Data-driven structural fatigue crack detection method and system based on violin plot method

Abstract

The present invention provides a data-driven structural fatigue crack detection method and system using a violin plot method, comprising the following steps: applying an excitation to one end of a structure to be tested, collecting acceleration response signals at multiple different locations of the structure to be tested using multiple acceleration sensors; rearranging the time domain data of the acceleration response signals at the multiple different locations in ascending order, and plotting a box plot of the time domain data at the different locations; performing kernel density trajectory estimation on the rearranged time domain data to obtain a kernel density estimation curve, and combining the kernel density estimation curve with the box plot to plot a violin plot; and determining fatigue cracks based on the plotted violin plot. This method can quickly and easily analyze massive amounts of data from various sensors, extract fatigue crack information, quickly and accurately extract dynamic characteristic information, and visualize the extent of fatigue damage, making it a lightweight detection technology.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring and safety early warning, and in particular to a data-driven violin plot method and system for detecting structural fatigue cracks. Background Art

[0002] Since the 21st century, infrastructure, civil, commercial, and industrial construction have developed rapidly. At the same time, the loads borne by old engineering structures have deviated from the original design objectives. In the new era, large-span, complex, long-life, and multifunctional modern structures are often exposed to harsh service environments for a long time. To ensure the normal, safe and stable operation of structures, the safety of construction structures has become a key issue of concern, and the demand for structural health monitoring has shown rapid growth. As structural health monitoring systems collect massive amounts of data, how to analyze the status of structures based on this data has become the core content of structural health monitoring. Currently, with the development of science and technology, especially the rapid development of information data analysis and processing technology, analysis methods with data as the core have rapidly emerged, triggering new thinking in structural health monitoring.

[0003] Under the condition that it is difficult to establish an accurate mechanism model, data-driven methods can achieve structural optimization control and evaluation, and can provide solutions for structural state fatigue crack analysis. Currently, the commonly used fatigue crack identification methods are mainly based on the known system and its dynamic output signal. The response data collected by the monitoring sensor is used to identify cracks through methods such as generalized likelihood ratio test and wavelet packet sensitivity identification. The generalized likelihood ratio test method is used to study fatigue cracks, aiming to detect the smallest crack size, but lacks the detection of different crack depths. The wavelet packet sensitivity identification method also requires obtaining external load information, and the forward and reverse operations performed in the time-frequency domain are computationally inefficient and the process is complicated. Currently, there is a lack of a lightweight detection technology that can quickly and easily analyze the massive data from various sensors, extract fatigue crack information, quickly and accurately extract dynamic characteristic information, and visualize the degree of fatigue damage. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a data-driven violin plot method and system for structural fatigue crack detection. This method can quickly and easily analyze massive data from various sensors, extract fatigue crack information, quickly and accurately extract dynamic characteristic information, and visualize the degree of fatigue damage. It is a lightweight detection technology.

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

[0006] A data-driven structural fatigue crack detection method using a violin plot method comprises the following steps:

[0007] Apply at one end of the structure to be tested Excitation: using multiple acceleration sensors to collect acceleration response signals at multiple different positions of the structure to be tested;

[0008] The time domain data of the acceleration response signals at multiple different locations are rearranged in order from small to large to obtain the minimum value, first quartile, median, third quartile and maximum value of the time domain data, and a box plot of the time domain data at different locations is drawn based on this;

[0009] Perform kernel density trajectory estimation on the time domain data after rearrangement at each position to obtain the kernel density estimation curve, and then combine the kernel density estimation curve with the box plot to draw a violin plot;

[0010] Fatigue cracks are judged based on the drawn violin plot: when there are no fatigue cracks in the structure, the violin plot will not produce a convexity and the graph will show a symmetrical distribution; if there are fatigue cracks, the violin plot will produce a convexity, the median will be offset, and it will move away from the center of symmetry as the degree of damage increases.

[0011] Preferably, the The excitation is a Gaussian distributed random excitation.

[0012] Preferably, the test structure is a cantilever beam, and an acceleration sensor is arranged along the length direction of the cantilever beam.

[0013] Preferably, the drawing of the box plots of the time domain data at different positions comprises the following steps:

[0014] Set the first median of the data obtained from the rearranged distribution as Q1, the third median as Q3, and calculate the interquartile moments:

[0015] IQR=Q3-Q1

[0016] Where, IQR is interquartile range;

[0017] At this time, the upper and lower limits of the box plot are:

[0018] MAX=Q3+1.5IQR

[0019] MIN=Q1-1.5IQR

[0020] Among them, MAX is the upper limit of the box plot, MIN is the lower limit of the box plot, the first median is Q1, and the third median is Q3.

[0021] Preferably, the drawing of the violin plot comprises the following steps:

[0022] Determine the upper and lower limits of the violin plot as the upper and lower limits of the box plot;

[0023] According to the upper and lower limits of the violin plot, extract the time domain data within the upper and lower limits after redistribution;

[0024] Perform kernel density estimation on the data within the upper and lower limits and draw the kernel density curve. The kernel density estimation method is as follows:

[0025]

[0026] Among them, x represents the data of one of the selected data points, n is the number of samples within the upper and lower limits, and h represents the interval width. When the data of point i is in [Xh / 2,X+h / 2], δ i =1, when the data of point i is not in [Xh / 2,X+h / 2], δ i =0.

[0027] After one-to-one correspondence between the value of the kernel density estimation at each point and the data of the point in the box plot, the kernel density estimation curve is obtained, and the violin plot is obtained by combining the curve with the box plot.

[0028] A system for detecting structural fatigue cracks using a data-driven violin plot method, comprising:

[0029] A detection module, comprising a plurality of acceleration sensors arranged on the structure to be tested;

[0030] The excitation application module applies the excitation to the end position of the structure to be tested. excitation;

[0031] A processor is configured to collect a response signal from each acceleration sensor and construct an acceleration response database; the processor rearranges the acceleration response data and plots a box plot of the time domain data at different positions; the processor performs kernel density trajectory estimation on the rearranged time domain data to obtain a kernel density estimation curve, and combines the kernel density estimation curve with the box plot to plot a violin plot; the processor performs fatigue crack judgment based on the plotted violin plot and outputs the result.

[0032] Beneficial effects of the present invention:

[0033] The present invention proposes a data-driven violin plot method and system for structural fatigue crack detection. The method can quickly and easily analyze massive data from various sensors, extract information about fatigue cracks, quickly and accurately extract dynamic characteristic information, and visualize the degree of fatigue damage. It is a lightweight detection technology. The method of the present invention targets the characteristics of fatigue cracks under multiple excitations, which produce a time-history data distribution curve that is different from the excitation distribution. The bulge of the kernel density trajectory curve in the violin plot clearly reflects the presence of fatigue cracks. The greater the bulge, the greater the degree of damage. As the median of the violin plot moves away from the center of symmetry, its value can reflect the size of the damage, and intuitively and accurately identify the location and degree of fatigue breathing cracks. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a flow chart of a data-driven structural fatigue crack detection method using a violin plot method according to an embodiment of the present invention;

[0035] Figure 2 : The distribution of violin plots and box plots at the same position under different crack depths in the numerical simulation of an embodiment of the present invention, where (a) is the response data, (b) is the violin plot, and (c) is the box plot;

[0036] Figure 3 : The distribution of violin plots and box plots at different locations under different crack positions in the numerical simulation of the embodiment of the present invention, where (a) is the response data, (b) is the violin plot, and (c) is the box plot;

[0037] Figure 4 : The distribution of violin plots and box plots at the same position under different crack depths in the experiment of the embodiment of the present invention, where (a) is the response data, (b) is the violin plot, and (c) is the box plot;

[0038] Figure 5 1 is the distribution of violin plots and box plots at different positions under different crack positions in the experiment of the embodiment of the present invention, where (a) is the response data, (b) is the violin plot, and (c) is the box plot. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, 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 intended to limit the present invention.

[0040] Example 1

[0041] During the long-term service of the structure, the complex environment causes a large number of tiny fatigue cracks. The cracks vibrate with the structure, showing a contact-separation "breathing" effect. After the damage accumulates, they continue to expand to a normally open state. When the local stiffness changes greatly, the nonlinearity generated will be significant, corresponding to a significant crack size. When the local stiffness changes insignificantly, the nonlinearity generated is smaller, which is consistent with the smaller crack depth. The present invention applies to the structure Excitation, when fatigue cracks exist, fatigue cracks The excitation signal is modulated to produce an abnormal distribution. At this time, the violin plot will have an obvious bulge. The greater the damage, the more obvious the bulge. The change in the median is numerically expressed to indicate the degree of damage.

[0042] The present invention provides a data-driven structural fatigue crack detection method using a violin plot method, such as Figure 1-5 As shown:

[0043] S1: Apply at one end of the structure to be tested Excitation, through multiple acceleration sensors to collect acceleration response signals at multiple different positions of the structure to be tested. Arrange multiple acceleration sensors on the structure to be tested, and electrically connect multiple acceleration sensors to the processor respectively. The processor is electrically connected to the power supply through the control switch. Multiple acceleration sensors form a detection group, and apply the acceleration response signals at the end position of the structure to be tested. The processor collects the response signal from each acceleration sensor and uses the response signal to establish an acceleration response database at different positions. In this embodiment, the excitation is a Gaussian distribution excitation.

[0044] S2: Rearrange the time domain data of the acceleration response signals at multiple different locations from small to large to obtain the minimum value, first quartile, median, third quartile, and maximum value of the time domain data, and use this to draw a box plot of the time domain data at different locations.

[0045] Specifically:

[0046] Set the first median of the data obtained from the rearranged distribution as Q1, the third median as Q3, and calculate the interquartile moments:

[0047] IQR=Q3-Q1

[0048] Where, IQR is interquartile range;

[0049] At this time, the upper and lower limits of the box plot are:

[0050] MAX=Q3+1.5IQR

[0051] MIN=Q1-1.5IQR

[0052] Among them, MAX is the upper limit of the box plot, MIN is the lower limit of the box plot, the first median is Q1, and the third median is Q3.

[0053] S3: Perform kernel density trajectory estimation on the rearranged time domain data to obtain the kernel density estimation curve, and combine the kernel density estimation curve with the box plot to draw a violin plot.

[0054] Specifically:

[0055] Determine the upper and lower limits of the violin plot as the upper and lower limits of the box plot;

[0056] According to the upper and lower limits of the violin plot, extract the time domain data within the upper and lower limits after redistribution;

[0057] Perform kernel density estimation on the data within the upper and lower limits and draw the kernel density curve. The kernel density estimation method is as follows:

[0058]

[0059] Among them, x represents the data of one of the selected data points, n is the number of samples within the upper and lower limits, and h represents the interval width. When the data of point i is in [Xh / 2,X+h / 2], δ i =1, when the data of point i is not in [Xh / 2,X+h / 2], δ i =0.

[0060] After one-to-one correspondence between the value of the kernel density estimation at each point and the data of the point in the box plot, the kernel density estimation curve is obtained, and the violin plot is obtained by combining the curve with the box plot.

[0061] S4: Fatigue cracks are judged based on the drawn violin plot: If there are no fatigue cracks in the structure, the violin plot will not have a convexity and the graph will be symmetrically distributed; if there are fatigue cracks, the violin plot will have a convexity, the median will be offset, and it will move away from the center of symmetry as the degree of damage increases.

[0062] Example 2, numerical simulation:

[0063] S1: Use ABAQUS to construct a cantilever beam. The geometric dimensions of the beam are: length (L = 300 mm), width (B = 25 mm), and thickness (H = 10 mm);

[0064] S2: Damage is set to fatigue crack

[0065] The opening and closing of a fatigue crack is considered a local contact problem. The interaction between the fatigue crack surfaces is modeled by treating one crack surface as the master surface and the other as the slave surface. During beam vibration, the fatigue crack exhibits three contact states:

[0066] (i) The crack is fully open, which means there is no contact between the primary and secondary surfaces.

[0067] (ii) All nodes on the secondary crack surface and the main crack surface are in contact, and the crack is completely closed.

[0068] (iii) Partial contact between the secondary crack surface and the main crack surface.

[0069] S3: Set the damage position along the length of the beam, and the distance from the damage position to the end is x c , the depth of the damage is a. In order to conveniently define the location and depth of the damage, the damage location and depth are defined as:

[0070] q=x c / L

[0071] p=a / H

[0072] Among them, x c represents the position of the damage location from the end, L is the length of the beam, q represents the relative position of the crack from the end, a represents the depth of the crack, H represents the thickness of the beam, and p represents the relative depth of the crack.

[0073] Three damage levels p were set, including p=7%, p=20% and p=41% damage levels; three relative damage positions q were q=0.040, q=0.450 and q=0.773, and the undamaged structure was set as the control.

[0074] S4: Set sensors along the length of the beam and select 10 points as the sensor locations.

[0075] S5: Б excitation is applied to the free end of the cantilever beam (using Gaussian distribution random excitation).

[0076] S6: Collect acceleration response at 10 points.

[0077] S7: Redistribute the time domain data at different locations and arrange them in order from small to large to obtain the minimum value, first quartile, median, third quartile, and maximum value of the data, and draw a box plot of the time domain data at different locations.

[0078] S8: Import the rearranged data from S7, perform kernel density trajectory estimation, combine the kernel density estimation curve with the box plot in step 2, and draw a violin plot. The method for drawing a violin plot is as follows:

[0079] (1) The upper and lower limits of the violin plot are the same as those of the box plot.

[0080] (2) Based on the upper and lower limits determined by the violin plot, extract the data that are redistributed and arranged within the upper and lower limits.

[0081] (3) Perform kernel density estimation on the data within the upper and lower limits and draw the kernel density curve. The kernel density estimation method is as follows:

[0082]

[0083] Among them, X represents the data of one of the selected data points, n is the number of samples within the upper and lower limits, and h represents the interval width. When the data of point i is in [Xh / 2,X+h / 2], δ i =1, when the data of point i is not in [Xh / 2,X+h / 2], δ i =0.

[0084] (4) After matching the value of the kernel density estimation at each point with the data of the point in the box plot one by one, the kernel density estimation curve is obtained, and the violin plot is obtained by combining the curve with the box plot.

[0085] S9: By Figure 2 、 Figure 3 It can be seen that when the structure is intact, the data is normally distributed. In contrast, as the crack depth increases, the median value shifts, indicating a gradually increasing skewed distribution. The degree of bulge clearly shows the extent of fatigue crack damage, and the violin plot clearly indicates the presence of damage at different locations.

[0086] Example 3, in terms of experiment:

[0087] S1: Three steel pieces were bonded together using a high-performance structural adhesive to form a cantilever beam with different crack parameters. The beam dimensions were L (300 mm) × B (25 mm) × H (10 mm).

[0088] S2: Set the damage position along the length of the beam, and the distance from the damage position to the end is x c , the depth of the damage is a. In order to conveniently define the location and depth of the damage, the damage location and depth are defined as:

[0089] q=x c / L

[0090] p=a / H

[0091] Among them, x c represents the position of the damage location from the end, L is the length of the beam, q represents the relative position of the crack from the end, a represents the depth of the crack, H represents the thickness of the beam, and p represents the relative depth of the crack.

[0092] Three damage levels p were set, namely p=7%, p=20% and p=41%; three relative damage positions q were q=0.040, q=0.450 and q=0.773, and the undamaged structure was set as the control.

[0093] S3: Use a laser side vibrometer to select 10 points along the length of the beam. The positions of the 10 points are consistent with the numerical simulation, and reflective powder is applied to these 10 points.

[0094] S4: Use the exciter to apply Б excitation to the free end of the cantilever beam (using Gaussian distribution random excitation)

[0095] S5: Automatic analysis by the laser vibrometer processor to obtain the acceleration response signals of 10 points

[0096] S6: Redistribute the time domain data at different locations and arrange them in order from small to large to obtain the minimum value, first quartile, median, third quartile, and maximum value of the data, and draw a box plot of the time domain data at different locations.

[0097] S7: Import the rearranged data from S6, perform kernel density trajectory estimation, combine the kernel density estimation curve with the box plot in step 2, and draw a violin plot.

[0098] S8: By Figure 4 、 Figure 5 Experimental results demonstrate a significant "breathing" effect of fatigue cracks, which modulates the excitation signal at the crack, deviating from the normal excitation signal distribution. As crack depth increases, the median shifts, indicating a progressively more skewed distribution. The degree of bulge clearly indicates the extent of fatigue crack damage, and violin plots clearly demonstrate the presence of damage at different locations.

[0099] Depend on Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 It can be obtained that the cracked beam is Numerical simulations and experiments demonstrate a significant "breathing" effect of fatigue cracks under excitation, causing the cracks to modulate the excitation signal, thereby deviating from the normal excitation signal distribution. The median value of a violin plot is used to quantitatively characterize the degree of distribution deviation. The bulge in the violin plot reflects the location and extent of the fatigue cracks. Analysis of the changes in the response signal deviation distribution reveals that when fatigue cracks are present, the violin plot will bulge. A larger bulge indicates a greater degree of damage, resulting in a larger shift in the median, which moves away from the center of symmetry as the damage level increases.

[0100] This method is based on the signal modulation characteristics of fatigue cracks, can effectively extract the damage location and extent, is sensitive to damage, and is suitable for expansion into practical applications.

[0101] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A data-driven structural fatigue crack detection method using a violin plot method, characterized in that: The following steps are involved: Applying È excitation at one end of the structure to be tested, and collecting acceleration response signals at multiple different positions of the structure to be tested through multiple acceleration sensors; The time domain data of the acceleration response signals at multiple different locations are rearranged in order from small to large to obtain the minimum value, first quartile, median, third quartile and maximum value of the time domain data, and a box plot of the time domain data at different locations is drawn based on this; Perform kernel density trajectory estimation on the time domain data after rearrangement at each position to obtain the kernel density estimation curve, and then combine the kernel density estimation curve with the box plot to draw a violin plot; Fatigue cracks are judged based on the drawn violin plot: if there are no fatigue cracks in the structure, the violin plot will not have any convexity and the graph will be symmetrically distributed; if there are fatigue cracks, the violin plot will have a convexity, the median will be offset, and it will move away from the symmetry center as the damage degree increases; The drawing of the violin plot comprises the following steps: Determine the upper and lower limits of the violin plot as the upper and lower limits of the box plot; According to the upper and lower limits of the violin plot, extract the time domain data within the upper and lower limits after redistribution; Perform kernel density estimation on the data within the upper and lower limits and draw the kernel density curve. The kernel density estimation method is as follows: Among them, x represents the data of one of the selected data points, n is the number of samples within the upper and lower limits, and h represents the interval width. When the data of point i is China Times, , when the data of point i is not China Times, ; After one-to-one correspondence between the value of the kernel density estimation at each point and the data of the point in the box plot, the kernel density estimation curve is obtained, and the violin plot is obtained by combining the curve with the box plot.

2. The data-driven violin plot method for structural fatigue crack detection according to claim 1, characterized in that: The È excitation is a Gaussian distributed random excitation.

3. The data-driven structural fatigue crack detection method using the violin plot method according to claim 1, characterized in that: The test structure is a cantilever beam, and an acceleration sensor is arranged along the length direction of the cantilever beam.

4. The data-driven structural fatigue crack detection method using the violin plot method according to claim 1, characterized in that: Drawing the box plots of the time domain data at different positions comprises the following steps: Set the first median of the data obtained by rearranging the distribution as , the third median is set to , calculate the interquartile range: Where, IQR is interquartile range; At this time, the upper and lower limits of the box plot are: Among them, MAX is the upper limit of the box plot, MIN is the lower limit of the box plot, and the first median is , the third median is .

5. A system for using the data-driven violin plot method for structural fatigue crack detection according to any one of claims 1 to 4, characterized in that: include: A detection module, comprising a plurality of acceleration sensors arranged on the structure to be tested; An excitation applying module applies an excitation to an end position of the structure to be tested; A processor, configured to collect a response signal from each acceleration sensor and construct an acceleration response database; The processor rearranges the acceleration response data and draws a box plot of the time domain data at different positions; the processor performs kernel density trajectory estimation on the rearranged time domain data to obtain a kernel density estimation curve, and combines the kernel density estimation curve with the box plot to draw a violin plot; the processor performs fatigue crack judgment based on the drawn violin plot and outputs the result.

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