A dense modal parameter extraction method and system based on random subspace

Abstract

The application discloses a dense modal parameter extraction method and system based on a random subspace, and the method comprises the following steps: collecting vibration response data of a research object, and then processing the data; according to the collected vibration response data, modal parameter identification is carried out by using an SSI-COV algorithm; for different bolt connection structure states, the modal parameters of each bolt connection structure in the state are identified, all modes are clustered by using a hierarchical clustering algorithm, and a steady-state diagram is obtained to identify real physical modes; the identified real physical modes of each bolt connection structure in the connection state are classified, and the damping ratio dispersion indexes in each real physical mode are calculated; and the change rule of the modal parameters with the change of the bolt connection structure state is obtained.

Description

Technical Field

[0001] This invention belongs to the field of state detection of rotor bolt connections in aero-engines, and specifically relates to a method and system for extracting dense modal parameters based on random subspace. Background Technology

[0002] Bolted connections are a common type of connection used in mechanical equipment across industries such as aerospace, shipbuilding, transportation, mining, petroleum, and chemicals. As one of the most widely used component connection methods in mechanical equipment, bolted connections play a crucial role in the assembly and maintenance of core mechanical equipment due to their high reliability and ease of assembly and disassembly. However, the introduction of bolted connections introduces discontinuity into the mechanical system, creating a transitional zone where the system's inherent performance changes. When bolted connections are subjected to extreme environments such as impact and vibration, the preload of the bolts decreases, leading to failure phenomena such as loosening, slippage, fatigue cracking, and fracture at the joint surface. This causes complex changes in the stiffness and damping of the entire system, resulting in a strong nonlinear response. Consequently, the integrity of the structure is compromised, ultimately affecting its safety and reliability. Therefore, bolted connections are also the weakest link in the entire mechanical system. The bolted joint is one of the main sources of nonlinear response; even small changes in the joint can cause changes in the system's modal parameters. Therefore, accurate identification of modal parameters is crucial for understanding changes in the system's structure. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides a dense modal parameter extraction method based on random subspace, which overcomes the previous method of extracting fault information only from the time domain, frequency domain, and time-frequency domain of the signal. It can obtain the fault characteristics of the signal from the direction of modal parameter identification and find fault information from the frequency and damping changes of the system.

[0004] To achieve the above objectives, the technical solution adopted by this invention is: a method for extracting dense modal parameters based on random subspaces, comprising the following steps:

[0005] Vibration response data of the research object are collected and then processed.

[0006] Based on the collected vibration response data, the SSI-COV algorithm is used to identify modal parameters;

[0007] For different bolted connection structural states, the modal parameters of each bolted connection structural state are identified, and all modes are clustered using a hierarchical clustering algorithm. The similarity value combining modal frequency and mode shape is used to measure the similarity between two modes, and a steady-state diagram is obtained to identify the real physical modes.

[0008] The modes identified under each bolted connection state are classified, and the damping ratio dispersion index under each mode is calculated. Taking the standard preload state as normal, the dispersion index of other connection states is compared with it to obtain the variation law of modal parameters as the bolted connection structural state changes.

[0009] The vibration response data of the research object is collected, and the data is then processed as follows:

[0010] First, the data length of the acquired vibration signal is selected. Since the recognition accuracy of the SSI-COV algorithm is related to the number of rows in the Toeplitz matrix, considering the impact of data length on the spectrum, calculation speed, and the impact of the number of matrix rows on the Toeplitz matrix, the following calculation is performed: i When the value is 625, the spectral condition number of the Toeplitz matrix reaches its minimum. A data length of 1250 points is selected, and five sets of signals are used for modal parameter identification.

[0011] In the SSI-COV algorithm, the cross-correlation function of the vibration response data is first used to represent the impact response function. Then, the calculated cross-correlation functions are used to form a covariance matrix. The eigenvalues ​​of the Toeplitz matrix are obtained through singular value decomposition, and the modal parameters of the structural system are identified. Based on the characteristics of the spectrum diagram of the bolted connection structure, an order interval is set. The upper limit of the order interval should be greater than the actual order. The upper limit of the system order is selected as n=30, and the lower limit is n=2.

[0012] For different bolted connection structural states, modal parameters are identified for each bolted connection structural state. Hierarchical clustering algorithm is used to cluster all modes. A similarity value combining modal frequencies and mode shapes is used to measure the similarity between two modes. When obtaining a steady-state diagram to identify the true physical modes, the steady-state diagram is used to determine the modal order of the system. The modal parameters of different order poles are compared with the modal parameters of adjacent order poles. When the distance between the modal parameters of different order poles and the modal parameters of adjacent order poles is less than the limit criteria of natural frequency, damping ratio, and mode shape, it is considered a stable order pole. Stable order poles form a stable axis, thus obtaining the true physical mode. Then, a similarity value combining modal frequencies and mode shapes is used to measure the similarity between two modes. The distance between two modes is calculated as follows:

[0013]

[0014] In the formula, Indicates the system structure of the first The natural frequency of the order, It is a modal guarantee criterion. The value represents the degree of correlation between two mode shapes. Its value is generally between 0 and 1. The larger the value, the greater the probability that the two compared mode shapes belong to the same mode order. The expression is as follows:

[0015]

[0016] In the formula, Indicates the first First-order mode shape and the second-order mode shape First-order mode shape, The above formula, which represents the conjugate transpose, can quantitatively determine the correlation between two mode shapes.

[0017] Then, the actual physical modes are identified from the steady-state diagram.

[0018] The limits for natural frequency, damping ratio, and mode shape are as follows:

[0019]

[0020] The distance threshold is 0.5; Indicates the system structure of the first Damping ratio of order, Indicates the system structure of the first +1 order natural frequency;

[0021] The actual physical modes identified under the connection states of each bolted connection structure are categorized. When calculating the damping ratio dispersion index for each state, the damping ratio under each connection state is presented in the form of a scatter plot. Then, a dispersion index is established to measure the degree of dispersion of the damping value under each connection state. The dispersion degree is used to characterize the relationship between the damping ratio and bolt loosening. The formula for the dispersion index is as follows:

[0022]

[0023] The larger the dispersion value, the more dispersed the damping ratio and the more complex the system structure.

[0024] This invention also provides a bolt connection condition detection system based on SSI-COV, including a data acquisition module, a modal parameter identification module, a real physical mode identification module, and a condition identification module;

[0025] The data acquisition module is used to collect vibration response data of the research object and then process the data;

[0026] The modal parameter identification module is used to identify modal parameters based on the collected vibration response data using the SSI-COV algorithm.

[0027] The real physical mode recognition module is used to identify the modal parameters of each bolted connection structure under different bolted connection structure states. It uses a hierarchical clustering algorithm to cluster all modes and uses a similarity value combining modal frequency and mode shape to measure the similarity between two modes, and obtains a steady-state diagram to identify the real physical modes.

[0028] The state recognition module is used to classify the real physical modes identified under the connection states of each bolted connection structure and calculate the damping ratio dispersion index under each state. Taking the standard preload state as normal, the dispersion index of other connection states is compared with it to obtain the variation law of modal parameters as the state of the bolted connection structure changes.

[0029] A computer device is also provided, including a processor and a memory. The memory is used to store a computer executable program. The processor reads part or all of the computer executable program from the memory and executes it. When the processor executes part or all of the executable program, it can realize the dense modal parameter extraction method based on random subspace described in this invention.

[0030] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of the dense modal parameter extraction method based on random subspaces as described in this invention.

[0031] Compared with the prior art, the present invention has at least the following beneficial effects:

[0032] Random subspace is a time-domain method that directly processes time-series signals without needing to convert them to the frequency domain, thus avoiding the impact of frequency resolution. This invention first uses a covariance-driven random subspace method to identify the modal parameters of the poles in a bolted connection structure. Then, a hierarchical clustering algorithm is used to cluster the poles to obtain a steady-state diagram. When most poles lie on a vertical line, the vertical cluster is considered the true physical mode, and its modal parameters are then extracted. The SSI-COV method not only has a solid theoretical foundation but also accurately identifies dense modes, overcoming the shortcomings of traditional modal identification methods such as EMD and HHT. To detect the degree of bolt loosening, this invention proposes a damping ratio dispersion as a loosening index. The accuracy and reliability of this invention are verified through experiments on bolted connection structures of aero-engine rotors. Modal parameters, as dynamic characteristic quantities in a structural system, can characterize changes in the dynamic behavior within the structure, thereby reliably detecting the state of bolted connection structures. Attached Figure Description

[0033] Figure 1 This is a set of signals under standard preload conditions.

[0034] Figure 2The rotor tie rod bolt distribution diagram: 1-24 represent the positions of the 24 bolts respectively.

[0035] Figure 3 This is the steady-state diagram for the standard preload condition.

[0036] Figure 4 A bar chart showing the number of poles at different frequencies.

[0037] Figure 5 This is a schematic diagram showing the frequency identification results of a set of signals under each connection state.

[0038] Figure 6 This is a schematic diagram showing the damping ratio identification results of the six sets of signals under each connection state. Detailed Implementation

[0039] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] To address the challenge of identifying dense modal parameters in bolted connections of aero-engine rotors, this invention proposes a dense modal parameter extraction method based on random subspace. This method extracts modal parameters under different bolted connection states, performs discreteness analysis, and observes the changing trends of system frequency and damping ratio. Furthermore, the discreteness value is used to quantitatively describe the tightness of the bolt connection. By measuring the connection state through the system's modal parameters, it can effectively characterize the essential changes in the system's structure. SSI-COV not only accurately identifies modal parameters but also effectively identifies dense modal parameters.

[0041] The purpose of this invention is to propose a dense modal parameter extraction method based on random subspace for modal parameter identification and state detection of large and complex mechanical structures, especially disc bolt connections.

[0042] To achieve the above objectives, the technical solution provided by this invention is: a design method for a dense modal parameter extraction method based on random subspaces, specifically including the following steps:

[0043] Step 1: Collect vibration response data of the research object, and then select the data length;

[0044] Step 2: Based on the characteristics of the vibration response data collected in Step 1, select the covariance-driven stochastic subspace method (SSI-COV) algorithm for modal parameter identification.

[0045] Step 3: For different bolted connection structure states, identify the modal parameters of each bolted connection structure state, use hierarchical clustering algorithm to cluster all modes, use the similarity value of modal frequency and mode shape to measure the similarity between two modes, and obtain steady state diagram to identify the real physical modes;

[0046] Step 4: Classify the modes identified in the connection states of each bolted connection structure, and calculate the damping ratio dispersion index under each mode; take the standard preload state as normal, and then compare the dispersion index of other connection states with it.

[0047] In step 1, the data length of the acquired vibration signals is first selected. Since the recognition accuracy of the SSI-COV algorithm is related to the number of rows in the Toeplitz matrix, the data length is chosen in relation to the Toeplitz matrix. Based on experience, this invention selects a data length of 1250 points. To ensure data integrity, this invention selects five sets of signals for modal parameter identification.

[0048] Step 2 requires selecting relevant parameters for the SSI-COV algorithm. In the SSI-COV algorithm, the cross-correlation function of the vibration response data is first used to represent the impact response function. Then, the calculated cross-correlation functions are used to form a covariance matrix (i.e., the Toeplitz matrix). Then, singular value decomposition is used to obtain the eigenvalues ​​of the Toeplitz matrix, thereby identifying the modal parameters of the structural system. The Toeplitz matrix is ​​a square matrix. In step 1, this invention selects... i =625 (1250 data points) The Toeplitz matrix. Based on the characteristics of the structure, an order interval is defined, with the upper limit of the order greater than the actual order. The upper limit of the system order is n=30, and the lower limit is n=2.

[0049] Step 3: In this invention, steady-state diagrams are used to determine the modal order of the system. The modal parameters of poles of different orders are compared with the modal parameters of adjacent poles. When the distance between the modal parameters of poles of different orders and the modal parameters of adjacent poles is less than a set limit criterion, it is considered a stable pole. Stable poles form a stable axis, also known as the true physical modes of the system. The limit criteria for natural frequency, damping ratio, and mode shape are as follows:

[0050]

[0051] Indicates the system structure of the first The natural frequency of the order, It is a modal guarantee criterion. The value represents the degree of correlation between two mode shapes. Its value is generally between 0 and 1. The larger the value, the greater the probability that the two compared mode shapes belong to the same mode order. The expression is as follows:

[0052]

[0053] In the formula, Indicates the first First-order mode shape and the second-order mode shape First-order mode shape, The above formula, which represents the conjugate transpose, can quantitatively determine the correlation between two mode shapes.

[0054] Then, a similarity value combining modal frequencies and mode shapes is used to measure the similarity between the two modes; the distance between the two modes is calculated as follows:

[0055]

[0056] If the distance between the two modes dij A very short distance threshold (d) indicates that the two modes have similar natural frequencies and mode shapes. Therefore, the two modes may contain the same physical modes and can be grouped into the same cluster through clustering. The lower the distance threshold d, the more clusters there are, and physical modes belonging to the same cluster may be separated into other clusters. Generally, when the number of measurement points is unlimited, a distance below 1 avoids including estimates of different physical modes in the same cluster, because the MAC between corresponding modal shapes should be close to zero. In this invention, a distance threshold of 0.5 achieved good results, and the true physical modes can be well identified from the obtained steady-state plot.

[0057] Step 4: To better observe the change in damping ratio with bolt tightness, this invention presents the damping ratio under various connection conditions as a scatter plot. Then, a dispersion index is established to measure the dispersion of the damping values ​​under each connection condition, thereby characterizing the relationship between the damping ratio and bolt loosening. The dispersion index formula is as follows:

[0058]

[0059] Dispersion value The larger the value, the more dispersed the damping ratio and the more complex the system structure.

[0060] In addition, the present invention can also provide a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and the processor can implement the dense modal parameter extraction method based on random subspace described in the present invention when executing part or all of the computed executable program.

[0061] Alternatively, a computer-readable storage medium may be provided, in which a computer program is stored, which, when executed by a processor, enables the implementation of the dense modal parameter extraction method based on random subspace described in this invention.

[0062] The device used for the computer-readable storage medium may be a laptop computer, tablet computer, desktop computer, or workstation.

[0063] The processor can be a graphics processing unit (GPU), a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0064] The memory described in this invention can be an internal storage unit of a laptop, tablet, desktop computer, mobile phone, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0065] Computer-readable storage media can include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM).

[0066] The present invention will be further illustrated below with reference to the accompanying drawings, using fault diagnosis based on bolt connection data from a rotor testing center as an example.

[0067] In this embodiment, vibration data of five bolt connection states with a sampling frequency of 6400Hz were used.

[0068] Step 1: First, collect the vibration response data of the research object, and then select the data length.

[0069] In step 1, the data length of the acquired vibration signals is first selected. Based on experience, this invention selects a data length of 1250 points. To ensure data integrity, this invention selects five sets of signals for modal parameter identification. Due to space limitations, only the first set of signals selected from four sensors is shown here. The selected time and frequency domains are as follows: Figure 1 As shown.

[0070] The five bolt connection states mentioned in this invention are standard pre-tightening, loosening three bolts, loosening twelve bolts, loosening all bolts once, and loosening all bolts twice. In a static impact test on a chassis test bench, 24 bolts on an aero-engine rotor were set to five states to simulate different degrees of bolt tightness. The bolt distribution diagram is shown below. Figure 2 As shown, the five states of bolt loosening are listed in Table 1.

[0071] Table 1. Five connection states of rotor bolt connections

[0072]

[0073] Based on the experimental data used in the specific implementation examples of this invention, a square wave with a mean of 0, a frequency of 1Hz, and an amplitude of 0.75A (A being the maximum amplitude) is used as input to excite the system structure. The excitation of the square wave signal can be approximately seen as the excitation of the impact signal.

[0074] Step 2: Based on the characteristics of the vibration response data collected in Step 1, select the covariance-driven random subspace method (SSI-COV) algorithm for modal parameter identification.

[0075] Step 3: For different connection structure states, identify the modal parameters in each state, use hierarchical clustering algorithm to cluster all modes, use a similarity value combining modal frequency and mode shape to measure the similarity between two modes, and obtain a steady state diagram to identify the real physical modes.

[0076] In step 3, the data is analyzed using a covariance-driven random subspace algorithm. Figure 3 Steady-state plots obtained for all standard preload conditions (where + represents all poles and · represents stable poles). Figure 3The lower curve is the power spectrum of the Burg algorithm based on the AR model. Clustering is performed according to the limits of natural frequency, damping ratio, and mode shape, as well as a distance threshold, resulting in 8 vertical axes. Physical modes are modes inherent to the structure itself and exist stably within the system. The more poles contained in each cluster, the greater the likelihood that it belongs to a true physical mode. Based on experience, a pole number threshold m=10 is used. In this invention, a cluster with more than 10 poles is considered a true physical mode. Taking a set of signals given in the standard preload state in step 1 as an example, the number of poles at different frequencies is as follows... Figure 4 As shown in Table 2, the actual physical modal parameters are listed.

[0077] Table 2. Identification of Real Physical Modal Parameters under Standard Pre-tensioning State

[0078]

[0079] Step 4: In order to better observe the change of damping ratio with the tightness of bolt connection, the present invention presents the damping ratio of each connection state in the form of a scatter plot, and then establishes a dispersion index to measure the dispersion of the damping value in each connection state, so as to characterize the relationship between damping ratio and bolt loosening.

[0080] Specifically, for each of the five bolt connection states, six sets of signals are selected, with each set containing four signal segments. The SSI-COV algorithm is used to identify the modal parameters of these six sets of signals for each state, based on the selection criteria for the actual physical modes in step 3. One set of data from each of the five states is selected for modal parameter identification, and its frequency changes are as follows: Figure 5 As shown, the frequency tends to increase in each state, and decreases as the bolt connection loosens. Since the frequency change trends of each group of signals are the same, they will not be shown here.

[0081] In modal parameter identification, besides frequency identification, damping ratio is also an important modal parameter. Due to the complexity of damping ratio, it generally cannot exhibit a linear change. Therefore, this invention proposes a dispersion index to measure the dispersion of damping ratio under different bolted connection states. According to the dispersion formula in step 4, the damping ratio dispersion diagrams for the six sets of signals identified under five bolted connection states are as follows: Figure 6 As shown in the figure, it can be clearly seen that as the degree of bolt loosening increases, the damping ratio generally increases, and the dispersion of the damping ratio becomes larger. To quantitatively describe this phenomenon, the dispersion of the damping ratio is listed in Table 3.

[0082] Table 3. Dispersion Index

[0083]

[0084] As shown in Table 3, the average damping ratio generally increases with the degree of bolt loosening, and the dispersion increases significantly with the degree of bolt loosening, which can be used as a metric. Therefore, by using modal parameter identification, not only frequency parameters but also damping ratio parameters can be obtained. By using dispersion to link the damping ratio with bolt loosening faults, this can be used as a standard for judging whether the bolt is loose.

[0085] 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, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for extracting dense modal parameters based on random subspaces, characterized in that, Includes the following steps: Vibration response data of the research object are collected and then processed. Based on the collected vibration response data, the SSI-COV algorithm is used to identify modal parameters; For different bolted connection structural states, modal parameters are identified for each state. Hierarchical clustering is used to cluster all modes. A similarity value combining modal frequencies and mode shapes is used to measure the similarity between two modes, resulting in a steady-state diagram to identify the true physical modes. The steady-state diagram is then used to determine the modal order of the system. Modal parameters at different order poles are compared with those at adjacent order poles. When the distance between the modal parameters at different order poles and those at adjacent order poles is less than the limits set by natural frequency, damping ratio, and mode shape, it is considered a stable order pole. These stable order poles form a stable axis, thus yielding the true physical modes. Finally, a similarity value combining modal frequencies and mode shapes is used to measure the similarity between two modes. The distance between two modes is calculated as follows: In the formula, Indicates the system structure of the first The natural frequency of the order, It is a modal guarantee criterion. The value represents the degree of correlation between two mode shapes, ranging from 0 to 1. The larger the value, the greater the probability that the two compared mode shapes belong to the same modal order. The expression is as follows: In the formula, Indicates the first First-order mode shape and the second-order mode shape First-order mode shape, The above equation, representing the conjugate transpose, can quantitatively determine the correlation between two mode shapes; then, the true physical modes are identified from the steady-state diagram; the limits for natural frequencies, damping ratios, and mode shapes are as follows: The distance threshold is 0.5; Indicates the system structure of the first Damping ratio of order, Indicates the system structure of the first +1 order natural frequency; The modes identified under each bolted connection state are classified, and the damping ratio dispersion index under each mode is calculated. Taking the standard preload state as normal, the dispersion index of other connection states is compared with it to obtain the variation law of modal parameters as the bolted connection structural state changes.

2. The method for extracting dense modal parameters based on random subspace according to claim 1, characterized in that, The vibration response data of the research object is collected, and the data is then processed as follows: First, the data length of the acquired vibration signal is selected. Since the recognition accuracy of the SSI-COV algorithm is related to the number of rows in the Toeplitz matrix, considering the impact of data length on the spectrum, calculation speed, and the impact of the number of matrix rows on the Toeplitz matrix, the following calculation is performed: i When the value is 625, the spectral condition number of the Toeplitz matrix reaches its minimum. A data length of 1250 points is selected, and five sets of signals are used for modal parameter identification.

3. The method for extracting dense modal parameters based on random subspace according to claim 1, characterized in that, In the SSI-COV algorithm, the cross-correlation function of the vibration response data is first used to represent the impact response function. Then, the calculated cross-correlation functions are used to form a covariance matrix. The eigenvalues ​​of the Toeplitz matrix are obtained through singular value decomposition, and the modal parameters of the structural system are identified. Based on the characteristics of the spectrum diagram of the bolted connection structure, an order interval is set. The upper limit of the order interval should be greater than the actual order. The upper limit of the system order is selected as n=30, and the lower limit is n=2.

4. The method for extracting dense modal parameters based on random subspace according to claim 1, characterized in that, The actual physical modes identified under the connection states of each bolted connection structure are categorized. When calculating the damping ratio dispersion index for each state, the damping ratio under each connection state is presented in the form of a scatter plot. Then, a dispersion index is established to measure the degree of dispersion of the damping value under each connection state. The dispersion degree is used to characterize the relationship between the damping ratio and bolt loosening. The formula for the dispersion index is as follows: Dispersion value The larger the value, the more dispersed the damping ratio and the more complex the system structure.

5. A bolt connection condition detection system based on SSI-COV, characterized in that, It includes a data acquisition module, a modal parameter recognition module, a real physical mode recognition module, and a state recognition module; The data acquisition module is used to collect vibration response data of the research object and then process the data; The modal parameter identification module is used to identify modal parameters based on the collected vibration response data using the SSI-COV algorithm. The real physical mode identification module is used to identify the modal parameters of various bolted connection structures under different structural states. It uses a hierarchical clustering algorithm to cluster all modes and employs a similarity value combining modal frequencies and mode shapes to measure the similarity between two modes, resulting in a steady-state diagram to identify the real physical modes. The steady-state diagram is then used to determine the modal order of the system. Modal parameters at different order poles are compared with those at adjacent order poles. When the distance between the modal parameters at different order poles and those at adjacent order poles is less than the limits set by natural frequency, damping ratio, and mode shape, it is considered a stable order pole. These stable order poles form a stable axis, thus yielding the real physical modes. Finally, a similarity value combining modal frequencies and mode shapes is used to measure the similarity between two modes. The distance between two modes is calculated as follows: In the formula, Indicates the system structure of the first The natural frequency of the order, It is a modal guarantee criterion. The value represents the degree of correlation between two mode shapes, ranging from 0 to 1. The larger the value, the greater the probability that the two compared mode shapes belong to the same modal order. The expression is as follows: In the formula, Indicates the first First-order mode shape and the second-order mode shape First-order mode shape, The above equation, representing the conjugate transpose, can quantitatively determine the correlation between two mode shapes; then, the true physical modes are identified from the steady-state diagram; the limits for natural frequencies, damping ratios, and mode shapes are as follows: The distance threshold is 0.5; Indicates the system structure of the first Damping ratio of order, Indicates the system structure of the first +1 order natural frequency; The state recognition module is used to classify the real physical modes identified under the connection states of each bolted connection structure and calculate the damping ratio dispersion index under each state. Taking the standard preload state as normal, the dispersion index of other connection states is compared with it to obtain the variation law of modal parameters as the state of the bolted connection structure changes.

6. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and the processor executing part or all of the computed executable program is capable of implementing the dense modal parameter extraction method based on random subspace as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the extraction method of dense modal parameters based on random subspace as described in any one of claims 1-4.

Images