A Directional Wavelet Multi-Scale Mode Derivative Method for Damage Detection of Shell Structures

Abstract

The present invention provides a method for detecting damage to a shell structure by using a directional wavelet multi-scale mode derivative quantity, belonging to the field of structural damage detection, including: obtaining the modal shape of the shell structure at any natural frequency and performing continuous Laplace transform calculation to obtain the mode derivative quantity; constructing a fourth integral function of a two-dimensional continuous mother wavelet and convolving it with the mode derivative quantity to respectively obtain various directional wavelet multi-scale mode derivative quantities; observing the damage identification effects of various directional wavelet multi-scale mode derivative quantities, selecting the two-dimensional continuous mother wavelet, angular parameter, and scale parameter with the best identification effect to construct the directional wavelet multi-scale mode derivative quantity, and judging the damage location according to the position where the singular peak appears in the figure. This method breaks through the limitation of the traditional vibration-based damage detection method that is insensitive to early weak damage of the shell structure, reduces the influence of noise on the damage identification performance, and can effectively locate and identify early weak damage of the shell structure in a noisy environment.

Description

Technical Field

[0001] The present invention relates to the technical field of structural damage detection, and particularly to a method for detecting damage to a shell structure by using a directional wavelet multi-scale mode derivative quantity. Background Art

[0002] During long-term service, shell structure facilities such as oil and gas storage tanks, nuclear facilities, main towers of wind turbines, power station boilers, and pressure pipelines will generate typical damages such as corrosion, cracks, and pits inside the structure. After accumulation, these damages will exacerbate the overall stability of the facilities, ultimately causing major safety accidents and seriously threatening the safe operation of shell structure facilities. In recent decades, a large number of studies have been conducted on damage detection methods for shell structures, and a damage detection system for shell structure facilities mainly based on vibration-based damage detection methods has gradually taken shape. However, there is no report on the research of constructing a directional wavelet multi-scale mode derivative quantity by combining the structural modal shape, the Laplace operator, and two-dimensional continuous wavelets and applying it to the damage detection of shell structures.

[0003] Damages to shell structure facilities mostly occur inside the structure, and the damage location cannot be directly judged visually. Traditional vibration-based damage detection methods cannot simultaneously meet the requirements of non-destructive testing, identifying early weak damages of the structure, anti-noise interference, and effectively identifying various typical damages. Therefore, the method of using traditional vibration-based damage detection methods to locate damages inside shell structures is not accurate enough. Summary of the Invention

[0004] To solve the above problems, the present invention provides a method for detecting damage to a shell structure by using a directional wavelet multi-scale mode derivative quantity. By constructing a mode derivative quantity and combining the concept of wavelet transform for improvement, a method for detecting damage to a shell structure based on a directional wavelet multi-scale mode derivative quantity is proposed.

[0005] To achieve the above object, the present invention provides the following technical solutions.

[0006] A method for detecting damage to a shell structure by using a directional wavelet multi-scale mode derivative quantity includes the following steps:

[0007] Obtain the modal shape of the shell structure to be detected at any natural frequency, perform continuous Laplace transform calculation on the modal shape to obtain a mode derivative quantity;

[0008] Select different two-dimensional continuous mother wavelets, respectively construct the fourth integral function of the two-dimensional continuous mother wavelet, and perform convolution with the mode derivative quantity to obtain respective directional wavelet multi-scale mode derivative quantities;

[0009] Observe the damage identification effects of the respective directional wavelet multi-scale mode derivative quantities, and determine the two-dimensional continuous mother wavelet with the best identification effect;

[0010] Select a two-dimensional continuous mother wavelet with the optimal identification effect, and successively select different angle parameters and scale parameters. Observe the damage identification effects of the multi-scale mode derivatives of wavelets in each direction respectively, and determine the angle parameter and scale parameter with the optimal identification effect;

[0011] Select a two-dimensional continuous mother wavelet, an angle parameter, and a scale parameter with the optimal identification effect, construct the multi-scale mode derivative of the directional wavelet, and judge the damage location according to the position of the singular peak in the mode derivative diagram.

[0012] Preferably, the continuous Laplace transform calculation of the mode shape to obtain the mode derivative includes the following steps:

[0013] Establish a finite element model of the damaged shell structure, conduct modal analysis and solution, and obtain the mode shape W(x1, x2) at any natural frequency;

[0014] Perform a continuous Laplace transform on the mode shape W(x1, x2) of the damaged shell structure to obtain the mode derivative:

[0015]

[0016] where, represents the first Laplace transform,

[0017] Preferably, the calculation of the multi-scale mode derivatives of wavelets in each direction includes the following steps:

[0018] Let the fourth integral of the two-dimensional continuous mother wavelet be a smooth function g(x1, x2), and convolve this function with the calculated mode derivative to obtain the multi-scale mode derivative of the directional wavelet:

[0019]

[0020] where a is the scale parameter, b1 and b2 are the translation parameters, φ is the angle parameter, is the multi-scale mode derivative of the directional wavelet.

[0021] Preferably, it further includes:

[0022] The calculated multi-scale mode derivative of the directional wavelet Before using it for damage identification, normalize this characteristic quantity to the interval [0, 1].

[0023] Preferably, the selection of the two-dimensional continuous mother wavelet includes 23 types of two-dimensional continuous mother wavelets. Compare the damage identification effects and select the two-dimensional continuous mother wavelet with the best identification performance.

[0024] Preferably, it further includes: The range of the angle parameter is:

[0025] i / 6π, where i = 0, 1, 2…11

[0026] Among them, there are a total of twelve parameter values representing directions.

[0027] Preferably, it further includes: the interval range of the scale parameter a is [1, 12].

[0028] Advantages of the present invention:

[0029] The present invention proposes a method for detecting damage to a shell structure using directional wavelet multi-scale mode derivatives. Compared with the effects of traditional vibration-based damage detection methods in the application of shell structures, it has the following advantages: The mode derivatives proposed in the present invention are obtained through continuous Laplace transforms of the mode shapes, having the ability to amplify the singular values caused by damage and overcoming the defect that traditional mode-based damage detection methods are insensitive to early weak damage to the structure. The directional wavelet multi-scale mode derivatives proposed in the present invention are improved by combining the concept of wavelet transform, having the effects of optimizing damage identification performance and smoothing noise. The present invention meets the requirements for early weak damage sensitivity, noise interference reduction, and applicability to various typical damages in shell structure damage identification, providing a new idea for damage detection methods for shell structure facilities in practical engineering. Description of the Drawings

[0030] Figure 1 It is a flow chart of the method of the present invention;

[0031] Figure 2 It is a finite element model diagram of a thin-walled cylinder structure according to an embodiment of the present invention;

[0032] Figure 3 It is a first-order modal shape diagram of a thin-walled cylinder structure according to an embodiment of the present invention;

[0033] Figure 4 It is a plane expansion diagram of the first-order modal shape of a thin-walled cylinder structure according to an embodiment of the present invention;

[0034] Figure 5 It is a diagram of mode derivatives according to an embodiment of the present invention;

[0035] Figure 6 It is a diagram of directional wavelet multi-scale mode derivatives under the optimal identification wavelet according to an embodiment of the present invention;

[0036] Figure 7 It is a diagram of directional wavelet multi-scale mode derivatives under the optimal identification angle according to an embodiment of the present invention;

[0037] Figure 8 It is a diagram of directional wavelet multi-scale mode derivatives under the optimal identification scale according to an embodiment of the present invention. Detailed Implementation Manner

[0038] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0039] Embodiment 1

[0040] A method for detecting damage to a shell structure based on a directional wavelet multi-scale mode derivative quantity, the flowchart is as Figure 1 shown, and it includes the following steps:

[0041] Step 1: Obtain the modal shape W(x1, x2) of the shell structure at any natural frequency, and perform continuous Laplace transform calculation on the modal shape to obtain a mode derivative quantity;

[0042] Step 2: Construct a fourth-order integral function of a two-dimensional continuous mother wavelet, and convolve it with the mode derivative quantity to obtain a directional wavelet multi-scale mode derivative quantity;

[0043] Step 3: Select different two-dimensional continuous mother wavelets, construct corresponding directional wavelet multi-scale mode derivative quantities, preliminarily observe the damage identification effect, and obtain the two-dimensional continuous mother wavelet with the best identification effect;

[0044] Step 4: Select different angle parameters, observe the damage identification effect again, and obtain the direction angle with the best identification effect;

[0045] Step 5: Select different scale parameters, finally observe the damage identification effect, obtain the scale parameter with the best identification effect, and judge the damage location according to the position where the singular peak appears in the identification diagram.

[0046] Specifically, the steps for obtaining the modal shape of the damaged shell structure in Step 1 include:

[0047] (1) Use the modeling software ANSYS to establish a finite element model of the damaged shell structure, set parameters such as the radius, height, material thickness, material density, material elastic modulus and Poisson's ratio of the shell structure, perform modal analysis and solution, and obtain the modal shape W(x1, x2) at any natural frequency. The modal shape of the shell structure is not limited to the modal displacement information at a specified natural frequency, and the modal shapes at each natural frequency can be used as analysis objects.

[0048] (2) Perform continuous Laplace transform on the modal shape W(x1, x2) of the damaged shell structure to obtain the mode derivative quantity:

[0049]

[0050] Where Represents a Laplace transform,

[0051] The modal derivative quantity shows obvious singular values at the structural damage location, and this characteristic quantity can usually be obtained by solving through the finite element difference method:

[0052]

[0053]

[0054]

[0055] In the formula, and are the modal curvatures of the shell along the two directions of x1 and x2 respectively, is the modal torsional curvature of the shell. Among them, l x1 and l x2 are the sampling point spacings along the two directions of x1 and x2 on the shell structure respectively.

[0056] Specifically, the calculation method of step two is as follows:

[0057] Let the fourth integral of the two-dimensional continuous mother wavelet be a smooth function g(x1, x2), and convolve this function with the calculated modal derivative quantity to obtain the directional wavelet multi-scale modal derivative quantity:

[0058]

[0059] In the formula, a is the scale parameter, b1 and b2 are the translation parameters, φ is the angle parameter, Ψ is the two-dimensional continuous mother wavelet.

[0060] In the formula, C Ψ is the discriminant function with respect to Ψ, expressed as:

[0061]

[0062] In the formula, is the Fourier transform of Ψ, is the angular frequency. If the two-dimensional mother wavelet Ψ satisfies C Ψ < ∞, then it is said to satisfy the admissibility condition.

[0063] Specifically, before using the calculated directional wavelet multi-scale modal derivative quantity for damage identification, this characteristic quantity needs to be normalized to the interval [0, 1].

[0064] Specifically, the specific operation method of Step 3 is to use 23 common two-dimensional continuous mother wavelets (such as Morlet wavelet, Mexican hat wavelet, Dog wavelet, Gaus wavelet, Fan wavelet, Pethat wavelet, Dogpow wavelet, Sinc wavelet, etc.), compare the damage identification effects, and select the two-dimensional continuous mother wavelet with the best identification performance.

[0065] Before preliminarily observing the damage identification effect of the constructed directional wavelet multi-scale mode derivative, the selected scale parameter a = 1 and the angle parameter φ = π. When performing damage identification on the shell structure, the two-dimensional continuous wavelet with the best identification effect is determined as the identification wavelet.

[0066] Specifically, the selected angle parameter φ in Step 4 is i / 6π, where i = 0, 1, 2…11, a total of twelve parameter values representing directions. Before observing the damage identification effect again for the constructed directional wavelet multi-scale mode derivative, the selected scale parameter a = 1. When performing damage identification on the shell structure, the angle parameter with the best identification effect is determined as the identification angle.

[0067] Specifically, the range of the scale parameter a that can be selected in Step 5 is [1, 12]. When performing damage identification on the shell structure, the scale parameter with the best identification effect is determined as the identification scale. Finally, the damage location of the shell structure is determined by observing the position of the singular peak in the identification diagram.

[0068] The working principle of the present invention is as follows: The dynamic response change of the shell structure caused by early weak damage is not obvious, and noise easily masks the dynamic response signal. The application of traditional vibration-based damage detection methods in shell structures is not ideal. Considering this, the present invention proposes to perform continuous Laplace transform on the modal shape of the shell structure to obtain a mode derivative, which is sensitive to early weak damage. Construct the fourth integral function of the two-dimensional continuous mother wavelet and convolve it with the mode derivative to obtain a directional wavelet multi-scale mode derivative, which has the effects of optimizing damage identification performance and smoothing noise. Finally, the damage location of the shell structure is located by observing the position of the singular peak in the damage diagram.

[0069] Embodiment 1

[0070] The present invention will be further described below with reference to the accompanying drawings through Embodiment 1:

[0071] The shell structure used in this example is a thin-walled cylinder with a radius of 10 m, a height of 20 m, a cylinder thickness of 10 mm, an elastic modulus of 201 GPa, and a density of 7850 kg / m 3, the Poisson's ratio is 0.3. The finite element used is the shell181 shell element. The model is divided into 50 parts along the axial direction of the cylinder and 120 parts along the circumferential direction, with a total of 6,000 elements planned. Each 0.4 m along the axial direction of the cylinder and every 3° along the circumferential direction is a unit node, and each unit node is regarded as a sampling point. Suppose there is a damaged area of 0.4 m × 1 m at the axial height of 10 m and circumferential angle of 45° of the thin-walled cylinder structure. The damage type is internal corrosion and peeling of the structure, and the damage degree is 10%.

[0072] As Figure 2 shown, a finite element model of the thin-walled cylinder structure with damage is established.

[0073] Perform modal analysis on the thin-walled cylinder structure with damage to obtain the modal vibration mode at any natural frequency of the shell structure, and select the first-order modal vibration mode as the analysis object.

[0074] As Figure 3 shown, the first-order modal vibration mode of the thin-walled cylinder structure with damage is obtained.

[0075] As Figure 4 shown, expand the first-order modal vibration mode of the thin-walled cylinder structure with damage obtained to a two-dimensional plane. Among them, h(m) represents the axial height direction of the thin-walled cylinder, θ(°) represents the circumferential angle direction of the thin-walled cylinder, W represents the modal vibration mode of the thin-walled cylinder, and it is difficult to directly judge the damage position from the vibration mode in the figure.

[0076] As Figure 5 shown, calculate the modal vibration mode derivative at the first natural frequency of the thin-walled cylinder structure with damage according to formulas (1)-(5). For easy observation, normalize this characteristic quantity to the interval [0,1]. It can be observed from the modal vibration mode derivative diagram that a large singular peak appears at the damaged area, and irregular protrusions appear in other areas, and the recognition effect is average.

[0077] Obtain the directional wavelet multi-scale modal vibration mode derivative at the first natural frequency of the thin-walled cylinder structure with damage according to formulas (6)-(7). For easy observation, normalize this characteristic quantity to the interval [0,1]. Before initially observing the damage recognition effect of the constructed directional wavelet multi-scale modal vibration mode derivative, the selected scale parameter a = 1 and angle parameter φ = π. After substituting different two-dimensional continuous mother wavelets for observation respectively, the two-dimensional continuous Morlet wavelet with the best recognition effect is selected.

[0078] As Figure 6 shown, initially perform damage recognition, and select the two-dimensional continuous Morlet wavelet as the recognition wavelet according to the quality of the recognition effect. It can be seen from the figure that an obvious singular peak appears at the damage position, but the recognition effect is not good, and the angle parameter and scale parameter need to be adjusted.

[0079] After determining the two-dimensional continuous Morlet wavelet as the recognition wavelet, the scale parameter a = 1 is selected, the angle parameter is adjusted, and it is observed that the angle parameter with the best recognition effect is φ = 0.

[0080] As Figure 7 shown, damage identification is carried out again. According to the quality of the recognition effect, the angle parameter φ = 0 is selected as the recognition angle. Compared with Figure 6 , some protrusions in the recognition area disappear and the recognition effect is better.

[0081] Determine the two-dimensional continuous Morlet wavelet as the recognition wavelet, determine the angle parameter φ = 0, adjust the scale parameter, and it is observed that the scale parameter with the best recognition effect is a = 3.

[0082] As Figure 8 shown, finally damage identification is carried out, and the scale parameter a = 3 is selected as the recognition scale. Compared with Figure 7 , there are only obvious singular peaks in the recognition area, and the irregular protrusions caused by noise interference have disappeared. The internal damage location of the shell structure can be determined according to the position of the singular peaks.

[0083] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for detecting damage to a shell structure using a directional wavelet multi-scale mode derivative quantity, characterized in that, It includes the following steps: Obtain the modal vibration mode at any natural frequency of the shell structure to be detected, perform continuous Laplace transform calculation on the modal vibration mode, and obtain the vibration mode derivative; Select different two-dimensional continuous mother wavelets, respectively construct the fourth integral functions of the two-dimensional continuous mother wavelets, and perform convolution with the vibration mode derivative to obtain the multi-scale vibration mode derivatives in each direction, and construct the multi-scale vibration mode derivative diagrams in each direction; Observe the damage identification effect of the multi-scale vibration mode derivative diagrams in each direction, and determine the two-dimensional continuous mother wavelet with the best identification effect; Select the two-dimensional continuous mother wavelet corresponding to the best identification effect, and sequentially select different angle parameters and scale parameters, respectively observe the damage identification effect of the multi-scale vibration mode derivative diagrams in each direction, and determine the angle parameter and scale parameter with the best identification effect; Select the two-dimensional continuous mother wavelet, angle parameter and scale parameter with the best identification effect, construct the multi-scale vibration mode derivative in the direction, and judge the damage location according to the position where the singular peak appears in the vibration mode derivative diagram; The continuous Laplace transform calculation of the modal vibration mode to obtain the vibration mode derivative includes the following steps: Establish a finite element model of the damaged shell structure, perform modal analysis and solution, and obtain the modal vibration mode W(x1,x2) at any natural frequency; Perform continuous Laplace transform on the modal vibration mode W(x1,x2) of the damaged shell structure to obtain the vibration mode derivative: Among them, represents a Laplace transform once, The selection of different two-dimensional continuous mother wavelets, respectively constructing the fourth integral functions of the two-dimensional continuous mother wavelets, and performing convolution with the vibration mode derivative to obtain the multi-scale vibration mode derivatives in each direction includes the following steps: Let the fourth integral of the two-dimensional continuous mother wavelet be a smooth function g(x1,x2), perform convolution on this function and the calculated vibration mode derivative to obtain the multi-scale vibration mode derivative in the direction: where a is the scale parameter, b1 and b2 are the translation parameters, φ is the angle parameter, Ψ is a two-dimensional continuous mother wavelet; where C Ψ is the discriminant function with respect to Ψ, expressed as: In the formula, is the Fourier transform of Ψ, is the angular frequency. If the two-dimensional mother wavelet Ψ satisfies C Ψ < ∞, it is said to satisfy the admissibility condition.

2. The directional wavelet multi-scale mode-derived quantity shell structure damage detection method according to claim 1, wherein It also includes: Calculated directional wavelet multi-scale mode derivative Before using for damage identification, the directional wavelet multi-scale mode derivative is normalized to the interval [0, 1].

3. The directional wavelet multi-scale mode derivative quantity shell structure damage detection method according to claim 1, characterized in that The selection of the two-dimensional continuous mother wavelet includes 23 types of two-dimensional continuous mother wavelets. Compare the damage identification effects and select the two-dimensional continuous mother wavelet with the best identification performance.

4. The directional wavelet multi-scale mode shape derivative-based shell structure damage detection method according to claim 1, characterized in that It also includes: The range of the angle parameter is: i / 6π, i = 0, 1, 2…11 Among them, there are a total of twelve direction parameter values.

5. The method for detecting damage of a directional wavelet multi-scale mode shape derivative quantity shell structure according to claim 1, wherein It also includes: The interval range of the scale parameter a is [1, 12].

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