Probabilistic impact position and energy identification method based on approximate Bayesian calculation

Abstract

The invention discloses a probabilistic impact position and energy identification method based on approximate Bayesian calculation. The method comprises an off-line training stage and an on-line monitoring stage, in the off-line training stage, a neural network is used for fitting the relationship among the impact position, the impact energy, the time difference of arrival and the maximum envelope amplitude; in the online monitoring stage, a proper distance function is selected, data generated by the neural network and online monitoring data are used for approximate Bayesian calculation, posterior probability distribution of impact positions and impact energy parameters is obtained by adopting a sequence Monte Carlo sampling algorithm, and finally probabilistic impact positioning and impact energy recognition are achieved. The method is verified in a 500mm * 500mm composite material plate-shaped structure, and the result shows that the method can carry out probabilistic impact positioning and impact energy under the condition of using a small number of sensors and has relatively high precision.

Description

Technical Field

[0001] The present invention relates to the field of structural health monitoring, and in particular to a probabilistic impact position and energy identification method based on approximate Bayesian calculation. Background Art

[0002] Engineering structures will inevitably be impacted by external objects during service and transportation, which will cause damage to the structure and directly threaten the safety and integrity of the structure. Manual regular inspection of the structure is time-consuming, labor-intensive, and has high maintenance costs. Therefore, real-time online impact monitoring of engineering structures is of great significance for maintaining the health and safety of the structure. Structural impact monitoring technology uses sensors to collect impact stress wave signals, uses signal processing methods to extract features, and uses specific algorithms to achieve impact location and impact energy identification. Bayesian reasoning plays an important role in structural health monitoring (SHM). It mainly uses monitoring data to update probability models to invert unknown parameters related to structural health monitoring. An important component of Bayesian reasoning is the calculation of likelihood functions. For impact monitoring systems, due to the complexity of the structure, boundary reflections, and noise interference, in many cases, it is impossible to derive the analytical expression of the likelihood function that associates monitoring data with impact position and energy. Summary of the invention

[0003] The purpose of this application is to address the deficiencies in the prior art 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, which makes the Bayesian inference probability framework applicable to the impact monitoring system.

[0004] To this end, some embodiments of the present application propose a probabilistic impact position and energy identification method based on approximate Bayesian calculation, which includes step 1, using multiple sensors to collect offline the first impact response signal of a known impact with a known impact position and a known impact energy and extract first feature data; step 2, designing a neural network structure and training the neural network, using the known impact position and the known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data; step 3, collecting online the second impact response signal of an unknown impact and extracting the first feature data for the second impact response signal; step 4, designing a neural network structure and training the neural network, using the known impact position and the known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data; step 5, collecting the second impact response signal of an unknown impact online and extracting the first feature data for the second impact response signal; step 6, designing a neural network structure and training the neural network, using the known impact position and the known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data; step 7, collecting the second impact response signal of an unknown impact online and extracting the first feature data for the second impact response signal; step 8, designing a neural network structure and training the neural network, using the known impact position and the known impact energy as the output layer of the neural network, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data; step 9, The second characteristic data is extracted from the impact response signal; step 4, using the two types of second characteristic data of the unknown impact arrival time difference and the envelope maximum amplitude monitored online and the neural network to build a Bayesian inference model without a likelihood function; step 5, selecting the distance function between the first characteristic data output by the neural network and the second characteristic data monitored online, and using the sequential Monte Carlo sampling algorithm to sample the unknown impact position parameters and unknown impact energy parameters in the Bayesian inference model without a likelihood function; and step 6, using the normal distribution to fit the posterior distribution of the impact position and impact energy parameters sampled by the sequential Monte Carlo sampling algorithm, respectively, to achieve probabilistic impact positioning and impact energy identification.

[0005] In some embodiments, step 1 includes deploying a sensor network on the structure, setting training points and impact energy, using corresponding impact energy to impact all training points in turn, obtaining 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 characteristic data.

[0006] In some embodiments, step 2 includes using the known impact position and the known impact energy as the input layer of the neural network, using the known feature data as the output layer of the neural network, selecting the number of hidden layers and the activation function, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data.

[0007] In some embodiments, step 3 includes obtaining, under online monitoring conditions, the second impact response signal of each unknown impact with an unknown impact position and an unknown impact energy through each sensor, and extracting the arrival time difference of the second impact response signals of different sensors and the maximum amplitude characteristics of the envelope of each second impact response signal.

[0008] In some embodiments, step 4 includes, according to Bayesian theorem, using the two types of second characteristic data of the unknown impact's arrival time difference and envelope maximum amplitude monitored online and the neural network to construct a Bayesian inference model without likelihood function;

[0009] In some embodiments, step 5 includes selecting a distance function between the known feature data output by the neural network and the second feature data monitored online, and sampling the unknown impact position parameters and unknown impact energy parameters using a sequential Monte Carlo sampling algorithm.

[0010] In some embodiments, step 6 includes fitting the posterior distributions of the unknown impact position parameters and unknown impact energy parameters sampled by the sequential Monte Carlo sampling algorithm using normal distribution, respectively, so as to perform probabilistic impact positioning and impact energy identification.

[0011] Due to the adoption of the above technical solution, the probabilistic impact position and energy identification method based on approximate Bayesian calculation provided by the present invention has the following beneficial technical effects:

[0012] First, the method of the present invention uses a neural network to fit the relationship between the impact position, impact energy and arrival time difference, and maximum envelope amplitude characteristic data, laying a foundation for the impact position and energy identification based on approximate Bayesian calculation without a likelihood function.

[0013] Second, the method of the present invention uses the approximate Bayesian calculation-sequential Monte Carlo method to achieve probabilistic impact location and impact energy identification, which has higher reliability than other deterministic impact location and impact energy identification methods.

[0014] Third, the method of the present invention uses a neural network to assist in the identification of impact position and energy based on approximate Bayesian calculations. Compared with traditional physical methods, it can complete more complex impact monitoring tasks and requires fewer sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1 Schematic diagram of the flow of the probabilistic impact position and energy identification method based on approximate Bayesian calculation according to the present invention.

[0017] Figure 2FIG. 1 is a schematic diagram of a sensor network in the method according to the present invention.

[0018] Figure 3A Schematic diagram of an impact stress wave signal according to the present invention.

[0019] Figure 3B FIG. 1 is a schematic diagram of the arrival time and signal envelope amplitude measurement according to the present invention.

[0020] Figure 4 Schematic diagram of the Matlab neural network fitting toolbox according to the present invention.

[0021] Figure 5 Schematic diagram of the flow chart of the sequential Monte Carlo sampling algorithm according to the present invention.

[0022] Figure 6 This is a schematic diagram of the arrangement of a composite material plate, sensors and training points according to an embodiment of the present invention.

[0023] Figure 7 Schematic diagram of a sequential Monte Carlo sampling result according to an embodiment of the present invention.

[0024] Figure 8 Schematic diagram of impact probability imaging positioning result according to an embodiment of the present invention.

[0025] Fig. 9 Schematic diagram of a probabilistic impact energy identification result according to an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention:

[0027] like Figure 1 As shown, some embodiments of the present application propose a probabilistic impact position and energy identification method based on approximate Bayesian calculation, and the method specifically includes the following steps: Step 1, offline collection of impact signals and feature extraction of known impacts;

[0028] Step 2, designing a neural network structure and training the neural network;

[0029] Step 3, online collection of impact signals and feature extraction;

[0030] Step 4, construct a Bayesian inference model without likelihood function;

[0031] Step 5, select distance function and sequential Monte Carlo sampling;

[0032] Step 6: Probabilistic impact location and impact energy identification.

[0033] Specifically, step 1 is to collect the impact signal and extract the features offline, such as Figure 2 As shown in FIG. 1 , the sensor network is arranged on the monitoring structure, the training points and the impact energy are set, the corresponding impact energy is used to impact all the training points in turn, and the impact response signal is obtained by using the data acquisition system in an offline state. The typical impact response signal is shown in FIG. Figure 3A As shown. In this step, the sensors forming the sensor network may be piezoelectric sensors, fiber grating sensors and acceleration sensors. The sensor network may be composed of a first sensor P1, a second sensor P2, a third sensor P3 and a fourth sensor P4 arranged in the boundary area of ​​the monitoring structure. For an impact with the training point as the impact source IS, each sensor will receive an impact response signal, such as an impact stress wave signal, such as Figure 2 As shown in FIG, the first sensor P1 receives the first impulse response signal W1 , the second sensor P2 receives the second impulse response signal W2 , the third sensor P3 receives the third impulse response signal W3 , and the fourth sensor P4 receives the fourth impulse response signal W4 .

[0034] The Fourier transform is used to observe the spectral components of each impulse response signal, and the wavelet transform is used to extract the narrowband Lamb wave signal with the maximum frequency component. The complex Morlet continuous wavelet transform of the impulse response signal S(t) is defined as follows:

[0035]

[0036] Among them, a is the expansion factor, b is the translation factor, "<>" represents the inner product, "" represents the conjugate, and ψ(t) is the complex Morlet mother wavelet function:

[0037]

[0038] In the formula, f c is the center frequency of the mother wavelet, f b is the mother wavelet bandwidth.

[0039] Adjust the scaling factor a and the mother wavelet bandwidth f b , complex Morlet wavelet transform is used to extract the narrowband Lamb wave signal with the largest frequency component in each impulse response signal. Figure 3B As shown, the Hilbert transform is used to extract the arrival time and envelope maximum amplitude of the narrowband Lamb wave signal with the largest frequency component. The arrival time of the narrowband Lamb wave signal with the largest frequency component in the impulse response signals of different sensors is subtracted to obtain arrival time difference feature data.

[0040] Step 2: design a neural network and train the neural network.

[0041] like Figure 4 As shown, the structure of the back propagation (BP) neural network is designed using the neural network fitting toolbox provided by Matlab. The impact position and energy are used as the input layer of the neural network, and the arrival time difference and the maximum amplitude of the envelope are used as the output layer of the neural network. The appropriate number of hidden layers is selected. In this embodiment, the number of hidden layers is 10, and it can also be 8, 9, 11, 12, etc., and the Sigmod activation function is used:

[0042]

[0043] The Levenberg-Marquardt algorithm is used to train the neural network, and the relationship between the impact position and impact energy and the two types of characteristic data, namely, the arrival time difference and the maximum amplitude of the envelope, is fitted.

[0044] Step 3: Online impact signal collection and feature extraction.

[0045] Under the online monitoring state, the impact signal of unknown impact position and impact energy is obtained, and the arrival time difference and envelope maximum amplitude characteristics are extracted according to the same signal processing method as step 1.

[0046] Step 4: Construct a Bayesian inference model without likelihood function.

[0047] Bayesian inference continuously updates unknown parameters through new observation data to obtain the posterior distribution of unknown parameters. The calculation formula is as follows:

[0048]

[0049] Where data is the arrival time difference and envelope maximum amplitude characteristic data obtained by online monitoring. θ is the unknown parameter: impact position x coordinate x I , impact position y coordinate parameter y I and impact energy parameter e I p(data|θ) is the likelihood function, which represents the probability of observing data data under given parameters θ. p(θ) is the prior distribution of the unknown parameters, which can be regarded as a uniform distribution when no prior information is available.

[0050] However, for the impact identification problem, in many cases it is impossible to derive the analytical expression of the likelihood function of the parameters. The approximate Bayesian calculation method directly randomly samples the parameters, which can effectively avoid this problem. If the sampling meets the specified tolerance conditions, it is accepted. Otherwise, the sampling is rejected. By repeatedly performing a large number of sampling simulations, the approximate posterior distribution p of each parameter such as the impact position coordinate parameter and the impact energy parameter can be obtained. ε (θ|data):

[0051]

[0052] Among them, data and data* are the characteristic data obtained by online monitoring and the parameter θ n,t Substitute the feature data generated by the neural network fitting, Δ(data,data * ) is a distance function used to calculate the gap between two data sets. ε is a tolerance. Using an adaptive tolerance can ensure that the effective operation of the algorithm will not result in a too low particle acceptance rate. Therefore, in this embodiment, the mean value of the gap between the previous generation of particles is used as the adaptive tolerance. n,k For samples that meet the tolerance ε condition, θ * is a sample from the random sampling population, and N is the total number of particles accepted.

[0053] Therefore, an approximate Bayesian inference model without a likelihood function can be constructed using the feature data of online monitoring and the feature data generated by neural network fitting.

[0054] Step 5: Select distance function and sequential Monte Carlo sampling.

[0055] Choose a suitable distance function Δ(data,data * ). For example, the distance function Δ(data,data) can be calculated using the Euler distance formula. * ):

[0056]

[0057] Among them, L is the data set data and data * Length.

[0058] According to Figure 5 The sequential Monte Carlo sampling algorithm shown is used to sample unknown impact position and impact energy parameters, including the steps of:

[0059] Step S51, determine the particle scale Z, the number of iterations K, k=1.

[0060] Step S52, initializing particle θ according to p(θ) i,k , i=1.

[0061] Step S53, the particle θ i,k Substitute the neural network to fit the generated data data * .

[0062] Step S54, if Δ(data,data * )≤ε, accept θ i,k , assign particle weights: N is the total number of particles accepted; otherwise, θ is discardedi,k . i=i+1.

[0063] Step S55, if i>Z, normalize the weight: Otherwise return to step S53.

[0064] Step S56: if k>K, obtain the approximate posterior distribution p ε (θ|data); otherwise k=k+1, return to step S52.

[0065] Step 6: Probabilistic impact location and impact energy identification.

[0066] The posterior distribution of the impact position and impact energy parameters obtained by the sequential Monte Carlo sampling algorithm are fitted using normal distribution to achieve probabilistic impact location and impact energy identification. Assume that after sampling, the means of the impact position x-coordinate, y-coordinate and impact energy posterior distribution are and The variances are and The correlation coefficient of the posterior distribution of the x-coordinate and y-coordinate of the impact position is ρ. Finally, the probability distribution of the impact position in the monitoring area is expressed as the standard form of a two-dimensional normal distribution:

[0067]

[0068] Where: is the impact position parameter X=(x I ,y I ) is the mean vector of the matrix; Σ is the covariance matrix: det(Σ) is the determinant of the covariance matrix of Σ.

[0069] The probability distribution of impact energy in the monitoring area is expressed as the standard form of one-dimensional normal distribution:

[0070]

[0071] Example:

[0072] The monitoring object of this embodiment is a carbon fiber / epoxy composite material plate structure, and an impact test study is performed on the structure. Figure 6 The figure shows the schematic diagram of the composite material board, sensors and training point settings. The size of the composite material board is 500mm×500mm×2mm (length×width×thickness), the material is T300 woven cloth, and the ply method is [0 / 90] 3s. A total of four piezoelectric sensors are arranged on the surface of the composite material plate. The sensors used are P-51 piezoelectric ceramic discs with a diameter of 8mm and a thickness of 0.25mm. The sensors are numbered P1, P2, P3, and P4, and the spacing is 360mm. The left and right ends of the plate are fixed with clamps, and the composite material plate is subjected to an impact test using a steel ball free-fall device. The weight of the ball is 1kg, and five levels of impact energy are set by adjusting the height, which are 0.2J, 0.4J, 0.6J, 0.8J and 1J respectively. Each grid intersection in the monitoring area is defined as an impact training point, so there are a total of 359 impact training points in the monitoring area. Impacts of different energies are carried out in turn at all impact training points, and the impact stress wave signals received by the four piezoelectric sensors are continuously collected using a data acquisition system with a sampling rate of 200kHz.

[0073] Taking the online monitoring impact event with the impact position of (325mm, 375mm) and the impact energy of 0.2J as an example, the method of the present invention is verified. Figure 7 As shown in the figure, it is the result of the sequential Monte Carlo sampling with a particle size of 5000 and an iteration number of 50. The impact probability imaging positioning and the probabilistic impact energy identification results obtained by the sequential Monte Carlo sampling are shown in Figure 8 and Fig. 9 As shown in the figure, the predicted impact position is (326.2mm, 375.6mm), and the predicted impact energy is 0.19J. The positioning error is 1.3mm, and the energy recognition error is only 0.01J, which can meet the needs of engineering applications.

[0074] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. Probabilistic impact location and energy identification method based on approximate Bayesian calculation, Features: include Step 1, using a plurality of arranged sensors to respectively collect offline first impact response signals of known impacts with known impact positions and known impact energies and extract first characteristic data; Step 2, designing a neural network structure and training the neural network, using the known impact position and the known impact energy as the input layer of the neural network, using the first feature data as the output layer of the neural network, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data; Step 3, online collecting a second impulse response signal of the unknown impulse and extracting second characteristic data from the second impulse response signal; Step 4, using the online monitored arrival time difference and envelope maximum amplitude of the unknown shock and two types of second characteristic data and the neural network to construct a Bayesian inference model without likelihood function; Step 5, selecting a distance function between the first feature data output by the neural network and the second feature data monitored online, and sampling the unknown impact position parameters and the unknown impact energy parameters in the Bayesian inference model without likelihood function using a sequential Monte Carlo sampling algorithm; Step 6, using normal distribution to fit the posterior distribution of the impact position and impact energy parameters sampled by the Sequential Monte Carlo Sampling Algorithm, respectively, to achieve probabilistic impact positioning and impact energy identification.

2. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 1 includes deploying a sensor network on the structure, setting training points and impact energy, using corresponding impact energy to impact all training points in turn, obtaining 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 characteristic data.

3. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 2 includes using the known impact position and the known impact energy as the input layer of the neural network, using the known feature data as the output layer of the neural network, selecting the number of hidden layers and the activation function, and training the neural network to fit the relationship between the known impact position and the known impact energy and the first feature data.

4. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 3 includes acquiring the second impact response signal of each unknown impact with unknown impact position and unknown impact energy through each sensor under an online monitoring state, and extracting the arrival time difference of the second impact response signals of different sensors and the maximum amplitude feature of the envelope of each second impact response signal.

5. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 4 includes, according to the Bayesian theorem, using the two types of second characteristic data of the unknown impact's arrival time difference and envelope maximum amplitude monitored online and the neural network to construct a Bayesian inference model without likelihood function.

6. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 5 includes selecting a distance function between the known characteristic data output by the neural network and the second characteristic data monitored online, and sampling the unknown impact position parameters and the unknown impact energy parameters using a sequential Monte Carlo sampling algorithm.

7. The probabilistic impact position and energy identification method based on approximate Bayesian calculation according to claim 1, Features: The step 6 includes fitting the posterior distributions of the unknown impact position parameters and the unknown impact energy parameters sampled by the sequential Monte Carlo sampling algorithm using normal distribution, respectively, so as to perform probabilistic impact positioning and impact energy identification.

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