Substructure modal identification method, device, and equipment capable of performing step-by-step and multiple measurements

Abstract

The present application discloses a substructure modal identification method, device, and equipment that can be measured step by step and multiple times. The method includes: using the non-linear frequency modulation modal decomposition algorithm, with the goal of minimizing the objective function, performing signal demodulation processing on the response data of each measurement point in each substructure of the engineering structure to obtain at least one order of target single-component data; each substructure has at least one common measurement point with at least one other substructure; based on the target single-component data, obtaining spectral data; according to the ratio of the spectral amplitudes of the same order at each measurement point in the spectral data, obtaining the modal amplitude of each order of each substructure; according to the modal amplitude of each order of each substructure, adjusting the modal amplitudes of the common measurement points of each substructure to be consistent to obtain the modal amplitude of each order of all measurement points; according to the modal amplitude of each order of all measurement points, judging the direction of the mode based on the minimization of the modal confidence criterion; according to the direction of the mode, obtaining the modal mode of the engineering structure.

Description

Technical Field

[0001] This application belongs to the technical field of modal identification, and particularly relates to a substructure modal identification method, device, and equipment that can be measured step by step and multiple times. Background Art

[0002] Modal identification, as a structural dynamics analysis technology, is based on the response data of sensors to determine the modal parameters of a structural system, such as damping, frequency, vibration mode, etc. This technology is widely used in aspects such as the monitoring, damage diagnosis, and optimal design of engineering structures. It can assist staff in better understanding the health status of the structural system, promptly discovering potential problems, and thus ensuring the safety of the structure.

[0003] Traditional modal identification methods require that the acquisition of all response data must be synchronized to ensure the accuracy of modal identification. However, for particularly complex structural systems, this usually requires deploying a large number of sensors in the structural system simultaneously. This method not only greatly increases the difficulty of obtaining response data but also significantly increases the cost of modal identification. Summary of the Invention

[0004] Embodiments of this application provide a substructure modal identification method, device, and equipment that can be measured step by step and multiple times, aiming to solve problems such as the existing modal identification methods not only increasing the difficulty of obtaining response data but also increasing the cost of modal identification.

[0005] In a first aspect, embodiments of this application provide a substructure modal identification method that can be measured step by step and multiple times, including: obtaining the response data of each measurement point in each substructure of an engineering structure; the response data of all measurement points in the same substructure are response data collected synchronously at the same time; the response data of measurement points in different substructures are response data collected step by step and multiple times at different times; each substructure has at least one common measurement point with at least one other substructure; for each response data, using the non-linear frequency modulation modal decomposition algorithm, with the goal of minimizing the objective function, perform signal demodulation processing on the response data to obtain at least one-order target single-component data; the objective function is used to evaluate the signal complexity of at least one single-component data; for each target single-component data, based on the target single-component data, obtain spectral data; for each substructure, according to the ratio of the spectral amplitudes of the same order at each measurement point in the spectral data, obtain the modal amplitude of each order of each substructure; according to the modal amplitude of each order of each substructure, adjust the modal amplitudes of the common measurement points of each substructure to be consistent to obtain the modal amplitude of each order of all measurement points of the engineering structure; according to the modal amplitude of each order of all measurement points of the engineering structure, based on the minimum of the modal confidence criterion, judge the direction of the vibration mode; according to the direction of the vibration mode, obtain the modal vibration mode of the engineering structure.

[0006] In one embodiment of the first aspect, the method further includes: determining multiple sets of initial adjustment parameters in the non-linear frequency modulation mode decomposition algorithm; optimizing the multiple sets of initial adjustment parameters by using a parameter-free heuristic optimization algorithm to obtain target adjustment parameters; the target adjustment parameters are used to obtain at least first-order target single-component data.

[0007] In one embodiment of the first aspect, optimizing the multiple sets of initial adjustment parameters by using a parameter-free heuristic optimization algorithm to obtain target adjustment parameters includes: in the current iteration number, determining the fitness corresponding to each set of initial adjustment parameters based on the objective function; constructing an initial position vector for each set of initial adjustment parameters, and determining a core position vector with the smallest fitness among the multiple initial position vectors; updating each initial position vector based on the core position vector to obtain a candidate position vector corresponding to each initial position vector; if the current iteration number does not meet the iteration number condition, updating the multiple initial position vectors by using the multiple candidate position vectors until the current iteration number meets the iteration number condition, and then determining the parameters in the position vector with the smallest fitness among the multiple candidate position vectors as the target adjustment parameters.

[0008] In one embodiment of the first aspect, updating each initial position vector based on the core position vector to obtain a candidate position vector corresponding to each initial position vector includes: aiming at the actual position difference being less than the preset position difference, updating each initial position vector according to the core position vector, the weight value, and the balance index to obtain a candidate position vector corresponding to each initial position vector; wherein, the position difference is used to characterize the position deviation rate of the candidate position vector compared with the core position vector, and the balance index is used to characterize the movable range of the initial position vector.

[0009] In one embodiment of the first aspect, aiming at the actual position difference being less than the preset position difference, the initial position vector is updated according to the core position vector, the weight value, and the balance index to obtain the candidate position vector, including: determining the initial value of the balance index within the first index interval and the weight value of each initial position vector among the multiple initial position vectors; using the core position vector, the initial value, and the weight value to update each initial position vector within the preset search domain to obtain the first position vector corresponding to each initial position vector; for each initial position vector, determining the candidate value of the balance index, and using the candidate value to update the initial value and using the first position vector to update the initial position vector until the candidate value is within the second index interval, and determining the first position vector as the second position vector; wherein, the candidate value is less than the initial value, the first index interval is adjacent to and greater than the second index interval; if the position deviation rate of each second position vector relative to the core position vector is within the preset deviation range, it is determined that the actual position difference is less than the preset position difference, the core position vector is updated to the position vector corresponding to the core position vector among the multiple second position vectors, and for each second position vector, the second position vector is updated using the core position vector and the weight value to obtain the candidate position vector; if there is one or more second position vectors whose position deviation rate relative to the core position vector is outside the preset deviation range, then for each second position vector, the second position vector is iteratively updated using the core position vector, the weight value, and the candidate value until the position deviation rate of each second position vector relative to the core position vector is within the preset deviation range, the core position vector is updated to the position vector corresponding to the core position vector among the multiple second position vectors, and for each second position vector, the second position vector is updated using the core position vector and the weight value to obtain the candidate position vector.

[0010] In one embodiment of the first aspect, updating the multiple initial position vectors using the multiple candidate position vectors includes: determining the fitness of each candidate position vector based on the objective function; if there is a candidate position vector among the other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, then updating the multiple candidate position vectors to the multiple initial position vectors; the other candidate position vectors include the position vectors among the multiple candidate position vectors except the candidate position vector corresponding to the core position vector; if the fitness of the candidate position vector corresponding to the core position vector is greater than or equal to the fitness of the other candidate position vectors, then each candidate position vector is updated based on the Levy flight algorithm until there is a candidate position vector among the other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, and updating the multiple candidate position vectors to the multiple initial position vectors.

[0011] In one embodiment of the first aspect, determining the fitness corresponding to each set of initial adjustment parameters based on the objective function includes: for each set of initial adjustment parameters, performing signal demodulation processing on the response data according to the non-linear frequency modulation modal decomposition algorithm using the initial adjustment parameters to obtain at least one initial single-component data; using the objective function to determine the signal complexity of each initial single-component data; and determining the minimum signal complexity among the at least one initial single-component data as the fitness corresponding to the initial adjustment parameters.

[0012] In a second aspect, an embodiment of the present application provides a substructure modal identification device that can perform step-by-step multiple measurements, including:

[0013] An acquisition module, configured to acquire response data of each measurement point in each substructure of the engineering structure; the response data of all measurement points in the same substructure are response data collected synchronously at the same time; the response data of measurement points in different substructures are response data collected step by step and multiple times at different times; each substructure has at least one common measurement point with at least one other substructure.

[0014] A decomposition module, configured to, for each response data, use the non-linear frequency modulation modal decomposition algorithm to perform signal demodulation processing on the response data with the goal of minimizing the objective function to obtain at least one-order target single-component data; the objective function is used to evaluate the signal complexity of at least one single-component data.

[0015] A transformation module, configured to, for each target single-component data, obtain spectral data based on the target single-component data.

[0016] An identification module, configured to, for each substructure, obtain the modal amplitude of each order of each substructure according to the ratio of the spectral amplitudes of the same order of each measurement point in the spectral data.

[0017] The identification module is further configured to, according to the modal amplitude of each order of each substructure, adjust the modal amplitude of the common measurement points of each substructure to be consistent to obtain the modal amplitude of each order of all measurement points of the engineering structure; according to the modal amplitude of each order of all measurement points of the engineering structure, determine the direction of the mode based on the minimization of the modal confidence criterion; and obtain the modal mode of the engineering structure according to the direction of the mode.

[0018] In a third aspect, an embodiment of the present application provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where when the processor executes the computer program, it implements the step-by-step multiple measurement substructure modal identification method provided in the first aspect above.

[0019] Fourthly, an embodiment of the present application provides a computer-readable storage medium storing a computer program, which when executed by a processor, implements the substructure modal identification method capable of step-by-step multiple measurements provided in the first aspect above.

[0020] It can be understood that the beneficial effects of the second aspect above can be referred to the relevant descriptions in the first aspect above, and will not be repeated here.

[0021] The beneficial effects of the embodiment of the present application compared with the prior art are as follows: Since the prior art requires synchronous acquisition of the response data of the structure, not only a large number of sensors need to be deployed simultaneously, but also it is necessary to ensure that these sensors can synchronously measure the response data of the structure, which increases the identification cost; at the same time, it also raises the requirement for the data acquisition accuracy of the sensors, resulting in the problem of excessive difficulty in obtaining response data. Therefore, the response data of the measurement points of different substructures obtained in the present application can be the response data collected step by step at different times, so as to greatly reduce the number of sensors that need to be synchronously deployed in large civil engineering structures. The requirement for data synchronization is greatly reduced, thereby reducing the difficulty of obtaining response data. Combining with the non-linear frequency modulation modal decomposition algorithm, with the minimum of the objective function as the goal, the response data is demodulated, so that the response data is decomposed into at least one-order target single-component data. In this way, by extracting the single-component data from the response data and establishing the relationship between the modal amplitude and the spectral amplitude of the target single-component signal, that is, adjusting the modal amplitudes of the common measurement points of each substructure to be consistent, the acquisition time synchronization of the response data of all measurement points of the engineering structure is no longer restricted. It only needs to ensure the data acquisition time synchronization among all measurement points in the same substructure. Even if two sensors are used to divide the engineering structure into multiple substructures each containing two measurement points and obtain the response data of multiple substructures separately, the accuracy of the modal shape identification of the engineering structure can still be guaranteed, so that the obtained modal shape can accurately reflect the health status of the engineering structure.

[0022] In addition, usually, noise will be dispersed into multiple frequency components. In multi-component data, cross-interference will occur between different components, which will reduce the signal-to-noise ratio of the signal and affect the accurate extraction and analysis of the signal. However, the single-component data in the present application only contains modal information of a specific order, so that the influence of noise will be relatively small. In this way, by performing spectral analysis on each target single-component data, the frequency response of each component can be depicted more precisely, thereby effectively reducing the errors caused by signal aliasing or interference. This refined analysis method enables the present method to more accurately extract the modal shape of the engineering structure during the modal identification process, which not only helps to improve the accuracy of modal shape identification, but also can greatly reduce the calculation amount and calculation time, and improve the overall analysis efficiency. Description of the Drawings

[0023] Figure 1 It is a schematic structural diagram of a substructure modal identification system that can be measured step by step and multiple times provided by an embodiment of the present application;

[0024] Figure 2 It is a schematic flow diagram of a substructure modal identification method that can be measured step by step and multiple times provided by an embodiment of the present application;

[0025] Figure 3a It is a schematic structural diagram of an engineering structure provided by an embodiment of the present application;

[0026] Figure 3b It is an example schematic diagram of response data in an engineering structure provided by an embodiment of the present application;

[0027] Figure 3c It is an example schematic diagram of decomposed response data provided by an embodiment of the present application;

[0028] Figure 3d It is an example schematic diagram of the time-frequency curve of decomposed response data provided by an embodiment of the present application;

[0029] Figure 3e It is an example schematic diagram of the wavelet spectrum of decomposed response data provided by an embodiment of the present application;

[0030] Figure 3f It is an example schematic diagram of the spectrum curve of decomposed response data provided by an embodiment of the present application;

[0031] Figure 4 It is a schematic flow diagram of another substructure modal identification method that can be measured step by step and multiple times provided by an embodiment of the present application;

[0032] Figure 5 It is a schematic flow diagram of another substructure modal identification method that can be measured step by step and multiple times provided by an embodiment of the present application;

[0033] Figure 6 It is a schematic flow diagram of another substructure modal identification method that can be measured step by step and multiple times provided by an embodiment of the present application;

[0034] Figure 7a It is an example schematic diagram of the balance index during the iteration process provided by an embodiment of the present application;

[0035] Figure 7b It is an example schematic diagram of the fitness convergence curve during the iteration process provided by an embodiment of the present application;

[0036] Figure 8 It is a schematic flow diagram of optimizing adjustment parameters provided by an embodiment of the present application;

[0037] Figure 9 It is an example schematic diagram of a fourth-order vibration mode provided by an embodiment of the present application;

[0038] Figure 10 It is an example schematic diagram of a fourth-order orthogonality verification provided by an embodiment of the present application;

[0039] Figure 11 It is a structural schematic diagram of a substructure modal identification device that can be measured step by step and multiple times provided by an embodiment of the present application;

[0040] Figure 12 It is a structural block diagram of a terminal device provided by an embodiment of the present application. Detailed implementation manners

[0041] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clear and understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0042] Traditional modal identification methods require that the acquisition of all response data must be synchronized to ensure the accuracy of modal identification. However, for particularly complex structural systems, this usually requires deploying a large number of sensors in the structural system at the same time. This method not only greatly increases the difficulty of obtaining response data, but also significantly increases the cost of modal identification.

[0043] Based on this, the embodiments of the present application provide a substructure modal identification method, device, and equipment that can be measured step by step and multiple times. The technical principle of this method is as follows: divide the engineering structure into substructures to obtain multiple substructures containing common measurement points; acquire the response data of each measurement point in each substructure; the response data of all measurement points in the same substructure needs to be the response data collected synchronously at the same time; the response data of the measurement points in different substructures can be the response data collected step by step and multiple times at different times. Each substructure has at least one common measurement point with at least one other substructure, and using the non-linear frequency modulation modal decomposition algorithm, with the goal of minimizing the objective function, decompose the response data into at least one order of single-component data. During the decomposition process, use a parameter-free heuristic optimization algorithm to optimize the adjustment parameters used in the non-linear frequency modulation modal algorithm, which can more accurately determine the most suitable adjustment parameters for the non-linear frequency modulation modal algorithm to improve the accuracy of single-component data decomposition. Then, through Fourier transform of each order of single-component signals, calculate the spectral data of the single-component signals within each substructure, and further obtain the frequency and amplitude corresponding to the spectral peaks in the spectral data. Further, according to the ratio of the modal amplitudes of each order of the engineering structure being the ratio of the spectral amplitudes of the same order at each measurement point, adjust the modal amplitudes of the common measurement points of each substructure to be consistent, and successively obtain the modal amplitudes of each order of the vibration mode at each measurement point and the frequencies corresponding to each order of single-component signals. Thus, the relative ratios of the modal amplitudes of each order of the engineering structure at each measurement point can be obtained; then, according to the relative ratios of each order of the vibration mode at each measurement point, use the modal confidence criterion to obtain the directions of each order of the vibration mode of the engineering structure, that is, first determine that the direction of the first-order vibration mode is all positive, and successively traverse the positive and negative direction situations of each measurement point of the second-order vibration mode, calculate the orthogonality between the first-order vibration mode and all possible second-order vibration mode directions, and based on the principle of the minimum modal confidence criterion, determine the direction of the second-order vibration mode. Similarly, the directions of other orders of vibration modes can be obtained. Thus, the modal vibration mode of the structure can be obtained. In this way, by extracting single-component data from the response data, the acquisition time of the response data of multiple measurement points is no longer restricted. Even if two sensors are used to separately obtain the response data of multiple measurement points, the accuracy of the modal vibration mode identification of the engineering structure can still be guaranteed, so that the obtained modal vibration mode can accurately reflect the health status of the engineering structure.

[0044] Figure 1 FIG. 4 is a schematic structural diagram of a substructure modal identification system that can be measured step by step and multiple times provided by the embodiments of the present application. The substructure modal identification method that can be measured step by step and multiple times provided by the embodiments of the present application can be applied to the substructure modal identification system 100 that can be measured step by step and multiple times. Refer to Figure 1 FIG. 4, this modal identification system 100 includes one or more sensors 101 and a terminal device 102.

[0045] Optionally, one or more sensors 101 are used to transmit response data of measurement points detecting a structure (such as a building structure) to the terminal device 102, so that the terminal device 102 performs modal identification of the structure based on the response data of each measurement point.

[0046] In a possible implementation, a communication connection is established between the sensor 101 and the terminal device 102 through a wired or wireless network. Optionally, the above-mentioned wireless network or wired network uses standard communication technologies and / or protocols. The network is usually the Internet, but can also be any network, including but not limited to any combination of a local area network (LAN), a metropolitan area network (MAN), a wide area network (WAN), a mobile, wired or wireless network, a private network or a virtual private network.

[0047] Optionally, the sensor 101 is an acceleration sensor, a vibrating wire sensor, etc. The acceleration sensor can be, but is not limited to, any one of the following: a piezoelectric acceleration sensor, a capacitive acceleration sensor, a laser interferometer acceleration sensor, and a MEMS acceleration sensor. Acceleration sensors have different characteristics and applicability in the field of structural modal identification. Selection can be made according to factors such as the required measurement range, accuracy, resolution, frequency response range, and environmental conditions. The embodiments of the present application do not limit this.

[0048] Optionally, the terminal device 102 can be a terminal device in various AI application scenarios. For example, the terminal device 102 can be a laptop computer, a tablet computer, a desktop computer, a vehicle-mounted terminal, a mobile device, etc. The mobile device can be various types of terminals such as a smart phone, a portable device, and a personal digital assistant. The embodiments of the present application do not specifically limit this.

[0049] Furthermore, an operating system can run on the terminal device 102. The operating system can include but is not limited to an Android system, an IOS system, a Linux system, Unix, a Windows system, etc. It can also include a user interface (UI) layer, and can provide display of modal identification results through the UI layer.

[0050] For the convenience of understanding and explanation, the following will Figures 2 to 11 elaborate in detail on the substructure modal identification, device, and equipment provided by the embodiments of the present application that can perform step-by-step multiple measurements.

[0051] Figure 2 The following shows a schematic flow chart of the substructure modal identification method provided by the embodiments of the present application that can perform step-by-step multiple measurements. As Figure 2 shown, the method includes:

[0052] 201. Obtain the response data of each measurement point in each sub-structure of the engineering structure; the response data of all measurement points in the same sub-structure are the response data collected synchronously at the same time; the response data of measurement points in different sub-structures are the response data collected at different times and in multiple steps; each sub-structure has at least one common measurement point with at least one other sub-structure.

[0053] Optionally, the engineering structure can be a structural system that needs to identify modal vibration modes, and the structural system can be a system composed of various structures, such as a structural system for civil engineering, a structural system for mechanical engineering, etc.

[0054] The response data can be data such as acceleration, velocity, or displacement generated by the engineering structure under external load excitation (i.e., system input excitation, such as white noise). The response data can be a time-varying signal with frequency varying over time. The external load excitation can be used to apply an external force to the engineering structure to make it vibrate, and the response data can be used to describe the vibration form of the structural system under the external load excitation, which can be specifically described by a vibration curve graph.

[0055] When studying the structural damage of the engineering structure or when it is necessary to optimize the structure of the engineering structure, it is necessary to determine the vibration situation of the engineering structure, and then it is necessary to perform modal identification on the engineering structure, and collect the response data of the engineering structure under environmental excitation by arranging sensors at each key node of the engineering structure, so as to obtain the response data of the engineering structure.

[0056] It should be noted that the sensors in the embodiments of the present application can be two or more. A sub-structure for synchronous measurement is constructed, and each sub-structure can be sequentially deployed at different positions (i.e., measurement points) of the engineering structure to measure the response data at the measurement points of the engineering structure.

[0057] In a possible implementation manner, the measurement of the engineering structure is divided into multiple sub-structures according to a preset number of measurement layers at one time. Each sub-structure includes at least two layers of structures. One sub-structure has at least one overlapping measurement point with at least one of the other sub-structures among the multiple sub-structures, that is, a common measurement point. The multiple sub-structures are sequentially measured to obtain at least one response data of each measurement point in the engineering structure.

[0058] As an example, assume that the engineering structure includes m1, m2, m3, and m4 from high to low. Two sensors are located on different two floors, that is, the two floors are used as a sub-structure for simultaneous measurement. The division forms of the sub-structures of the engineering structure can be, for example: [m1, m2], [m2, m3], [m3, m4], or, [m1, m2], [m1, m3], [m1, m4], or, [m1, m2], [m1, m3], [m3, m4], and so on.

[0059] It can be understood that the number of groups of response data obtained at each measurement point is determined based on the sub-structure assigned to the measurement point. Combining the above example, for the division form of the sub-structures [m1, m2], [m2, m3], [m3, m4] for measurement, 1 group of response data of the m1 floor, 2 groups of response data of the m2 floor, 2 groups of response data of the m3 floor, and 1 group of response data of the m4 floor are obtained.

[0060] 202. For each group of response data, using the non-linear frequency modulation mode decomposition algorithm, with the goal of minimizing the objective function, perform signal demodulation processing on the response data to obtain at least one-order target single-component data; the objective function is used to evaluate the signal complexity of at least one-order single-component data.

[0061] It can be understood that the single-component data only includes a signal with one frequency value. For example, the single-component data can be a first-order frequency signal or a second-order frequency signal, etc.

[0062] The response data of the engineering structure can be composed of the superposition of several orders of modal vibration modes, and then the non-linear frequency modulation mode decomposition algorithm is used to decompose the structural response data into single-component signals corresponding to each order of modes.

[0063] Optionally, use the non-linear frequency modulation mode decomposition algorithm (Nonlinear Chirp Mode Decomposition, NCMD) to perform demodulation processing on the response data to achieve the decomposition of the response data. Specifically, perform frequency demodulation on the time-varying signal with a wider bandwidth, and then the time-varying signal can be converted into at least one narrowband signal.

[0064] Specifically, the non-linear frequency modulation mode (Nonlinear Chirp Mode, NCM) can be represented by the following function:

[0065] (Formula 1)

[0066] Among them, represents the non-linear frequency modulation mode, can be expressed as the instantaneous amplitude, t is the time variable, can be expressed as the instantaneous frequency, can be represented as the initial phase.

[0067] The response data can be the superposition of multiple non - linear frequency modulation modes, which can be specifically represented by the following formula: (Formula 2)

[0068] Where, represents the response data, can be Gaussian white noise, Q represents the total number of modes, and i represents the mode order. And for the response data frequency demodulation can be represented by the following formula: (Formula 3)

[0069] Where, and can be the demodulated signal, can be represented as the frequency function of the demodulation operator, represents the instantaneous amplitude.

[0070] Where, the instantaneous amplitude can be reconstructed by Formula 4:

[0071] (Formula 4)

[0072] At the bandwidth of the demodulated signal and is the smallest, and the signal decomposition problem can be represented by the following formula:

[0073] (Formula 5)

[0074] (Formula 6)

[0075] Where, Formula 5 indicates that the bandwidth of the demodulated signal and is the smallest, can be represented as the L2 norm, represents the second - order derivative of, represents the second - order derivative of, Formula 6 is the constraint condition, and the constrained problem can be solved by the augmented Lagrangian multiplier method. The purpose of Formula 5 and Formula 6 is to find a set of demodulated signals and , minimizing the sum of squares of the L2 norm of its second derivative and satisfying the constraint conditions of Formula 6, thereby realizing the decomposition of the response data to obtain at least one single-component data.

[0076] See Figure 3a , Figure 3a shows a schematic structural diagram of an engineering structure provided by an embodiment of the present invention. As Figure 3a shown, the engineering structure can be a metal frame structure, and the engineering structure can be composed of 5 layers of metal frames, including the first layer, the second layer, the third layer, the fourth layer, and the fifth layer. The sub-structure contains two layers, that is, two sensors, the acceleration sensor 31 and the acceleration sensor 32, measure two layers simultaneously, and the 5 layers are divided into four sub-structures: [the first layer, the second layer], [the second layer, the third layer], [the third layer, the fourth layer], [the fourth layer, the fifth layer]. These two sensors sequentially measure the floors in the sub-structure from low to high according to the floor height order to obtain at least one set of response data of each measurement point in the engineering structure. The measurement order is successively as Figure 3a shown in (a), (b), (c), (d) in

[0077] When modal identification of the engineering structure is required, an environmental excitation, such as white noise, can be input to the engineering structure, and then the acceleration sensors are used to measure sequentially from low to high to collect the response data of the engineering structure under the environmental excitation.

[0078] See Figure 3b , Figure 3b shows an example schematic diagram of response data in an engineering structure provided by an embodiment of the present application. As Figure 3b shown, the curve a can represent the response data of the fifth-layer metal frame in the engineering structure.

[0079] In practical applications, a synchronous sub-structure measurement group is constructed by two or more sensors. By gradually moving the measurement group, the measurement group can be successively used to collect the structural response data of different layers of metal frames. For example, two sensors are used to collect the structural response data of the first and second layers of the metal frame, and after the collection is completed, the sensors are moved to the second and third layers of the metal frame, and so on; sensors can also be arranged in each layer of the metal frame, and then the structural response data of each layer of the metal frame can be collected simultaneously. The specific method can be user-defined.

[0080] See Figure 3c , Figure 3c shows an example schematic diagram of decomposing response data provided by an embodiment of the present invention. As Figure 3cAs shown, curve a can represent the response data of the fifth-layer metal frame in the engineering structure. Curve b1 can be the single-component data 1 obtained by decomposing the response data of the fifth-layer metal frame in the engineering structure using NCMD (i.e., the component represents the first order). Curve c1 can be the single-component data 2 obtained by decomposing the response data of the fifth-layer metal frame in the engineering structure using NCMD (i.e., the component represents the second order), and so on. Curve d1 and curve e1 can respectively represent the single-component data 3 (i.e., the component represents the third order) and single-component data 4 (i.e., the component represents the fourth order) obtained by decomposing the response data of the fifth-layer metal frame in the engineering structure using NCMD.

[0081] Furthermore, Figure 3d It shows an example schematic diagram of the time-frequency curve for decomposing response data provided by an embodiment of the present invention. Among them, curve b2 is the time-frequency curve of single-component data 1, curve c2 is the time-frequency curve of single-component data 2, curve d2 is the time-frequency curve of single-component data 3, and curve e2 is the time-frequency curve of single-component data 4. Figure 3e It shows an example schematic diagram of the wavelet spectrum for decomposing response data provided by an embodiment of the present invention. Among them, curve b3 is the wavelet spectrum of single-component data 1, curve c3 is the wavelet spectrum of single-component data 2, curve d3 is the wavelet spectrum of single-component data 3, and curve e3 is the wavelet spectrum of single-component data 4. Figure 3f It shows an example schematic diagram of the frequency spectrum curve for decomposing response data provided by an embodiment of the present invention. Among them, curve b4 is the frequency spectrum curve of single-component data 1, curve c4 is the frequency spectrum curve of single-component data 2, curve d4 is the frequency spectrum curve of single-component data 3, and curve e4 is the frequency spectrum curve of single-component data 4.

[0082] 203. For each target single-component data, based on the target single-component data, obtain the frequency spectrum data.

[0083] Optionally, perform Fourier transform on the target single-component data; obtain the frequency spectrum data of the target single-component signal.

[0084] It can be understood that the amplitude corresponding to each peak in the frequency spectrum data is the amplitude of the vibration mode corresponding to this order of the engineering structure. In the same sub-structure, there are two or more synchronous sensors. By performing Fourier transform to obtain the frequency spectrum amplitudes of each order of target single-component data at different measurement points, the relative ratio of the amplitudes corresponding to each order of vibration modes at different measurement points within the sub-structure can be obtained. By this method, the relative ratio of the amplitudes of each order of vibration modes at each measurement point can be obtained.

[0085] 204. For each sub-structure, according to the ratio of the frequency spectrum amplitudes of the same order at each measurement point in the frequency spectrum data, obtain the amplitudes of each order of vibration modes of each sub-structure.

[0086] 205. Adjust the modal amplitudes of the common measurement points of each sub-structure to be consistent according to the modal amplitudes of each order of each sub-structure, so as to obtain the modal amplitudes of each order of all measurement points of the engineering structure.

[0087] Optionally, the response data of the engineering structure is decomposed into multi-order single-component signals, and the frequency corresponding to the spectral peak of the single-component signal is the natural vibration frequency of the engineering structure.

[0088] 206. Based on the modal amplitudes of each order of all measurement points of the engineering structure, judge the direction of the mode shape by minimizing the modal confidence criterion.

[0089] 207. Obtain the modal mode shape of the engineering structure according to the direction of the mode shape.

[0090] The method provided by the embodiments of the present application takes into account that the prior art requires synchronous acquisition of the response data of the structure. It not only needs to deploy a large number of sensors simultaneously, but also must ensure that these sensors can synchronously measure the response data of the structure, increasing the identification cost. At the same time, it also raises the requirements for the data acquisition accuracy of the sensors, which results in the problem of excessive difficulty in obtaining response data. Therefore, among the at least one set of response data of each measurement point in the engineering structure obtained by the present application, the response data collected at different times can be used to greatly reduce the synchronous deployment amount of the sensors. The requirement for data synchronization is greatly reduced, thereby reducing the difficulty of obtaining response data. Combining with the non-linear frequency modulation modal decomposition algorithm, with the minimum of the objective function as the goal, the response data is demodulated, so that the response data is decomposed into at least one-order target single-component data. In this way, by extracting the single-component data from the response data and establishing the relationship between the modal amplitude and the spectral amplitude of the target single-component signal, the modal amplitudes of the common measurement points of each sub-structure are adjusted to be consistent. Therefore, the acquisition time synchronization of the response data of all measurement points is no longer restricted, and only the data acquisition time synchronization between different measurement points of the same sub-structure needs to be ensured. Even if two sensors are used to obtain the response data of different measurement points of multiple sub-structures step by step and multiple times, the accuracy of the modal mode shape identification of the engineering structure can still be guaranteed, so that the obtained modal mode shape can accurately reflect the health status of the engineering structure.

[0091] In addition, usually, noise is dispersed into multiple frequency components. In multi-component data, cross-interference occurs between different components, which reduces the signal-to-noise ratio of the signal and affects the accurate extraction and analysis of the signal. However, the single-component data in this application only contains modal information of a specific order, making the influence of noise relatively small. In this way, by performing spectral analysis on each target single-component data, the frequency response of each component can be depicted more precisely, thereby effectively reducing the errors caused by signal aliasing or interference. This refined analysis method enables the method to more accurately extract the modal vibration modes of engineering structures during the modal identification process, which not only helps to improve the accuracy of modal vibration mode identification, but also can greatly reduce the calculation amount and calculation time, and improve the overall analysis efficiency.

[0092] In one embodiment of this application, in order to improve the accuracy of the response data decomposition by the non-linear frequency modulation modal decomposition algorithm, the embodiment of this application also provides a parameter-free heuristic optimization algorithm to optimize the adjustment parameters used in the non-linear frequency modulation modal decomposition algorithm. Therefore, this method further includes: determining multiple groups of initial adjustment parameters in the non-linear frequency modulation modal decomposition algorithm; and using the parameter-free heuristic optimization algorithm to optimize the multiple groups of initial adjustment parameters to obtain target adjustment parameters; the target adjustment parameters are used to obtain at least one order of target single-component data.

[0093] Optionally, when the current iteration number is 1, the multiple groups of initial adjustment parameters are randomly generated.

[0094] Optionally, in the non-linear frequency modulation modal decomposition algorithm, the involved adjustment parameters include two types: the number of modal decompositions and the penalty parameter.

[0095] In some embodiments, the adjustment parameters may include the number of modal decompositions k in the non-linear frequency modulation modal decomposition algorithm, the penalty coefficient α for controlling the filtering bandwidth of the non-linear frequency modulation modal decomposition algorithm, and the penalty coefficient β for controlling the increment smoothness of the instantaneous frequency during the iteration process. Among them, the smaller the penalty coefficient α, the narrower the bandwidth of the demodulated signal, and the smaller the penalty coefficient β, the smoother the increment of the instantaneous frequency.

[0096] As an example, the target adjustment parameters can be the adjustment parameters when the accuracy of decomposing the response data into at least one single-component data based on the non-linear frequency modulation modal decomposition algorithm is optimal, and the initial adjustment parameters can be the adjustment parameters when the non-linear frequency modulation modal decomposition algorithm can decompose the structural response data into at least one single-component data.

[0097] When modal identification of an engineering structure is required, a non-linear frequency modulation modal decomposition algorithm for decomposing response data is determined, and initial adjustment parameters related to demodulation processing in the non-linear frequency modulation modal decomposition algorithm are determined. Furthermore, a parameter-free heuristic optimization algorithm, namely the Dynamic Swarm Hunting Optimizer (DSHO), can be used to optimize the initial adjustment parameters, and the sample entropy is used as the objective function of the initial adjustment parameters, so as to obtain the target adjustment parameters.

[0098] In one embodiment of the present application, with reference to Figure 4 , a parameter-free heuristic optimization algorithm is used to optimize multiple groups of initial adjustment parameters to obtain target adjustment parameters, including:

[0099] 401. In the current iteration number, the fitness corresponding to each group of initial adjustment parameters is determined based on the objective function.

[0100] Among them, the objective function can be the sample entropy (Sample Entropy, SampEn).

[0101] In practical applications, the fitness can be used to characterize the similarity or matching degree between the reference signal or ideal signal of the initial single-component data obtained after decomposing the response data by the non-linear frequency modulation modal decomposition algorithm using the initial adjustment parameters. Taking the sample entropy as the objective function, the fitness is specifically used to characterize the signal complexity of the initial single-component data.

[0102] It can be understood that the smaller the fitness, the smaller the signal complexity of the single-component data, and further indicates that the decomposition effect of the non-linear frequency modulation modal decomposition algorithm on the response data is better.

[0103] Among them, the current iteration number refers to the number of the current iteration in the iteration process.

[0104] Optionally, with reference to Figure 5 , determining the fitness corresponding to each group of initial adjustment parameters based on the objective function includes the following steps:

[0105] 4011. For each group of initial adjustment parameters, signal demodulation processing is performed on the response data according to the non-linear frequency modulation modal decomposition algorithm using the initial adjustment parameters to obtain at least one initial single-component data.

[0106] 4012. The signal complexity of each initial single-component data is determined using the objective function.

[0107] In a possible implementation manner, taking the sample entropy as the objective function, the signal complexity of each initial single-component data can be determined using the objective function in the following manner:

[0108] Represent the single-component data as: , where N represents the length of the single-component data. Then, divide each single-component data sequence into different subsequences, each with a length of m. The subsequence can be understood as the sequence of m consecutive values starting from in .

[0109] For a given similarity tolerance r, define two subsequences and (where I ≠ J) to be similar if the maximum absolute difference between their corresponding elements does not exceed r, that is holds for all 0 ≤ k < m.

[0110] For each I (1 ≤ I ≤ N - m), calculate how many J (1 ≤ J ≤ N - m, J ≠ I) there are such that and are similar, and denote this quantity as .

[0111] Calculate the average value of all , denoted as:

[0112] (Equation Seven)

[0113] For m + 1, repeat the above steps to calculate and .

[0114] denotes how many J (1 ≤ J ≤ N - m - 1, J ≠ I) there are such that and are similar. denotes the average value of

[0115] After that, calculate the objective function SampEn(m, r, N) according to the following formula:

[0116] (Equation Eight)

[0117] It can be seen from this that the value of the objective function calculated based on the above initial single-component data is the fitness of the initial single-component data.

[0118] 4013. Determine the minimum signal complexity among at least one initial single-component data as the fitness corresponding to the initial adjustment parameter.

[0119] 402. Construct the initial position vectors of each group of initial adjustment parameters, and determine the core position vector with the minimum fitness among multiple initial position vectors.

[0120] In some embodiments, coordinates for describing the adjustment parameters can be defined based on the dimension of the adjustment parameters, and position vectors are randomly generated within a preset search domain.

[0121] For example, the adjustment parameters may include the number of modal decompositions Q, the penalty coefficient α for controlling the filtering bandwidth of the nonlinear frequency modulation modal decomposition algorithm, and the penalty coefficient β for controlling the incremental smoothness of the instantaneous frequency during the iterative process. Then, based on the dimension of the adjustment parameters, the position vector for describing the adjustment parameters can be defined as (Q, α, β). Furthermore, random values can be taken within the preset search domain of each adjustment parameter, that is, the values of each adjustment parameter are randomly determined to generate multiple initial position vectors.

[0122] Specifically, the position vector of the adjustment parameter can be determined by the following formula:

[0123] (Equation Nine)

[0124] Where, can be the upper limit of the preset search domain, can be the lower limit of the preset search domain, can be a random number between (0, 1), can be expressed as the position vector of the w-th adjustment parameter among all the parameters to be optimized, and w can represent any one of the position vectors of all the adjustment parameters.

[0125] 403. Update each initial position vector based on the core position vector to obtain the candidate position vector corresponding to each initial position vector; if the current iteration number does not meet the iteration number condition, then update the multiple initial position vectors using the multiple candidate position vectors until the current iteration number meets the iteration number condition, and then determine the parameters in the position vector with the minimum fitness among the multiple candidate position vectors as the target adjustment parameters.

[0126] It can be understood that after updating the multiple initial position vectors using the multiple candidate position vectors, steps 402 and 403 are re-executed until the current iteration number meets the iteration number condition, and then the iteration can be stopped.

[0127] Among them, updating each initial position vector based on the core position vector to obtain a candidate position vector corresponding to each initial position vector includes: for each initial position vector, aiming at the actual position difference being less than the preset position difference, updating the initial position vector according to the core position vector, the weight value, and the balance index to obtain the candidate position vector; where the position difference is used to characterize the position deviation rate of the candidate position vector relative to the core position vector, and the balance index is used to characterize the movable range of the initial position vector.

[0128] In one embodiment of the present application, with reference to Figure 6 , aiming at the actual position difference being less than the preset position difference, updating the initial position vector according to the core position vector, the weight value, and the balance index to obtain the candidate position vector, including:

[0129] 601. Determine the initial value of the balance index within the first index interval and the weight value of each initial position vector among the multiple initial position vectors.

[0130] Optionally, the balance index is related to the current iteration number, and the balance index is used to determine the update direction of the position vector iteration. The update direction of the position vector iteration may include determining the update direction of the target adjustment parameter within all preset search domains, or determining the update direction of the target adjustment parameter based on the region corresponding to all position vectors in the current iteration. The region corresponding to all position vectors in the current iteration may be the region determined based on the global coordinates of each position vector in the preset search domain in the current iteration.

[0131] In some embodiments, based on the fitness of each initial position vector and the total fitness value of the multiple initial position vectors, determine the weight value of the initial position vector among the multiple initial position vectors.

[0132] Specifically, the weight value can represent the positional relationship between each position vector within the preset search domain. The larger the weight value, the farther the relative position of this position vector to other position vectors within the preset search domain.

[0133] During each iteration, the current iteration number can be determined, and then the balance index can be determined according to the current iteration number.

[0134] Specifically, the balance index is determined by the following formula:

[0135] (Formula Ten)

[0136] Among them, can represent the current iteration number, can represent the maximum iteration number, can be a random number between (0, 1), can be the balance index corresponding to the current iteration number.

[0137] Refer to Figure 7a and Figure 7b , Figure 7a shows an example schematic diagram of the balance index during an iteration provided by an embodiment of the present invention. Figure 7b shows an example schematic diagram of the fitness convergence curve during an iteration provided by an embodiment of the present invention. As Figure 7a shown, the abscissa is the number of iterations, and the ordinate is the value of the balance index. As Figure 7b shown, the abscissa is the number of iterations, and the ordinate is the value of the fitness. It can be known from Figure 7a that the balance index is a changing value within the interval (0, 2), and as time goes by, that is, the balance index shows a decreasing trend as the number of iterations increases. Thus, through the balance index it can be ensured that as the iteration progresses, the optimization process can ensure convergence, thereby obtaining the minimum value of the objective function (i.e., fitness). The size of the balance index determines whether the direction of the later iteration is to explore more widely within the preset search domain or to conduct in-depth development in the current domain. When the balance index is higher during the early iteration process of the optimization process, it has a wider exploration ability, so that it can jump out of the local optimal solution and then search for the global optimal solution. When entering the later stage of the optimization process, when the optimization result is close to the optimal solution (i.e., the position vector corresponding to the target adjustment parameter), the algorithm enters key development and focuses on retrieving the possible optimal solutions nearby. Thus, the balance index is an important index for weighing the extensive exploration and key development of the algorithm, and it is only related to the current number of iterations.

[0138] During each iteration process, based on the fitness of all position vectors, the relative position between each position vector and other position vectors can also be determined, that is, the weight value occupied by the position vector among all position vectors is determined. Specifically, the weight value can be determined by the following formula:

[0139] (Formula XI)

[0140] where represents the weight value of the w-th position vector, represents the fitness of the w-th position vector, and Num represents the maximum population number for iterative update, that is, the number of position vectors.

[0141] 602. Use the core position vector, the initial value, and the weight value to update the initial position vector within the preset search domain to obtain the first position vector corresponding to each initial position vector.

[0142] Optionally, determine the position difference vector between each initial position vector and the core position vector, and update the initial position vector within a preset search domain according to the balance index, the position weight value, and the position difference vector to obtain the first position vector.

[0143] The position difference vector is used to represent the relative position between each initial position vector and the core position vector within the preset search domain.

[0144] Specifically, the following formula can be used to determine the position difference vector:

[0145] (Formula XII)

[0146] Where, can represent the w-th position difference vector, can represent the coordinates of the core position vector within the preset search domain, can be the coordinates of the w-th initial position vector within the search domain.

[0147] After obtaining the position difference vector, when the balance index is within the first index interval, for each initial position vector, the initial position vector can be updated within the preset search domain according to the balance index, the weight value, and the position difference vector to obtain the first position vector. Specifically, the initial position vector can be updated through the following formula:

[0148] (Formula XIII)

[0149] Where, can represent the weight value of the w-th initial position vector, can represent the balance index corresponding to the current iteration number, can be the position difference vector of the w-th initial position vector, can represent the first position vector obtained after updating the w-th initial position vector.

[0150] It should be noted that updating the initial position vector within the preset search domain is to update all the initial position vectors including the core position vector. It can be understood that the core position vector also corresponds to a first position vector. That is to say, when using the first position vector to update the initial position vector, the core position vector will be re-determined among the updated initial position vectors.

[0151] 603. For each initial position vector, determine a candidate value of the balance index, update the initial value using the candidate value, and update the initial position vector using the first position vector until the candidate value is within the second index interval, and determine the first position vector as the second position vector; wherein, the candidate value is less than the initial value, the first index interval is adjacent to and greater than the second index interval.

[0152] Exemplarily, the first index interval is [1, 2], and the second index interval is [0, 1).

[0153] It can be understood that updating the initial value using the candidate value and updating the initial position vector using the first position vector means that there is also a sub-iteration process in the entire large iteration process of the algorithm. The sub-iteration process includes a first sub-iteration process and a second sub-iteration process. The first sub-iteration process corresponds to the iteration process when the balance index is within the first index interval, and the second sub-iteration process corresponds to the iteration process when the balance index is within the second index interval.

[0154] Optionally, the candidate value being less than the initial value means that the balance index is assigned in a gradually decreasing manner.

[0155] 604. If the position deviation rate of each second position vector relative to the core position vector is within the preset deviation range, determine that the actual position difference is less than the preset position difference, update the core position vector to the position vector corresponding to the core position vector among the multiple second position vectors, and for each second position vector, update the second position vector using the core position vector and the weight value to obtain a candidate position vector.

[0156] Optionally, if the position deviation rate of the second position vector relative to the core position vector is within the preset deviation range, determine the parameter average value of the second position vector, and update the second position vector according to the parameter average value, the balance index, the weight value, and the core position vector to obtain a candidate position vector.

[0157] Wherein, the parameter average value is the coordinate average value of the second position vector.

[0158] Specifically, the parameter average value can be the coordinate average value from the first second position vector to the i-th second position vector.

[0159] Optionally, the position deviation rate can represent the ratio of the relative position between each second position vector and the core position vector within the preset search domain to the second position vector. Then, when the position deviation rate is less than the preset deviation range (such as satisfying the position deviation rate ), it can be stated that there is a relatively close relative position between the second position vector and the core position vector in the current iteration number, that is, the region where the global optimal solution is located is relatively narrow, and thus the region where the global optimal solution is located can be further updated.

[0160] As an example, according to the parameter average value and the position difference vector corresponding to the second position vector, determine the parameter sharing information corresponding to the second position vector, and update each second position vector according to the parameter sharing information and the core position vector to obtain the candidate position vector corresponding to each second position vector (briefly, update the initial adjustment parameter according to the parameter sharing information).

[0161] Specifically, the parameter sharing information can be determined by the following formula:

[0162] (Formula XIV)

[0163] wherein, can be the parameter average value of the first second position vector to the y-th second position vector, can be the position difference vector between the y-th second position vector and the core position vector, can be the weight of the parameter average value of the first second position vector to the y-th second position vector in the parameter sharing information, and the value is any random number in (0, 1). It should be noted that the core position vector here is the core position vector among multiple second position vectors, that is, the position vector corresponding to the original core position vector among multiple second position vectors. y corresponds to w one by one.

[0164] After obtaining the parameter sharing information of each second position vector, the second position vector can be updated according to the parameter sharing information of each second position vector and the core position vector to obtain the candidate position vector.

[0165] Specifically, the following formula can be used to update the second position vector :

[0166] (Formula XV)

[0167] 605. If there is one or more second position vectors whose position deviation rate from the core position vector is outside the preset deviation range, then for each second position vector, use the core position vector, the weight value, and the candidate value to iteratively update the second position vector until the position deviation rate of each second position vector from the core position vector is within the preset deviation range. Update the core position vector to the position vector corresponding to the core position vector among multiple second position vectors, and for each second position vector, use the core position vector and the weight value to update the second position vector to obtain the candidate position vector.

[0168] It can be understood that the core position vector in the iterative update of the second position vector using the core position vector, weight value, and candidate value in step 605 refers to the position vector corresponding to the core position vector among multiple second position vectors.

[0169] Optionally, after obtaining the parameter average value, for each second position vector, the second position vector can be updated according to the parameter average value, balance index (where the value of the balance index here is the candidate value), weight value, and core position vector.

[0170] Specifically, the second position vector can be updated using the following formula:

[0171] (Formula XVI)

[0172] Wherein, can be expressed as the parameter average value of the first second position vector to the y-th second position vector, can be expressed as the position vector obtained after updating the y-th second position vector (i.e., the updated y-th second position vector).

[0173] It can be understood that the second position vector is iteratively updated using Formula XVI until the position deviation rate of each second position vector relative to the core position vector is within the preset deviation range, at which point the iteration stops, and Formulas XIV and XV are used to update the second position vector obtained in the last iteration to obtain the candidate position vector corresponding to the second position vector.

[0174] In one embodiment of the present application, updating the multiple initial position vectors using the multiple candidate position vectors includes: determining the fitness of each candidate position vector based on the objective function; if there is a candidate position vector among other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, then updating the multiple candidate position vectors to the multiple initial position vectors; other candidate position vectors include the position vectors among the multiple candidate position vectors except the candidate position vector corresponding to the core position vector.

[0175] If the fitness of the candidate position vector corresponding to the core position vector is greater than or equal to the fitness of other candidate position vectors, then each candidate position vector is updated based on the Levy flight algorithm until there is a candidate position vector among other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, and the multiple candidate position vectors are updated to the multiple initial position vectors.

[0176] Optionally, for each candidate position vector, determine the candidate adjustment parameter corresponding to the candidate position vector, perform signal demodulation processing on the response data according to the non-linear frequency modulation modal decomposition algorithm using the candidate adjustment parameter, and obtain at least one candidate single-component data; use the objective function to determine the signal complexity of each candidate single-component data; determine the minimum signal complexity among the at least one candidate single-component data as the fitness of the candidate position vector.

[0177] In some embodiments, each candidate position vector is updated based on the following Formula XVII and Formula XVIII until there is a candidate position vector among other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, and the candidate position vector is updated to the initial position vector.

[0178] (Formula XVII)

[0179] Wherein, can represent the z-th candidate position vector, can represent the y-th updated candidate position vector, and z and y correspond one by one. Specifically, the Levy flight algorithm can be represented by the following formula:

[0180] (Formula XVIII)

[0181] Wherein, and can both be random numbers in (0, 1), can represent the gamma function, and in the formula the value of can be 1.5.

[0182] Exemplarily, in order to better understand the optimization steps of using the parameter-free heuristic optimization algorithm, that is, the Dynamic Swarm Hunting Optimizer (DSHO), to optimize multiple groups of initial adjustment parameters to obtain the target adjustment parameters in the embodiments of the present application, refer to Figure 8 , including:

[0183] S81, randomly generate multiple groups of initial adjustment parameters in the non-linear frequency modulation modal decomposition algorithm, and determine the initial position vector corresponding to each group of initial adjustment parameters.

[0184] S82, determine the fitness of each group of initial position vectors, and determine the core position vector from all the initial position vectors according to the fitness.

[0185] S83, determine the balance index corresponding to the current iteration number .

[0186] S84, judge the balance index Is it greater than 1? If so, execute step S85; if not, execute step S86.

[0187] S85, update the candidate position vector using the first position vector, and execute step S810.

[0188] S86, determine the position deviation rate E, and judge whether the position deviation rate E is greater than 0.5. If so, execute step S87; if not, execute step S88.

[0189] S87, update the candidate position vector using the second position vector, and execute step S810.

[0190] S88, determine the parameter sharing information , and execute step S89.

[0191] S89, update the second position vector, update the candidate position vector using the updated second position vector, and execute step S810.

[0192] S810, judge whether there is a fitness in other candidate position vectors that is less than the fitness of the candidate position vector corresponding to the core position vector . If so, execute step S811; if not, execute step S812.

[0193] S811, update the core position vector based on the position vectors in all candidate position vectors whose fitness is less than that of the core position vector.

[0194] S812, update each candidate position vector based on the Levy flight algorithm, and execute step S813.

[0195] S813, judge whether there is a fitness in other candidate position vectors that is less than the fitness of the candidate position vector corresponding to the core position vector . If so, execute step S811; if not, execute step S814.

[0196] S814, judge whether the current iteration number meets the iteration number condition. If so, execute step S815; if not, execute step S83.

[0197] S815, determine the parameters in the position vector with the minimum fitness among the multiple candidate position vectors of the current iteration number as the target adjustment parameters.

[0198] It should be noted that Figure 8 only a simple description of the above steps S81 - S815 is given. For details, please refer to the content of the above steps S81 - S815.

[0199] In practical applications, the optimal solution corresponding to the current iteration number can be the candidate position vector in the current iteration number.

[0200] In a specific implementation, the global optimal solution can be determined from the search domain of the adjustment parameter through the above method, and the region where the global optimal solution is located can be gradually converged through the balance index. As the iteration progresses, the balance index shows a gradually decreasing trend, so as to determine the target adjustment parameter for optimizing the initial mode decomposition algorithm, improving the accuracy of the target adjustment parameter. Moreover, since there are no other adjustment parameters involved in the parameter-free heuristic optimization algorithm, when using the parameter-free heuristic optimization algorithm to optimize the adjustment parameters in the non-linear frequency modulation mode decomposition algorithm, no more adjustment parameters will be introduced, reducing the influence of excessive hyperparameters on the adjustment parameters in the optimization of the non-linear frequency modulation mode decomposition algorithm.

[0201] In one embodiment of the present application, with the goal of adjusting the modal amplitudes of each order at the common measurement points of each sub-structure to be consistent, the modal amplitudes of each order in each sub-structure are adjusted to obtain the modal amplitudes of each order at all measurement points; based on the modal amplitudes of each order at all measurement points, the direction of the mode shape is judged based on the minimization of the modal confidence criterion; according to the direction of the mode shape, the modal mode shape of the engineering structure is obtained.

[0202] Optionally, by performing Fourier transform on each order of single-component signals, spectral data is obtained. By performing Fourier transform on each order of single-component signals, the spectral data of the single-component signals within each sub-structure is calculated, and then the frequency and amplitude corresponding to the spectral peak in the spectral data are obtained. Further, since the modal amplitude of each order of the engineering structure is the ratio of the spectral amplitudes of each order, by adjusting the modal amplitudes at the common measurement points of each sub-structure to be consistent, the amplitude of each order of the mode shape at each measurement point and the frequency corresponding to each order of single-component signals are obtained in sequence. Thus, the relative ratio of the modal amplitudes of each order of the engineering structure at each measurement point can be obtained; then, according to the relative ratio of each order of the mode shape at each measurement point, the direction of each order of the mode shape of the engineering structure is obtained using the modal confidence criterion, that is, first determine that the direction of the first-order mode shape is all positive, and then traverse the positive and negative direction situations of each measurement point of the second-order mode shape in sequence, calculate the orthogonality between the first-order mode shape and all possible second-order mode shape directions, and based on the principle of the minimum modal confidence criterion, the direction of the second-order mode shape is determined. Similarly, the directions of other orders of mode shapes can be obtained, so as to obtain the modal parameters such as the frequency and mode shape of the overall engineering structure. It can be understood that the frequency corresponding to each peak in the frequency data (i.e., the Fourier spectrum) is the natural vibration frequency of the structure (the ratio of the spectral peaks of each layer in each order is the modal amplitude).

[0203] Optionally, the MAC value between two-order modal mode shape vectors is calculated using the MAC formula. The calculation formula of the MAC value is:

[0204] (Equation XIX)

[0205] Wherein, and represent the i-th order and j-th order mode shape vectors respectively.

[0206] It should be noted that the orthogonality between two modes is evaluated according to the magnitude of the MAC value. The closer the MAC value is to 1, the more correlated the two modes are; the smaller the MAC value (close to 0), the less correlated the two modes are.

[0207] Through the method provided by this application, it is possible to obtain a more accurate mode shape of the engineering structure without being interfered by noise and without removing false modes.

[0208] As an example, the response data of the five-story metal frame in Figure 3a is identified by the substructure mode identification method provided by the embodiments of this application, which can be measured step by step and multiple times. The final frequency results of each order obtained by using the Stochastic Subspace Identification (SSI) algorithm to identify the response data of the five-story metal frame in Figure 3a are shown in Table 1.

[0209]

[0210] Based on Table 1, it can be seen that the substructure mode identification method provided by the embodiments of this application, which can be measured step by step and multiple times, has little difference in identification accuracy from the random subspace algorithm and can meet the accuracy requirements of engineering structures. However, this method does not require all measurement points to be time-synchronized during the acquisition of response data, and does not need to remove false modes and determine the system order during the mode identification process, which reduces human intervention in the mode identification process, avoids the subjectivity of the identification structure, and improves the accuracy of mode shape identification.

[0211] Furthermore, referring to Figure 9 , Figure 9 is an example schematic diagram of the 4th order mode shape obtained by using the substructure mode identification method provided by the embodiments of this application, which can be measured step by step and multiple times, to identify the response data of the five-story metal frame in Figure 3a . Among them, curve b5 is the mode shape curve of the first order, curve c5 is the mode shape curve of the second order, curve d5 is the mode shape curve of the third order, and curve e5 is the mode shape curve of the fourth order. Figure 10 is an example schematic diagram for verifying the 4th order orthogonality. Figure 10 The abscissa in

[0212] It should be noted that although the operations of the method of the present application are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result.

[0213] Figure 11 It is a block diagram of a substructure modal identification device capable of step-by-step multiple measurements according to an embodiment of the present application.

[0214] As Figure 11 shown, the substructure modal identification device capable of step-by-step multiple measurements includes: an acquisition module 1101, a decomposition module 1102, a transformation module 1103, an identification module 1104, and a parameter optimization module 1105. Among them,

[0215] The acquisition module 1101 is used to acquire the response data of each measurement point in each substructure of the engineering structure; the response data of all measurement points in the same substructure are response data collected synchronously at the same time; the response data of measurement points in different substructures are response data collected step by step and multiple times at different times; each substructure has at least one common measurement point with at least one other substructure.

[0216] The decomposition module 1102 is used to perform signal demodulation processing on each response data by using the non-linear frequency modulation modal decomposition algorithm with the goal of minimizing the objective function, so as to obtain at least one order of target single-component data; the objective function is used to evaluate the signal complexity of at least one single-component data.

[0217] The transformation module 1103 is used to obtain spectral data based on each target single-component data for each target single-component data.

[0218] The identification module 1104 is used to obtain the modal amplitude of each order of each substructure according to the ratio of the spectral amplitudes of the same order of each measurement point in the spectral data for each substructure.

[0219] The identification module 1104 is further used to adjust the modal amplitudes of the common measurement points of each substructure to be consistent according to the modal amplitudes of each order of each substructure, so as to obtain the modal amplitudes of each order of all measurement points of the engineering structure; based on the modal amplitudes of each order of all measurement points of the engineering structure, judge the direction of the mode shape based on the minimization of the modal confidence criterion; according to the direction of the mode shape, obtain the modal mode shape of the engineering structure.

[0220] In some embodiments, the parameter optimization module 1105 is used to determine multiple groups of initial adjustment parameters in the non-linear frequency modulation modal decomposition algorithm; optimize the multiple groups of initial adjustment parameters by using a parameter-free heuristic optimization algorithm to obtain target adjustment parameters; the target adjustment parameters are used to obtain at least one order of target single-component data.

[0221] In some embodiments, the parameter optimization module 1105 is specifically configured to,

[0222] In the current iteration number, determine the fitness corresponding to each set of initial adjustment parameters based on the objective function.

[0223] Construct the initial position vector of each set of initial adjustment parameters, and determine the core position vector with the minimum fitness among the multiple initial position vectors.

[0224] Update each initial position vector based on the core position vector to obtain the candidate position vector corresponding to each initial position vector; if the current iteration number does not meet the iteration number condition, update the multiple initial position vectors using the multiple candidate position vectors until the current iteration number meets the iteration number condition, then determine the parameters in the position vector with the minimum fitness among the multiple candidate position vectors as the target adjustment parameters.

[0225] In some embodiments, the parameter optimization module 1105 is specifically configured to aim at the actual position difference being less than the preset position difference, and update each initial position vector according to the core position vector, the weight value, and the balance index to obtain the candidate position vector corresponding to each initial position vector; wherein, the position difference is used to characterize the position deviation rate of the candidate position vector compared with the core position vector, and the balance index is used to characterize the movable range of the initial position vector.

[0226] In some embodiments, the parameter optimization module 1105 is specifically configured to,

[0227] Determine the initial value of the balance index within the first index interval and the weight value of each initial position vector among the multiple initial position vectors.

[0228] Use the core position vector, the initial value, and the weight value to update each initial position vector within the preset search domain to obtain the first position vector corresponding to each initial position vector.

[0229] For each initial position vector, determine the candidate value of the balance index, and use the candidate value to update the initial value and use the first position vector to update the initial position vector until the candidate value is within the second index interval, and determine the first position vector as the second position vector; wherein, the candidate value is less than the initial value, and the first index interval and the second index interval are adjacent and the first index interval is greater than the second index interval.

[0230] If the position deviation rate of each second position vector compared with the core position vector is within the preset deviation range, determine that the actual position difference is less than the preset position difference, then update the position vector corresponding to the core position vector among the multiple second position vectors to the core position vector, and for each second position vector, update the second position vector using the core position vector and the weight value to obtain the candidate position vector.

[0231] If there is one or more second position vectors whose position deviation rate from the core position vector is outside the preset deviation range, then for each second position vector, the second position vector is iteratively updated using the core position vector, the weight value, and the candidate value until the position deviation rate of each second position vector from the core position vector is within the preset deviation range. Then, the position vector corresponding to the core position vector among the multiple second position vectors is updated to the core position vector, and for each second position vector, the second position vector is updated using the core position vector and the weight value to obtain the candidate position vector.

[0232] In some embodiments, the parameter optimization module 1105 is specifically configured to,

[0233] Determine the fitness of each candidate position vector based on the objective function.

[0234] If there is a candidate position vector among other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, then the multiple candidate position vectors are updated to multiple initial position vectors; other candidate position vectors include the position vectors among the multiple candidate position vectors except the candidate position vector corresponding to the core position vector.

[0235] If the fitness of the candidate position vector corresponding to the core position vector is greater than or equal to the fitness of other candidate position vectors, then each candidate position vector is updated based on the Levy flight algorithm until there is a candidate position vector among other candidate position vectors whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, and the multiple candidate position vectors are updated to multiple initial position vectors.

[0236] In some embodiments, the parameter optimization module 1105 is specifically configured to,

[0237] For each set of initial adjustment parameters, the response data is subjected to signal demodulation processing according to the non - linear frequency - modulated mode decomposition algorithm using the initial adjustment parameters to obtain at least one - order initial single - component data.

[0238] Determine the signal complexity of each order of initial single - component data using the objective function.

[0239] Determine the smallest signal complexity among the at least one - order initial single - component data as the fitness corresponding to the initial adjustment parameters.

[0240] It should be noted that for the information interaction, execution process, etc. between the above - mentioned devices, since they are based on the same concept as the method embodiment of the present application, for their specific functions and the technical effects brought, reference can be specifically made to the method embodiment part, and details are not described herein again.

[0241] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated into a processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of this application. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0242] Next, refer to Figure 12 , Figure 12 which shows a schematic structural diagram of a terminal device suitable for implementing the embodiments of the present application. As Figure 12 shown, the computer system 1200 includes a central processing unit (CPU) 1201, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 1202 or the program loaded from the storage section 1208 into the random access memory (RAM) 1203. In the RAM 1203, various programs and data required for the operation instructions of the system are also stored. The CPU 1201, ROM 1202, and RAM 1203 are connected to each other via a bus 1204. The input / output (I / O) interface 1205 is also connected to the bus 1204.

[0243] The following components are connected to the I / O interface 1205; an input section 1206 including a keyboard, a mouse, etc.; an output section 1207 including such as a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker; a storage section 1208 including a hard disk, etc.; and a communication section 1209 including a network interface card such as a LAN card, a modem, etc. The communication section 1209 performs communication processing via a network such as the Internet. A drive 1210 is also connected to the I / O interface 1205 as needed. A removable medium 1211, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1210 as needed so that the computer program read from it can be installed into the storage section 1208 as needed.

[0244] Specifically, according to the embodiments of the present application, as referred to above with reference to the flowchart Figure 2The described process may be implemented as a computer software program. For example, embodiments of the present application include a computer program product that includes a computer program carried on a computer-readable medium, the computer program including program code for performing the method shown in the flowchart. In such an embodiment, the computer program includes program code for performing the method shown in the flowchart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication section 1209, and / or installed from the removable medium 1211. When the computer program is executed by the central processing unit (CPU) 1201, the above functions defined in the system of the present application are performed.

[0245] It should be noted that the computer-readable medium shown in the present application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. And in the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted by any suitable medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0246] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operation instructions of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the foregoing module, program segment, or part of code includes one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two connected blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operation instructions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0247] The units or modules involved in the embodiments described in the present application can be implemented in software or in hardware. The described units or modules can also be provided in a processor. For example, it can be described as: a processor includes a violator detection unit, a multi-modal detection unit, and an identification unit. Among them, the names of these units or modules do not constitute a limitation to the units or modules themselves in some cases.

[0248] As another aspect, the present application also provides a computer-readable storage medium, which may be included in the terminal device described in the above embodiments, or may exist separately without being assembled into the terminal device. The above computer-readable storage medium stores one or more programs, and when the above programs are executed by one or more processors, the substructure modal identification method that can be measured step by step and multiple times described in the present application is performed. For example, it can execute Figure 2 each step of the substructure modal identification method that can be measured step by step and multiple times as shown.

[0249] The embodiments of the present application provide a computer program product, which includes instructions that, when run, cause the method described in the embodiments of the present application to be executed. For example, it can execute Figure 2 each step of the substructure modal identification method that can be measured step by step and multiple times as shown.

[0250] The above description is only a preferred embodiment of the present application and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of disclosure involved in the present application is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the foregoing disclosure concept. For example, the technical solutions formed by mutually replacing the above features with the technical features (but not limited to) having similar functions disclosed in the present application.

[0251] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A substructure modal identification method capable of multiple step-by-step measurements, characterized in that: The method comprises: Obtain the response data of each measurement point in each substructure of the engineering structure; the response data of all measurement points of the same substructure are response data collected synchronously at the same time; the response data of measurement points of different substructures are response data collected multiple times at different times; each substructure has at least one common measurement point with other substructures; For each response data, a nonlinear frequency modulation mode decomposition algorithm is used to perform signal demodulation processing on the response data with the objective of minimizing the objective function, so as to obtain at least first-order target single component data; the objective function is used to evaluate the signal complexity of the at least first-order target single component data; For each of the target single component data, obtaining spectrum data based on the target single component data; For each substructure, the amplitude of each order of vibration mode of each substructure is obtained according to the ratio of the amplitude of the same order spectrum of each measurement point in the spectrum data; According to the vibration mode amplitudes of each substructure, the vibration mode amplitudes of the common measurement points of each substructure are adjusted to be consistent, so as to obtain the vibration mode amplitudes of all measurement points of the engineering structure; According to the amplitudes of each order vibration mode at all measurement points of the engineering structure, the direction of the vibration mode is determined based on the minimization of the modal confidence criterion; According to the direction of the vibration mode, the modal vibration mode of the engineering structure is obtained.

2. The substructure modal identification method capable of multiple step-by-step measurements according to claim 1 is characterized in that: The method further comprises: Determining multiple groups of initial adjustment parameters in the nonlinear frequency modulation mode decomposition algorithm; The multiple groups of initial adjustment parameters are optimized using a parameter-free heuristic optimization algorithm to obtain target adjustment parameters; the target adjustment parameters are used to obtain the at least first-order target single component data.

3. The substructure modal identification method capable of multiple step-by-step measurements according to claim 2, characterized in that: The method of optimizing the multiple groups of initial adjustment parameters using a non-parameterized heuristic optimization algorithm to obtain target adjustment parameters includes: In the current iteration number, determining the fitness corresponding to each set of initial adjustment parameters based on the objective function; Constructing an initial position vector for each set of initial adjustment parameters, and determining a core position vector with the minimum fitness among multiple initial position vectors; Based on the core position vector, each initial position vector is updated to obtain a candidate position vector corresponding to each initial position vector; if the current number of iterations does not meet the iteration number condition, the multiple initial position vectors are updated using multiple candidate position vectors until the current number of iterations meets the iteration number condition, and the parameters in the position vector with the smallest fitness among the multiple candidate position vectors are determined as the target adjustment parameters.

4. The substructure modal identification method capable of multiple step-by-step measurements according to claim 3 is characterized in that: The updating each initial position vector based on the core position vector to obtain a candidate position vector corresponding to each initial position vector includes: With the goal of making the actual position difference smaller than the preset position difference, each initial position vector is updated according to the core position vector, the weight value and the balance index to obtain a candidate position vector corresponding to each initial position vector; wherein the position difference is used to characterize the position deviation rate of the candidate position vector compared to the core position vector, and the balance index is used to characterize the movable range of the initial position vector.

5. The substructure modal identification method capable of multiple step-by-step measurements according to claim 4, characterized in that: The step of taking the actual position difference less than the preset position difference as a goal, updating each of the initial position vectors according to the core position vector, the weight value, and the balance index, and obtaining a candidate position vector corresponding to each of the initial position vectors includes: Determining an initial value of the balance index within a first index interval and a weight value of each initial position vector among the multiple initial position vectors; Using the core position vector, the initial value and the weight value, each of the initial position vectors is updated in a preset search domain to obtain a first position vector corresponding to each of the initial position vectors; For each initial position vector, determine a candidate value of the balance index, and use the candidate value to update the initial value and use the first position vector to update the initial position vector until the candidate value is within a second index interval, and determine the first position vector as the second position vector; wherein the candidate value is smaller than the initial value, and the first index interval is adjacent to and larger than the second index interval; If the position deviation rate of each of the second position vectors compared to the core position vector is within a preset deviation range, it is determined that the actual position difference is less than the preset position difference, the core position vector is updated to a position vector corresponding to the core position vector among the plurality of second position vectors, and for each of the second position vectors, the second position vector is updated using the core position vector and the weight value to obtain the candidate position vector; If there are one or more second position vectors whose position deviation rate compared to the core position vector is outside the preset deviation range, then for each of the second position vectors, the second position vector is iteratively updated using the core position vector, the weight value and the candidate value until the position deviation rate of each of the second position vectors compared to the core position vector is within the preset deviation range, the core position vector is updated to the position vector corresponding to the core position vector among the multiple second position vectors, and for each of the second position vectors, the second position vector is updated using the core position vector and the weight value to obtain the candidate position vector.

6. The substructure modal identification method capable of multiple step-by-step measurements according to claim 3, characterized in that: The method of updating the plurality of initial position vectors by using the plurality of candidate position vectors comprises: Determining the fitness of each candidate position vector based on the objective function; If there is a fitness of the candidate position vector corresponding to the core position vector among the other candidate position vectors which is smaller than the fitness of the candidate position vector corresponding to the core position vector, the multiple candidate position vectors are updated to the multiple initial position vectors; the other candidate position vectors include position vectors among the multiple candidate position vectors except the candidate position vector corresponding to the core position vector; If the fitness of the candidate position vectors corresponding to the core position vector are greater than or equal to the fitness of other candidate position vectors, each candidate position vector is updated based on the Levy flight algorithm until there is a candidate position vector whose fitness is less than the fitness of the candidate position vector corresponding to the core position vector, and the multiple candidate position vectors are updated to the multiple initial position vectors.

7. The substructure modal identification method capable of multiple step-by-step measurements according to claim 3 is characterized in that: The determining the fitness corresponding to each group of initial adjustment parameters based on the objective function includes: For each group of initial adjustment parameters, performing signal demodulation processing on the response data according to a nonlinear frequency modulation mode decomposition algorithm using the initial adjustment parameters to obtain at least one initial single component data; Determine the signal complexity of each initial single component data using the objective function; The minimum signal complexity in at least one initial single component data is determined as the fitness corresponding to the initial adjustment parameter.

8. A substructure modal identification device capable of multiple step-by-step measurements, characterized in that: include: An acquisition module, used to acquire response data of each measurement point in each substructure of the engineering structure; The response data of all measurement points of the same substructure are the response data collected synchronously at the same time; The response data of the measurement points of different substructures are the response data collected multiple times at different times and in different steps; Each substructure has at least one common measurement point with other substructure; A decomposition module is used to perform signal demodulation processing on each response data by using a nonlinear frequency modulation mode decomposition algorithm with the objective of minimizing the objective function, so as to obtain at least first-order target single component data; The objective function is used to evaluate the signal complexity of the at least first-order target single component data; A transformation module, configured to obtain spectrum data based on each target single component data; An identification module, for obtaining, for each substructure, the amplitude of each order of vibration mode of each substructure according to the ratio of the amplitude of the same order spectrum of each measurement point in the spectrum data; The identification module is further used to adjust the vibration mode amplitudes of the common measurement points of each substructure to be consistent according to the vibration mode amplitudes of each order of each substructure, so as to obtain the vibration mode amplitudes of each order of all measurement points of the engineering structure; to determine the direction of the vibration mode based on minimization of the modal confidence criterion according to the vibration mode amplitudes of each order of all measurement points of the engineering structure; and to obtain the modal vibration mode of the engineering structure according to the direction of the vibration mode.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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