CN111488710A - Structure damage identification method based on self-adaptive WOA-VMD and range entropy - Google Patents
Structure damage identification method based on self-adaptive WOA-VMD and range entropy Download PDFInfo
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Abstract
The invention provides a structure damage identification method based on self-adaptive WOA-VMD and range entropy, which comprises the following steps: 1) acquiring an acceleration time-course signal of the civil structure under random excitation; 2) performing self-adaptive decomposition on the signals obtained in the step 1) by using a WOA-VMD method, and obtaining an optimal parameter combination when ensuring that a fitness function is minimum; 3) taking the optimal parameter combination as a standard combination of VMD decomposition, and decomposing signals of a health state and a damage state to obtain IMF components of each order; 4) calculating the range entropy of the first-order IMF component under each working condition in the step 3), and judging whether the structure generates initial damage or not through entropy change. The method comprises the steps of firstly utilizing a WOA algorithm to realize signal self-adaptive decomposition of the VMD, then utilizing the VMD to decompose the vibration signal, calculating the range entropy of the first component, and judging whether the structure is damaged or not according to fluctuation.
Description
Technical Field
The invention relates to a structure health monitoring technology, in particular to a structure damage identification method based on self-adaptive WOA-VMD and range entropy.
Background
The service life of a large-scale structure is dozens of years or even hundreds of years, damage accumulation and resistance attenuation of a structure system are inevitably caused under the combined action of environmental erosion, material aging, long-term effect and fatigue effect of load, mutation effect of disaster factors and the like, and catastrophic accidents can be caused under extreme conditions. Therefore, in order to ensure the safety, integrity and durability of the structure, the large-scale structure which is built for use needs to adopt effective means to monitor and evaluate the damage degree and the safety state. With the improvement of testing means and analysis technology, structural health monitoring systems are arranged in some built and established large-scale structures at home and abroad to monitor and evaluate the damage and safety states of the structures.
As a core technology of bridge health monitoring, structural damage identification becomes a research hotspot in recent years, and is widely verified through experiments. In the process of identifying the damage of the bridge, the most important work is to determine the change of the structural state according to the structural response of different excitations, search parameters which are relevant to structural characteristics and sensitive to structural damage, and identify the damage of the structure according to the change of the parameters.
However, in the study and application of damage identification, raw sampling data without preprocessing is often directly used. The bridge structure is usually located in a complex external environment, under the influence of various factors, a bridge health monitoring system is always interfered by noise, and a large amount of state information of the structure is hidden in the noise, so that the damage identification rate is low, and the damage of the structure cannot be accurately identified directly through sampling data. The traditional damage identification methods have certain application ranges and also have some defects, such as being easily influenced by environmental factors and being difficult to identify the initial damage of the structure so as to finish early warning, so that the practicability and the effectiveness are limited.
Disclosure of Invention
The invention aims to solve the technical problem of providing a structure damage identification method based on self-adaptive WOA-VMD and range entropy aiming at the defects in the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a structure damage identification method based on adaptive WOA-VMD and range entropy comprises the following steps:
1) acquiring an acceleration time-course signal of the civil structure under random excitation, and recording the acceleration time-course signal as X;
2) performing self-adaptive decomposition on the signal X obtained in the step 1) by using a WOA-VMD method, and obtaining an optimal parameter combination (α, K) when ensuring that a fitness function is minimum;
α is a penalty parameter, wherein the smaller α is, the larger the bandwidth of each component is, and the smaller the bandwidth is otherwise;
the method comprises the following specific steps:
2.1) carrying out self-adaptive decomposition on the signal X obtained in the step 1) by utilizing a VMD method;
2.2) introducing a whale optimization algorithm WOA to perform parameter optimization on the VMD, and when the fitness function is minimum, obtaining an optimal parameter combination;
the fitness function mean envelope spectral entropy (MEE) is defined as:
wherein, a (j) is envelope curve of signal, pja (j) is a normalized form of envelope, K is the number of IMF components obtained by VMD, and represents the envelope entropy value of each IMF component, and obviously, the smaller the MEE, the signalThe more apparent the content. Therefore, the parameter optimization of the VMD is converted into the minimization problem of the fitness function;
3) the optimal parameter combination is used as a standard combination of VMD decomposition, and signals of a health state and a damage state are decomposed to obtain IMF components of each order;
4) calculating the range entropy of the first-order IMF component under each working condition in the step 3), and judging whether the structure is damaged or not through entropy change, namely judging whether the structure is damaged or not according to entropy fluctuation.
The invention has the following beneficial effects:
the method can effectively overcome the defects of the existing monitoring method, and can effectively diagnose the working conditions of single damage, multiple losses, initial damage and the like.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a flow chart of the WOA-VMD algorithm of an embodiment of the present invention;
FIG. 3 is a diagram of the acceleration time course of a benchmark raw signal in a healthy state according to an embodiment of the present invention;
FIG. 4 is a graph of the convergence of the WOA-VMD fitness function of an embodiment of the present invention;
FIG. 5 is a diagram illustrating acceleration time courses of benchmark decomposition results in a healthy state according to an embodiment of the present invention;
FIG. 6 is a diagram of a WOA-VMD original signal and a spectrum of a decomposition result of a benchmark original signal in a healthy state according to an embodiment of the present invention;
FIG. 7 is case 1 in an embodiment of the present invention: entropy diagram of each working condition under single damage state;
FIG. 8 is case 2 in an embodiment of the present invention: entropy diagrams of various working conditions under multiple damage states;
FIG. 9 is case 3 in an embodiment of the present invention: working condition 1 entropy diagram under different rigidity losses;
FIG. 10 is case 3 in an embodiment of the present invention: working condition 2 entropy diagram under different rigidity losses;
FIG. 11 is case 3 in an embodiment of the present invention: working condition 3 entropy diagram under different rigidity losses;
fig. 12 is case 3 in the embodiment of the present invention: working condition 4 entropy diagram under different rigidity losses;
fig. 13 is case 3 in the embodiment of the present invention: working condition 5 entropy value graph under different rigidity losses;
FIG. 14 is case 3 in an embodiment of the present invention: and (4) working condition 6 entropy value graphs under different rigidity losses.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, a structure damage identification method based on adaptive WOA-VMD and range entropy includes the following steps:
1) collecting vibration signals: acquiring an acceleration time-course signal of the civil structure under random excitation, and recording the acceleration time-course signal as X;
2) performing self-adaptive decomposition on the signal X obtained in the step 1) by using a WOA-VMD method, and obtaining an optimal parameter combination (α, K) when ensuring that a fitness function is minimum;
α is a penalty parameter, wherein the smaller α is, the larger the bandwidth of each component is, and the smaller the bandwidth is otherwise;
2.1) carrying out self-adaptive decomposition on the signal X obtained in the step 1) by utilizing a VMD method;
the basic theory of the VMD algorithm is as follows:
the VMD algorithm converts the decomposition problem of the signal into a variation framework for processing, and adaptively decomposes the signal by seeking an optimal solution of a variation model. The variation modal decomposition algorithm comprises two problems of constructing a variation framework and solving variation. And realizing self-adaptive signal decomposition by searching an optimal solution of the constraint variational model, and solving the center frequency and bandwidth of each Intrinsic Mode Function (IMF) component in the updating process of the variational model by iteration. And finally, finishing an iteration process according to the characteristics of the self-adaptive subdivided signal frequency band to obtain a series of narrow-band components.
The specific steps of VMD are as follows:
1) for each mode ukAnd (t) calculating a correlation analysis signal by using Hilbert transform to obtain a single-sided spectrum.
2) For each mode, the spectrum of the mode is shifted to "baseband", mixing an index tuned to the respective estimated center frequency.
3) By frequency-shifted H1The gaussian method estimates the bandwidth of the analysis signal, and obtains the following constraint variation problem:
wherein { ukAnd { omega } andkrepresents each order mode and its center frequency, respectively.
In order to effectively solve the constraint variation problem, a secondary penalty factor and a Lagrange multiplier are introduced. Thus, the augmented Lagrangian expression is rewritten as:
solving by adopting an Alternating Direction Multiplier Method (ADMM), wherein the IMF components and the corresponding center frequencies are updated by the following formula:
when the mode and the center frequency of each order are updated respectively, the Lagrange multiplier is also updated according to the following formula:
the updating process is repeated until the error tolerance is satisfied, and the constraint condition is as follows:
the value is typically 10-6 and all IMF components are obtained in the cyclic process described above.
2.2) introducing a whale optimization algorithm WOA to perform parameter optimization on the VMD, and when the fitness function is minimum, obtaining an optimal parameter combination;
the VMD algorithm is a time domain signal processing method which needs preset parameters, and when the parameter combination is selected differently, the signal decomposition is influenced. In view of the above, the whale optimization algorithm WOA is introduced to select the optimal parameter combination. The flow of the WOA-VMD algorithm is shown in FIG. 2.
The Whale Optimization Algorithm (WOA) performs mathematical simulation on a hunting process of a spiral bubble net strategy, shrinkage and enclosure, spiral position updating and random hunting mechanism of whales which continuously approach a hunting object, and has the characteristics of less adjusting parameters, strong global convergence, high convergence speed and the like. The WOA mathematical model includes 3 stages of wraparound predation, bubble net attack prey, and random search predation. The basic theory of the WOA algorithm is as follows:
the whales in the standing position can identify their location and surround them when looking for prey. The specific mathematical model is
In the formula, t is the current iteration times; x is the currently obtained prey position vector; x is whale position vector; a and C are coefficient vectors defined as
In the formula, a is a convergence factor and linearly decreases from 2 to 0 along with the increase of the iteration times; r is a random vector between [0,1 ].
To establish a mathematical model of whale's bubble net attack behavior, two methods were designed to simulate this behavior, as follows:
a shrink wrap mechanism. Only a needs to be reduced to achieve this behavior, and it is noted that a shrinks as a decreases. And updating spiral positions. The whale with a standing head continuously approaches to a prey in a spiral motion mode, and the mathematical model of the spiral motion is as follows:
to simulate this synchronization behavior, assume that the selection of either the shrink-wrap mechanism or the spiral position update probability is 50%. The mathematical model is as follows:
in the formula, p is a random number on [0,1 ]. The whale sitting in the head can randomly update the position of an individual to prey on prey. The whale carries out random search according to the mutual positions, and the specific process is as follows:
in the formula
To be from the current groupRandomly selected individual position vectors.
Parameter optimization is carried out on the VMD through the WOA, the traditional process of repeated trial and error by manpower can be avoided, and the characteristics of few adjusting parameters, simple structure, high convergence speed and the like of the WOA algorithm are combined, so that the parameter combination of the VMD is rapidly optimized, and the signal decomposition effect is improved.
A fitness function;
the information entropy represents the information quantity of the random variable from the macroscopic view and is a measure of the orderliness and uncertainty of the random variable, and the larger the information entropy is, the more the information quantity is, the larger the uncertainty is.
Similar to the entropy, the fitness function mean envelope spectral entropy (MEE) is defined as:
wherein, a (j) is envelope curve of signal, pja (j) is a normalized version of the envelope. K is the number of IMF components obtained by the VMD and represents the envelope entropy value of each IMF component. Clearly, the smaller the MEE, the more apparent the content of the signal. Therefore, the parameter optimization process of the VMD is intuitively described as a minimization problem of the fitness function.
3) The optimal parameter combination is used as a standard combination of VMD decomposition, and signals of a health state and a damage state are decomposed to obtain IMF components of each order;
the procedure is the same as 2.1), but the optimal parameter combination obtained by step 2) is used.
4) Calculating the range entropy of the first-order IMF component under each working condition in the step 3), and judging whether the structure generates damage or not through entropy change: including single lesions, multiple lesions, and primary lesions.
Selecting a first IMF component under each working condition, and calculating a range entropy, wherein the formula of the range entropy is as follows:
wherein
Representing the distance between the two state vectors,
each conditional probability is represented.
In order to verify the effectiveness of the method provided by the invention, an ASCE benchmark model is taken as an example here to identify the structural damage of several common damages, such as single damage, multiple damage and initial damage, and the specific application process is as follows:
1) case 1: occurrence of single injury
The ASCE benchmark model is a four-layer framework model. Firstly, selecting a healthy state to acquire time-course signals of 1 sensor, wherein the acceleration time-course in the healthy state is shown in figure 3, and selecting an optimal parameter combination by using a WOA-VMD algorithm, wherein the convergence curve is shown in figure 4, and the optimal parameter combination is (308, 4). VMD decomposition is again performed and the components are shown in fig. 5. The original signal and the frequency spectrum of each component are shown in fig. 6. It can be seen that the components contain the importance information of the original signal. And the first IMF component has the most important information.
And selecting different layers and respectively having one inclined strut to lose efficacy, namely the rigidity is 0. The operating conditions are shown in table 1. And acquiring acceleration signals of 1 sensor under each working condition. The first component was selected and its ApE, SaE and RnE were calculated, the results are shown in fig. 7.
TABLE 1
| Damage numbering | Description of |
| 0 | State of |
| 1 | Failure of No. 24 diagonal brace of |
| 2 | Second tier No. 53 bracing |
| 3 | Failure of No. 82 diagonal brace of |
| 4 | Failure of No. 87 diagonal brace of |
| 5 | Failure of No. 111 diagonal brace of |
| 6 | Fourth layer 115 brace failure |
And (4) analyzing results: it can be seen that ApE, SaE cannot identify structural damage, and RnE can better identify a single damage of a structure no matter where the damage occurs in the structure.
2) Case 2: multiple lesions occur
And on the basis of the condition 1, combining all working conditions and identifying multiple damages to the benchmark model. The operating conditions are shown in table 2.
TABLE 2
And acquiring acceleration signals of 1 sensor under each working condition, and decomposing the acceleration signals by using the VMD, wherein the result is shown in the figure. The original signal and the frequency spectrum of each component are shown in the figure. The first scores were selected and their apes, SaE and RnE calculated, the results are shown in figure 8,
and (4) analyzing results: it can be seen that ApE, SaE cannot identify multiple lesions of a structure, and RnE can both better identify multiple lesions of a structure.
3) Case 3: initial injury occurs
On the basis of the cases 1 and 2, one working condition is selected, and the benchmark model is subjected to initial damage identification under different degrees of rigidity loss. The operating conditions are shown in table 3.
TABLE 3
| Damage numbering | Description of Damage | Variation of |
| 0 | State of health | Without |
| 1 | First layer No. 24 bracing | 0-100％ |
| 2 | No. 53 bracing of second floor | 0-100％ |
| 3 | No. 82 third-layer diagonal bracing | 0-100％ |
| 4 | No. 87 third-layer diagonal bracing | 0-100％ |
| 5 | No. 111 diagonal brace of fourth layer | 0-100％ |
| 6 | Fourth layer 115 # bracing | 0-100％ |
And acquiring acceleration signals of 1 sensor under each working condition, and decomposing the acceleration signals by using the VMD, wherein the result is shown in the figure. The original signal and the frequency spectrum of each component are shown in the figure. The first component was selected and its ApE, SaE and RnE calculated, the results are shown in fig. 9-14.
And (4) analyzing results: it can be seen that ApE and SaE cannot identify the initial damage of the structure, and RnE can better identify the initial damage of the structure, thereby realizing damage early warning.
The invention specifies how to apply WOA-VMD and range entropy to carry out damage identification of the structure. By combining the analysis of the embodiment, the result of the damage identification of the structure shows that the method has better sensitivity, can well identify single damage, multiple damages and initial damage, and can internally detect whether the structure generates damage only by 1s of sampling signals, thereby better improving the damage identification capability.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (2)
1. A structure damage identification method based on self-adaptive WOA-VMD and range entropy is characterized by comprising the following steps:
1) acquiring an acceleration time-course signal of the civil structure under random excitation, and recording the acceleration time-course signal as X;
2) performing self-adaptive decomposition on the signal X obtained in the step 1) by using a WOA-VMD method, and obtaining an optimal parameter combination (α, K) when ensuring that a fitness function is minimum;
α is a penalty parameter, wherein the smaller α is, the larger the bandwidth of each component is, and the smaller the bandwidth is otherwise;
the method comprises the following specific steps:
2.1) carrying out self-adaptive decomposition on the signal X obtained in the step 1) by utilizing a VMD method;
2.2) introducing a whale optimization algorithm WOA to perform parameter optimization on the VMD, and when the fitness function is minimum, obtaining an optimal parameter combination;
3) the optimal parameter combination is used as a standard combination of VMD decomposition, and signals of a health state and a damage state are decomposed to obtain IMF components of each order;
4) calculating the range entropy of the first-order IMF component under each working condition in the step 3), and judging whether the structure is damaged or not through entropy change.
2. The adaptive WOA-VMD and range entropy based structural damage identification method of claim 1, wherein the fitness function defined in step 2) is mean envelope spectral entropy (MEE):
wherein, a (j) is envelope curve of signal, pjand a (j) is a normalization form of an envelope line, K is the number of IMF components obtained by VMD, and represents an envelope entropy value of each IMF component.
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