A structural damage detection method and device for nonlinear systems

Abstract

The present invention provides a method and device for detecting structural damage of a nonlinear system, which relates to the field of nondestructive testing technology. The method includes: applying an excitation force to a test piece to be inspected, vibrating the test piece to be inspected based on the excitation force, collecting signals from the test piece to be inspected to obtain an excitation signal and a response signal, combining the excitation signal and the response signal with multiple imported orders to construct initial NARX models of different orders, screening a target NARX model from the multiple initial NARX models based on the Akaike information criterion and optimizing it, comparing the order information in the optimized NARX model to be inspected with the order information in the reference NARX model, and determining whether the test piece to be inspected has defects based on the order comparison results. A nonlinear model is constructed and optimized based on the signal data of the test piece to be inspected, so that the model accurately represents the structural characteristics of the test piece to be inspected, thereby determining whether the test piece to be inspected has defects.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of nondestructive testing, and in particular to a method and device for detecting structural damage of a nonlinear system. Background Art

[0002] A nonlinear system is one in which the change in output is disproportionate to the change in input; it is characterized by a nonlinear relationship between input and output. Nondestructive testing (NDT) utilizes modern technology and equipment to detect defects within and on the surface of a specimen, exploiting changes caused by structural anomalies or defects within the material without damaging or affecting the performance of the object being tested. In NDT of microcracks in metal specimens, defects within the specimen can cause nonlinear mechanical behavior. Parameter identification methods for nonlinear systems can capture these nonlinear characteristics, enabling defect detection and location. However, different materials, structures, and testing conditions may require different nonlinear models to describe them. While a variety of nonlinear models are currently available, such as the Hammerstein model and the Wiener model, selecting an appropriate model remains challenging in practical applications. If the selected model is not well-suited to the specific NDT problem, inaccurate identification results may result, compromising defect detection and assessment. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method and device for detecting structural damage of a nonlinear system in view of the deficiencies in the prior art.

[0004] The technical solution of the present invention to solve the above technical problems is as follows:

[0005] A structural damage detection method for a nonlinear system comprises the following steps:

[0006] Applying an exciting force to the test piece to be tested by a modal force hammer to cause the test piece to vibrate. During the application of the exciting force, a laser vibrometer is used to collect signals from the test piece to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon.

[0007] importing a plurality of order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screening a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, optimizing the target NARX model by the least squares method, and obtaining a NARX model to be tested;

[0008] The order information in the NARX model to be inspected is compared with the order information in the reference NARX model, and whether the test piece to be inspected has defects is determined according to the order comparison result.

[0009] Another technical solution of the present invention to solve the above technical problems is as follows:

[0010] A structural damage detection device for a nonlinear system, comprising:

[0011] a signal acquisition module, configured to apply an excitation force to a test piece to be inspected by using a modal force hammer to cause the test piece to vibrate, and to acquire signals from the test piece to be inspected by using a laser vibrometer during the application of the excitation force, thereby obtaining an excitation signal corresponding to the excitation force and a response signal corresponding to the vibration phenomenon;

[0012] a model construction module, configured to import a plurality of order combinations, construct initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screen out a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, and optimize the target NARX model by the least squares method to obtain a NARX model to be tested;

[0013] The defect detection module is used to compare the order information in the NARX model to be detected with the order information in the reference NARX model, and determine whether the test piece to be detected has defects according to the order comparison result.

[0014] The present invention has the following beneficial effects: a NARX model is established using the input and output data of the test piece to be tested, the model order is determined using the AIC criterion, and the parameters of the determined model are estimated using the least squares method to generate an optimal NARX model, thereby completing the modeling of the nonlinear system in which the test piece to be tested resides. Parameter residuals are generated using the order information of the baseline NARX model of the defect-free test piece and the order information of the NARX model to be tested of the test piece to be tested. A set threshold is used to compare the parameter residuals with the parameter residuals to determine whether the test piece has defects, thereby achieving the purpose of defect detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flow chart of a structural damage detection method for a nonlinear system provided by an embodiment of the present invention;

[0016] Figure 2 A structural diagram of a structural damage detection method provided by an embodiment of the present invention;

[0017] Figure 3 A schematic diagram of a test piece to be tested provided in an embodiment of the present invention;

[0018] Figure 4 This is a module block diagram of a structural damage detection device for a nonlinear system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0020] like Figure 1 As shown, an embodiment of the present invention provides a method for detecting structural damage of a nonlinear system, comprising the following steps:

[0021] Applying an exciting force to the test piece to be tested by a modal force hammer to cause the test piece to vibrate. During the application of the exciting force, a laser vibrometer is used to collect signals from the test piece to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon.

[0022] importing a plurality of order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screening a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, optimizing the target NARX model by the least squares method, and obtaining a NARX model to be tested;

[0023] The order information in the NARX model to be inspected is compared with the order information in the reference NARX model, and whether the test piece to be inspected has defects is determined according to the order comparison result.

[0024] It should be understood that since a modal force hammer is used to apply an exciting force to the test piece to cause it to vibrate, the force signal is the excitation signal of the test piece to be tested, and the vibration displacement function of the test piece to be tested under the corresponding force signal is also called the response function (i.e., the response signal). Since the change in the output of the test piece to be tested is not proportional to the change in the input, the test piece to be tested is regarded as a nonlinear system.

[0025] In an embodiment of the present invention, a nonlinear model is constructed and optimized using the signal data of the test piece to be tested, so that the model accurately represents the structural characteristics of the test piece to be tested, thereby determining whether the test piece to be tested has defects. Because micro-defects on the test piece can produce nonlinear effects, a model of the nonlinear system in which the test piece is located is established by analyzing the excitation signal and the response signal, thereby determining whether the structure contains defects. In other words, based on the nonlinear effects produced by the test piece, a nonlinear model is constructed using data that can express the nonlinearity of the test piece, and the model parameters are optimized to make the model more accurately represent the characteristics of the test piece, thereby determining whether the test piece has defects.

[0026] Preferably, an excitation force is applied to the test piece to be tested by a modal force hammer to cause the test piece to vibrate. During the application of the excitation force, a laser vibrometer is used to collect signals from the test piece to be tested, and an excitation signal corresponding to the excitation force and a response signal corresponding to the vibration phenomenon are obtained, respectively, including:

[0027] like Figure 2 and Figure 3 As shown in the figure, a 250mm long, 50mm wide, and 2mm thick ordinary aluminum alloy sheet was selected as the test piece. A microcrack with a width (d) of 0.1cm was created on the test piece, and the test piece was fixed with a fixture. Nine test contacts were set in an area 160mm long and 30mm wide on the test piece. The equipment used included a modal force hammer connected to a Julight laser vibrometer, a control unit with an acquisition card, a VSM-TEST signal processing platform, and a Vibro Remote Console laser controller. The modal force hammer applied an excitation force to the test piece, causing it to vibrate. The Julight laser vibrometer recorded the vibration of the test piece in real time and collected the input and output signals of the test piece.

[0028] Based on the size, material, and metal plate defect range of the test piece, set the laser focal length through the Vibro Remote Console laser controller and select the appropriate laser vibrometer acquisition system parameters (including laser focal length, acquisition channel, sampling frequency, trigger settings, and preprocessing function). Specifically:

[0029] Set the laser focal length. The laser vibrometer control unit, which includes the acquisition card, sets the basic parameters of the laser vibrometer signal channel based on the basic data from the impact hammer. Channel 1 is set as the input channel with a sensitivity of 2.42 mV / N, and Channel 2 is set as the output channel. Using the Vibro Remote Console laser controller, set the laser vibrometer acquisition system to a sampling frame rate of 5.12 kHz, 1600 selected spectral lines, and a bandwidth of 2 kHz, based on the test piece's size, material, and metal sheet defect range. Use linear averaging mode excitation, with trigger delay set to -20 ms, trigger threshold set to 0.4%, and trigger hysteresis set to 0.2%. The vibration of the test piece to be inspected is recorded in real time using the VSM-TEST signal processing platform of the laser vibrometer. The windowing function of the input signal is set to a rectangular window function, and the windowing function of the output signal is set to an exponential window function. The main window offset is 5 ms and the attenuation constant is 100 ms. In the preprocessing stage, a high-pass filter is applied to the signal with 3dB frequency 1 at 5 Hz and 3dB frequency 2 at 1.2 kHz to add the corresponding windowing function to the signal and perform preliminary processing such as signal noise reduction.

[0030] Based on the laser vibrometer's detection parameters, set up a test schedule formatted as an excitation signal in the negative Z-axis direction and a response signal in the positive Z-axis direction. The schedule is tailored to the size of the test piece, and the input excitation signal and output response signal are collected. Once the test is completed according to the schedule, the response and excitation signals can be exported.

[0031] It should be understood that the number and arrangement of detection contacts of the laser vibrometer on the test piece are selected according to the determined size of the test piece to be tested, hammer excitation is applied to the test piece to be tested in sequence according to the test sequence in the set test plan, and the response signal and excitation signal of each time period are collected by the signal collector of the laser vibrometer.

[0032] Preferably, before the step of importing multiple order combinations, the method further comprises:

[0033] The autoregressive order interval of the autoregressive order is set, the input order interval of the exogenous input order is set, and corresponding orders are obtained from the autoregressive order interval and the input order interval according to the set combination parameters to combine and obtain multiple order combinations;

[0034] Or multiple combinations of autoregressive orders and exogenous input orders can be set to obtain multiple order combinations.

[0035] The autoregressive order of a set of order combinations can be set to [1, 2, 3], and the exogenous input order can be set to [1, 2].

[0036] Preferably, the order combination includes an autoregressive order and an exogenous input order;

[0037] The constructing of initial NARX models corresponding to different orders by combining the excitation signal and the response signal with a plurality of orders respectively includes:

[0038] The excitation signal is mapped to the response signal according to the autoregressive order and the exogenous input order to obtain an initial NARX model. In this process, all order combinations are processed to obtain multiple initial NARX models. The initial NARX model is:

[0039] y(k)=F[y(k-1),…,y(kn a ),u(kn b ),u(kn b -1),…,u(kn b -n k )]+e(k),

[0040] Where y(k) is the response signal (i.e., the response signal delay of the test piece at the kth moment), u(k) is the excitation signal (i.e., the excitation signal delay of the test piece at the kth moment), F[·] is a nonlinear function, and n a is the autoregressive order, n b is the time delay, which represents the time difference between the exogenous input (i.e., the stimulus signal) and the output (i.e., the response signal), n k is the exogenous input order, e(k) is the error term of the model, y(k-1) is the output signal delay of the past moment, y(kn a ) is the past n a The output signal delay at the moment, u(kn b ) is the hysteresis of the input signal. The actual impact of the input signal is from n b The moment begins, u(kn b -n k ) is the past n k The input signal at n moments (i.e. the delayed part of the input) has an actual impact on the input signal. b The moment begins.

[0041] Specifically, the NARX neural network is used to perform regression analysis on the excitation signal and the response signal, and the excitation signal is mapped to the response signal according to the set order combination to obtain the NARX model.

[0042] Generally, the NARX model is widely used in black box modeling of nonlinear systems. It represents the relationship between the input and output signals of a nonlinear system. The output signal at the current moment is composed of a weighted combination of the input and output signals at the past moments. The general expression of the NARX model is as follows:

[0043] y(k)=F[y(k-1),…,y(kn a ),u(k-1),…,u(kn k )]+e(k),

[0044] Among them, y(k) is the output signal of the nonlinear system, u(k) is the input signal of the nonlinear system, F[·] is the nonlinear function, and n a is the order of autoregression, n k is the order of the exogenous input term, e(k) is the error term of the model, which is usually assumed to be white noise, y(k-1) is the output signal delay of the previous output, y(kn a ) is the first n a The output signal delay of each output, u(k-1) is the input signal delay of the previous input, u(kn k ) is the first n k The input signal is delayed for each input.

[0045] It should be understood that both the excitation signal and the response signal have timing information (both include signals at k moments), and the use of multiple delayed input and output signals can better capture the dynamic behavior and nonlinear relationship of the nonlinear system of the test piece to be tested. The NARX neural network is a neural network based on an autoregressive model with time series modeling capabilities. It is suitable for prediction and time series analysis. It maps the input sequence to the output sequence through regression analysis, and uses the previous output and the current input to predict the current output. The NARX model includes autoregressive (AR) and exogenous (EX) input terms; the AR term represents the lagged value of the output, and the EX term represents the external input variable that may affect the output. The time delay of the NARX neural network refers to the time difference between the time when the input data reaches the neuron and the time when the neuron responds to the output when the network processes time series data.

[0046] In the embodiment of the present invention, the NARX (nonlinear autoregressive with external input) neural network is a powerful tool for structural damage detection. The model combines the advantages of traditional autoregressive models and neural networks and can process and predict the behavior of nonlinear systems.

[0047] Preferably, the step of selecting a target NARX model corresponding to an optimal order combination from a plurality of the initial NARX models based on the Akaike Information Criterion comprises:

[0048] Parameters of the multiple initial NARX models are obtained respectively to obtain multiple model parameters, and the multiple model parameters are calculated respectively using the Akaike information criterion expression to obtain the Akaike information criterion values ​​of the multiple initial NARX models, wherein the Akaike information criterion expression is:

[0049] AIC=2k-2ln(L),

[0050] Where AIC is the Akaike information criterion value, k is the number of model parameters, and L is the maximum likelihood estimate;

[0051] An initial NARX model and an optimal order combination corresponding to the minimum value among the Akaike information criterion values ​​of the multiple initial NARX models are selected to obtain a target NARX model corresponding to the optimal order combination.

[0052] The process of solving the maximum likelihood estimate is: calculating the model parameters of each initial NARX model through the likelihood function, including: under given observation data (stimulus signal and response signal), by adjusting the model parameters so that the probability distribution predicted by the model is closest to the actual observation data (that is, the likelihood function value is the largest), and obtaining the function value (that is, the maximum likelihood estimate corresponding to each initial NARX model).

[0053] It should be understood that the AIC criterion (i.e., Akaike Information Criterion) is an information criterion, an indicator for evaluating the overall optimal configuration, which is a weighted function of fitting accuracy and the number of unknown parameters. The likelihood function is a function of the parameters of a statistical model. The likelihood function measures the probability of observing the observation data x given the model parameters θ. When the observation data x (i.e., the stimulus signal and the response signal) are given, the likelihood function L(θ|x) about the model parameters θ is numerically equal to the probability of the corresponding variable observation data after the given parameters θ, expressed as:

[0054] L(θ|x)=P(x|θ).

[0055] In the embodiment of the present invention, the AIC criterion balances the goodness of fit and complexity of the model, selects and compares the model to select the most suitable order combination from multiple groups of order combinations, and finds the model that best expresses the mapping relationship between the stimulus signal and the response signal.

[0056] Preferably, before the step of optimizing the target NARX model by the least squares method, the method further comprises:

[0057] The target NARX model is solved based on the parameters of the target NARX model to obtain a predicted response signal, which is:

[0058]

[0059] in, is the predicted response signal, y(k) is the response signal, u(k) is the excitation signal, n a is the autoregressive order, n b is the time delay, n k is the exogenous input order, β0 is the intercept, β n is the autoregressive coefficient, γ n is the exogenous input coefficient.

[0060] In an embodiment of the present invention, the closer the predicted value is to the actual value, the higher the fitting effect of the model is, and the more it can represent the nonlinear system of the test piece to be tested. Therefore, the predicted value of the model is calculated based on the model parameters, and the model parameters are optimized according to the predicted value, so that when the optimized model makes a prediction, its predicted value gradually approaches the actual value, so that the model can better represent the test piece to be tested.

[0061] Preferably, the optimization of the target NARX model by the least square method to obtain the NARX model to be detected includes:

[0062] The response signal and the predicted response signal of the target NARX model are calculated using an objective function expression to obtain an objective function value. The objective function expression is:

[0063]

[0064] Among them, J(θ) is the objective function value, y(k) is the response signal, To predict the response signal, N is the total number of model parameters;

[0065] The objective function value is minimized to obtain the NARX model to be tested.

[0066] In the embodiment of the present invention, the least squares optimization algorithm is used to optimize the model parameters, which not only improves the prediction performance of the model, but also improves the accuracy, so that the nonlinear model of the test piece to be tested can be closer to the actual output signal collected.

[0067] Preferably, the minimization of the objective function value to obtain the NARX model to be detected includes:

[0068] The objective function value is derived by a derivative equation to obtain the optimal model parameters. The derivative equation is:

[0069]

[0070] Among them, J(θ) is the objective function value, θ is the model parameter;

[0071] The target NARX model is updated with the optimal model parameters to obtain the NARX model to be detected.

[0072] It should be understood that the model parameters θ = {β0, β1, β2, ..., β n ,γ1,γ2,…,γ n}, β is the coefficient of the autoregressive part of the NARX model, γ is the coefficient of the exogenous input part of the NARX model, and β0 is the intercept. Updating the NARX model parameters using the optimal model parameters involves replacing the coefficients of the autoregressive part, the coefficients of the exogenous input part, and the intercept of the NARX model with the optimal exogenous input part coefficients, the optimal exogenous input part coefficients, and the optimal intercept obtained by differentiation.

[0073] Preferably, the process of constructing the benchmark NARX model includes:

[0074] Applying an exciting force to a non-defective specimen using a modal dynamometer to cause the non-defective specimen to vibrate, and collecting signals from the non-defective specimen using a laser vibrometer during the application of the exciting force to obtain an excitation signal corresponding to the exciting force and a reference response signal corresponding to the vibration phenomenon;

[0075] A plurality of order combinations are imported, and initial benchmark NARX models corresponding to different orders are constructed by respectively combining the excitation signal and the benchmark response signal with the plurality of order combinations. A target benchmark NARX model corresponding to the optimal order combination is screened out from the plurality of initial benchmark NARX models based on the Akaike information criterion, and the target benchmark NARX model is optimized by the least squares method to obtain a benchmark NARX model.

[0076] Preferably, comparing the order information in the NARX model to be inspected with the order information in the reference NARX model, and determining whether the test piece to be inspected has defects according to the order comparison result, includes:

[0077] An order combination is extracted from the NARX model to be detected to obtain the autoregressive order to be detected and the exogenous input order to be detected. An order combination is extracted from the benchmark NARX model to obtain the benchmark autoregressive order and the benchmark exogenous input order. The difference between the autoregressive order to be detected and the benchmark autoregressive order is calculated to obtain a regression order error. The difference between the exogenous input order to be detected and the benchmark exogenous input order is calculated to obtain an exogenous order error. It is judged whether the regression order error and the exogenous order error meet the corresponding error thresholds respectively, and whether the test piece to be detected has defects is determined based on the judgment results.

[0078] It should be understood that the order information in the NARX model is the optimal order combination. For example, the order information in the NARX model to be tested is the optimal order combination of the NARX model to be tested, that is, the order combination corresponding to the construction of the initial NARX model. The error threshold of the regression order error is different from the error threshold of the exogenous order error. If there are defects in the test piece to be tested, it will often manifest itself in the impact on the stiffness, mass distribution, vibration mode, etc. of the structure, which may change the dynamic characteristics of the system, requiring the model to adjust its order to better fit and predict the nonlinear dynamic response of the structure. Therefore, the change in the model order is used to determine whether the test piece to be tested has defects.

[0079] In an embodiment of the present invention, by comparing the autoregressive order and exogenous input order of the NARX model to be tested of a defect-free specimen and the baseline NARX model of a defective specimen, the residual of the parameter change of the NARX model to be tested compared with the baseline NARX model can be obtained, which can reveal the changes in the structural dynamic characteristics of the test piece to be tested when defects exist, thereby achieving the purpose of defect detection.

[0080] like Figure 4 As shown, an embodiment of the present invention provides a structural damage detection device for a nonlinear system, comprising:

[0081] a signal acquisition module, configured to apply an exciting force to a test piece to be inspected by using a modal force hammer to cause the test piece to vibrate, and to acquire signals from the test piece to be inspected by using a laser vibrometer during the application of the exciting force, thereby obtaining an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon;

[0082] a model construction module, configured to import a plurality of order combinations, construct initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screen out a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, and optimize the target NARX model by the least squares method to obtain a NARX model to be tested;

[0083] The defect detection module is used to compare the order information in the NARX model to be detected with the order information in the reference NARX model, and determine whether the test piece to be detected has defects according to the order comparison result.

[0084] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0085] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described devices and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0086] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the module division is only a logical function division. In actual implementation, other division methods may be used. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not performed.

[0087] Modules described as separate components may or may not be physically separate, and components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of these modules may be selected based on actual needs to achieve the objectives of the embodiments of the present invention.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A structural damage detection method for a nonlinear system, characterized in that: The steps include: Applying an exciting force to the test piece to be tested by a modal force hammer to cause the test piece to vibrate. During the application of the exciting force, a laser vibrometer is used to collect signals from the test piece to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon. importing a plurality of order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screening a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, optimizing the target NARX model by the least squares method, and obtaining a NARX model to be tested; Comparing the order information in the NARX model to be inspected with the order information in the reference NARX model, and determining whether the test piece to be inspected has defects according to the order comparison result; The method of selecting a target NARX model corresponding to an optimal order combination from the multiple initial NARX models based on the Akaike Information Criterion includes: Parameters of the multiple initial NARX models are obtained respectively to obtain multiple model parameters, and the multiple model parameters are calculated respectively using the Akaike information criterion expression to obtain the Akaike information criterion values ​​of the multiple initial NARX models, wherein the Akaike information criterion expression is: AIC=2k-2ln(L), Where AIC is the Akaike information criterion value, k is the number of model parameters, and L is the maximum likelihood estimate; Selecting an initial NARX model and an optimal order combination corresponding to a minimum value among the Akaike information criterion values ​​of the multiple initial NARX models to obtain a target NARX model corresponding to the optimal order combination; Before the step of optimizing the target NARX model by the least squares method, the method further includes: The target NARX model is solved based on the parameters of the target NARX model to obtain a predicted response signal, which is: in, is the predicted response signal, y(k) is the response signal, u(k) is the excitation signal, n a is the autoregressive order, n b is the time delay, n k is the exogenous input order, β0 is the intercept, β n is the autoregressive coefficient, γ n is the exogenous input coefficient; The method of optimizing the target NARX model by the least square method to obtain the NARX model to be detected includes: The response signal and the predicted response signal of the target NARX model are calculated using an objective function expression to obtain an objective function value. The objective function expression is: Among them, J(θ) is the objective function value, y(k) is the response signal, To predict the response signal, N is the total number of model parameters; The objective function value is minimized to obtain the NARX model to be tested.

2. The structural damage detection method according to claim 1, characterized in that: The order combination includes an autoregressive order and an exogenous input order; The constructing of initial NARX models corresponding to different orders by combining the excitation signal and the response signal with a plurality of orders respectively includes: The excitation signal is mapped to the response signal according to the autoregressive order and the exogenous input order to obtain an initial NARX model. In this process, all order combinations are processed to obtain multiple initial NARX models. The initial NARX model is: y(k)=F[y(k-1),…,y(k-n a ),u(k-n b ),u(k-n b -1),…,u(k-n b -n k )]+e(k), Among them, y(k) is the response signal, u(k) is the excitation signal, F[·] is the nonlinear function, n a is the autoregressive order, n b is the time delay, n k is the exogenous input order, and e(k) is the error term of the model.

3. The structural damage detection method according to claim 1, characterized in that: The minimization of the objective function value to obtain the NARX model to be detected includes: The objective function value is derived by a derivative equation to obtain the optimal model parameters. The derivative equation is: Among them, J(θ) is the objective function value, θ is the model parameter; The target NARX model is updated with the optimal model parameters to obtain the NARX model to be detected.

4. The structural damage detection method according to claim 1, characterized in that: The construction process of the benchmark NARX model includes: Applying an exciting force to a non-defective specimen using a modal dynamometer to cause the non-defective specimen to vibrate, and collecting signals from the non-defective specimen using a laser vibrometer during the application of the exciting force to obtain an excitation signal corresponding to the exciting force and a reference response signal corresponding to the vibration phenomenon; A plurality of order combinations are imported, and initial benchmark NARX models corresponding to different orders are constructed by respectively combining the excitation signal and the benchmark response signal with the plurality of order combinations. A target benchmark NARX model corresponding to the optimal order combination is screened out from the plurality of initial benchmark NARX models based on the Akaike information criterion, and the target benchmark NARX model is optimized by the least squares method to obtain a benchmark NARX model.

5. The structural damage detection method according to claim 1, characterized in that: The step of comparing the order information in the NARX model to be inspected with the order information in the reference NARX model, and determining whether the test piece to be inspected has defects according to the order comparison result, includes: An order combination is extracted from the NARX model to be detected to obtain the autoregressive order to be detected and the exogenous input order to be detected. An order combination is extracted from the benchmark NARX model to obtain the benchmark autoregressive order and the benchmark exogenous input order. The difference between the autoregressive order to be detected and the benchmark autoregressive order is calculated to obtain a regression order error. The difference between the exogenous input order to be detected and the benchmark exogenous input order is calculated to obtain an exogenous order error. It is judged whether the regression order error and the exogenous order error meet the corresponding error thresholds respectively, and whether the test piece to be detected has defects is determined based on the judgment results.

6. A structural damage detection device for a nonlinear system, characterized in that: include: a signal acquisition module, configured to apply an excitation force to a test piece to be inspected by using a modal force hammer to cause the test piece to vibrate, and to acquire signals from the test piece to be inspected by using a laser vibrometer during the application of the excitation force, thereby obtaining an excitation signal corresponding to the excitation force and a response signal corresponding to the vibration phenomenon; a model construction module, configured to import a plurality of order combinations, construct initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the plurality of order combinations, screen out a target NARX model corresponding to the optimal order combination from the plurality of initial NARX models based on the Akaike Information Criterion, and optimize the target NARX model by the least squares method to obtain a NARX model to be tested; a defect detection module, configured to compare the order information in the NARX model to be detected with the order information in the reference NARX model, and determine whether the test piece to be detected has defects according to the order comparison result; The method of selecting a target NARX model corresponding to an optimal order combination from the multiple initial NARX models based on the Akaike Information Criterion includes: Parameters of the multiple initial NARX models are obtained respectively to obtain multiple model parameters, and the multiple model parameters are calculated respectively using the Akaike information criterion expression to obtain the Akaike information criterion values ​​of the multiple initial NARX models, wherein the Akaike information criterion expression is: AIC=2k-2ln(L), Where AIC is the Akaike information criterion value, k is the number of model parameters, and L is the maximum likelihood estimate; Selecting an initial NARX model and an optimal order combination corresponding to a minimum value among the Akaike Information Criterion values ​​of the multiple initial NARX models to obtain a target NARX model corresponding to the optimal order combination; Before the step of optimizing the target NARX model by the least squares method, the method further includes: The target NARX model is solved based on the parameters of the target NARX model to obtain a predicted response signal, which is: in, is the predicted response signal, y(k) is the response signal, u(k) is the excitation signal, n a is the autoregressive order, n b is the time delay, n k is the exogenous input order, β0 is the intercept, β n is the autoregressive coefficient, γ n is the exogenous input coefficient; The method of optimizing the target NARX model by the least square method to obtain the NARX model to be detected includes: The response signal and the predicted response signal of the target NARX model are calculated using an objective function expression to obtain an objective function value. The objective function expression is: Among them, J(θ) is the objective function value, y(k) is the response signal, To predict the response signal, N is the total number of model parameters; The objective function value is minimized to obtain the NARX model to be tested.

7. The structural damage detection device according to claim 6, characterized in that: The order combination includes an autoregressive order and an exogenous input order; In the model construction module, the initial NARX models corresponding to different orders are constructed by combining the excitation signal and the response signal with a plurality of orders, including: The excitation signal is mapped to the response signal according to the autoregressive order and the exogenous input order to obtain an initial NARX model. In this process, all order combinations are processed to obtain multiple initial NARX models. The initial NARX model is: y(k)=F[y(k-1),…,y(k-n a ),u(k-n b ),u(k-n b -1),…,u(k-n b -n k )]+e(k), Among them, y(k) is the response signal, u(k) is the excitation signal, F[·] is the nonlinear function, n a is the autoregressive order, n b is the time delay, n k is the exogenous input order, and e(k) is the error term of the model.

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