Probabilistic impact location and energy identification method based on approximate bayesian computation
Patent Information
- Application Number
- CN202411295222.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-16
- Publication Date
- 2026-10-13
- Estimated Expiration
- 2044-09-16
AI Technical Summary
贝叶斯推理的一个重要组成部分是似然函数的计算，对于冲击监测系统而言，由于结构的复杂性、边界反射以及噪声干扰等因素影响，在很多情况下无法推导监测数据与冲击位置、能量相关联的似然函数的解析表达式
[0012]第一、本发明中的方法利用神经网络拟合冲击位置、冲击能量与到达时间差、最大包络振幅特征数据的关系，为无似然函数情况下基于近似贝叶斯计算的冲击位置及能量识别奠定了基础。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of structural health monitoring, and in particular to a probabilistic method for identifying impact location and energy based on approximate Bayesian computation. Background Technology
[0002] Engineering structures inevitably suffer impacts from external objects during service and transportation, causing damage and directly threatening their safety and integrity. Regular manual inspections are time-consuming, labor-intensive, and costly. Therefore, real-time online impact monitoring of engineering structures is crucial for maintaining their health and safety. Structural impact monitoring technology utilizes sensors to collect impact stress wave signals, employs signal processing methods for feature extraction, and uses specific algorithms to locate the impact and identify its energy. Bayesian inference plays a vital role in structural health monitoring (SHM), primarily using monitoring data to update probabilistic models and inversely derive unknown parameters related to structural health monitoring. A key component of Bayesian inference is the calculation of the likelihood function. For impact monitoring systems, due to structural complexity, boundary reflections, and noise interference, it is often impossible to derive an analytical expression for the likelihood function relating monitoring data to impact location and energy. Summary of the Invention
[0003] The purpose of this application is to address the shortcomings of the existing technology and propose a more effective probabilistic impact location and energy identification method based on Approximate Bayesian computation (ABC) in the absence of a likelihood function, making the Bayesian inference probability framework applicable to impact monitoring systems.
[0004] To this end, some embodiments of this application propose a probabilistic impact location and energy identification method based on approximate Bayesian computation, which includes: Step 1, using multiple sensors to offline collect first impact response signals of known impacts with known impact locations and known impact energies, and extracting first feature data, the first feature data including time difference of arrival and maximum envelope amplitude; Step 2, designing a neural network structure and training the neural network, using the known impact location and known impact energy as the input layer of the neural network, and the first feature data as the output layer of the neural network, training the neural network to fit the relationship between the known impact location and the known impact energy and the first feature data; Step 3, online collecting second impact signals of unknown impacts. The impact response signal is analyzed, and second feature data is extracted from the second impact response signal; step 4: using the two types of second feature data, namely the arrival time difference and the maximum amplitude of the envelope of the unknown impact monitored online, and the neural network, a Bayesian inference model without likelihood function is constructed; step 5: the distance function between the first feature data output by the neural network and the second feature data monitored online is selected, and the unknown impact location parameter and unknown impact energy parameter in the Bayesian inference model without likelihood function are sampled using a sequential Monte Carlo sampling algorithm; and step 6: the posterior distribution of the impact location and impact energy parameters sampled by the sequential Monte Carlo sampling algorithm are fitted with a normal distribution to realize probabilistic impact location and impact energy identification.
[0005] In some embodiments, step 1 includes deploying a sensor network on the structure, setting training points and impact energy, sequentially impacting all training points with corresponding impact energy, acquiring the first impact response signal collected by each sensor in the sensor network using a data acquisition system in an offline state, and extracting the arrival time difference between different first impact response signals and the maximum amplitude of the envelope of each first impact response signal as the first feature data.
[0006] In some embodiments, step 2 includes using the known impact location and known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, selecting the number of hidden layers and activation function, and training the neural network to fit the relationship between the known impact location and the known impact energy and the first feature data.
[0007] In some embodiments, step 3 includes, under online monitoring conditions, acquiring the second impact response signal of each unknown impact with unknown impact location and unknown impact energy through each of the sensors, and extracting the arrival time difference of the second impact response signals from different sensors and the maximum amplitude characteristics of the envelope of each second impact response signal.
[0008] In some embodiments, step 4 includes constructing an likelihood-free Bayesian inference model using two types of second feature data—the arrival time difference and the maximum amplitude of the envelope—based on Bayes' theorem and the neural network.
[0009] In some embodiments, step 5 includes selecting a distance function between the first feature data output by the neural network and the second feature data monitored online, and using a sequence Monte Carlo sampling algorithm to sample the unknown impact location parameter and the unknown impact energy parameter.
[0010] In some embodiments, step 6 includes fitting the posterior distributions of the unknown impact location parameters and unknown impact energy parameters obtained by the sequence Monte Carlo sampling algorithm with a normal distribution, so as to perform probabilistic impact localization and impact energy identification.
[0011] Due to the adoption of the above technical solution, the beneficial technical effects of the probabilistic impact location and energy identification method based on approximate Bayesian calculation provided by this invention are as follows:
[0012] First, the method in this invention utilizes a neural network to fit the relationship between impact location, impact energy, arrival time difference, and maximum envelope amplitude characteristic data, laying the foundation for impact location and energy identification based on approximate Bayesian calculations in the absence of likelihood functions.
[0013] Secondly, the method in this invention utilizes the approximate Bayesian computation-sequence Monte Carlo method to achieve probabilistic impact location and impact energy identification, which has higher reliability compared to other deterministic impact location and impact energy identification methods.
[0014] Third, the method in this invention utilizes neural networks to assist in the identification of impact location and energy based on approximate Bayesian calculations. Compared with traditional physical methods, it can complete more complex impact monitoring tasks and requires fewer sensors. Attached Figure Description
[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is a flowchart illustrating the probabilistic impact location and energy identification method based on approximate Bayesian calculation according to the present invention.
[0017] Figure 2This is a schematic diagram of the sensor network in the method according to the present invention.
[0018] Figure 3A This is a schematic diagram of the impact stress wave signal according to the present invention.
[0019] Figure 3B This is a schematic diagram of the arrival time and signal envelope amplitude measurement according to the present invention.
[0020] Figure 4 This is a schematic diagram of the Matlab neural network fitting toolbox according to the present invention.
[0021] Figure 5 This is a schematic diagram of the sequence Monte Carlo sampling algorithm according to the present invention.
[0022] Figure 6 This is a schematic diagram illustrating the composite material plate, sensor, and training point setup according to an embodiment of the present invention.
[0023] Figure 7 This is a schematic diagram of the sequence Monte Carlo sampling results according to an embodiment of the present invention.
[0024] Figure 8 This is a schematic diagram of the impact probability imaging localization result according to an embodiment of the present invention.
[0025] Figure 9 This is a schematic diagram of the probabilistic impact energy identification results according to an embodiment of the present invention. Detailed Implementation
[0026] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention:
[0027] like Figure 1 As shown, some embodiments of this application propose a probabilistic impact location and energy identification method based on approximate Bayesian computation. The method specifically includes the following steps: Step 1, offline acquisition of impact signals and feature extraction of known impacts;
[0028] Step 2: Design the neural network structure and train the neural network;
[0029] Step 3: Online acquisition of impact signals and feature extraction;
[0030] Step 4: Construct a Bayesian inference model without likelihood function;
[0031] Step 5: Select the distance function and sequence Monte Carlo sampling;
[0032] Step 6: Probabilistic impact location and impact energy identification.
[0033] Specifically, step 1 involves offline acquisition of impact signals and feature extraction, such as... Figure 2 As shown, this includes deploying a sensor network on the monitoring structure, setting training points and impact energies, sequentially impacting all training points with corresponding impact energies, and acquiring impact response signals using a data acquisition system in an offline state. A typical impact response signal is shown below. Figure 3A As shown. The sensors forming the sensor network in this step can be piezoelectric sensors, fiber Bragg grating sensors, and accelerometers. The sensor network can consist of a first sensor P1, a second sensor P2, a third sensor P3, and a fourth sensor P4 arranged in the boundary region of the monitored structure. For an impact IS with the training point as the impact source, each sensor receives an impact response signal, such as an impact stress wave signal, like... Figure 2 The diagram shows that the first sensor P1 receives the first impact response signal W1, the second sensor P2 receives the second impact response signal W2, the third sensor P3 receives the third impact response signal W3, and the fourth sensor P4 receives the fourth impact response signal W4.
[0034] The spectral components of each impulse response signal are observed using Fourier transform, and the narrowband Lamb wave signal with the maximum frequency component is extracted using wavelet transform. The complex Morlet continuous wavelet transform of the impulse response signal S(t) is defined as follows:
[0035] (1)
[0036] Where a is the scaling factor and b is the translation factor, "Indicates inner product," "Indicates conjugate, For the complex Morlet mother wavelet function:
[0037] (2)
[0038] In the formula, f c f is the center frequency of the mother wavelet. b The bandwidth of the mother wavelet.
[0039] Adjusting the scaling factor a and the mother wavelet bandwidth f b The narrowband Lamb wave signal with the largest frequency component in each impulse response signal is extracted using complex Morlet wavelet transform. For example... Figure 3B As shown, the arrival time and maximum envelope amplitude of the narrowband Lamb wave signal with the largest frequency component are extracted using Hilbert transform. The arrival times of the narrowband Lamb wave signals with the largest frequency components in the impact response signals of different sensors are subtracted to obtain arrival time difference feature data.
[0040] Step 2: Design the neural network and train the neural network.
[0041] like Figure 4 As shown, the backpropagation (BP) neural network structure is designed using the neural network fitting toolbox provided by Matlab. The impact location and energy are used as the input layer of the neural network, and the arrival time difference and maximum envelope amplitude are used as the output layer. An appropriate number of hidden layers is selected; in this embodiment, 10 hidden layers are used, but 8, 9, 11, 12, etc., are also possible. The Sigmoid activation function is used.
[0042] (3)
[0043] A neural network was trained using the Levenberg-Marquardt algorithm to fit the relationship between the impact location and impact energy and two types of feature data: the time difference of arrival and the maximum amplitude of the envelope.
[0044] Step 3: Online impact signal acquisition and feature extraction.
[0045] Under online monitoring, the impact signal with unknown impact location and impact energy is acquired, and the arrival time difference and maximum amplitude of the envelope are extracted using the same signal processing method as in step 1.
[0046] Step 4: Construct a Bayesian inference model without likelihood function.
[0047] Bayesian inference continuously updates the unknown parameters using new observation data to obtain the posterior distribution of the unknown parameters. The calculation formula is as follows:
[0048] (4)
[0049] Here, 'data' represents the arrival time difference and envelope maximum amplitude characteristic data obtained from online monitoring. Unknown parameter: x-coordinate of impact location Impact position y-coordinate parameters and impact energy parameters . Let be the likelihood function, representing the likelihood given parameters. The probability of observing the data. The prior distribution of unknown parameters can be regarded as a uniform distribution when no prior information is available.
[0050] However, for impact identification problems, it is often impossible to derive analytical expressions for the likelihood functions of the parameters. Approximate Bayesian computation methods, which directly perform random sampling of the parameters, can effectively avoid this problem. Sampling is accepted if it meets the specified tolerance conditions; otherwise, it is rejected. By repeatedly performing numerous sampling simulations, approximate posterior distributions of various parameters, such as impact location coordinates and impact energy, can be obtained. :
[0051] (5)
[0052] Where data and data* represent the feature data obtained from online monitoring and the parameters, respectively. Substitute the feature data generated by the neural network fitting, This is a distance function used to calculate the difference between two datasets. As a tolerance, using an adaptive tolerance ensures that the effective operation of the algorithm does not result in an excessively low particle acceptance rate. Therefore, in this embodiment, the mean of the particle gap from the previous generation is used as the adaptive tolerance. To meet tolerance Conditional samples, It is a sample from a random population, where N is the total number of particles accepted.
[0053] Therefore, an approximate Bayesian inference model without likelihood function can be constructed by using feature data from online monitoring and feature data generated by neural network fitting.
[0054] Step 5: Select the distance function and sequence Monte Carlo sampling.
[0055] Choose an appropriate distance function For example, the Euler distance formula can be used to calculate the distance function. :
[0056] (6)
[0057] Where L represents the datasets data and data * The length.
[0058] According to such Figure 5 The Monte Carlo sampling algorithm shown sampled unknown impact locations and impact energy parameters, including the following steps:
[0059] Step S51: Determine the particle size Z and the number of iterations K, k = 1.
[0060] Step S52, according to Initialize particles , i = 1.
[0061] Step S53, the particles Substitute into a neural network to fit and generate data * .
[0062] Step S54, if ,accept Assign weights to particles: N is the total number of particles accepted; otherwise, they are discarded. i = i + 1.
[0063] Step S55, if i > Z, normalize the weights: , i = 1, 2, …, N; otherwise return to step S53.
[0064] Step S56: If k > K, obtain the approximate posterior distribution. Otherwise, k = k + 1, return to step S52.
[0065] Step 6: Probabilistic impact location and impact energy identification.
[0066] The posterior distributions of the impact location and impact energy parameters obtained by the Monte Carlo sampling algorithm are fitted using a normal distribution to achieve probabilistic impact localization and impact energy identification. Assume that after sampling, the mean values of the x-coordinate, y-coordinate of the impact location, and the posterior distribution of the impact energy are respectively... , and The variances are respectively , and The correlation coefficient between the posterior distributions of the impact location's x and y coordinates is: Finally, the probability distribution of the impact location within the monitoring area is expressed in the standard form of a two-dimensional normal distribution:
[0067] (7)
[0068] In the formula: Impact position parameters The mean vector; It is the covariance matrix: ; for The determinant of the covariance matrix.
[0069] The probability distribution of impact energy within the monitoring area is expressed in the standard form of a one-dimensional normal distribution:
[0070] (8)
[0071] Example:
[0072] In this embodiment, the monitoring object is a carbon fiber / epoxy composite material plate structure, and impact tests are conducted on the structure. Figure 6 The diagram shown illustrates the composite material plate, sensor, and training point setup. The composite material plate measures 500 mm × 500 mm × 2 mm (length × width × thickness), is made of T300 woven fabric, and has a [0 / 90] layering pattern. 3s Four piezoelectric sensors, P-51 type piezoelectric ceramic discs with a diameter of 8 mm and a thickness of 0.25 mm, were deployed on the surface of the composite material plate. The sensors were numbered P1, P2, P3, and P4, with a spacing of 360 mm. The plate was fixed at both ends using clamps, and an impact test was conducted on the composite material plate using a free-fall steel ball device. The ball weighed 1 kg, and five impact energy levels were set by adjusting the height: 0.2 J, 0.4 J, 0.6 J, 0.8 J, and 1 J. Each grid intersection point within the monitoring area was defined as an impact training point, resulting in a total of 359 impact training points within the monitoring area. Impacts of different energies were sequentially applied to all impact training points, and the impact stress wave signals received by the four piezoelectric sensors were continuously acquired using a data acquisition system with a sampling rate of 200 kHz.
[0073] The method of this invention is verified using an online monitoring impact event with an impact location of (325 mm, 375 mm) and an impact energy of 0.2 J as an example. Figure 7 The image shows the Monte Carlo sampling results for a particle size of 5000 and 50 iterations. The impact probability imaging localization and probabilistic impact energy identification results obtained from the Monte Carlo sampling are shown below. Figure 8 and Figure 9 As shown, the predicted impact location is (326.2 mm, 375.6 mm), and the predicted impact energy is 0.19 J. The positioning error is 1.3 mm, and the energy identification error is only 0.01 J, which meets the requirements of engineering applications.
[0074] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.
Claims
1. A probabilistic impact location and energy identification method based on approximate Bayesian computation, characterized in that: include Step 1: Using multiple sensors, the first impact response signal of a known impact with a known impact location and known impact energy is collected offline and the first feature data is extracted. The first feature data includes the time difference of arrival and the maximum amplitude of the envelope. Step 2: Design a neural network structure and train the neural network, using the known impact location and known impact energy as the input layer of the neural network, and the first feature data as the output layer of the neural network, to train the neural network to fit the relationship between the known impact location and the known impact energy and the first feature data; Step 3: Acquire the second impact response signal of the unknown impact online and extract the second feature data from the second impact response signal; Step 4: Construct a Bayesian inference model without likelihood function using the two types of second feature data, namely the arrival time difference and the maximum amplitude of the envelope of the unknown impact, which are monitored online, and the neural network. Step 5: Select the distance function between the first feature data output by the neural network and the second feature data monitored online, and use the sequence Monte Carlo sampling algorithm to sample the unknown impact location parameters and unknown impact energy parameters in the Bayesian inference model without likelihood function; Step 6: Fit the posterior distributions of the impact location and impact energy parameters obtained by the Monte Carlo sampling algorithm of the sequence using a normal distribution, so as to realize probabilistic impact localization and impact energy identification.
2. The probabilistic impact location and energy identification method based on approximate Bayesian computation according to claim 1, characterized in that: Step 1 includes deploying a sensor network on the structure, setting training points and impact energy, using the corresponding impact energy to sequentially impact all training points, and using a data acquisition system to acquire the first impact response signals collected by each sensor in the sensor network in an offline state, and extracting the arrival time difference between different first impact response signals and the maximum amplitude of the envelope of each first impact response signal as the first feature data.
3. The probabilistic impact location and energy identification method based on approximate Bayesian computation according to claim 1, characterized in that: Step 2 includes using the known impact location and known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, selecting the number of hidden layers and activation function, and training the neural network to fit the relationship between the known impact location and the known impact energy and the first feature data.
4. The probabilistic impact location and energy identification method based on approximate Bayesian computation according to claim 1, characterized in that: Step 3 includes, under online monitoring conditions, acquiring the second impact response signal of each unknown impact with unknown impact location and unknown impact energy through each of the sensors, and extracting the arrival time difference of the second impact response signals from different sensors and the maximum amplitude characteristics of the envelope of each second impact response signal.
5. The probabilistic impact location and energy identification method based on approximate Bayesian computation according to claim 1, characterized in that: Step 5 includes selecting the distance function between the first feature data output by the neural network and the second feature data monitored online, and using a sequence Monte Carlo sampling algorithm to sample the unknown impact location parameters and unknown impact energy parameters.