Structural Damage Diagnosis Method Based on Gaussian Mixture Model and Nested Transmission Distance

Abstract

The present invention discloses a structural damage diagnosis method based on a Gaussian mixture model and a nested transmission distance, belonging to the field of structural health monitoring. The method includes tracking the probability distributions of guided wave signal features of a structure in a healthy state and in damaged states with different degrees through a Gaussian mixture model, proposing a nested transmission distance, taking the nested transmission distance between the Gaussian mixture model of the signal features of the structure in damaged states with different degrees and the reference Gaussian mixture model of the structure in the healthy state as a damage quantification index, establishing a quantitative relationship between the nested transmission distance and the damage degree, and further estimating the damage of the target structure. The structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance of the present invention realizes a Gaussian mixture model difference metric with good linearity and accuracy, and can achieve reliable structural damage quantification evaluation under the influence of the uncertainty of time-varying service conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and particularly to a structural damage diagnosis method based on a Gaussian mixture model and nested transmission distances. Background Art

[0002] Structural health monitoring technology has a wide range of application prospects in improving the use safety and reliability of structures; at the same time, structural health monitoring technology replaces regular maintenance with on-demand maintenance, saving the maintenance cost of structures. With the increasing demand for structural health monitoring, a variety of health monitoring technologies have been developed based on combinations of different sensors, systems, and diagnostic methods, such as vibration monitoring, strain monitoring, guided wave monitoring, acoustic emission monitoring, etc. Among these technologies, guided wave monitoring technology is widely used due to its characteristics of long propagation distance, large monitoring range, and sensitivity to small damages.

[0003] In structural health monitoring, structural damage quantification diagnosis technology that can diagnose the degree of structural damage has very important application value. However, in actual engineering applications, time-varying service conditions such as load, temperature, humidity, and boundary conditions directly affect the reliability of the results of structural damage quantification diagnosis. Guided wave monitoring technology mainly conducts damage diagnosis by monitoring the change degree of the signal compared with the reference signal on a healthy structure. During actual monitoring, signal features such as signal amplitude difference, energy difference, and correlation moment are used to measure the change degree of the guided wave signal, and then the severity of structural damage is evaluated according to the magnitudes and change situations of these signal features. However, in addition to damage, time-varying service conditions also cause changes in signals and their features, and the signal changes caused by damage and time-varying service conditions are mixed with each other, making it difficult to reliably evaluate structural damage. Therefore, suppressing the uncertain influence of time-varying service conditions is crucial for achieving reliable guided wave monitoring.

[0004] To achieve reliable damage diagnosis under the influence of uncertainties in time-varying service conditions, in the existing technologies, relationship models between signal features and damage degrees are generally established through methods such as Gaussian regression, support vector machines, and neural networks to achieve quantitative diagnosis of structural damage. However, due to the influence of complex time-varying service conditions, the relationship models in these methods are complex, the training process has a large amount of calculations, and a large number of training data with known damage degree labels are required. To solve this problem, one method is to characterize the random influence of time-varying conditions through the Gaussian mixture model of signal features and diagnose structural damage through the change of the Gaussian mixture model. For example, the literature (Chakraborty D, Kovvali N, Papandreou-Suppappola A, et al. An adaptive learning damage estimation method for structural health monitoring. Journal of Intelligent Material Systems and Structures, 2015, 26(2): 125-143.) proposed to combine the change of Gaussian components contained in the Gaussian mixture model with the structural physical crack propagation model to achieve quantitative diagnosis of the crack length of the aluminum plate structure under the influence of temperature; the literature (Rogers T J, Worden K, Fuentes R, et al. A Bayesian non-parametric clustering approach for semi-supervised structural health monitoring. Mechanical Systems and Signal Processing, 2019, 119: 100-119.) proposed to use the appearance of new Gaussian components in the Gaussian mixture model of signal features as a warning of crack propagation and combine non-destructive testing methods to measure the actual structural crack length. However, in the Gaussian mixture models relied on by these methods, new Gaussian components will also appear due to the change of the signal feature distribution caused by the change of service conditions, so the reliability of diagnosing structural damage by these methods needs to be improved. Another method is to evaluate the state of the structure according to the difference measurement methods such as Kullback Leibler divergence, Mahalanobis squared distance, and normalized probability similarity between Gaussian mixture models. However, these measurement methods cannot linearly measure the change of Gaussian mixture models and are mostly used for early warning of structural damage.

[0005] In summary, although the Gaussian mixture model and its dissimilarity measure are effective means to suppress the influence of uncertainty, the existing dissimilarity measurement methods for Gaussian mixture models still need to be optimized, and there is a lack of an effective structural damage quantification diagnosis method based on the dissimilarity measure of Gaussian mixture models. Summary of the Invention

[0006] To solve the above problems, the present invention provides a structural damage diagnosis method based on Gaussian mixture models and nested transportation distances, effectively realizing reliable quantitative diagnosis of structural damages such as cracks under the influence of uncertainty in time-varying service conditions.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] The structural damage diagnosis method based on Gaussian mixture models and nested transportation distances of the present invention includes:

[0009] Step S11: Obtain signal feature samples of training structural members;

[0010] The specific steps of step S11 include:

[0011] Step S111: Under a simulated time-varying service environment, collect guided wave signals of the training structural members at different damage degrees;

[0012] Step S112: Determine the damage degree corresponding to each guided wave signal on each training structural member;

[0013] Step S113: Extract damage factors to obtain the signal feature samples;

[0014] Step S12: Randomly select n signal feature samples from the signal feature samples obtained when all the training structural members are in a healthy state to form a reference sample set, where n is a natural number greater than 0;

[0015] Step S13: Based on the reference sample set, establish a reference Gaussian mixture model corresponding to the reference sample set through a density peak clustering probability modeling algorithm;

[0016] Step S14: Construct training sample sets under different damage degrees;

[0017] Step S15: Based on the training sample sets, establish corresponding training Gaussian mixture models through the density peak clustering probability modeling algorithm;

[0018] Step S16: According to the calculation method of the nested transportation distance, calculate the training nested transportation distance NTD between the training Gaussian mixture model of each training structural member and the reference Gaussian mixture model;

[0019] Step S17, obtain the damage level L corresponding to the training nested transmission distance NTD;

[0020] Step S18, establish a damage quantification model through polynomial fitting.

[0021] In a specific embodiment, the expression of the damage quantification model is as follows:

[0022] L(NTD, w) = w0 + w1NTD + w2NTD 2 +...+ w p NTD p ,

[0023] where L is the damage level, NTD is the training nested transmission distance, {w i |i = 1, 2,..., p} are the coefficients of the polynomial, and p is the order of the polynomial;

[0024] In a specific embodiment, the coefficients {w i |i = 1, 2,..., p} of the polynomial can be obtained by the least squares method based on the training nested transmission distance NTD and the damage level L.

[0025] In a specific embodiment, the order p can be set to 3.

[0026] The above-mentioned structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance further includes

[0027] Step S21, in the monitoring state, collect n signal feature samples under the time-varying service state of the target structural member;

[0028] Step S22, based on the n signal feature samples of the target structural member, form a monitoring sample set;

[0029] Step S23, based on the monitoring sample set, establish a corresponding monitoring Gaussian mixture model through the density peak clustering probability modeling algorithm;

[0030] Step S24, according to the calculation method of the nested transmission distance, calculate the monitoring nested transmission distance NTD' between the monitoring Gaussian mixture model and the reference Gaussian mixture model;

[0031] Step S25, substitute the monitoring nested transmission distance NTD' into the damage quantification model to calculate the damage level of the target structural member.

[0032] The above density peak clustering probability modeling algorithm includes

[0033] Step S31, based on the sample set O = {o1,..., o i ,…, o n}, estimating the probability density ρ of each sample o in it through Gaussian kernel density estimation i as follows: i The calculation formula is as follows:

[0034]

[0035] where n is the number of samples o in the sample set O, the dimension of the sample o is D, d is the Euclidean distance between the sample o in the sample set O and o, d is the truncation distance, and the expression of the truncation distance d is as follows: i The sample o i has a dimension of D, d ij is the sample o in the sample set O i and o j The Euclidean distance between them, d c is the truncation distance, and the truncation distance d c The expression is as follows:

[0036]

[0037] where d Z (o i ) is the distance between the sample o i and the Zth sample closest to the distance o i . In a specific embodiment, Z takes the value of represents the largest integer not exceeding x;

[0038] Step S32, calculate the minimum distance δ of each sample o i The calculation formula is as follows: i The calculation formula is as follows:

[0039]

[0040] Step S33, calculate the product λ of the probability density ρ of each sample o i and the minimum distance δ i The calculation formula is as follows: i The product λ i The calculation formula is as follows:

[0041] λ i =ρ i ×δ i ;

[0042] Step S34, calculate the threshold λ of the product λ i The calculation formula is as follows: min The calculation formula is as follows:

[0043]

[0044] where is the probability density ρ of all samples o in the sample set O i as follows: iThe mean value;

[0045] Step S35: Select the samples that satisfy the following inequality as class centers, and cluster the remaining samples in the sample set O into the class to which the nearest class center belongs based on the nearest neighbor principle, to obtain an initial clustering result;

[0046] λ i > λ min & δ i > d c ;

[0047] Step S36: If there is a class in the initial clustering result that contains fewer samples than the sample dimension D, remove this class and the corresponding samples to obtain a final clustering result. At this time, the total number of samples is n';

[0048] Step S37: Based on the final clustering result, calculate the mean value and covariance matrix of each class, and at the same time calculate the ratio of the number of samples contained in each class to the total number of samples n' to obtain the weight value corresponding to each class;

[0049] Step S38: Use the mean value, covariance matrix, and weight value of each class obtained in Step S37 as initialization parameters, and use the expectation maximization algorithm to establish the Gaussian mixture model Ф of the sample set O. The probability density function expression of the Gaussian mixture model Ф is as follows:

[0050]

[0051] where K is the number of Gaussian components in the Gaussian mixture model Ф, k = 1, 2,..., K, w k is the weight value of the k-th Gaussian component, is the k-th Gaussian component, The probability density function expression is as follows:

[0052]

[0053] where μ k and Σ k are respectively the mean value and covariance matrix, |·| is the determinant of the matrix, and T represents the matrix transpose symbol.

[0054] The above calculation method of the nested transmission distance includes,

[0055] Step S41: Denote the two Gaussian mixture models as Φ 0 and Φ 1 , and denote the Gaussian components in the Gaussian mixture model Φ 0 as i = 1, 2,..., K 0 K 0For the Gaussian mixture model Φ 0 the number of Gaussian components in; the Gaussian mixture model Φ 1 the Gaussian components in are denoted as j = 1, 2, …, K 1 , K 1 For the Gaussian mixture model Φ 1 the number of Gaussian components in, the Gaussian mixture model Φ 0 the Gaussian components in and the Gaussian mixture model Φ 1 the Gaussian components in the optimal transport distance between is calculated as follows:

[0056]

[0057] where and are respectively the mean and covariance matrix of the Gaussian component 0 in the Gaussian mixture model Φ , and are respectively the mean and covariance matrix of the Gaussian component 1 in the Gaussian mixture model Φ ;

[0058] Step S42, the nested transport distance NTD between the Gaussian mixture model Φ 0 and the Gaussian mixture model Φ 1 is calculated as follows:

[0059]

[0060] where is and the optimal transport distance between, is the joint distribution when the Gaussian components and are two individuals, φ ∈ Π(w 0 , w 1 ) indicates that the joint distribution obeys the marginal constraints and are the weights of the Gaussian components in the Gaussian mixture model Φ 0 , are the weights of the Gaussian components in the Gaussian mixture model Φ 1 . In a specific embodiment, linear programming can be used to find the minimum solution of under this marginal constraint, and take the minimum solution as the Gaussian mixture model Φ0 and the Gaussian mixture model Φ 1 of the nested transmission distance NTD.

[0061] In a specific embodiment, the damage factor DI 1,i is calculated as follows:

[0062]

[0063]

[0064]

[0065] where t0 and t1 are the start time and end time of the intercepted guided wave signal segment respectively, τ is the time lag parameter, and r si is the cross-correlation between the guided wave signal f i (t) and the reference signal f s (t), and r ss (τ) is the cross-correlation of the reference signal f s (t) with itself. In a specific embodiment, the reference signal f s (t) is the average signal between the two signals first obtained for each training structural member.

[0066] In a specific embodiment, the damage factor DI 2,i is calculated as follows:

[0067]

[0068] where t0 and t1 are the start time and end time of the intercepted guided wave signal segment respectively, f i (t) is the guided wave signal, and f s (t) is the reference signal.

[0069] In a specific embodiment, the expression of the signal feature sample o i is as follows,

[0070] o i = [DI 1,i , DI 2,i T ,

[0071] where the superscript T is the matrix transpose symbol.

[0072] Advantageous effects: The structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance of the present invention realizes a good difference metric of the Gaussian mixture model in terms of linearity and accuracy; it can achieve a reliable quantitative assessment of structural damage under the influence of the uncertainty of time-varying service conditions; the implementation process is simple and efficient. ​

[0073] To make the above features and advantages of the invention more obvious and understandable, specific embodiments are given below and will be described in detail in conjunction with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 Schematic diagram of the positions of the monitored structure and the piezoelectric sensor in a specific embodiment of the present invention.

[0075] Figure 2 Flowchart of the structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance of the present invention.

[0076] Figure 3 For Figure 2 Specific step flowchart of step S11 in

[0077] Figure 4 Schematic diagram of the distribution of signal feature samples on a training structural member under different crack lengths.

[0078] Figure 5 Schematic diagram of the signal feature distribution in the reference sample set O0 and the Gaussian component distribution of the reference Gaussian mixture model.

[0079] Figure 6 Schematic diagram of the damage quantification model curve based on the third-order polynomial and the curves of the training structural members S1 to S5.

[0080] Figure 7 Schematic diagram of the monitored Gaussian mixture model corresponding to the signal feature samples collected from the target structural member at different crack lengths under the time-varying service state, Figure 7 In which (a) is a schematic diagram of the monitored Gaussian mixture model corresponding to the signal feature samples collected from the target structural member without cracks under the time-varying service state, Figure 7 In which (b) is a schematic diagram of the monitored Gaussian mixture model corresponding to the signal feature samples collected from the target structural member with a crack length of 2 mm under the time-varying service state, Figure 7 In which (c) is a schematic diagram of the monitored Gaussian mixture model corresponding to the signal feature samples collected from the target structural member with a crack length of 4 mm under the time-varying service state, Figure 7 In which (d) is a schematic diagram of the monitored Gaussian mixture model corresponding to the signal feature samples collected from the target structural member with a crack length of 6 mm under the time-varying service state.

[0081] Figure 8 Schematic diagram of the calculation results of the monitored nested transmission distance during the monitoring process.

[0082] Figure 9 Schematic diagram of the estimated crack length, actual crack length, and absolute error of the target structural member.

[0083] In the drawings, like reference numerals refer to like elements. Detailed Description of the Invention

[0084] For the purpose of making the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0085] In this specific embodiment, a random load is used as a time-varying service condition, a lug is used as the structure to be monitored, the crack length at the hole edge of the lug is regarded as the degree of damage, and combined with the guided wave damage monitoring technology, the implementation process of the method of the present invention is specifically described by taking the quantitative diagnosis of the crack length at the hole edge under the time-varying service condition of a random load as an example.

[0086] Figure 1 It is a schematic diagram of the structure to be monitored and the positions of piezoelectric sensors in a specific embodiment of the present invention. As Figure 1 shown, the structure 1 to be monitored is a lug structure with a width of 90 mm, a length of 245 mm, and a radius of 45 mm for its semi-circular part. There is a simulated damage on the structure 1 to be monitored, and the simulated damage is an ear hole 11 with a diameter of 25 mm. There is a crack 12 at the hole edge of the ear hole 11. Piezoelectric sensors PZT1 and PZT2 are arranged beside the ear hole 11 to monitor the crack 12 at the hole edge. The piezoelectric sensor PZT1 serves as the excitation element of the guided wave signal, and the piezoelectric sensor PZT2 serves as the response element of the guided wave signal. The propagation direction of the crack 12 at the hole edge is vertically downward. The distance from the center of the piezoelectric sensor PZT1 to the lower edge of the structure 1 to be monitored is 25 mm, the distance from the center of the piezoelectric sensor PZT1 to the diameter of the semi-circular part is 120 mm. The piezoelectric sensor PZT2 is horizontal with the piezoelectric sensor PZT1 and is located in the semi-circular part. The distance from the center of the piezoelectric sensor PZT2 to the center of the piezoelectric sensor PZT1 is 140 mm.

[0087] Figure 2 The flowchart of the structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance of the present invention is shown, which specifically includes:

[0088] Step S11, obtaining the signal feature samples of the training structural members. As Figure 3 shown, the step S11 specifically includes,

[0089] Step S111, in a simulated time-varying service environment, collect guided wave signals of training structural members at different damage degrees. More specifically, use 5 lug structures as shown in Figure 1 as training structural members. The target structural member is of the same configuration as the lug structure shown in Figure 1 . Under random loads, conduct guided wave monitoring tests on 5 training structural members respectively. During the propagation process of the structural crack 12, collect guided wave signals at the same time interval continuously. For each training structural member, the first 30 guided wave signals are all obtained when the structure is healthy, that is, when the structural crack 12 has not propagated.

[0090] Step S112, determine the structural crack length corresponding to each guided wave signal on each training structural member, that is, the damage degree. More specifically, during the test process of each training structural member, use an electron microscope to observe and measure the actual length of the structural crack 12. Whenever the structural crack 12 propagates 1 mm, record the order of the current guided wave signal. When the structural crack 12 of each training structural member propagates to 15 mm, stop the collection of guided wave signals and the observation of the structural crack. By means of linear fitting, determine the structural crack length corresponding to each guided wave signal on the training structural member.

[0091] Step S113, extract damage factors, obtain multi-dimensional signal features of the training structural members, and acquire signal feature samples. In this specific embodiment, a total of two damage factors are extracted to form two-dimensional signal features, that is, D = 2. Among them, the first damage factor DI i extracted based on the guided wave signal f 1,i is calculated as follows:

[0092]

[0093]

[0094]

[0095] where t0 and t1 are the start time and end time of the intercepted guided wave signal segment respectively, τ is the time lag parameter, r si is the cross-correlation between the guided wave signal f i (t) and the reference signal f s (t), r ss (τ) is the cross-correlation between the reference signal f s (t) and itself. In this specific embodiment, the reference signal f s (t) takes the average signal between the first two signals obtained for each training structural member.

[0096] Based on the guided wave signal f i(t) The second damage factor DI extracted 2,i is calculated as follows:

[0097]

[0098] where t0 and t1 are the start time and end time of the intercepted guided wave signal segment respectively, and f i (t) is the guided wave signal, and f s (t) is the reference signal.

[0099] Two damage factors extracted by the above calculation method are used to form the signal feature sample o i of the guided wave signal f i , that is, o i = [DI 1,i , DI 2,i T , where the superscript T is the matrix transpose symbol.

[0100] For the guided wave signals obtained from the training structural members, signal feature samples are extracted by the above method. Each signal feature sample has a corresponding structural crack length, that is, a corresponding damage degree. The signal features obtained under different damage degrees form training sample sets under different damage degrees, and each training sample set has a corresponding known damage degree. Figure 4 shows the distribution of signal feature samples on a training structural member under different crack lengths. The horizontal axis is the first damage factor DI1, and the vertical axis is the second damage factor DI2. The distribution of signal feature samples when the crack lengths are 0mm, 0 - 3mm, 3 - 6mm, 6 - 9mm, 9 - 12mm, and 12 - 15mm is as shown Figure 4 in.

[0101] Step S12, construct a reference sample set O0. More specifically, the signal feature samples corresponding to 30 guided wave signals obtained from each training structural member in a healthy state are collected, and 50 signal feature samples are randomly selected from them to form the reference sample set O0.

[0102] Step S13, based on the reference sample set O0, establish the reference Gaussian mixture model Φ0 corresponding to the reference sample set O0 through the density peak clustering probability modeling algorithm in step S3.

[0103] The step S3 more specifically includes:

[0104] Step S31, based on the sample set O = {o1, …, o i , …, o n}, estimate the probability density ρ i of each sample o i by Gaussian kernel density estimation. The calculation formula is as follows:​

[0105]

[0106] Among them, n is the number of samples o in the sample set O i The dimension of the sample o i is D, and d ij is the Euclidean distance between the sample point o i and o j in the sample set O, and d c is the truncation distance. The estimation expression of the truncation distance d c is as follows:

[0107]

[0108] Among them, d Z (o i ) is the distance between the sample o i and the Z-th sample closest to the distance o i . In a specific embodiment, Z takes the value of represents the largest integer not exceeding x;

[0109] Step S32, calculate the minimum distance δ i of each sample o i , and the calculation formula is as follows:

[0110]

[0111] Step S33, calculate the product λ i of the probability density ρ i of each sample o i and the minimum distance δ i , and the calculation formula is as follows:

[0112] λ i = ρ i × δ i ;

[0113] Step S34, calculate the threshold λ i of the product λ min , and the calculation formula is as follows:

[0114]

[0115] Among them, is the mean value of the probability density ρ i of all samples o i in the sample set O;

[0116] Step S35: Select the samples that satisfy the following inequality as the class centers, and cluster the remaining samples in the sample set O into the class to which the nearest class center belongs based on the nearest neighbor principle to obtain an initial clustering result;

[0117] λ i >λ min &δ i >d c ;

[0118] Step S36: If there is a class in the initial clustering result that contains fewer samples than the dimension D, remove this class and the corresponding samples to obtain a final clustering result. At this time, the total number of samples is n';

[0119] Step S37: Based on the final clustering result, calculate the mean and covariance matrix of each class, and at the same time calculate the ratio of the number of samples contained in each class to the total number of samples n' to obtain the weight corresponding to each class;

[0120] Step S38: Take the mean, covariance matrix, and weight of each class obtained in Step S37 as initialization parameters, and use the expectation-maximization algorithm to establish the Gaussian mixture model Ф of the sample set O. The probability density function expression of the Gaussian mixture model Ф is as follows:

[0121]

[0122] where K is the number of Gaussian components in the Gaussian mixture model Ф, k = 1, 2,..., K, w k is the weight of the k-th Gaussian component, is the k-th Gaussian component, and the probability density function expression of

[0123]

[0124] is as follows: k and Σ k are the mean and covariance matrix of respectively, |·| is the determinant of the matrix, and T represents the matrix transpose symbol.

[0125] In Step S13, the sample set O in Step S3 is the reference sample set O0. Figure 5 shows the signal feature distribution in the reference sample set O0 and the Gaussian component distribution of the reference Gaussian mixture model, as Figure 5 shown. The horizontal axis is the first damage factor DI1, and the vertical axis is the second damage factor DI2.

[0126] Step S14: Construct a training sample set O mj , more specifically, for a training structural member Sm , a training sample set O is constructed every 5 signal feature samples mj , where the subscript m is the serial number of the training structural member, m = 1, 2, 3, 4, 5, and the subscript j is the serial number of the training sample set, j = 1, 2, 3, …. In this specific embodiment, the signal feature samples of each training structural member are arranged in the order of the acquisition time of their corresponding guided wave signals, and a training sample set O is constructed every 5 signal feature samples mj , that is, take a signal feature sample every 5, and take it out together with the previous 49 signal feature samples to form a training sample set O mj , the crack length corresponding to this signal feature sample is the crack length of this training sample set O mj , denoted as L mj , the training sample set O mj contains 50 signal feature samples. In this specific embodiment, when constructing a training sample set O for each training structural member mj , O m1 to O m9 may all have the problem of insufficient sample size. For the training sample set O with insufficient sample size mj , it can be supplemented by randomly extracting from the benchmark sample set O0. For example, the training sample set O m1 only has 5 signal feature samples from the training structural member S m , and the other 45 signal feature samples can be randomly selected from the benchmark sample set O0.

[0127] Step S15, for each training structural member S m , based on the training sample set O mj , through the density peak clustering probability modeling algorithm in the step S3, establish the corresponding training Gaussian mixture model Φ mj . In the step S15, the sample set O in the step S3 is the training sample set O mj .

[0128] Step S16, according to the calculation method of the nested transmission distance, calculate the training nested transmission distance NTD m between the training Gaussian mixture model Φ mj of each training structural member S and the benchmark Gaussian mixture model Φ0 mj .

[0129] Step S17, obtain the crack length L mj corresponding to the nested transmission distance NTD mj .

[0130] Step S18, in this specific embodiment, establish a damage quantification model with the nested transmission distance NTD as the input and the crack length L as the output through a third-order polynomial. The expression is

[0131] L(NTD, w) = w0 + w1NTD + w2NTD 2 + w3NTD 3 ,

[0132] where w0, w1, w2, and w3 are the coefficients of the polynomial, based on the nested transmission distance NTD of the training structural member mj and the corresponding crack length L mj , and the coefficients of the polynomial are determined by the least squares method.

[0133] Figure 6 shows the damage quantification model curve based on the third-order polynomial and the curves of the training structural members S1 to S5, as Figure 6 shown, the horizontal axis is the nested transmission distance NTD, and the vertical axis is the crack length L.

[0134] Step S21, in the monitoring state, for a target structural member, in the time-varying service state, based on the calculation methods of the two damage factors in the step S113, obtain 50 signal feature samples.

[0135] Step S22, based on the 50 signal feature samples of the target structural member, construct a monitoring sample set O'.

[0136] Step S23, through the density peak clustering probability modeling algorithm in the step S3, establish a monitoring Gaussian mixture model Φ' corresponding to the monitoring sample set O', in the step S23, the sample set O in the step S3 is the monitoring sample set O'. Figure 7 shows the monitoring Gaussian mixture models corresponding to the signal feature samples collected at different crack lengths of the target structural member in the time-varying service state, as Figure 7 shown, the horizontal axis is the first damage factor DI1, and the vertical axis is the second damage factor DI2, Figure 7 where (a) is the monitoring Gaussian mixture model corresponding to the signal feature samples collected when the target structural member has no crack in the time-varying service state, Figure 7 where (b) is the monitoring Gaussian mixture model corresponding to the signal feature samples collected when the crack length of the target structural member is 2 mm in the time-varying service state, Figure 7 where (c) is the monitoring Gaussian mixture model corresponding to the signal feature samples collected when the crack length of the target structural member is 4 mm in the time-varying service state, Figure 7 where (d) is the monitoring Gaussian mixture model corresponding to the signal feature samples collected when the crack length of the target structural member is 6 mm in the time-varying service state.

[0137] Step S24: Calculate the monitoring nested transmission distance NTD' between the monitoring Gaussian mixture model Φ' and the reference Gaussian mixture model Φ0 according to the calculation method of the nested transmission distance. Figure 8 Shows the calculation results of the monitoring nested transmission distance during the monitoring process, as Figure 8 shown. The horizontal axis is the number of monitoring times, that is, the number of times the structure is monitored within a period of time, and the vertical axis is the monitoring nested transmission distance NTD'.

[0138] Step S25: Substitute the monitoring nested transmission distance NTD' into the damage quantification model obtained in the above step S18, and calculate the estimated crack length L' of the target structural member, which is the damage degree of the target structural member. Figure 9 Shows the estimated crack length, actual crack length and absolute error of the target structural member, as Figure 9 shown. The horizontal axis is the number of monitoring times, and the vertical axis is the crack length. As can be seen from Figure 9 , the consistency between the estimated crack length calculated by the method of the present invention and the actual crack length is high, indicating that the method of the present invention has high accuracy. Among them, the absolute error is the absolute value of the difference between the estimated crack length and the actual crack length at each monitoring moment. During the monitoring process, the maximum absolute error does not exceed 2 mm, and the average absolute error is 0.6 mm. Therefore, through the structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance of the present invention, reliable crack length diagnosis under the influence of time-varying service conditions can be realized.

[0139] Among them, the calculation method of the nested transmission distance in the above step S16 and the above step S24 includes:

[0140] Step S41: Denote the two Gaussian mixture models as Φ 0 and Φ 1 respectively. The Gaussian components in the Gaussian mixture model Φ 0 are denoted as i = 1, 2,..., K 0 , where K 0 is the number of Gaussian components in the Gaussian mixture model Φ 0 ; the Gaussian components in the Gaussian mixture model Φ 1 are denoted as j = 1, 2,..., K 1 , where K 1 is the number of Gaussian components in the Gaussian mixture model Φ 1 . The optimal transmission distance 0 between the Gaussian component in the Gaussian mixture model Φ 1 and the Gaussian component in the Gaussian mixture model Φ is calculated as follows:

[0141]

[0142] Among them, and are the mean and covariance matrix of the Gaussian component 0 in the Gaussian mixture model Φ respectively, and are the mean and covariance matrix of the Gaussian component 1 in the Gaussian mixture model Φ respectively;

[0143] Step S42, the calculation formula of the nested transmission distance NTD between the Gaussian mixture model Φ 0 and the Gaussian mixture model Φ 1 is as follows:

[0144]

[0145] Among them, is and the optimal transmission distance between, is the joint distribution when the Gaussian components and are two individuals, φ ∈ Π(w 0 , w 1 ) indicates that the joint distribution obeys the marginal constraints and is the weight of the Gaussian component in the Gaussian mixture model Φ 0 , is the weight of the Gaussian component in the Gaussian mixture model Φ 1 . In a specific embodiment, the minimum solution of under this marginal constraint can be found by linear programming, and the minimum solution is used as the nested transmission distance NTD between the Gaussian mixture model Φ 0 and the Gaussian mixture model Φ 1 .

[0146] Although the present invention has been disclosed above with embodiments, it is not intended to limit the present invention. Any person with ordinary knowledge in the technical field can make some changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be subject to that defined by the appended patent application scope.

Claims

1. A structural damage diagnosis method based on Gaussian mixture model and nested transmission distance, characterized in that including Step S11: Obtain signal feature samples of training structural members; Step S12: Randomly select n signal feature samples from all the signal feature samples obtained under the healthy state of the training structural members to form a benchmark sample set, where n is a natural number greater than 0; Step S13: Based on the benchmark sample set, establish a benchmark Gaussian mixture model corresponding to the benchmark sample set through a density peak clustering probability modeling algorithm; Step S14: Construct training sample sets under different damage degrees; Step S15: Based on the training sample sets, establish corresponding training Gaussian mixture models through the density peak clustering probability modeling algorithm; Step S16: According to the calculation method of the nested transmission distance, calculate the training nested transmission distance NTD between the training Gaussian mixture model of each training structural member and the benchmark Gaussian mixture model; Step S17: Obtain the damage degree L corresponding to the training nested transmission distance NTD; Step S18: Establish a damage quantification model through polynomial fitting; The calculation method of the nested transmission distance includes Step S41, denote the two Gaussian mixture models as Gaussian mixture model Φ 0 and Gaussian mixture model Φ 1 . The Gaussian components in the Gaussian mixture model Φ 0 are denoted as K 0 , where K 0 is the number of Gaussian components in the Gaussian mixture model Φ 0 . The Gaussian components in the Gaussian mixture model Φ 1 are denoted as K 1 , where K 1 is the number of Gaussian components in the Gaussian mixture model Φ 0 . The optimal transport distance between the Gaussian components 1 in the Gaussian mixture model Φ and the Gaussian components in the Gaussian mixture model Φ Among them, and are the mean and covariance matrix of the Gaussian component 0 in the Gaussian mixture model Φ respectively; and are the mean and covariance matrix of the Gaussian component 1 in the Gaussian mixture model Φ respectively. Step S42, the Gaussian mixture model Φ 0 and the Gaussian mixture model Φ 1 The calculation formula for the nested transmission distance NTD between them is as follows: Among them, is and the optimal transmission distance between, is the joint distribution of the Gaussian component and the Gaussian component when they are two individuals, φ ∈ Π(w 0 , w 1 ) indicates that the joint distribution obeys the marginal constraints and is the weight of the Gaussian component in the Gaussian mixture model Φ 0 in, is the weight of the Gaussian component in the Gaussian mixture model Φ 1 in.

2. The structural damage diagnosis method based on the Gaussian mixture model and nested transmission distance according to claim 1, wherein further including Step S21: Under the monitoring state, collect n signal feature samples under the time-varying service state of the target structural member; Step S22: Based on the n signal feature samples of the target structural member, form a monitoring sample set; Step S23: Based on the monitoring sample set, establish a corresponding monitoring Gaussian mixture model through the density peak clustering probability modeling algorithm; Step S24: According to the calculation method of the nested transmission distance, calculate the monitoring nested transmission distance NTD' between the monitoring Gaussian mixture model and the benchmark Gaussian mixture model; Step S25: Substitute the monitoring nested transmission distance NTD' into the damage quantification model to calculate the damage degree of the target structural member.

3. The structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance according to claim 1, characterized in that, The said Step S11 includes Step S111: Under the simulated time-varying service environment, collect guided wave signals of the training structural members under different damage degrees; Step S112: Determine the damage degree corresponding to each guided wave signal on each training structural member; Step S113: Extract damage factors to obtain the signal feature samples.

4. The structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance according to claim 1, characterized in that The expression of the damage quantification model is as follows: L(NTD, w) = w0 + w1NTD + w2NTD 2 +...+ w p NTD p , where L is the degree of damage, NTD is the training nested transmission distance, and {w i |i = 1, 2, …, p} are the coefficients of the polynomial, and p is the order of the polynomial.

5. The structural damage diagnosis method based on the Gaussian mixture model and the nested transmission distance according to claim 4, characterized in that, By the least squares method, the coefficients {w i | i = 1, 2, …, p} of the polynomial are obtained based on the training nested transmission distance NTD and the damage degree L.

6. The structural damage diagnosis method based on the Gaussian mixture model and nested transmission distance according to any one of claims 1-2, characterized in that The density peak clustering probability modeling algorithm includes Step S31, based on the sample set O = {o1, …, o i , …, o n}, use Gaussian kernel density estimation to estimate the probability density ρ i of each sample o i , and the calculation formula is as follows: where n is the number of the sample o in the sample set O i and the dimension of the sample o i is D, and d ij is the Euclidean distance between the sample o i and o j in the sample set O, and the expression of the truncation distance d c is as follows: c ​ where d Z (o i ) is the distance between the sample o i and the Z-th sample closest to o i ; Step S32, calculate the minimum distance δ i for each of the samples o i , and the calculation formula is as follows: Step S33, calculate the probability density ρ i for each sample o i and the product λ i of the minimum distance δ i , and the calculation formula is as follows: λ i = ρ i × δ i ; Step S34, calculate the product λ i threshold λ min , and the calculation formula is as follows: wherein, is the mean value of the probability density ρ i for all samples o i in the sample set O; Step S35: Select samples that satisfy the following inequality as class centers, and based on the nearest neighbor principle, cluster the remaining samples in the sample set O into the class to which the nearest class center belongs to obtain an initial clustering result; λ i > λ min & δ i > d c ; Step S36: If there is a class in the initial clustering result that contains a number of samples less than the dimension D, remove this class and the corresponding samples to obtain a final clustering result. At this time, the total number of samples is n'; Step S37: On the basis of the final clustering result, calculate the mean and covariance matrix of each class, and at the same time calculate the ratio of the number of samples included in each class to the total number of samples n' to obtain the weight corresponding to each class; Step S38: Using the mean value, covariance matrix, and weight value of each category obtained in step S37 as initialization parameters, establish a Gaussian mixture model Ф of the sample set O using the expectation-maximization algorithm. The probability density function expression of the Gaussian mixture model Ф is as follows: where K is the number of Gaussian components in the Gaussian mixture model Ф, k = 1, 2, …, K, and w k is the weight of the k-th Gaussian component, is the k-th Gaussian component, and the expression of its probability density function is as follows: where μ k and Σ k are the mean value and covariance matrix of respectively, |·| is the determinant of the matrix, and T represents the matrix transpose symbol.

7. The structural damage diagnosis method based on the Gaussian mixture model and nested transmission distance according to claim 3, wherein The damage factor DI 1,i is calculated as follows: where \(t_0\) and \(t_1\) are the start time and end time of the intercepted guided wave signal segment respectively, \(\tau\) is the time lag parameter, and \(r\) si is the cross - correlation between the guided wave signal \(f\) i (t) and the reference signal \(f\) s (t), and \(r\) ss (\(\tau\)) is the auto - correlation of the reference signal \(f\) s (t) with itself.

8. The structural damage diagnosis method based on the Gaussian mixture model and nested transmission distance as claimed in claim 7, wherein The damage factor DI 2,i is calculated as follows: where t0 and t1 are the start time and end time of the intercepted guided wave signal segment respectively, and f i (t) is the guided wave signal, and f s (t) is the reference signal.

9. The structural damage diagnosis method based on the Gaussian mixture model and nested transmission distance according to claim 8, wherein, The signal feature sample o i has the following expression: o i = [DI 1,i , DI 2,i T ,​ where the superscript T is the matrix transpose symbol.

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