A time-varying structure vibration sensor arrangement method that maximizes conditional probability

Abstract

The application discloses a time-varying structure vibration sensor arrangement method for maximizing conditional probability, and belongs to the technical field of structural dynamics vibration testing.The application establishes a sensor arrangement mode set at discrete time points in the whole operation process of a time-varying structure according to the dynamic characteristics of the whole operation process of the time-varying structure, determines important degrees of freedom in the whole operation process of the time-varying structure by calculating the importance probability of the candidate degrees of freedom for the optimal arrangement of the time-varying structure sensor, selects the affinity matrix of the candidate degrees of freedom by calculating the optimal arrangement of the candidate degrees of freedom in the whole operation process of the time-varying structure sensor, and the spatial correlation between the candidate degrees of freedom is characterized, and the secondary degrees of freedom in the whole operation process of the time-varying structure are quantitatively and accurately selected by maximizing the minimum conditional probability.The sensor measurement degree of freedom set obtained according to the application is used for sensor array arrangement, the classification and cooperative collection of structural dynamics vibration information by the sensor array are realized, and the structural dynamics vibration information collection capability of the time-varying structure in the whole operation process is improved.

Description

Technical Field

[0001] This invention belongs to the field of structural dynamics vibration testing technology, and relates to a method for arranging time-varying structural vibration sensors to maximize conditional probability. Background Technology

[0002] The increasing complexity and sophistication of modern equipment places higher demands on the reliability and safety of structures. Modal analysis, as an important means of evaluating structural dynamic characteristics, provides crucial support for structural design and analysis. While theoretical modal analysis based on numerical methods is efficient and easy to operate, it cannot accurately obtain operational status information due to model simplification and the difficulty in simulating real working environments. Therefore, starting from the inverse problem, obtaining time-varying dynamic characteristics of structures based on system identification is particularly important. Operational modal analysis based on experimental methods, which identifies measured response data of operating equipment, can accurately obtain physical information under real working environments, evaluate the dynamic characteristics of equipment in real time, and monitor its health status, thus attracting widespread attention. As a measurement point layout problem in operational modal analysis, sensor optimization aims to obtain comprehensive, reliable, and accurate structural response information by deploying as few sensors as possible, providing a data foundation for subsequent modal parameter identification. Optimization is mainly based on three criteria: vibration signal intensity, parameter estimation error, and modal reconstruction effect. Representative methods include modal kinetic energy method, QR decomposition method, effective independence method, and spatial domain sampling method. However, existing research mainly focuses on time-invariant structures with fixed structural characteristics.

[0003] Modern equipment often exhibits significant time-varying characteristics during operation. For example, fuel consumption during a launch vehicle's flight causes significant changes in the vehicle's mass; aerodynamic heating in hypersonic vehicles increases the structural temperature, leading to significant changes in structural stiffness; and deformable vehicles alter their shape during flight to improve performance, causing simultaneous changes in both mass and stiffness. Current sensor optimization methods for structural dynamic testing are incomplete and insufficient in acquiring dynamic response information for these time-varying structures, necessitating effective sensor placement optimization for such structures. Summary of the Invention

[0004] To address the contradiction between the significant time-varying dynamic characteristics of time-varying structures during operation and the inability to adjust sensor placement, this invention primarily aims to provide a sensor optimization placement method that fully considers the dynamic characteristics of time-varying structures. Based on the dynamic characteristics of the time-varying structure throughout its operation, a set of sensor placement methods for discrete moments throughout the entire operation is established. The importance probabilities of candidate degrees of freedom for optimal sensor placement throughout the entire operation are calculated to determine the important degrees of freedom. An affinity matrix is ​​calculated to characterize the spatial correlation between candidate degrees of freedom. By maximizing the minimum conditional probability, the secondary degrees of freedom throughout the entire operation of the time-varying structure are quantitatively and accurately selected. Sensor placement based on the sensor measurement degree-of-freedom set obtained according to this invention improves the comprehensive ability to acquire structural dynamic vibration information of time-varying structures throughout their operation.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a method for arranging time-varying structural vibration sensors to maximize conditional probability, comprising the following steps:

[0007] Step 1: Establish a time-varying characteristic model of the time-varying structure based on its operating conditions, and determine the final number of sensor measurement degrees of freedom n according to the target mode, the time-varying structure environment, and the test system conditions. U .

[0008] Step 2: Taking into account both the characteristic period of the time-varying structure's operation and computational efficiency, a quasi-static analysis method is used to discretize the entire time-varying structure's operation into n... s The state at each discrete moment is characterized, and the discrete characterization results are passed to the structural finite element model for modal analysis to obtain the structural dynamics information at the current moment.

[0009] Step 3: Since sensor measurement points can only be placed on the structural surface, nodes inside the finite element model and nodes under boundary constraints are eliminated based on physical limitations. Rotational degrees of freedom that cannot be measured are also eliminated, retaining only the degrees of freedom that can be used to directly measure the sensors. This set of candidate degrees of freedom is used for subsequent optimization of the time-varying structural sensor layout. The number of candidate degrees of freedom is denoted as n. L This effectively eliminates potential invalid sensor placement methods and improves the efficiency of sensor optimization.

[0010] Step 4: Utilize a time-invariant structure sensor optimization placement method to optimize the sensor placement based on the current discrete-time state, obtaining the corresponding time-varying structure discrete-time sensor placement method. Update the time step and iteratively calculate, traversing all discrete-time states throughout the entire operation to obtain the time-varying structure discrete-time sensor placement method at each moment during the entire operation of the time-varying structure, forming a set of discrete-time sensor placement methods for the entire operation of the time-varying structure.

[0011] Step 5: Determine the important sensor degrees of freedom throughout the entire operation of the time-varying structure. Perform statistical analysis on the set of sensor arrangement methods at discrete moments throughout the entire operation of the time-varying structure obtained in Step 4, and calculate the frequency n of each degree of freedom in the candidate set of optimal sensor arrangement for the entire operation of the time-varying structure within the set of sensor arrangement methods at discrete moments throughout the entire operation of the time-varying structure. i (i = 1, 2, ..., n) L Then, the importance probability vector of the candidate degree-of-freedom set for the optimal arrangement of the time-varying structure sensor throughout its operation is calculated. in This represents the importance probability of the candidate degrees of freedom for the optimal arrangement of the i-th time-varying structural sensor throughout its operation. A higher importance probability indicates that it will obtain richer vibration information during the entire operation of the time-varying structure. Sensors with an importance probability exceeding the importance degree of freedom probability threshold p0 are classified as important sensors. The basic testing capability of the final sensor arrangement is guaranteed by using important sensors. A balance is struck between the importance probability distribution of the candidate degrees of freedom set for the optimal arrangement of the time-varying structural sensor throughout its operation and the number of measurement degrees of freedom n of the final sensor. U A threshold p0 is set for the probability of important degrees of freedom throughout the operation of the time-varying structure. Degrees of freedom whose importance probability in the optimized arrangement of the time-varying structure's sensors is greater than p0 are considered important degrees of freedom throughout the operation of the time-varying structure. If the number of important degrees of freedom throughout the operation of the time-varying structure reaches the final number of sensor measurement degrees of freedom n... U Then, the top n candidate degrees of freedom with the highest importance probability will be optimized throughout the operation of the time-varying structure sensor. U The candidate degrees of freedom for the optimal arrangement of a time-varying structure sensor throughout its operation are used as the final set of sensor measurement degrees of freedom, D. U If the number of important degrees of freedom throughout the operation of the time-varying structure is less than the number of degrees of freedom measured by the final sensor, n... U Then all important degrees of freedom of the time-varying structure throughout its operation will be added to the sensor measurement degree of freedom set D. m Within the sensor's set of degrees of freedom, the number of degrees of freedom is denoted as n. m Furthermore, it is necessary to further determine the secondary degrees of freedom of the time-varying structure throughout its operation based on the correlation of the vibration characteristics of the time-varying structure, and proceed to step six.

[0012] Step Six: Calculate the candidate degrees of freedom for the time-varying structure sensor during its entire operation, and select the affinity matrix M.A The correlation between candidate degrees of freedom for optimal arrangement of time-varying structure sensors throughout the entire operation process is quantitatively calculated. Based on the frequency of each degree of freedom in the candidate degree of freedom set for optimal arrangement of time-varying structure sensors at discrete moments in the sensor arrangement mode set throughout the entire operation process, the affinity matrix M for selecting candidate degrees of freedom for optimal arrangement of time-varying structure sensors is calculated. A .

[0013] Step six describes the selection of the affinity matrix M for candidate degrees of freedom. A Quantitative calculation based on formula (1):

[0014]

[0015] Among them, M A It is a square matrix whose dimension is related to the number of candidate degrees of freedom of the time-varying structure sensor's optimized layout throughout its operation, and is n. L ×n L SA (i,j) This represents the probability that degree-of-freedom i is selected when a candidate degree-of-freedom i is selected during the entire optimized layout of the time-varying structure sensor. The probability of degree-of-freedom j being selected is calculated as follows:

[0016]

[0017] Where, n (i,j) The frequency of degree-of-freedom i being selected when a candidate degree-of-freedom i is selected in the set of sensor arrangement methods at discrete moments throughout the operation of the time-varying structure; the frequency n of candidate degree-of-freedom i in the set of sensor arrangement methods at discrete moments throughout the operation of the time-varying structure. i When the value is 0, i.e., when candidate degree of freedom i has never been selected, SA is defined. (i,j) =0, (j=1,2,…n) L ).

[0018] Step 7: Select the affinity matrix M based on the candidate degrees of freedom of the time-varying structure sensor during its entire operation optimization. A Calculate the minimum conditional probability minSA of the candidate degrees of freedom i for the remaining time-varying structural sensor arrangement during the entire operation of each set of degrees of freedom not included in the sensor measurement measurement set. (j,i) j∈D m The remaining time-varying structure sensor optimization placement candidate degrees of freedom, corresponding to the minimum conditional probability with the largest probability, are taken as secondary degrees of freedom for the entire time-varying structure operation and added to the sensor measurement degree of freedom set D. mWithin this framework, the selection of secondary degrees of freedom throughout the entire operation of the time-varying structure is quantitatively achieved, further enhancing the spatial information acquisition capability of the sensor arrangement for the vibration characteristics of the time-varying structure. If there is more than one candidate degree of freedom for the optimal arrangement of the remaining time-varying structure sensors corresponding to the largest minimum conditional probability, the degree of freedom corresponding to the second smallest probability with the largest probability is selected, and so on. If there are two or more candidate degrees of freedom for the optimal arrangement of the remaining time-varying structure sensors with completely identical conditional probability distributions, the degree of freedom with the smaller number is selected and added as a secondary degree of freedom throughout the operation of the time-varying structure, and added to the sensor measurement degree of freedom set D. m Inside.

[0019] Step 8: If the sensor measures the set of degrees of freedom D m The number of degrees of freedom n m =n u Then the set of sensor measurement degrees of freedom D at this time will be... m As the final set of sensor measurement degrees of freedom D U Stop iteration if the sensor measures the set of degrees of freedom D. m The number of degrees of freedom n m <n u Then return to step seven and iteratively expand the secondary degrees of freedom of the time-varying structure throughout its operation.

[0020] Step Nine: Based on the target mode, time-varying structural environment, test system conditions, and the final number of sensor measurement degrees of freedom n U The probability threshold p0 for important degrees of freedom is used to determine the final sensor measurement degree of freedom set D output from step six. U Or the final set of sensor measurement degrees of freedom D output from step eight. U The final set of sensor measurement degrees of freedom, D, is output. U This enables the optimization of the arrangement of time-varying structural vibration sensors.

[0021] It also includes step ten: based on the final sensor measurement degree-of-freedom set D output from step nine. U By deploying sensors, the number of sensors can be reduced while ensuring the acquisition of time-varying structural dynamic vibration information. This enables the sensor array to classify and collaboratively acquire time-varying structural dynamic vibration information, thereby improving the ability to acquire structural dynamic vibration information of time-varying structures throughout their operation.

[0022] Beneficial effects:

[0023] 1. The present invention discloses a method for maximizing the conditional probability of time-varying structural vibration sensor arrangement. Based on the time-varying characteristics of the structure throughout the entire operation, a set of sensor arrangement schemes for each moment is obtained. The method uses the affinity matrix of the candidate degrees of freedom of the time-varying structural sensor arrangement to perform quantitative calculations, thereby improving the information acquisition capability of the sensor arrangement method for the dynamic characteristics of the time-varying structure throughout the entire operation.

[0024] 2. The present invention discloses a method for maximizing the conditional probability of time-varying structural vibration sensor arrangement. Based on the importance probability of the candidate degree-of-freedom set for the optimized arrangement of time-varying structural sensor throughout its operation, the important degrees of freedom of the time-varying structure throughout its operation are determined in the candidate degree-of-freedom set for the optimized arrangement of time-varying structural sensor throughout its operation, thereby improving the information acquisition capability of the sensor arrangement method for the dynamic characteristics of the time-varying structure throughout its operation.

[0025] 3. The present invention discloses a method for maximizing the conditional probability of time-varying structural vibration sensor arrangement. It adopts a quasi-static analysis method to discretize the entire process of time-varying structural operation, and transmits the discrete characterization results to the structural finite element model for modal analysis. It uses a time-invariant structural sensor optimization arrangement method to establish a set of sensor arrangement methods for discrete moments throughout the entire process of time-varying structural operation, thereby achieving the acquisition of dynamic characteristics of the entire process of time-varying structural operation while taking into account both computational accuracy and efficiency.

[0026] 4. The present invention discloses a method for maximizing the conditional probability of time-varying structural vibration sensor arrangement, which is highly versatile for engineering problems, applicable to various time-varying processes, can support high-quality acquisition of time-varying structural vibration signals, enhance the ability to acquire structural dynamic characteristics, and solve engineering technical problems related to time-varying structures in the field of structural dynamics. Attached Figure Description

[0027] Figure 1 This is a flowchart of the time-varying structural vibration sensor arrangement method according to the present invention;

[0028] Figure 2 This is a schematic diagram of the moving mass-beam geometric model of the present invention.

[0029] Figure 3 The time-varying characteristics of the velocity and displacement of the moving mass block in this invention;

[0030] Figure 4 This invention describes the time-varying frequency process of the first four modal frequencies of a moving mass-beam time-varying structure. Figure 4 (a) represents the first-order modal frequency. Figure 4 (b) represents the second-order modal frequency. Figure 4 (c) represents the third-order modal frequency. Figure 4 (d) represents the fourth-order modal frequency;

[0031] Figure 5 This is a typical time sensor arrangement for implementing the present invention;

[0032] Figure 6 This is the probability distribution of the importance of the candidate degree-of-freedom set in the implementation of this invention;

[0033] Figure 7The optimized placement results of the moving mass-beam sensor are as follows: Detailed Implementation

[0034] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0035] The flowchart of the time-varying structural vibration sensor arrangement method of this invention is as follows: Figure 1 As shown.

[0036] Example 1:

[0037] The specific implementation steps of the time-varying structural vibration sensor arrangement method that maximizes conditional probability disclosed in this embodiment are as follows.

[0038] Step 1: Taking a moving mass-beam structure as an example, considering the first four vibration modes of the structure, and taking into account the target mode, time-varying structural environment, and test system conditions, the final sensor measurement degrees of freedom are determined to be 8. Its geometric model is as follows: Figure 2 As shown, a mass block with a mass of 4.866 kg slides from the left end to the right end under traction. Its velocity and displacement time-varying characteristics are as follows: Figure 3 As shown in Table 1, the geometric dimensions and material parameters of the beam in the moving mass-beam time-varying structure of the present invention are as follows.

[0039] Table 1 Beam Geometric Dimensions and Material Parameters

[0040]

[0041] Step Two: The entire operation process of the moving mass-beam time-varying structure was discretized using a quasi-static analysis method. Since the fourth vibration mode caused by the mass movement changes the fastest, with a characteristic period of approximately 5 seconds, a time step of 0.025 seconds was used to discretize the entire operation process, considering both the characteristic period of the moving mass-beam time-varying structure and overall computational efficiency. This resulted in 1001 discrete time-states. Finite element modal analysis was then performed at each time step to obtain the structural dynamics information. The time-varying process of the first four modal frequencies of the moving mass-beam time-varying structure is as follows: Figure 4 As shown.

[0042] Step 3: The moving mass-beam finite element model has 17 nodes. Only the lateral translational degree of freedom is considered, for a total of 17 degrees of freedom. The two degrees of freedom at the two end constraints are removed. The remaining 15 degrees of freedom are candidates for the full-process optimization of the moving mass-beam time-varying structure sensor arrangement, ranging from 2 to 16.

[0043] Step 4: Using the QR decomposition method, a time-invariant structural sensor optimization placement method, the sensor placement is optimized for the moving mass-beam time-varying structural state at each discrete time step, resulting in 1001 sets of sensor placement methods for the discrete moments of the time-varying structure. Based on this, a set of sensor placement methods for the entire discrete moments of the moving mass-beam time-varying structure operation is established. Without loss of generality, Figure 5 The sensor arrangement is shown at 5s and 12.5s, when the mass block is located at 1 / 8 and 1 / 2 of the beam, respectively.

[0044] Step 5: Determine the important degrees of freedom throughout the entire operation of the moving mass-beam time-varying structure. Perform statistical analysis on the sensor arrangement set of discrete moments throughout the entire operation of the moving mass-beam time-varying structure obtained in Step 4. Calculate the frequency of each degree of freedom in the candidate set of optimal sensor arrangement throughout the entire operation of the moving mass-beam time-varying structure within the set of discrete sensor arrangement methods. Then, calculate the probability distribution of the importance of the candidate set of optimal sensor arrangement throughout the entire operation of the moving mass-beam time-varying structure, as shown below. Figure 6 As shown. Balancing the importance probability distribution of the candidate degrees of freedom set for the time-varying structure sensor layout throughout its operation with the final number of sensor measurement degrees of freedom, a probability threshold of 0.8 for the important degrees of freedom throughout the operation of the time-varying structure is set. Degrees of freedom 4 and 14 have a selection probability of 0.94, which is greater than the probability threshold of 0.8, while the selection probabilities of the remaining nodes are all less than 0.8. Therefore, the important degrees of freedom throughout the operation of the time-varying structure are 4 and 14. Since their number is less than the final number of sensor measurement degrees of freedom (8), the important degrees of freedom throughout the operation of the time-varying structure are added to the sensor measurement degree of freedom set D. m Furthermore, it is necessary to supplement the secondary degrees of freedom of the moving mass-beam time-varying structure throughout its operation.

[0045] Step Six: To quantitatively calculate the correlation between candidate degrees of freedom for the optimal arrangement of sensors in a time-varying moving mass-beam structure throughout its operation, the affinity matrix M for selecting candidate degrees of freedom is calculated based on the frequency of each degree of freedom in the candidate degree of freedom set at discrete moments during the operation of the time-varying moving mass-beam structure sensor. A for

[0046]

[0047] Step 7: Select the affinity matrix M based on the candidate degrees of freedom of the moving mass-beam time-varying structure sensor during the entire operation optimization. A Calculate the minimum conditional probability minSA of the residual moving mass of each set of degrees of freedom not included in the sensor measurement - the minimum conditional probability of candidate degrees of freedom i for the optimal arrangement of sensors throughout the entire operation of the time-varying beam structure.(j,i) , where j∈{4,14}, i∈{2,3,5,6,7,8,9,10,11,12,13,15,16}, and sorted in descending order of probability, as shown in Table 2.

[0048] Table 2 Selection of Minimum Conditional Probability in the First Round

[0049]

[0050] For the remaining moving mass-beam time-varying structure sensor, the candidate degrees of freedom 2 and 16 have the largest minimum probability of 0.77, and their second smallest probability distributions are also the same. Therefore, degree 2, with the smaller degree of freedom number, is not selected as the minor degree of freedom for the entire operation of the moving mass-beam time-varying structure, and is added to the sensor measurement degree of freedom set D. m Inside.

[0051] Step 8: First replenishment of moving mass - after the second degree of freedom of the time-varying beam structure has been completed throughout its operation, the sensor measures the degree of freedom set D. m ={2, 4, 14}, with n degrees of freedom m =3, which is less than the final number of degrees of freedom n measured by the sensor. U =8, then return to step seven and iterate 5 more times, supplementing degrees of freedom 16, 7, 11, 9, and 5 as secondary degrees of freedom throughout the entire operation of the moving mass-beam time-varying structure, and adding the sensor measurement degree of freedom set D. m After six rounds of iteration, the sensor measurement degree of freedom set D... m ={2, 4, 5, 7, 9, 11, 14, 16}, with n degrees of freedom. m =8, which equals the final number of degrees of freedom for sensor measurement, n. U The set of sensor measurement degrees of freedom D at this time m As the final set of sensor measurement degrees of freedom D U Stop iterating.

[0052] Step Nine: Based on the target mode, time-varying structural environment, test system conditions, and the final number of sensor measurement degrees of freedom n U =8. The probability threshold for important degrees of freedom p0 = 0.8. The final sensor measurement degree of freedom set D output from step eight is... U The output is the final set of sensor measurement degrees of freedom, D. U This enables the optimization of the arrangement of time-varying structural vibration sensors.

[0053] Step 10: Based on the final sensor measurement degree of freedom set D output from Step 9. U Arrange sensors, such as Figure 7As shown, while ensuring the acquisition requirements of the dynamic vibration information of the moving mass-beam time-varying structure, the number of sensors is reduced, and the sensor array is used to classify and coordinate the acquisition of the dynamic vibration information of the moving mass-beam time-varying structure, thereby improving the ability to acquire the structural dynamic vibration information of the moving mass-beam time-varying structure throughout its operation.

[0054] To evaluate the effectiveness of the method of this invention, the maximum singular value ratio (SVR) was used as the evaluation criterion. Without considering the time-varying characteristics of the structure, and only based on the structural dynamics at t = 12.5s, i.e., when the mass block is at the midpoint of the beam, the sensor placement optimization using the QR decomposition method was used as a reference. The sensor placement quality of this method was evaluated throughout the entire operation of the moving mass-beam time-varying structure. The maximum singular value ratio is the ratio of the non-zero maximum to the minimum singular values ​​of the measurement mode matrix. A ratio closer to 1 indicates better linear independence of each mode and a more optimized sensor placement.

[0055] Throughout the operation of the moving mass-beam time-varying structure, the average SVR of the sensor arrangement obtained by this method is 1.93, while the average result of the sensor arrangement under time-invariant conditions is 2.31. This method shows a 16.5% performance improvement. The comparison results indicate that this method effectively achieves the classified and coordinated acquisition of dynamic vibration information of time-varying structures, and improves the ability to acquire structural dynamic vibration information of time-varying structures throughout the entire operation.

[0056] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for arranging time-varying structural vibration sensors to maximize conditional probability, characterized in that: Includes the following steps, Step 1: Establish a time-varying characteristic model of the time-varying structure based on its operating conditions, and determine the final number of sensor measurement degrees of freedom n according to the target mode, the time-varying structure environment, and the test system conditions. U ; Step 2: Taking into account both the characteristic period of the time-varying structure's operation and computational efficiency, a quasi-static analysis method is used to discretize the entire time-varying structure's operation into n... s The state at each discrete moment is characterized, and the discrete characterization results are passed to the structural finite element model for modal analysis to obtain the structural dynamics information at the current moment. Step 3: Since sensor measurement points can only be placed on the structural surface, nodes inside the finite element model and nodes under boundary constraints are eliminated based on physical limitations. Rotational degrees of freedom that cannot be measured are also eliminated, retaining only the degrees of freedom that can be used to directly measure the sensors. This set of candidate degrees of freedom is used for subsequent optimization of the time-varying structural sensor layout. The number of candidate degrees of freedom is denoted as n. L This effectively eliminates potential ineffective sensor placement methods and improves the efficiency of sensor optimization placement. Step 4: Utilize the time-invariant structure sensor optimization arrangement method to optimize the sensor arrangement for the current discrete time step structure state, and obtain the corresponding time-varying structure discrete time sensor arrangement method; update the time step and iteratively calculate, traversing all discrete time states throughout the entire operation to obtain the time-varying structure discrete time sensor arrangement method at each moment during the entire operation of the time-varying structure, forming a set of discrete time sensor arrangement methods for the entire operation of the time-varying structure. Step 5: Determine the important sensor degrees of freedom throughout the entire operation of the time-varying structure; perform statistical analysis on the sensor arrangement set at discrete moments throughout the entire operation of the time-varying structure obtained in Step 4, and calculate the frequency n of each degree of freedom in the candidate set of optimal sensor arrangement throughout the entire operation of the time-varying structure in the set of sensor arrangement methods at discrete moments throughout the entire operation of the time-varying structure. i (i = 1, 2, ..., n) L Then, the importance probability vector of the candidate degree-of-freedom set for the optimal arrangement of the time-varying structure sensor throughout its operation is calculated. in This represents the importance probability of the candidate degrees of freedom for the i-th time-varying structural sensor during its entire optimized layout. A higher importance probability indicates that it will obtain richer vibration information during the entire operation of the time-varying structure. Sensors with importance probabilities exceeding the importance degree of freedom probability threshold p0 are classified as important sensors. The basic testing capability of the final sensor layout is guaranteed by using important sensors. A balance is struck between the importance probability distribution of the candidate degrees of freedom set for the optimized layout of the time-varying structural sensor and the number of measurement degrees of freedom n of the final sensor. U Set a threshold p0 for the probability of important degrees of freedom throughout the operation of the time-varying structure. Degrees of freedom whose importance probability in the optimized arrangement of the time-varying structure sensors is greater than p0 are considered important degrees of freedom throughout the operation of the time-varying structure. If the number of important degrees of freedom throughout the operation of the time-varying structure reaches the final number of sensor measurement degrees of freedom n... U Then, the top n candidate degrees of freedom with the highest importance probability will be optimized throughout the operation of the time-varying structure sensor. U The candidate degrees of freedom for the optimal arrangement of a time-varying structure sensor throughout its operation are used as the final set of sensor measurement degrees of freedom, D. U ; If the number of important degrees of freedom throughout the entire operation of the time-varying structure is less than the number of degrees of freedom measured by the final sensor, n U Then all important degrees of freedom of the time-varying structure throughout its operation will be added to the sensor measurement degree of freedom set D. m Within the sensor's set of degrees of freedom, the number of degrees of freedom is denoted as n. m Furthermore, it is necessary to further determine the secondary degrees of freedom of the time-varying structure throughout its operation based on the correlation of the vibration characteristics of the time-varying structure, and proceed to step six. Step Six: Calculate the candidate degrees of freedom for the time-varying structure sensor during its entire operation, and select the affinity matrix M. A The correlation between candidate degrees of freedom for optimal arrangement of time-varying structure sensors throughout the entire operation process is quantitatively calculated. Based on the frequency of each degree of freedom in the candidate degree of freedom set for optimal arrangement of time-varying structure sensors at discrete moments in the sensor arrangement mode set throughout the entire operation process, the affinity matrix M for selecting candidate degrees of freedom for optimal arrangement of time-varying structure sensors is calculated. A ; Step 7: Select the affinity matrix M based on the candidate degrees of freedom of the time-varying structure sensor during its entire operation optimization. A Calculate the minimum conditional probability min SA of the candidate degrees of freedom i for the remaining time-varying structural sensor arrangement during the entire operation of each set of degrees of freedom not included in the sensor measurement measurement set. (j,i) j∈D m The remaining candidate degrees of freedom for the optimal arrangement of the time-varying structure sensors throughout the entire operation are sorted in descending order of probability. The degree of freedom corresponding to the minimum conditional probability with the largest value is taken as the secondary degree of freedom for the entire operation of the time-varying structure and added to the sensor measurement degree of freedom set D. m Within this framework, the selection of secondary degrees of freedom throughout the entire operation of the time-varying structure is quantitatively realized, further enhancing the spatial information acquisition capability of the sensor arrangement for the vibration characteristics of the time-varying structure. If there is more than one candidate degree of freedom for the optimal arrangement of the remaining time-varying structure sensors corresponding to the largest minimum conditional probability, the degree of freedom corresponding to the second smallest probability with the largest probability is selected, and so on. If there are two or more candidate degrees of freedom for the optimal arrangement of the remaining time-varying structure sensors with completely identical conditional probability distributions, the degree of freedom with the smaller number is selected and added as a secondary degree of freedom throughout the operation of the time-varying structure, and added to the sensor measurement degree of freedom set D. m Inside; Step 8: If the sensor measures the set of degrees of freedom D m The number of degrees of freedom n m =n u Then the set of sensor measurement degrees of freedom D at this time will be... m As the final sensor measurement degree of freedom set D U Stop iteration; If the sensor measures the set of degrees of freedom D m The number of degrees of freedom n m <n u Then return to step seven and iteratively expand the secondary degrees of freedom of the time-varying structure throughout its operation; Step Nine: Based on the target mode, time-varying structural environment, test system conditions, and the final number of sensor measurement degrees of freedom n U The probability threshold p0 for important degrees of freedom is used to optimize the arrangement of time-varying structural vibration sensors, and the final sensor measurement degree of freedom set D output from step six is ​​used. U Or the final set of sensor measurement degrees of freedom D output from step eight. U The final set of sensor measurement degrees of freedom, D, is output. U This enables the optimization of the arrangement of time-varying structural vibration sensors.

2. The method for maximizing conditional probability arrangement of time-varying structural vibration sensors as described in claim 1, characterized in that: Step six describes the selection of the affinity matrix M for candidate degrees of freedom. A Quantitative calculation based on formula (1): Among them, M A It is a square matrix whose dimension is related to the number of candidate degrees of freedom of the time-varying structure sensor's optimized layout throughout its operation, and is n. L ×n L SA (i,j) This represents the probability that degree-of-freedom i is selected when a candidate degree-of-freedom i is selected during the entire optimized layout of the time-varying structure sensor. The probability of degree-of-freedom j being selected is calculated as follows: Where, n (i,j) The frequency of degree-of-freedom i being selected when a candidate degree-of-freedom i is selected in the set of sensor arrangement methods at discrete moments throughout the operation of the time-varying structure; the frequency n of candidate degree-of-freedom i in the set of sensor arrangement methods at discrete moments throughout the operation of the time-varying structure. i When the value is 0, i.e., when candidate degree of freedom i has never been selected, SA is defined. (i,j) =0, (j=1,2,…n) L ).

3. A method for maximizing conditional probability arrangement of time-varying structural vibration sensors as described in claim 1 or 2, characterized in that... It also includes step ten: based on the final sensor measurement degree-of-freedom set D output from step nine. U By deploying sensors, the number of sensors can be reduced while ensuring the acquisition of time-varying structural dynamic vibration information. This enables the sensor array to classify and collaboratively acquire time-varying structural dynamic vibration information, thereby improving the ability to acquire structural dynamic vibration information of time-varying structures throughout their operation.

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