204.

[0043] Furthermore, the dual-structure measurement matrix consists of an M×M dimensional identity matrix Φ1 and an M×(NM) dimensional random Bernoulli matrix Φ2; the number of rows M of the dual-structure measurement matrix is ​​determined by the compression ratio CR and the length N of the original mechanical vibration signal, and the number of columns N of the dual-structure measurement matrix is ​​determined by the length N of the original mechanical vibration signal. Its formula can be expressed as:

[0044]

[0045] Where Φ1 is an M-dimensional identity matrix, Φ2 is an M×(NM) random Bernoulli matrix, Y is the observation obtained after compressed measurement, and X is the original signal sample of length N.

[0046] In a preferred embodiment of the present invention, the method further includes determining whether the dual-structure measurement matrix satisfies the conditions based on the finite isometric property formula. If the conditions are met, the dual-structure measurement matrix is ​​used for compressed sensing. If the conditions are not met, the number of rows in the dual-structure measurement matrix is ​​adjusted until the conditions are met.

[0047] Specifically, let the dual-structure measurement matrix Φ be an M×N matrix of the form [I,B], where the non-zero terms of the Bernoulli matrix B conform to... Random numbers, the Bernoulli distribution is a discrete probability distribution where the random variable has only two possible values, typically 0 or 1. In a random Bernoulli matrix, each element takes the value 1 with probability p and the value 0 with probability 1-p. When the measured value satisfies... Then [I,B] satisfies the K-order RIP property, and the proof is as follows:

[0048]

[0049] Since the random Bernoulli matrix B satisfies the RIP property, the boundary of the second term on the right is:

[0050]

[0051] Because the elements in the random Bernoulli matrix B satisfy Therefore, we can conclude that:

[0052]

[0053] Where A1 represents the coefficient that determines the minimum measured value M, log represents the logarithm, which can be base 10, or initially base irrational number e, or other commonly used bases; this invention does not limit this. K represents the sparsity of the signal. Where x is an N-dimensional sparse vector. The length of x1 is M, and the length of x2 is NM.

[0054] This invention, by adjusting the number of rows in the dual-structure measurement matrix to ensure that the dual-structure measurement matrix meets certain conditions, can guarantee accurate signal reconstruction in compressed sensing, enabling the original signal to be effectively reconstructed from a small amount of measurement data, thereby achieving data compression and efficient transmission.

[0055] In some embodiments of the present invention, the size of the observation matrix obtained after steps 101-102 is (204, 512). The observed value of each signal sample obtained after passing through this observation matrix with a sparse sample size of 200 and a length of 512 is 204. This step significantly reduces the amount of mechanical vibration signal data required, lowers the data transmission and storage pressure, and also ensures accurate reconstruction of the original signal.

[0056] 104. At the edge computing node, the compressed mechanical vibration signal observations are reconstructed using a greedy algorithm to obtain the reconstructed mechanical vibration signal;

[0057] In this embodiment of the invention, the sparse coefficient estimate can be obtained locally at the edge node using the SAMP algorithm. The mechanical vibration signal is then reconstructed based on the sparse coefficient estimate, and the details of the signal are recovered through sparse representation to obtain the reconstructed signal.

[0058] It is understandable that executing locally on edge nodes can reduce the amount of data transmission and has advantages such as strong real-time performance, reduced load on the central server, and protection of data security and privacy. This embodiment can guarantee data security to a certain extent.

[0059] 105. At the edge computing node, determine whether the error between the reconstructed mechanical vibration signal and the original mechanical vibration signal meets the set threshold requirement, and then dynamically adjust the compression ratio;

[0060] In this embodiment of the invention, the dynamic compression ratio is determined by the error between the original mechanical vibration signal and the reconstructed mechanical vibration signal; the error can be the mean square error, the signal-to-noise ratio, and the peak signal-to-noise ratio.

[0061] For example, the formula for calculating the error can be:

[0062]

[0063] Where error is the relative error between the calculated recovered signal and the original signal, measuring the degree of difference between the recovered signal and the original signal, x or,i Let x represent the i-th sample value of the original signal (original mechanical vibration signal). rec,i Let represent the i-th sample value of the recovered signal (reconstructed mechanical vibration signal), and n be the number of observations, i.e., the number of samples. By calculating the square root of the sum of squares of the differences between the corresponding samples of the original signal and the recovered signal, and the square root of the sum of squares of the original signal samples, and then dividing the two, the relative error is obtained, thereby quantitatively evaluating the degree to which the recovered signal restores the original signal.

[0064] When the error exceeds the set threshold, the dynamic compression ratio is adjusted as follows:

[0065] CR new =max[CR(1-factor),CR min ]

[0066] If the error does not exceed the set threshold, the dynamic compression ratio is adjusted as follows:

[0067] CR new=min[CR(1+factor),CR max ]

[0068] Among them, CR new The compression ratio is represented by CR, which represents the value from the previous iteration (i.e., the current compression ratio). Factor represents the scaling factor that controls the adjustment of the compression ratio. min CR represents the minimum compression ratio. max This indicates the maximum compression ratio.

[0069] This invention dynamically adjusts the compression ratio (CR) by calculating and determining whether the recovery error between the reconstructed signal and the original signal meets the set threshold requirements, and in turn adjusts the parameters of the dual-structure measurement matrix to optimize the reconstruction effect and ensure the best observation value.

[0070] 106. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the dynamic compression ratio until the optimal mechanical vibration signal observation value is obtained.

[0071] Since the compression ratio affects the number of rows in the dual-structure measurement matrix, the dual-structure measurement matrix will be dynamically adjusted once the compression ratio is changed. This embodiment can dynamically change the dual-structure measurement matrix by using this adaptive dynamic compression ratio. By adjusting the observation values, it solves the problem that the observation values ​​obtained by compressing different signals with a fixed observation matrix cannot reconstruct the best results, thus ensuring good final signal reconstruction accuracy.

[0072] The process of dynamically adjusting the dual-structure measurement matrix based on error feedback is expressed as follows:

[0073] Y = ΦX = ΦΨS = ΘS

[0074]

[0075] Where Y is the observation obtained after compressed measurement, n is the number of observations, Φ is the dual-structure measurement matrix, Ψ is the N-dimensional sparse basis matrix, Θ is the sensing matrix, and S is the sparse coefficient. During the iteration process, Lasso regression is used to make the recovered signal as close as possible to the original signal. ‖·‖2 is the l2 norm, ‖·‖1 is the l1 norm, and λ is the regularization parameter that controls the model complexity and sparsity.

[0076] Using the above formula, an adaptive dynamic measurement matrix was designed with error feedback. By adjusting the observed values, the problem that a fixed observation matrix cannot reconstruct the best results from observations compressed for different signals was solved, ensuring good final signal reconstruction accuracy. This embodiment can reduce computational complexity while ensuring signal reconstruction accuracy.

[0077] 107. At the central server, the optimal mechanical vibration signal observation value is reconstructed using a greedy algorithm to obtain the final reconstructed mechanical vibration signal.

[0078] In this embodiment of the invention, the optimized best observations and the new dual-structure measurement matrix can be transmitted to the central server. The central server then reconstructs the mechanical vibration signal to obtain the final reconstructed signal. The powerful computing capabilities of the central server can quickly complete these numerous matrix operations and iterative solutions, significantly shortening the signal reconstruction time and improving processing efficiency.

[0079] It is understood that in this embodiment of the invention, steps 101-106 are implemented through edge computing nodes, and step 107 is implemented through a central server. Between steps 106 and 107, the edge computing nodes transmit the optimal mechanical vibration signal observation values ​​to the central server through wired or wireless communication networks. The central server then processes the data calculated by each edge computing node. This method utilizes edge computing technology to preprocess the mechanical vibration signal, improving the flexibility and efficiency of condition monitoring. At the edge computing nodes, the reconstruction accuracy can be effectively optimized, significantly improving the signal recovery quality, while also reducing the computational burden on the central server.

[0080] In some embodiments of this invention, a power transmission integrated test bench (DDS) is used to collect fault signals from the parallel gearbox. The test bench mainly includes a drive motor, a two-stage planetary gearbox, a two-stage parallel gearbox, and a programmable heavy-duty brake. An accelerometer is installed on the right intermediate shaft, positioned vertically, to monitor the faulty outer ring bearing on the right side of the parallel gear intermediate shaft. This experiment uses an NI9234 signal acquisition card and a vibration accelerometer (e.g., PCB352C03) at a sampling frequency of 25600Hz and a motor speed of 20Hz to collect the outer ring bearing fault signal. The acquisition length is set to 2048 points. To quantitatively and intuitively evaluate the model's reconstruction performance, Mean Absolute Error (MAE), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), and Pearson Correlation Coefficient (PCC) are introduced to evaluate the model's reconstruction accuracy. The calculation formulas for these four evaluation indicators are as follows:

[0081]

[0082] Where, x i Represents the original signal. This represents the reconstructed signal, and N represents the length of the original signal sample.

[0083] The results of comparing the method proposed in this invention with several other different reconstruction methods are shown in Table 1:

[0084] Table 1 Comparison of key parameters of the present invention on the DDS dataset.

[0085]

[0086] As shown in Table 1, the multi-structure dynamic compressed sensing vibration signal reconstruction method proposed in this invention outperforms other algorithms in terms of signal reconstruction accuracy. Furthermore, this invention utilizes edge computing technology to preprocess the mechanical vibration signal, enhancing the flexibility and efficiency of condition monitoring; at the edge computing nodes, the reconstruction accuracy can be effectively optimized, significantly improving the recovery quality of the mechanical vibration signal while reducing the computational burden on the central server.

[0087] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing mechanical vibration signals from multi-structure dynamic compressed sensing based on edge computing, characterized in that, The method is applied to edge computing nodes and central servers, and the method includes:

101. Acquire raw mechanical vibration signals through edge computing nodes; 102. At the edge computing node, the original mechanical vibration signal is processed by a sparse decomposition algorithm to obtain a sparse mechanical vibration signal; the sparse mechanical vibration signal is composed of the product of the sparse basis matrix and the sparse coefficients.

103. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the initial compression ratio to obtain the compressed mechanical vibration signal observation value; the compressed mechanical vibration signal observation value is composed of the product of the sensing matrix and the sparse coefficients; the sensing matrix is ​​composed of the product of the dual-structure measurement matrix and the sparse basis matrix; 104. At the edge computing node, the compressed mechanical vibration signal observations are reconstructed using a greedy algorithm to obtain the reconstructed mechanical vibration signal; 105. When determining at the edge computing node whether the error between the reconstructed mechanical vibration signal and the original mechanical vibration signal meets the set threshold requirement, the compression ratio is dynamically adjusted accordingly.

106. At the edge computing node, the sparsed mechanical vibration signal is compressed and sensed based on the dual-structure measurement matrix corresponding to the dynamic compression ratio until the optimal mechanical vibration signal observation value is obtained.

107. At the central server, the optimal mechanical vibration signal observation value is reconstructed using a greedy algorithm to obtain the final reconstructed mechanical vibration signal.

2. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 1, is characterized in that... The original mechanical vibration signal is processed using a sparse decomposition algorithm to obtain a sparsed mechanical vibration signal, which includes: Select an initial dictionary; the size of the initial dictionary is greater than the dimension of the original mechanical vibration signal; The sparse coding method is used to find the sparse coefficients in the dictionary for each original mechanical vibration signal sample; The dictionary is updated based on the obtained sparse coefficients and the original mechanical vibration signal; Through iterative processes of sparse coding and dictionary updates, the sparsed mechanical vibration signal is obtained when the convergence condition is met.

3. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 1, is characterized in that... The dual-structure measurement matrix consists of an M×M identity matrix Φ1 and an M×(NM)-dimensional random Bernoulli matrix Φ2; the number of rows M of the dual-structure measurement matrix is ​​determined by the compression ratio CR and the length N of the original mechanical vibration signal, and the number of columns N of the dual-structure measurement matrix is ​​determined by the length N of the original mechanical vibration signal.

4. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 3, is characterized in that... The formula for calculating the number of rows in the dual-structure measurement matrix is ​​as follows: M = N - CR × N Where CR represents the current compression ratio and N represents the length of the original mechanical vibration signal.

5. A method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 3 or 4, characterized in that... The method further includes determining whether the dual-structure measurement matrix meets the conditions based on the finite isometric property formula. If the conditions are met, the dual-structure measurement matrix is ​​used for compressed sensing. If the conditions are not met, the number of rows in the dual-structure measurement matrix is ​​adjusted.

6. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 5, is characterized in that... The conditions are: Where A1 represents the coefficient that determines the minimum measured value M, log represents the logarithm, and K represents the sparsity of the signal.

7. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 1, is characterized in that... The optimal mechanical vibration signal observation is obtained by multiplying the dual-structure measurement matrix with the optimal original mechanical vibration signal; the optimal original mechanical vibration signal is determined by the sparse basis matrix and the optimal sparse coefficients.

8. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 7, is characterized in that... The formula for solving the optimal sparsity coefficient S is expressed as follows: Where S is the sparsity coefficient, n is the number of observations, Y is the mechanical vibration signal observation obtained after compressed measurement, Θ is the sensing matrix, ‖·‖2 is the l2 norm, ‖·‖1 is the l1 norm, and λ is the regularization parameter that controls the model complexity and sparsity.

9. The method for reconstructing mechanical vibration signals based on edge computing using multi-structure dynamic compressed sensing, as described in claim 1, is characterized in that... The dynamic compression ratio is determined by the error between the original mechanical vibration signal and the reconstructed mechanical vibration signal; When the error exceeds the set threshold, the dynamic compression ratio is adjusted as follows: CR new =max[CR(1-factor),CR min ] If the error does not exceed the set threshold, the dynamic compression ratio is adjusted as follows: CR new =min[CR(1+factor),CR max ] Among them, CR new The compression ratio is represented by CR, which represents the value from the previous iteration (i.e., the current compression ratio). Factor represents the scaling factor that controls the adjustment of the compression ratio. min CR represents the minimum compression ratio. max This indicates the maximum compression ratio.

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