CN117708734A - Structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition and storage medium - Google Patents
Structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition and storage medium Download PDFInfo
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Abstract
The invention discloses a structural damage identification method and a storage medium based on improved self-adaptive noise complete integrated empirical mode decomposition, and dynamic response of a structure is obtained through continuous vibration test; calculating the power spectral density of each order mode based on an improved self-adaptive noise complete integrated empirical mode decomposition and a spectral feature inspection method; adopting a power spectrum density secondary peak suppression algorithm to overcome the influence of a modal aliasing phenomenon in a decomposition result on classification accuracy; carrying out frequency domain clustering on the processed modal components by adopting K-means++, and extracting damage sub-signals; calculating the characteristics of instantaneous amplitude, phase and the like, constructing a composite energy factor, and automatically judging the existence and the damage position of the structural damage according to a PELT algorithm. The invention provides a PSD secondary peak suppression frequency domain clustering algorithm based on improved self-adaptive noise complete integrated empirical mode decomposition, which extracts damage characteristic sub-signals; a robust composite energy damage recognition factor is constructed, and visualization and automatic early warning processing of damage existence and damage positions are realized through PELT.
Description
Technical Field
The invention relates to the technical field of engineering detection, in particular to a structural damage identification method and a storage medium based on improved self-adaptive noise complete integrated empirical mode decomposition.
Background
In the prior art, the health diagnosis of the wharf is mainly performed according to the dynamic characteristics of the structure, such as frequency, mode, strain energy and the like. However, the external excitation of the normal structure is contradictory with the white noise excitation condition of the prior modal parameter identification, and the damage detection lack of sensitivity by utilizing the modal characteristics greatly weakens the structure damage identification effect.
Disclosure of Invention
The invention aims to solve the technical problem of providing a structural damage identification method and a storage medium based on improved self-adaptive noise complete integrated empirical mode decomposition, which can realize the visualization of damage existence and damage position and automatic early warning treatment.
In order to solve the technical problems, the invention provides a structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition, which comprises the following steps:
step 1, obtaining the dynamic response of a structure through a continuous vibration test;
step 2, calculating the power spectral density of each order mode based on an improved self-adaptive noise complete integrated empirical mode decomposition and a spectral feature inspection method;
step 3, adopting a power spectrum density secondary peak suppression algorithm to overcome the influence of a modal aliasing phenomenon in a decomposition result on classification accuracy;
step 4, carrying out frequency domain clustering on the processed modal components by adopting K-means++, and extracting damage sub-signals;
and 5, calculating characteristics such as instantaneous amplitude, phase and the like, constructing a composite energy factor, and automatically judging the existence and the damage position of the structural damage according to a PELT algorithm.
In step 1, the dynamic response signals are displacement, speed and acceleration.
In step 2, based on the improved adaptive noise complete integrated empirical mode decomposition (Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, icemdan) and the spectral feature inspection method, the power spectral density of each order mode is calculated specifically as follows: decomposing the vibration signal into n IMFs and 1 residual term r (t) by icemdan, namely:
wherein x (T) represents an original signal representing a number of time samples T;
calculation of the power spectral Density (Power Spectral density, PSD) the original signal x (t) is considered as an energy-limited sequence, assuming N=2 M M is the minimum positive integer when N is more than or equal to T, and FFT [ x (T) is obtained by performing fast Fourier transform on the original signal]Thereby obtaining an estimated value of PSD:
where fs denotes the sampling frequency. The k-th value of PSD corresponds to the frequency:
in the step 3, the influence of the modal aliasing phenomenon on classification accuracy in the decomposition result is specifically overcome by adopting a power spectrum density secondary peak suppression algorithm: assuming PSD frequency rangeEnclose as [ f 1 ,f N ]The core idea of local linear kernel regression is to minimize the weighted least squares formula:
where h represents bandwidth, K (·) represents kernel function, gaussian kernel function is used, resulting inAs an estimate of the restricted linear estimator g (x), a>As an estimate of the marginal effect β (x):
to overcome the problem of bandwidth parameter selection, the adaptive bandwidth is obtained by using a least square cross-validation method, and the idea is to minimize the function:
wherein the method comprises the steps ofIs composed of g (X) k ) When the prediction of the kth observation point is generated, the point is omitted to form the observation point, so that a curve SPSD with a smoothed PSD is automatically obtained;
finding the peak point of the SPSD by using the find_peaks function in the Scipy library, detecting the local maximum of a group of data according to the concept of terrain protrusion, setting Promence=0.2×max (SPSD), and identifying the peak point only when the promence of a certain peak is higher than 0.2×max (SPSD), so as to further perform next peak suppression.
The p peaks of the SPSD are assumed to be found, and the coordinates of the peak points are as follows:
(H 1 ,SPSD(H 1 )),...,(H p ,SPSD(H p )),H 1 ＜H p
wherein (H) m ,SPSD(H m ) M is more than or equal to 1 and less than or equal to p, and represents the coordinates of a main peak, and the rest is the coordinates of each secondary peak; the SPSD is also subjected to peak identification after the negative number, at least p-1 and at most p+1 peaks and valleys of the SPSD are obtained, and coordinates of the peaks and valleys are assumed to be:
(L 1 ,SPSD(L 1 )),(L 2 ,SPSD(L 2 )),(L 3 ,SPSD(L 3 )),...
determining the frequency ranges of each main peak and each secondary peak under different conditions according to peak-valley, weighting each secondary peak in the PSD after determining the frequency range corresponding to each secondary peak, wherein the weighting coefficient is in the form of an index of the ratio of each secondary peak to the main peak, and the calculation formula is as follows:
where f is the frequency range of the secondary peak j, c is a constant indicating the degree of weighting of the secondary peak, taking c=4.
In step 4, frequency domain clustering is performed on the processed modal components by adopting K-means++, and the extracting of the damage sub-signals is specifically as follows: after obtaining the PSD after secondary peak inhibition, calculating the frequency f of the ith IMF k CSD at:
wherein F is i * WPSD corresponding to the ith IMF;
taking each CSD as a data object, clustering the objects with common data characteristics by adopting K-means++, thereby realizing automatic and robust reconstruction of IMFs, selecting Euclidean distance as a synchronization measure, and standardizing the CSD before clustering, wherein the formula is as follows:
the profile coefficient is selected to provide a reference for the optimal cluster number, and the profile coefficient of the sample i is assumed to be classified into a cluster A, and the profile coefficient of the cluster are defined as follows:
where a (i) represents the average distance of sample i from other samples in the same cluster and b (i) represents the minimum value of the average distance of sample i to samples in other clusters. The value range of the profile coefficient SC is [ -1,1], the larger the value is, the more reasonable and effective the clustering result obtained by selecting the clustering number corresponding to the value is, and the selection of the classification number can be judged through the profile coefficient curve.
In step 5, calculating characteristics such as instantaneous amplitude and phase, constructing a composite energy factor, and automatically judging existence of structural damage and damage positions according to a PELT algorithm, wherein the specific steps are as follows: the corresponding formula for the Hilbert transform is:
wherein c (t) refers to the signal to be transformed; after Hilbert transformation, an analytic signal is obtainedThe instantaneous amplitude and phase can be obtained from the resolved signal:
when the structure of the system itself changes or the state of the system changes into an abnormal state, the energy of the system itself also changes, so the energy generally can better reflect structural damage, and the calculation formulas of the instantaneous energy and a certain signal energy are as follows:
phase changes are typically caused when structural systems are damaged or abnormal; in addition, the change condition of the information contained in the signal is indirectly known by analyzing the phase slope; thus, after the energy and phase characteristics are obtained, the damage index is constructed based on the energy, phase slope, respectively:
wherein E is h (t)、E d (t) represents energy obtained under healthy and injured conditions, PS h 、PS d Respectively representing the slopes of the phases under the conditions of health and damage, and fitting a linear regression equation according to the least square method principle to obtain the linear regression equation;
DI based (E) With DI (PS) Fusion construction of a composite energy factor:
the PELT algorithm is implemented by minimizing the following cost function:
wherein,is a local cost function for evaluating the time point tau j To tau j+1 Fitting goodness of time series column segments; />k (·, ·) is the RBF kernel function; beta is a penalty term to control the total number of change points, preventing overfitting, where beta = 1; m is the total number of detected change points, and the existence of structural damage and the damage position can be automatically judged.
Correspondingly, a structural damage identification storage medium based on improved self-adaptive noise complete integrated empirical mode decomposition stores a computer program, and the program realizes an asynchronous intermittent measurement-oriented power distribution network estimation fusion method when being executed by a processor.
The beneficial effects of the invention are as follows: the invention can solve two problems of structural damage identification under complex excitation: aliasing of multiple types of signals, robust damage identification and automatic early warning; aiming at the aliasing effect of multiple types of signals, a PSD secondary peak suppression frequency domain clustering algorithm based on ICEEMDAN is provided, and damage characteristic sub-signals are extracted; constructing a robust composite energy damage recognition factor, and judging the existence and the damage position of damage through a PELT algorithm; the visualization and automatic early warning treatment of the existence and the positions of the damage can be realized.
Drawings
Fig. 1 is an aerial view of an experimental model of a high pile wharf according to the present invention.
Fig. 2 is a side view of an experimental model of a high pile wharf of the present invention.
FIG. 3 is a graph showing acceleration response of each node under 10% damage condition according to the present invention.
FIG. 4 (a) is an IMF1-IMF4 and a corresponding PSD plot obtained from node No. 5 via ICEEMDAN under 10% damage conditions according to the present invention.
FIG. 4 (b) is an IMF5-IMF8 obtained by ICEEMDAN for node No. 5 under 10% damage condition and a corresponding PSD map.
FIG. 4 (c) is a PSD plot of IMF9-IMF12 and corresponding IMF12 obtained from node No. 5 via ICEEMDAN under 10% damage conditions according to the present invention.
Fig. 5 is a diagram of IMFs classification results obtained by the PSD sub-peak suppression frequency domain clustering algorithm of the present invention.
Fig. 6 is a schematic diagram of the reconstruction result of different types of signals according to the present invention.
FIG. 7 is a graph of a composite energy factor of the present invention.
FIG. 8 is a graph of the results of automatic determination by the PELT algorithm of the present invention.
FIG. 9 is a schematic flow chart of the method of the present invention.
Detailed Description
As shown in fig. 9, a structural damage identification method based on improved adaptive noise complete integrated empirical mode decomposition includes the following steps:
step 1: and obtaining the dynamic response of the structure through continuous vibration test, wherein the dynamic response signals are displacement, speed and acceleration.
Step 2: based on an improved self-adaptive noise complete integrated empirical mode decomposition and a spectral feature inspection method, calculating the power spectral density of each order mode comprises the following steps:
according to research, the dynamic response of a structural body in actual engineering is usually non-stable and nonlinear, and is formed by aliasing of multiple types of signals. Poor lesion recognition results if used directly. Therefore, the automatic extraction of the damage sensitive signals needs to be realized by adopting the modes of decomposition, reclassification and reconstruction. The empirical mode decomposition (Empirical Mode Decomposition, EMD) is capable of decomposing the signal into several eigenmode functions (Intrinsic Mode Functions, IMFs), whereas the complete integrated empirical mode decomposition (Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, icemdan) with improved adaptive noise greatly improves the decomposition effect by introducing the concept of noise and local mean. Decomposing the vibration signal into n IMFs and 1 residual term r (t) by icemdan, namely:
where x (T) represents an original signal representing a number of time samples T.
The calculation of the power spectral density (Power Spectral Density, PSD) regards the original signal x (t) as an energy-limited sequence. Let n=2 M M is the minimum positive integer when N is more than or equal to T, and FFT [ x (T) is obtained by performing fast Fourier transform on the original signal]Thereby obtaining an estimated value of PSD:
where fs denotes the sampling frequency. The k-th value of PSD corresponds to the frequency:
step 3: the method for overcoming the influence of the modal aliasing phenomenon on the classification accuracy in the decomposition result by adopting a power spectrum density secondary peak suppression algorithm comprises the following steps:
to aid classification, the PSD may also be integrated to obtain a cumulative spectral distribution (Cumulative Spectral Distribution, CSD) at frequency to obtain its spectral features. However, multimodal in PSD can give rise to a stepped CSD result, causing an extension of its overall morphology, which can have an impact on classification accuracy. Therefore, it is necessary to propose a PSD sub-peak suppression algorithm for overcoming the influence of the modal aliasing phenomenon.
In view of the fact that there are usually multiple "burrs" in the PSD corresponding to each IMF component in the decomposition result, multiple extreme points are obtained by directly identifying, and the true peak point position cannot be determined, so it is considered to perform smoothing on the PSD first. To reduce the parameter selection problem, local linear kernel regression is chosen for smoothing. Let PSD frequency range be [ f 1 ,f N ]Office (bureau)The core idea of the partial linear kernel regression is to minimize the weighted least squares formula:
where h represents bandwidth, K (·) represents kernel function, here Gaussian kernel function is used. Thereby obtainingAs an estimate of the restricted linear estimator g (x), a>As an estimate of the marginal effect β (x):
to overcome the problem of bandwidth parameter selection, the adaptive bandwidth is obtained by using a least square cross-validation method, and the idea is to minimize the function:
wherein the method comprises the steps ofIs composed of g (X) k ) When the prediction of the kth observation point is generated, the point is omitted. Thus, the PSD smoothed curve SPSD is automatically obtained.
The invention uses find_peaks function in Scipy library to find peak point of SPSD, and detects local maximum of a group of data according to concept of topography salient. Setting Prominine=0.2×max (SPSD), only when prominine of a certain peak is higher than 0.2×max (SPSD), it is recognized, and further, the next peak suppression is performed.
Assuming that p peaks of the SPSD are found altogether, the peak point coordinates are in order:
(H 1 ,SPSD(H 1 )),...,(H p ,SPSD(H p )),H 1 ＜H p
wherein (H) m ,SPSD(H m ) M is more than or equal to 1 and less than or equal to p, and represents the coordinates of the main peak, and the rest is the coordinates of each secondary peak. And (3) carrying out peak identification after taking the negative number of the SPSD, so as to obtain at least p-1 and at most p+1 peaks and valleys of the SPSD, wherein the coordinates of the peaks and the valleys are assumed to be:
(L 1 ,SPSD(L 1 )),(L 2 ,SPSD(L 2 )),(L 3 ,SPSD(L 3 )),...
the frequency range of each main peak and each secondary peak under different conditions can be determined according to the peak valley. After the frequency range corresponding to each secondary peak is determined, weighting each secondary peak in the PSD, wherein the weighting coefficient is in the form of an index of the ratio of each secondary peak to the main peak, and the calculation formula is as follows:
where f is the frequency range of the secondary peak j and c is a constant indicating the degree to which the secondary peak is weighted. The algorithm used in the method is carried out in the environment of Python 3.9.9, and the version of the scipy library used is 1.7.3.
Step 4: carrying out frequency domain clustering on the processed modal components by adopting K-means++, and extracting damage sub-signals, wherein the method comprises the following steps:
after obtaining the PSD after secondary peak inhibition, calculating the frequency f of the ith IMF k CSD at:
wherein F is i * The WPSD corresponding to the ith IMF.
K-means++ is an improvement on a K-means clustering algorithm, and a central point is selected in a mode of introducing random probability, so that the problem of local optimal solution possibly caused by randomly initializing the central point in the traditional K-means algorithm is avoided. And taking each CSD as a data object, and clustering the objects with common data characteristics by adopting K-means++, so that automatic and robust reconstruction of IMFs is realized. In order to obtain a better clustering effect, the Euclidean distance is selected as a synchronization measure, and the CSD is standardized before clustering, and the formula is as follows:
in addition, the profile factor is selected to provide a reference for the optimal number of clusters, and assuming that the sample i is classified into a cluster a, the profile factor and the profile factor of the sub-cluster are defined as:
where a (i) represents the average distance of sample i from other samples in the same cluster and b (i) represents the minimum value of the average distance of sample i to samples in other clusters. The value range of the profile coefficient SC is [ -1,1], the larger the value is, the more reasonable and effective the clustering result obtained by selecting the clustering number corresponding to the value is, and the selection of the classification number can be judged through the profile coefficient curve.
Step 5: calculating characteristics such as instantaneous amplitude, phase and the like, constructing a composite energy factor, judging whether damage exists according to whether damage perception indexes exceed a threshold value or not, and comprising the following steps:
the hilbert transform (Hilbert Transform, HT) technique is suitable for processing vibration response data of buildings under complex excitation and can provide some unique information. The formula corresponding to HT is:
wherein c (t) refers to the signal to be transformed. After HT, an analytic signal can be obtainedThe instantaneous amplitude and phase can be obtained from the resolved signal:
when the structure of the system itself changes or the state of the system becomes abnormal, the energy of the system itself changes, so the energy can better reflect the structural damage in general. The calculation formula of the instantaneous energy and a certain signal energy is as follows:
phase is one of the important features of a signal, which is very sensitive to small changes in the signal and to relative timing changes. Phase changes are typically caused when structural systems are damaged or abnormal; in addition, the change condition of the information contained in the signal can be indirectly known by analyzing the phase slope. Thus, after the energy and phase characteristics are obtained, the damage index is constructed based on the energy, phase slope, respectively:
wherein E is h (t)、E d (t) represents energy obtained under healthy and damaged conditions, respectively. PS (PS) h 、PS d And respectively representing the slopes of the phases under the conditions of health and damage, and fitting a linear regression equation according to the least square method principle to obtain the phase-change detector.
Due to the fact that the dynamic response of the structure is not stable, the signal to noise ratio is low, the aliasing is of multiple types under complex excitation, DI is comprehensively considered (E) With DI (PS) And fusing, namely constructing more sensitive combined damage indexes based on energy and phase information, so as to improve the sensitivity and robustness of structural damage identification and realize the effect of accurately identifying the existence, the damage position and the damage degree of structural damage. DI based (E) With DI (PS) Fusion construction of a composite energy factor:
pruning accurate linear time algorithm (Pruned Exact Linear Time, PELT) is an efficient algorithm for detecting points of structural change in time series data. This algorithm combines dynamic planning and pruning techniques to ensure that the optimal set of breakpoints is found within a linear time. The core of the PELT algorithm is to minimize the following cost function:
wherein,is a local cost function for evaluating the time point tau j To tau j+1 Fitting goodness of time series segments of (c). Here->k (·, ·) is the RBF kernel function. Beta is a penalty term to control the total number of change points, preventing overfitting, where beta = 1.M is the total number of detected change points. The method can automatically judge the existence of structural damage and the damage position.
As shown in fig. 1 to 7, a structural damage identification method and device based on improved adaptive noise-complete integrated empirical mode decomposition are used for identifying pile foundation damage of a high pile wharf under wave excitation.
In the present invention we first construct an experimental model of a high pile wharf, which is placed in a special basin that simulates the effects of wind, waves and currents. The detailed construction of the model can be seen in fig. 1 and 2. In particular, on the front side of the model, acceleration sensors were installed every 0.1m of the second pile from top to bottom, for a total of 13. The main function of these sensors is to capture vibrations perpendicular to the dock front. Pile body damage of different degrees is set according to the percent of rigidity reduction. The injury width and experimental conditions were respectively: the width at 5% injury is 4mm; the width at 10% injury is 9mm; the width at 30% injury was 24mm.
In the experiment, regular waves are used for excitation, the period of the waves is set to be 1 second, the water depth is 1 meter, and the wave height is 0.1 meter. The aim of the experiment is to collect and analyze acceleration response data of the pile body before and after damage occurs.
The damage identification method specifically comprises the following steps:
step 1: and acquiring the acceleration response of the current state and the sound state of the structure.
The acquisition equipment adopts a DH5920 dynamic signal acquisition analysis system to realize multichannel parallel synchronous acquisition, the single-channel sampling frequency is 1000Hz, and the vibration pickup adopts a YD-186 type piezoelectric acceleration sensor to acquire acceleration signals of 13 nodes of the pile foundation model under wave excitation by using the DH5920 vibration pickup, as shown in figure 3.
Step 2: based on the improved adaptive noise complete integrated empirical mode decomposition and spectral feature verification method, the signal decomposition results and the power spectral densities of the modes of each order are shown in fig. 4 (a) - (c). It can be seen that each IMF component is arranged from high frequency to low frequency, and as a result, a modal aliasing phenomenon exists, such as a dual-peak phenomenon exists in PSD corresponding to IMF1-2, and the frequency of IMF2-3 is all around 100 Hz. The mode aliasing phenomenon in the decomposition result is overcome by adopting a power spectrum density secondary peak suppression algorithm, and the processed mode components are subjected to frequency domain clustering by adopting K-means++, so that damaged sub-signals are extracted. The classification result and the reconstruction result are shown in fig. 5 and 6, respectively. Wherein the graph (a) is a local bending response, changes greatly only when waves arrive, contains structural local damage information, and is a damage characteristic sub-signal required for research; (b) Representing a global bending response that exhibits a tendency to decay gradually over a short period of time following the impact, useful for identifying wave impacts; (c) And (d) represent the rigid body dynamic response quasi-static response, respectively, both without significant impact-induced features; (e) represents a baseline drift term.
Step 3: and calculating the characteristics of instantaneous amplitude, phase and the like, constructing a composite energy factor, and automatically judging the existence and the damage position of the structural damage according to a PELT algorithm, wherein the characteristics are shown in fig. 7 and 8.
According to the damage identification result, the whole curves obtained under different damage degrees all show a trend of ascending and then descending, and reach the maximum value at the node 5 or 6, and as the damage is arranged between the nodes 5-6, the existence and the damage position of the pile foundation damage can be identified through the composite energy factor. In addition, the three obtained curves have obvious magnitude relation, which indicates that the index successfully identifies the damage degree of the pile foundation. According to the PELT algorithm result, the method can realize automatic early warning of the existence and the damage position of the damage.
The invention can effectively realize multi-type signal extraction in the dynamic response of the structure under complex excitation, and the problems of damage existence and damage position discrimination, and provides a new means for automatic early warning of the damage during the service period of the structure.
Claims (10)
1. The structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition is characterized by comprising the following steps of:
step 1, obtaining the dynamic response of a structure through a continuous vibration test;
step 2, calculating the power spectral density of each order mode based on an improved self-adaptive noise complete integrated empirical mode decomposition and a spectral feature inspection method;
step 3, adopting a power spectrum density secondary peak suppression algorithm to overcome the influence of a modal aliasing phenomenon in a decomposition result on classification accuracy;
step 4, carrying out frequency domain clustering on the processed modal components by adopting K-means++, and extracting damage sub-signals;
and 5, calculating characteristics such as instantaneous amplitude, phase and the like, constructing a composite energy factor, and automatically judging the existence and the damage position of the structural damage according to a PELT algorithm.
2. The method for identifying structural damage based on improved adaptive noise-complete-integration empirical mode decomposition according to claim 1, wherein in step 1, the dynamic response signal is displacement, velocity, acceleration.
3. The structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition according to claim 1, wherein in step 2, based on the improved self-adaptive noise complete integrated empirical mode decomposition and a spectral feature inspection method, the power spectral density of each order mode is calculated specifically as follows: decomposing the vibration signal into n IMFs and 1 residual term r (t) by icemdan, namely:
wherein x (T) represents an original signal representing a number of time samples T;
calculation of the power spectral density the original signal x (t) is considered as an energy-limited sequence, assuming n=2 M M is the minimum positive integer when N is more than or equal to T, and FFT [ x (T) is obtained by performing fast Fourier transform on the original signal]Thereby obtaining an estimated value of PSD:
wherein fs represents the sampling frequency, and the frequency corresponding to the kth value of the PSD is:
4. the structural damage identification method based on improved adaptive noise complete integrated empirical mode decomposition according to claim 1, wherein in step 3, the power spectral density secondary peak suppression algorithm is adopted to overcome the influence of the modal aliasing phenomenon on the classification accuracy in the decomposition result specifically comprises the following steps: let PSD frequency range be [ f 1 ,f N ]The core idea of local linear kernel regression is to minimize the weighted least squares formula:
where h represents bandwidth, K (·) represents kernel function, gaussian kernel function is used, resulting inAs an estimate of the restricted linear estimator g (x), a>As an estimate of the marginal effect β (x):
to overcome the problem of bandwidth parameter selection, the adaptive bandwidth is obtained by using a least square cross-validation method, and the idea is to minimize the function:
wherein the method comprises the steps ofIs composed of g (X) k ) When the prediction of the kth observation point is generated, the point is omitted to formThus, a curve SPSD after PSD smoothing is automatically obtained;
finding the peak point of the SPSD by using the find_peaks function in the Scipy library, detecting the local maximum of a group of data according to the concept of terrain protrusion, setting Promence=0.2×max (SPSD), and identifying the peak point only when the promence of a certain peak is higher than 0.2×max (SPSD), so as to further perform next peak suppression.
5. The structural damage identification method based on improved adaptive noise-complete integrated empirical mode decomposition of claim 4, wherein p peaks of the SPSD are assumed to be found altogether, and the coordinates of the peak points are in turn:
(H 1 ,SPSD(H 1 )),...,(H p ,SPSD(H p )),H 1 ＜H p
wherein (H) m ,SPSD(H m ) M is more than or equal to 1 and less than or equal to p, and represents the coordinates of a main peak, and the rest is the coordinates of each secondary peak; the SPSD is also subjected to peak identification after the negative number, at least p-1 and at most p+1 peaks and valleys of the SPSD are obtained, and coordinates of the peaks and valleys are assumed to be:
(L 1 ,SPSD(L 1 )),(L 2 ,SPSD(L 2 )),(L 3 ,SPSD(L 3 )),...
determining the frequency ranges of each main peak and each secondary peak under different conditions according to peak-valley, weighting each secondary peak in the PSD after determining the frequency range corresponding to each secondary peak, wherein the weighting coefficient is in the form of an index of the ratio of each secondary peak to the main peak, and the calculation formula is as follows:
where f is the frequency range of the secondary peak j and c is a constant.
6. The method for structural damage identification based on improved adaptive noise-complete-integration empirical-mode decomposition of claim 5, wherein c represents the degree to which the secondary peak is weighted, taking c = 4.
7. The structural damage identification method based on improved adaptive noise complete integrated empirical mode decomposition according to claim 1, wherein in step 4, frequency domain clustering is performed on processed modal components by using K-means++, and the damage sub-signals are extracted specifically as follows: after obtaining the PSD after secondary peak inhibition, calculating the frequency f of the ith IMF k CSD at:
wherein F is i * WPSD corresponding to the ith IMF;
taking each CSD as a data object, clustering the objects with common data characteristics by adopting K-means++, thereby realizing automatic and robust reconstruction of IMFs, selecting Euclidean distance as a synchronization measure, and standardizing the CSD before clustering, wherein the formula is as follows:
the profile coefficient is selected to provide a reference for the optimal cluster number, and the profile coefficient of the sample i is assumed to be classified into a cluster A, and the profile coefficient of the cluster are defined as follows:
wherein a (i) represents the average distance between the sample i and other samples in the same cluster, and b (i) represents the minimum value of the average distance between the sample i and the samples in other clusters; the value range of the profile coefficient SC is [ -1,1], the larger the value is, the more reasonable and effective the clustering result obtained by selecting the clustering number corresponding to the value is, and the selection of the classification number is judged through the profile coefficient curve.
8. The structural damage identification method based on improved self-adaptive noise complete integrated empirical mode decomposition according to claim 1, wherein in step 5, the characteristics of instantaneous amplitude, phase and the like are calculated, and a composite energy factor is constructed, and the existence of structural damage and the damage position are automatically judged according to a PELT algorithm specifically as follows: the corresponding formula for the Hilbert transform is:
wherein c (t) refers to the signal to be transformed; after Hilbert transformation, an analytic signal is obtainedThe instantaneous amplitude and phase can be obtained from the resolved signal:
when the structure of the system itself changes or the state of the system changes into an abnormal state, the energy of the system itself also changes, so the energy generally can better reflect structural damage, and the calculation formulas of the instantaneous energy and a certain signal energy are as follows:
phase changes are typically caused when structural systems are damaged or abnormal; in addition, the change condition of the information contained in the signal is indirectly known by analyzing the phase slope; thus, after the energy and phase characteristics are obtained, the damage index is constructed based on the energy, phase slope, respectively:
wherein E is h (t)、E d (t) represents energy obtained under healthy and injured conditions, PS h 、PS d Respectively representing the slopes of the phases under the conditions of health and damage, and fitting a linear regression equation according to the least square method principle to obtain the linear regression equation;
DI based (E) With DI (PS) Fusion construction of a composite energy factor:
the PELT algorithm is implemented by minimizing the following cost function:
wherein,is a local cost function for evaluating the time point tau j To tau j+1 Fitting goodness of time series column segments; />k (·, i) is an RBF kernel function; beta is punishment item, M is the total number of detected change points, and the existence and the damage position of the structural damage can be automatically judged.
9. The method for structural damage identification based on improved adaptive noise-complete-integration empirical-mode decomposition of claim 8, wherein β = 1, is used to control the total number of change points to prevent overfitting.
10. A structural damage identification storage medium based on improved adaptive noise-complete-integration empirical-mode decomposition, having stored thereon a computer program which, when executed by a processor, implements a structural damage identification method based on improved adaptive noise-complete-integration empirical-mode decomposition as claimed in any one of claims 1 to 9.
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