Nonlinear system-based structural damage testing method and apparatus

Abstract

The present invention relates to the technical field of non-destructive testing, and provides a nonlinear system-based structural damage testing method and apparatus. The method comprises: applying an excitation force to a test object under test, so that said test object vibrates under the excitation force, performing signal acquisition on said test object by means of a laser vibrometer to obtain an excitation signal and a response signal, using the excitation signal and the response signal together with a plurality of imported order combinations to construct initial NARX models corresponding to different orders, screening out a target NARX model from among the plurality of initial NARX models on the basis of the Akaike information criterion and optimizing the target NARX model to obtain an NARX model under test, comparing order information in the NARX model under test with order information in a reference NARX model, and determining, on the basis of an order comparison result, whether said test object has a defect. A nonlinear model is constructed by means of signal data capable of expressing nonlinearity of a test object under test, parameter optimization is performed on the model, so that the model more accurately represents characteristics of said test object, and then whether said test object has a defect is determined.

Description

A method and apparatus for structural damage detection in nonlinear systems Technical Field

[0001] This invention relates to the field of nondestructive testing technology, specifically to a method and apparatus for detecting structural damage in nonlinear systems. Background Technology

[0002] A nonlinear system is a system in which the change in output is disproportionate to the change in input, characterized by a nonlinear relationship between the input and output. Nondestructive testing (NDT) refers to the use of modern technology and equipment to inspect for defects inside and on the surface of a specimen by utilizing changes caused by abnormalities or defects in the internal structure of the material, without damaging or affecting the performance of the object being tested. In the NDT of microcracks in metal specimens, the presence of defects leads to nonlinear mechanical behavior. Parameter identification methods for nonlinear systems can capture these nonlinear characteristics, thereby enabling defect detection and location. However, different materials, structures, and testing conditions may require different nonlinear models to describe them. Although various nonlinear models are available, such as the Hammerstein model and the Wiener model, selecting a suitable model remains challenging in practical applications. If the chosen model is not well-suited to the specific NDT problem, it may lead to inaccurate identification results, affecting 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 apparatus for detecting structural damage in nonlinear systems, addressing the shortcomings of the prior art.

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

[0005] A method for detecting structural damage in a nonlinear system includes the following steps:

[0006] A modal force measuring hammer is used to apply an excitation force to the test piece to induce vibration. During the application of the excitation force, a laser vibration meter is used to collect signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon.

[0007] Multiple order combinations are imported, and initial NARX models of different orders are constructed by the excitation signal and the response signal with the multiple order combinations respectively. Based on the Akaike information criterion, the target NARX model corresponding to the optimal order combination is selected from the multiple initial NARX models. The target NARX model is optimized by the least squares method to obtain the NARX model to be detected.

[0008] The order information in the NARX model to be tested is compared with the order information in the benchmark NARX model, and the presence of defects in the test piece is determined based on the order comparison results.

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

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

[0011] The signal acquisition module is used to apply an excitation force to the test piece through a modal force measuring hammer to cause the test piece to vibrate. During the application of the excitation force, a laser vibration meter is used to acquire signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon.

[0012] The model building module is used to import multiple order combinations, construct initial NARX models of different orders by combining the excitation signal and the response signal with the multiple order combinations, select the target NARX model corresponding to the optimal order combination from the multiple initial NARX models based on the Akaike information criterion, and optimize the target NARX model by the least squares method to obtain the NARX model to be detected.

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

[0014] The beneficial effects of this invention are as follows: A NARX model is established using the input and output data of the test specimen; the AIC criterion is used to determine the model order; and the least squares method is used to estimate the parameters of the ordered model, generating the optimal NARX model and completing the modeling of the nonlinear system containing the test specimen. Parametric residuals are generated using the order information of the baseline NARX model of the defect-free specimen and the order information of the NARX model to be tested on the test specimen. By comparing the residuals with a set threshold, the presence of defects in the specimen is determined, thus achieving the purpose of defect detection. Attached Figure Description

[0015] Figure 1 is a flowchart of a structural damage detection method for a nonlinear system provided in an embodiment of the present invention;

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

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

[0018] Figure 4 is a block diagram of the structural damage detection device for nonlinear systems provided in an embodiment of the present invention. Detailed Implementation

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

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

[0021] A modal force measuring hammer is used to apply an excitation force to the test piece to induce vibration. During the application of the excitation force, a laser vibration meter is used to collect signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon.

[0022] Multiple order combinations are imported, and initial NARX models of different orders are constructed by the excitation signal and the response signal with the multiple order combinations respectively. Based on the Akaike information criterion, the target NARX model corresponding to the optimal order combination is selected from the multiple initial NARX models. The target NARX model is optimized by the least squares method to obtain the NARX model to be detected.

[0023] The order information in the NARX model to be tested is compared with the order information in the benchmark NARX model, and the presence of defects in the test piece is determined based on the order comparison results.

[0024] It should be understood that since a vibration force is applied to the test piece using a modal force measuring hammer to make the test piece vibrate, the force signal is the excitation signal of the test piece. The vibration displacement function of the test piece under the corresponding force signal is also called the response function (i.e., response signal). Since the change in the output of the test piece is not proportional to the change in the input, the test piece is regarded as a nonlinear system.

[0025] In this embodiment of the invention, since micro-defects on the specimen will produce nonlinear effects, a model of the nonlinear system containing the specimen is established by analyzing the excitation signal and response signal, thereby determining whether the structure contains defects. That is, based on the nonlinear effects produced by the specimen, a nonlinear model is constructed using data that can express the nonlinearity of the specimen. The model's parameters are optimized to make the model more accurately represent the characteristics of the specimen, thus determining whether the specimen has defects.

[0026] Preferably, a modal force measuring hammer is used to apply an excitation force to the test specimen to induce vibration. During the application of the excitation force, a laser vibration meter is used to acquire signals from the test specimen, obtaining the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon, including:

[0027] As shown in Figures 2 and 3, a standard aluminum alloy sheet with a length of 250 mm, a width of 50 mm, and a thickness of 2 mm was selected as the test piece. A microcrack with a width (d) of 0.1 cm was created on the test piece, and a fixture was used to fix the test piece. Nine test contacts were set in an area with a length of 160 mm and a width of 30 mm on the test piece. The equipment used included a modal force measuring hammer connected to a Julight laser vibrometer, a control unit with a data acquisition card, a VSM-TEST signal processing platform, and a Vibro Remote Console laser controller. The modal force measuring 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, acquiring the input and output signals of the test piece.

[0028] Based on the size, material, and defect range of the metal plate of the test specimen, the laser focal length is set via the Vibro Remote Console laser controller. Appropriate parameters for the laser vibrometer acquisition system are selected, including laser focal length, acquisition channels, sampling frequency, trigger settings, and preprocessing functions.

[0029] The laser vibrometer's control unit, including the acquisition card, sets the basic parameters of the laser vibrometer's signal channels based on the force hammer's baseline data. Channel one is set as the input channel with a sensitivity of 2.42 mV / N, and channel two is set as the output channel. Using the Vibro Remote Console laser controller, the sampling frame rate of the laser vibrometer's acquisition system is set to 5.12 kHz, the selected spectral line number to 1600, and the bandwidth to 2 kHz, based on the size, material, and defect range of the tested piece. Linear averaging mode excitation is used, with a trigger delay of -20 ms, a trigger threshold of 0.4%, and a trigger hysteresis of 0.2%. The vibration of the test specimen 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 5ms and the attenuation constant is 100ms. In the preprocessing stage, a high-pass filter is applied to the signal, with 3dB frequency 1 being 5Hz and 3dB frequency 2 being 1.2KHz, in order to add the corresponding windowing function to the signal and perform preliminary processing such as signal noise reduction.

[0030] Based on the detection parameters of the laser vibrometer, the test plan is formatted as excitation signal in the negative Z-axis direction and response signal in the positive Z-axis direction. The test plan is then set according to the dimensions of the test piece, and the input excitation signal and output response signal are collected. After completing the test according to the test plan, the response signal and excitation signal can be exported.

[0031] It should be understood that the number and arrangement of the laser vibrometer's detection contacts on the test piece are selected according to the determined size of the test piece. The hammering excitation is applied to the test piece in sequence according to the test order in the set test plan. The response signal and excitation signal of each time period are collected by the signal acquisition device of the laser vibrometer.

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

[0033] Set the autoregressive order interval for the autoregressive order and the input order interval for the exogenous input order. According to the set combination parameters, obtain the corresponding orders from the autoregressive order interval and the input order interval and combine them to obtain multiple order combinations.

[0034] Alternatively, multiple combinations of autoregressive order and exogenous input order 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 construction of initial NARX models of different orders by combining the excitation signal and the response signal with multiple orders 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. This process is repeated for all order combinations to obtain multiple initial NARX models. The initial NARX model is as follows:

[0039] ,

[0040] in, In response to the signal, As an excitation signal, It is a nonlinear function. Let the order be the autoregressive order. Time delay represents the time difference between the exogenous input (i.e., the excitation signal) and the output (i.e., the response signal). For exogenous input order, This is the error term of the model. The output signal is delayed by a time interval from the previous moment. For the past The output signal delay at each moment Due to the lag of the input signal, the actual impact of the input signal is from From the moment on, For the past The input signal at time t (i.e., the delayed part of the input), the actual effect of the input signal from 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 to represent the relationship between the input and output signals of a nonlinear system. It is composed of the current output signal, which is a weighted combination of the input and output signals from past time points. The general expression of the NARX model is as follows:

[0043] ,

[0044] in, For the output signal of a nonlinear system, For the input signal of a nonlinear system, It is a nonlinear function. Let be the order of the autoregression. Let the order of the exogenous input term be . The error term of the model is usually assumed to be white noise. The output signal is delayed by the previous output. For the front The output signal delay of each output The input signal is delayed by the previous input. For the front The input signal is delayed.

[0045] It should be understood that both the excitation and response signals possess temporal information. The NARX neural network is a type of neural network based on an autoregressive model, possessing temporal modeling capabilities and suitable for prediction and time series analysis. It maps the input sequence to the output sequence through regression analysis and uses previous outputs and current inputs to predict the current output. The NARX model includes an autoregressive (AR) component and an exogenous (EX) component as input terms; the AR term represents the lag value of the output, while the EX term represents external input variables that may affect the output. The time delay in a NARX neural network refers to the time difference between the arrival time of input data at a neuron and the neuron's response output time when processing temporal data.

[0046] In this embodiment of the 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 handle and predict the behavior of nonlinear systems.

[0047] Preferably, the step of selecting the target NARX model corresponding to the optimal order combination from multiple initial NARX models based on the Akaike information criterion includes:

[0048] Parameters of multiple initial NARX models are obtained, resulting in multiple model parameters. The Akaike Information Criterion expression is then used to calculate the Akaike Information Criterion values ​​for each of the multiple initial NARX models. The Akaike Information Criterion expression is as follows:

[0049] ,

[0050] in, This is the value of the Akaike Information Criterion. The number of model parameters, This is the maximum likelihood estimate;

[0051] The initial NARX model corresponding to the minimum value among the multiple initial NARX models and the optimal order combination are selected to obtain the target NARX model corresponding to the optimal order combination.

[0052] The process of solving the maximum likelihood estimate is as follows: the model parameters of each initial NARX model are calculated through the likelihood function, including: under given observation data (excitation signal and response signal), the function value (i.e. the maximum likelihood estimate corresponding to each initial NARX model) is obtained when the model parameters are adjusted so that the probability distribution predicted by the model is closest to the actual observation data (i.e. the likelihood function value is the maximum) is maximized.

[0053] It should be understood that the AIC criterion (i.e., the Akaike Information Criterion) is an information criterion, an index for evaluating the overall optimal configuration. It 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. It measures the probability of observing observed data x given model parameters θ. Given observed data x (i.e., the excitation signal and the response signal), the likelihood function L(θ|x) with respect to model parameters θ is numerically equal to the probability of observing the corresponding variable given parameters θ, expressed as:

[0054] L(θ|x)=P(x|θ).

[0055] In this embodiment of the invention, the AIC criterion balances the goodness of fit and complexity of the model, selects the most suitable combination of orders from multiple combinations of orders by selecting and comparing models, and finds the model that best expresses the mapping relationship between the excitation signal and the response signal.

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

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

[0058] ,

[0059] in, To predict the response signal, In response to the signal, As an excitation signal, Let the order be the autoregressive order. For time delay, For exogenous input order, The intercept is... These are the autoregressive coefficients. These are the exogenous input coefficients.

[0060] In this embodiment of the invention, the closer the predicted value is to the actual value, the higher the fitting effect of the model and the more representative it is of the nonlinear system of the test piece. 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 the predicted value of the optimized model gradually approaches the actual value when making predictions, making the model more representative of the test piece.

[0061] Preferably, optimizing the target NARX model using the least squares method to obtain the NARX model to be detected includes:

[0062] The objective function value is obtained by calculating the response signal and the predicted response signal of the target NARX model using an objective function expression. The objective function expression is as follows:

[0063] ,

[0064] in, The objective function value, In response to the signal, To predict the response signal, This represents the total number of model parameters.

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

[0066] In this embodiment of the invention, the least squares optimization algorithm is used to optimize the model parameters, which not only improves the predictive performance of the model, but also improves the accuracy, making the nonlinear model of the test piece more closely approximate the actual output signal collected.

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

[0068] The optimal model parameters are obtained by differentiating the objective function value using the derivative equation, which is:

[0069] ,

[0070] in, The objective function value, These are model parameters;

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

[0072] It should be understood that model parameters , These are the coefficients of the autoregressive component of the NARX model. These are the coefficients of the exogenous input component of the NARX model. The intercept is used to update the parameters of the NARX model using the optimal model parameters. This involves replacing the coefficients of the autoregressive part, the coefficients of the exogenous input part, and the intercept of the NARX model with the coefficients of the optimal exogenous input part obtained by differentiation, the coefficients of the optimal exogenous input part, and the optimal intercept.

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

[0074] A modal force measuring hammer is used to apply an excitation force to a defect-free specimen to induce vibration. During the application of the excitation force, a laser vibration meter is used to collect signals from the defect-free specimen, thereby obtaining the excitation signal corresponding to the excitation force and the reference response signal corresponding to the vibration phenomenon.

[0075] Multiple order combinations are imported, and initial benchmark NARX models of different orders are constructed by combining the excitation signal and the reference response signal with the multiple order combinations. Based on the Akaike information criterion, the target benchmark NARX model corresponding to the optimal order combination is selected from the multiple initial benchmark NARX models. The target benchmark NARX model is optimized by the least squares method to obtain the benchmark NARX model.

[0076] Preferably, the step of comparing the order information in the NARX model to be tested with the order information in the benchmark NARX model, and determining whether the test piece to be tested has defects based on the order comparison result, includes:

[0077] The order combination is extracted from the NARX model to be tested to obtain the autoregressive order and the exogenous input order to be tested. The 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 tested and the benchmark autoregressive order is calculated to obtain the regression order error. The difference between the exogenous input order to be tested and the benchmark exogenous input order is calculated to obtain the exogenous order error. It is determined whether the regression order error and the exogenous order error meet the corresponding error thresholds. Based on the determination results, it is determined whether the test piece to be tested has defects.

[0078] It should be understood that the error threshold for regression order error differs from the error threshold for exogenous order error. If a test specimen has defects, these defects often manifest in its impact on the structure's stiffness, mass distribution, vibration modes, etc., potentially altering the system's dynamic characteristics. This necessitates adjusting the model's order to better fit and predict the structure's nonlinear dynamic response. Therefore, determining the presence of defects in the test specimen involves assessing changes in the model's order.

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

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

[0081] The signal acquisition module is used to apply an excitation force to the test piece through a modal force measuring hammer to cause the test piece to vibrate. During the application of the excitation force, a laser vibration meter is used to acquire signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon.

[0082] The model building module is used to import multiple order combinations, construct initial NARX models of different orders by combining the excitation signal and the response signal with the multiple order combinations, select the target NARX model corresponding to the optimal order combination from the multiple initial NARX models based on the Akaike information criterion, and optimize the target NARX model by the least squares method to obtain the NARX model to be detected.

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

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

[0085] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the above-described device and module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

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

[0087] The modules described as separate components may or may not be physically separate. Similarly, the components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the objectives of the embodiments of the present invention, depending on actual needs.

[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 within the protection scope of the present invention.

Claims

1. A method for detecting structural damage in a nonlinear system, characterized in that, Includes the following steps: A modal force measuring hammer is used to apply an excitation force to the test piece to induce vibration. During the application of the excitation force, a laser vibration meter is used to collect signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon. Multiple order combinations are imported, and initial NARX models of different orders are constructed by the excitation signal and the response signal with the multiple order combinations respectively. Based on the Akaike information criterion, the target NARX model corresponding to the optimal order combination is selected from the multiple initial NARX models. The target NARX model is optimized by the least squares method to obtain the NARX model to be detected. The order information in the NARX model to be tested is compared with the order information in the benchmark NARX model, and the presence of defects in the test piece is determined based on the order comparison results.

2. The defect detection method according to claim 1, characterized in that, The order combination includes autoregressive order and exogenous input order; The construction of initial NARX models of different orders by combining the excitation signal and the response signal with multiple orders 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. This process is repeated for all order combinations to obtain multiple initial NARX models. The initial NARX model is as follows: ， in, In response to the signal, As an excitation signal, It is a nonlinear function. Let the order be the autoregressive order. For time delay, For exogenous input order, This is the error term of the model.

3. The defect detection method according to claim 1, characterized in that, The selection of the target NARX model corresponding to the optimal order combination from multiple initial NARX models based on the Akaike information criterion includes: Parameters of multiple initial NARX models are obtained, resulting in multiple model parameters. The Akaike Information Criterion (AIC) values ​​are then calculated for each of these model parameters using the Akaike Information Criterion expression. The Akaike Information Criterion expression is as follows: ， in, This is the value of the Akaike Information Criterion. The number of model parameters, This is the maximum likelihood estimate; The initial NARX model corresponding to the minimum value among the multiple initial NARX models and the optimal order combination are selected to obtain the target NARX model corresponding to the optimal order combination.

4. The defect detection method according to claim 1, characterized in that, Before the step of optimizing the target NARX model using the least squares method, the method further includes: The target NARX model is solved based on its parameters to obtain a predicted response signal, which is: ， in, To predict the response signal, In response to the signal, As an excitation signal, Let the order be the autoregressive order. For time delay, For exogenous input order, The intercept is... These are the autoregressive coefficients. These are the exogenous input coefficients.

5. The defect detection method according to claim 4, characterized in that, The optimization of the target NARX model using the least squares method to obtain the NARX model to be detected includes: The objective function value is obtained by calculating the response signal and the predicted response signal of the target NARX model using an objective function expression. The objective function expression is as follows: ， in, The objective function value, In response to the signal, To predict the response signal, This represents the total number of model parameters. The objective function value is minimized to obtain the NARX model to be detected.

6. The defect detection method according to claim 5, characterized in that, The process of minimizing the objective function value to obtain the NARX model to be detected includes: The optimal model parameters are obtained by differentiating the objective function value using the derivative equation, which is: ， in, The objective function value, These are model parameters; The target NARX model is updated using the optimal model parameters to obtain the NARX model to be detected.

7. The defect detection method according to claim 1, characterized in that, The construction process of the benchmark NARX model includes: A modal force measuring hammer is used to apply an excitation force to a defect-free specimen to induce vibration. During the application of the excitation force, a laser vibration meter is used to collect signals from the defect-free specimen, thereby obtaining the excitation signal corresponding to the excitation force and the reference response signal corresponding to the vibration phenomenon. Multiple order combinations are imported, and initial benchmark NARX models of different orders are constructed by combining the excitation signal and the reference response signal with the multiple order combinations. Based on the Akaike information criterion, the target benchmark NARX model corresponding to the optimal order combination is selected from the multiple initial benchmark NARX models. The target benchmark NARX model is optimized by the least squares method to obtain the benchmark NARX model.

8. The defect detection method according to claim 1, characterized in that, The step of comparing the order information in the NARX model to be tested with the order information in the benchmark NARX model, and determining whether the test piece to be tested has defects based on the order comparison result, includes: The order combination is extracted from the NARX model to be tested to obtain the autoregressive order and the exogenous input order to be tested. The 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 tested and the benchmark autoregressive order is calculated to obtain the regression order error. The difference between the exogenous input order to be tested and the benchmark exogenous input order is calculated to obtain the exogenous order error. It is determined whether the regression order error and the exogenous order error meet the corresponding error thresholds. Based on the determination results, it is determined whether the test piece to be tested has defects.

9. A structural damage detection device for a nonlinear system, characterized in that, include: The signal acquisition module is used to apply an excitation force to the test piece through a modal force measuring hammer to cause the test piece to vibrate. During the application of the excitation force, a laser vibration meter is used to acquire signals from the test piece to obtain the excitation signal corresponding to the excitation force and the response signal corresponding to the vibration phenomenon. The model building module is used to import multiple order combinations, construct initial NARX models of different orders by combining the excitation signal and the response signal with the multiple order combinations, select the target NARX model corresponding to the optimal order combination from the multiple initial NARX models based on the Akaike information criterion, and optimize the target NARX model by the least squares method to obtain the NARX model to be detected. The defect detection module is used to compare the order information in the NARX model to be tested with the order information in the benchmark NARX model, and determine whether the test piece to be tested has defects based on the order comparison result.

10. The defect detection system according to claim 9, characterized in that, The order combination includes autoregressive order and exogenous input order; In the model construction module, the construction of initial NARX models of different orders by combining the excitation signal and the response signal with multiple orders 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. This process is repeated for all order combinations to obtain multiple initial NARX models. The initial NARX model is as follows: ， in, In response to the signal, As an excitation signal, It is a nonlinear function. Let the order be the autoregressive order. For time delay, For exogenous input order, This is the error term of the model.

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