Structural damage detection method and device for nonlinear system

Abstract

The invention provides a structural damage detection method and device for a nonlinear system, and relates to the technical field of nondestructive detection. The method comprises the following steps: applying excitation force to a to-be-detected test piece, vibrating the to-be-detected test piece based on the excitation force, performing signal acquisition on the to-be-detected test piece to obtain an excitation signal and a response signal, constructing initial NARX models of different orders by combining the excitation signal and the response signal with a plurality of imported orders respectively, and calculating the initial NARX models according to the initial NARX models. And screening a target NARX model from the plurality of initial NARX models based on an akaike information criterion, optimizing the target NARX model, comparing order information in the NARX model to be detected obtained by optimization with order information in the reference NARX model, and determining whether the test piece to be detected has defects according to an order comparison result. The nonlinear model is constructed and optimized through the signal data of the to-be-detected test piece, so that the model accurately represents the structural characteristics of the to-be-detected test piece, and then whether the to-be-detected test piece has defects or not is judged.

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 a system in which the change in output is not proportional to the change in input, and its characteristic is that there is a nonlinear relationship between input and output. Nondestructive testing refers to the use of modern technology and equipment to inspect defects inside and on the surface of the specimen by using changes caused by abnormal internal structure or defects in the material without damaging or affecting the performance of the object being tested. In the nondestructive testing of microcracks in metal specimens, when there are defects in the specimen, its mechanical behavior will show nonlinear characteristics. The parameter identification method of nonlinear systems can capture these nonlinear characteristics, thereby realizing the detection and location of defects. However, different materials, structures and testing conditions may require different nonlinear models to describe. Although there are currently a variety of nonlinear models available, such as the Hammerstein model and the Wiener model, it is still challenging to select a suitable model in practical applications. If the selected model is not well adapted to the specific nondestructive testing problem, it may lead to inaccurate identification results and affect the detection and evaluation of defects. 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 of 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 inspected by means of 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 multiple order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the multiple order combinations, selecting a target NARX model corresponding to the optimal order combination from the multiple 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 detected;

[0008] The order information in the NARX model to be inspected is compared with the order information in the reference NARX model, and it is determined whether the test piece to be inspected has defects 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 is used to apply an exciting force to the test piece to be inspected through a modal force hammer to make the test piece to be inspected vibrate. During the process of applying the exciting force, a laser vibrometer is used to collect signals from the test piece to be inspected to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon;

[0012] A model building module, used for 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 out 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 detected;

[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 beneficial effects of the present invention are as follows: a NARX model is established by using the input data and output data of the test piece to be tested, the model order is determined by using the AIC criterion, and the parameters of the model obtained by the order determination are estimated by using the least square method to generate the optimal NARX model, thereby completing the modeling of the nonlinear system in which the test piece to be tested is located. The order information of the benchmark 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 are used to generate parameter residuals, and the parameter residuals are compared according to the set threshold value 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 by an embodiment of the present invention;

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

[0019] The principles and features of the present invention are described below in conjunction with 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, a structural damage detection method for a nonlinear system provided by an embodiment of the present invention includes the following steps:

[0021] Applying an exciting force to the test piece to be inspected by means of 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 multiple order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the multiple order combinations, selecting a target NARX model corresponding to the optimal order combination from the multiple 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 detected;

[0023] The order information in the NARX model to be inspected is compared with the order information in the reference NARX model, and it is determined whether the test piece to be inspected has defects 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 make it 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 the embodiment of the present invention, a nonlinear model is constructed and optimized through the signal data of the test piece to be tested, so that the model can accurately represent the structural characteristics of the test piece to be tested, and then determine whether the test piece to be tested has defects. Since micro defects on the test piece will 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, so as to determine whether the structure contains defects. That is, through the nonlinear effect generated by the test piece, a nonlinear model is constructed using data that can express the nonlinearity of the test piece, and the parameters of the model are optimized, so that the model can more accurately represent the characteristics of the test piece and determine whether the test piece has defects.

[0026] Preferably, an exciting force is applied to the test piece to be inspected 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 be inspected, and an excitation signal corresponding to the exciting 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 piece of ordinary aluminum alloy sheet with a length of 250mm, a width of 50mm and a thickness of 2mm is selected as the test piece to be tested. A micro crack with a width (d) of 0.1cm is made on the test piece to be tested, and the test piece to be tested is fixed with a fixture. Nine test contacts are set in an area with a length of 160mm and a width of 30mm in the test piece to be tested. The equipment used includes a modal force hammer connected to the 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 applies an exciting force to the test piece to vibrate the test piece to be tested, and the Julight laser vibrometer records the vibration of the test piece to be tested in real time, and collects the input signal and output signal of the test piece to be tested.

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

[0029] Set the laser focal length; the control unit of the laser vibrometer with acquisition card sets the basic parameters of the laser vibrometer signal channel according to the basic data of the hammer; among them, channel 1 is set as the input channel with a sensitivity of 2.42mV / N, channel 2 is set as the output channel, and the sampling frame rate of the laser vibrometer acquisition system is set to 5.12KHz, the selected spectrum line is 1600, and the bandwidth is 2KHz according to the size, material, and metal plate defect range of the tested piece through the Vibro Remote Console laser controller. Use linear average mode excitation, set the trigger delay to -20ms, the trigger threshold to 0.4%, and the trigger hysteresis to 0.2%. The vibration conditions of the test piece to be inspected are recorded in real time through the VSM-TEST signal processing platform of the laser vibrometer, and 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. 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 being 5 Hz and 3dB frequency 2 being 1.2 kHz, so as to add the corresponding windowing function to the signal and perform preliminary processing such as signal noise reduction.

[0030] According to the detection parameters of the laser vibrometer, the format of the test plan is set as the excitation signal in the negative direction of the Z axis and the response signal in the positive direction of the Z axis. The test plan is set according to the size of the test piece to be tested, and the input excitation signal and the output response signal are collected. After the test is completed according to the test plan, the response signal and the excitation signal 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 are 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 initial NARX models corresponding to different orders are constructed by combining the excitation signal and the response signal with a plurality of the orders, respectively, including:

[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, 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 actual impact of the input signal is n b The moment begins.

[0041] Specifically, the excitation signal and the response signal are regressed through the NARX neural network, 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 signal and the output signal at the past moment. 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, and y(kn a ) is the first n a The output signal delay of the 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 timing 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] The parameters of the multiple initial NARX models are obtained respectively to obtain multiple model parameters, and the multiple model parameters are calculated respectively by the Akaike information criterion expression to obtain the Akaike information criterion values ​​of the multiple initial NARX models, and the Akaike information criterion expression is:

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

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

[0051] The initial NARX model and the optimal order combination corresponding to the minimum value among the Akaike information criterion values ​​of the multiple initial NARX models are selected to obtain the 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), 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 the minimum information criterion (an information criterion), which is an indicator for evaluating the comprehensive optimal configuration, and is a weighted function of the 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 observed data x given the model parameters θ. When the observed data x (i.e., the stimulus signal and the response signal) is given, the likelihood function L(θ|x) about the model parameter θ is numerically equal to the probability of the corresponding variable observed data after the given parameter 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 excitation 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 the 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 by an objective function expression to obtain an objective function value, and 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 detected.

[0066] In the embodiment of the present invention, the least squares optimization algorithm is used to optimize the model parameters, which can not only improve the prediction performance of the model, but also improve 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, and 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. The parameter update of the NARX model through the optimal model parameters is to replace the coefficient of the autoregressive part, the coefficient of the exogenous input part and the intercept of the NARX model with the coefficient of the optimal exogenous input part, the coefficient of the optimal exogenous input part 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 by means of a modal force hammer so as to cause the non-defective specimen to vibrate, and in the process of applying the exciting force, collecting signals from the non-defective specimen by means of a laser vibrometer 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 using the excitation signal and the benchmark response signal and 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; 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, comprises:

[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; a difference calculation is performed between the autoregressive order to be detected and the benchmark autoregressive order to obtain a regression order error; a difference calculation is performed between the exogenous input order to be detected and the benchmark exogenous input order 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 according to 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, so that the model needs to adjust its order to better fit and predict the nonlinear dynamic response of the structure. Therefore, it is determined whether the test piece to be tested has defects by judging the change in the model order.

[0079] In an embodiment of the present invention, by comparing the autoregressive order and the exogenous input order of the NARX model to be tested of a defect-free specimen and the benchmark NARX model of a defective specimen, the residual of the parameter change of the NARX model to be tested compared with the benchmark NARX model can be obtained, which can reveal the change of 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 is used to apply an exciting force to the test piece to be inspected through a modal force hammer to make the test piece to be inspected vibrate. During the process of applying the exciting force, a laser vibrometer is used to collect signals from the test piece to be inspected to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon;

[0082] A model building module, used for 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 out 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 detected;

[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 article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0085] Those skilled in the art can 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 only schematic, for example, the division of modules is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0087] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose 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 principle of the present invention should be included in the protection scope 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 inspected by means of 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 multiple order combinations, constructing initial NARX models corresponding to different orders by respectively combining the excitation signal and the response signal with the multiple order combinations, selecting a target NARX model corresponding to the optimal order combination from the multiple 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 detected; The order information in the NARX model to be inspected is compared with the order information in the reference NARX model, and it is determined whether the test piece to be inspected has defects according to the order comparison result.

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 initial NARX models corresponding to different orders are constructed by combining the excitation signal and the response signal with a plurality of the orders, respectively, 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, and 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 is characterized in that: The method 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 includes: The parameters of the multiple initial NARX models are obtained respectively to obtain multiple model parameters, and the multiple model parameters are calculated respectively by the Akaike information criterion expression to obtain the Akaike information criterion values ​​of the multiple initial NARX models, and the Akaike information criterion expression is: AIC = 2k-2ln(L), Among them, AIC is the Akaike information criterion value, k is the number of model parameters, and L is the maximum likelihood estimate; The initial NARX model and the optimal order combination corresponding to the minimum value among the Akaike information criterion values ​​of the multiple initial NARX models are selected to obtain the target NARX model corresponding to the optimal order combination.

4. The structural damage detection method according to claim 1, characterized in that: 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.

5. The structural damage detection method according to claim 4, characterized in that: 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 by an objective function expression to obtain an objective function value, and 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 detected.

6. The structural damage detection method according to claim 5, 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, and 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.

7. 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 by means of a modal force hammer so as to cause the non-defective specimen to vibrate, and in the process of applying the exciting force, collecting signals from the non-defective specimen by means of a laser vibrometer 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 using the excitation signal and the benchmark response signal and 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; the target benchmark NARX model is optimized by the least squares method to obtain a benchmark NARX model.

8. 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; a difference calculation is performed between the autoregressive order to be detected and the benchmark autoregressive order to obtain a regression order error; a difference calculation is performed between the exogenous input order to be detected and the benchmark exogenous input order 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 according to the judgment results.

9. A structural damage detection device for a nonlinear system, characterized in that: include: A signal acquisition module is used to apply an exciting force to the test piece to be inspected through a modal force hammer to make the test piece to be inspected vibrate. During the process of applying the exciting force, a laser vibrometer is used to collect signals from the test piece to be inspected to obtain an excitation signal corresponding to the exciting force and a response signal corresponding to the vibration phenomenon; A model building module, used for 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 out 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 detected; 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.

10. The structural damage detection device according to claim 9, characterized in that: The order combination includes an autoregressive order and an exogenous input order; In the model building 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 respectively, 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, and 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.

Images