Abstract
In the paper, a simple-supported wooden beam is used as the research object to identify the damage of the wood beam by finite element analysis and experimental research. First, ANSYS was used to establish the solid finite element model of the wood beam before and after the damage, and then the discrete wavelet transform was performed on the curvature mode of the wood beam before and after the damage, and the wavelet coefficient difference index was obtained after obtaining the high frequency wavelet coefficients. Then, the damage location of the wood beam was judged according to the sudden peak of the wavelet coefficient difference index, and the damage degree of the wood beam was estimated by fitting the relationship between the wavelet coefficient difference index and the degree of damage. Finally, the index was verified by the wooden beam test. The results show that the wavelet coefficient difference index can accurately identify the damaged location of the wood beams. The degree of damage to the wood beams at the damage location can be quantitatively estimated by fitting the relationship between the wavelet coefficient difference index and the degree of damage at the damage location. The research results provide a theoretical basis to identify wooden beam damage.
1. Introduction
Wood beams are the main load bearing elements of the historic timber structure; under the influence of environmental conditions, sudden disasters, human damage, and other factors, wood beams are prone to damage, affecting the safety, applicability, and durability of the wood structure of ancient buildings. They can seriously lead to the collapse of the entire wood structure. Therefore, the study of the identification of structural damage to wood beams is significant.
The three difficulties of time, spatial location, and damage level should be addressed in structural damage identification, and damage identification methods have been created to address the problems mentioned earlier [1, 2]. Structural damage can cause changes in the physical characteristics of the structure and in the modal parameters of the structure. As a result, the change in the modal parameters before and after the damage may be used to determine structural damage [3]. Some scholars have done much work on the early state damage detection of beams, and some research results have been achieved [4–6]. He et al. [7] showed that the index of the curvature modal difference could indicate the location of the damage and the degree of a cantilever beam. Xiang et al. [8] suggested the curvature-based modal utility information entropy as the damage detection index, and numerical modeling and testing on supported beams confirmed its validity. Ren et al. [9] studied the sensitivity of the natural frequency, the curvature mode, and the difference in the curvature mode to the damage of wooden beams and conducted a numerical simulation analysis on the wooden beams. Based on the first-order curvature mode difference index, the influence of noise pollution and mesh density on recognition accuracy was studied. However, some researchers have found that curvature modes are ineffective in identifying slight damage [10]. Therefore, we need to propose a new method to solve these problems.
The wavelet transform has the property of local amplification of the mutation signal in the time and frequency domains; so, it can determine the location and degree of minor damage that occurs in the structure. Janeliukstis et al. [11] suggested a damage identification algorithm based on the modal structural vibration wavelet transform, and the effectiveness of the proposed method was confirmed with finite element models of aluminum beams in different damaged parts. Bao et al. [12] performed the continuous wavelet transform of the curvature mode of the structure before and after damage. They obtained the wavelet coefficient difference index, which was shown to accurately discriminate the damage site and the degree of damage to the structure by finite element simulation and testing of the supported beam. Machorrolopez et al. [13] proposed a method of acoustic emission signal combined with continuous wavelet transform, and the proposed method was validated by concrete subjected to bending tests. The results showed that the method could identify the damaged state of concrete beams by the transformed wavelet energy index.
The abovemrntioned research results carry out relevant damage identification studies on different structures as research objects but relatively few damage identification studies on individual wood beam structures. This paper proposes a damage identification method based on the curvature mode and wavelet transform for simple-supported wooden beams. Compared to other methods, this method can better reflect the location of the damage to the wooden beam structure and has a particular sensitivity to the degree of damage. The degree of damage to the wooden beam at the damage location is quantitatively estimated by fitting the relationship equation between the difference index of the wavelet coefficient difference index at the damage location and the degree of damage. Specifically, first, ANSYS is used to build a solid finite element model of the wooden beam before and after damage and perform modal analysis. Then, the curvature mode of the wooden beam before and after the damage is subjected to a discrete wavelet transform to obtain high frequency wavelet coefficients and obtain the wavelet coefficient difference index. Then, the damage location of the wooden beam is judged according to the sudden change peak of the wavelet coefficient difference index, and the degree of the wooden beam is estimated by fitting the relationship between the wavelet coefficient difference index and the degree of damage. Second, the index was verified by wooden beam tests; finally, the limitations and challenges of the method are given in the conclusion.
2. Materials and Methods
2.1. Principle of Damage Identification in the Curvature Mode
According to the material mechanics theory, the static bending force of the beam is expressed as follows:where is the curvature, is the curvature radius, is the bending moment of the beam cross section, and is the flexural rigidity of the beam section.
According to the theory of material mechanics, the curvature function in any section of the beam is expressed as follows:where is the j order curvature modal, and is the modal coordinates. According to formulas (1) and (2), structural damage leads to a reduction in structural stiffness, which results in an increase in the vibration of the curvature mode. Therefore, sudden change in vibration of the curvature mode in a certain order can be used to diagnose structural damage.
To obtain the curvature mode of the structure before and after damage, the calculation must be performed with the central difference method based on the displacement mode [14, 15]. Under the premise that the displacement mode and the vibration mode of the equally spaced discrete unit nodes are known, the curvature mode is defined as follows:where represents the order of curvature modal at points, and represent lossless and lossy states, and is the distance between adjacent nodes.
2.2. Principles of Wavelet Transform Damage Identification
For any function , the continuous wavelet transform iswhere is the wavelet coefficient, is the wavelet function, is the complex conjugate of , and and are the translation and scale factors.
In an application, it is necessary to discretize the continuous wavelet. Its binary wavelet transform can be expressed as follows:
When , the above equation is the discrete wavelet transform.
2.3. Selection of Wavelet Functions
In signal analysis, choosing and building the appropriate wavelet function is essential. The results of different wavelet functions for the same problem differ in practice. Therefore, when using wavelet analysis to detect mutation signals, it is necessary to combine the analyzed signal’s characteristics with the research purpose and select the appropriate wavelet function for local mutation detection. In this paper, we refer to the process and principles of wavelet selection in the literature [16, 17], combine the analyzed signal’s characteristics, and finally select the bior6.8 wavelet function.
2.4. Structural Damage Identification Index
This paper uses the curvature mode indicator as the input signal. The bior6.8 wavelet is selected to perform the three-layer discrete wavelet transform to obtain the high-frequency wavelet coefficients and then make the difference to getwhere is the difference of wavelet coefficients at node under the order curvature mode before and after structural damage. and are the wavelet coefficients at node in the curvature mode before and after damage.
2.5. Damage Identification Steps
(1)First, a modal analysis was performed on the members of the wooden beam to obtain their first-order curvature modal data before and after damage.(2)The bior6.8 wavelet is used to perform the three-layer discrete wavelet transform in the first-order curvature mode before and after the damage and obtain the high-frequency wavelet coefficients and then make the difference to get the wavelet coefficient difference index.(3)The damage location was localized on the basis of the sudden peak of the wavelet coefficient difference index. The degree of damage to the wooden beam was estimated by fitting the relationship equation between the wavelet coefficient difference index and the degree of damage.2.6. Numerical Simulations
This paper uses a simple-supported timber beam as the research object for the localization of damage and the study of the degree of damage. The wood beam (width 160 mm and height 200 mm) with a span of 2400 mm and a net span of 2200 mm, and the specific dimensional arrangement of the wood beam is shown in Figure 1. To obtain the parameters related to the wood timber property in the finite element model of the simple-supported wood beam, the authors conducted wood timber property tests on the same batch of poplar wood beams. All tests were collected, fabricated, and tested according to national standards [18, 19], part of the test procedure is shown in Figure 2, and the results of the timber property tests of the wood beam are shown in Table 1.
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The three-dimensional solid model of the wood beam is simulated by the Solid185 unit with finite element ANSYS. The mesh cell size is 40 mm, the wood beam model is meshed by sweep command, and a total of 1960 solid cells are divided, as shown in Figure 3. The model x-axis is the beam length direction, the y-axis is the beam section height direction, and the z-axis is the beam section width direction. That means that the left end of the model constrains , , , , and , the right end constrains , , , and , and is constrained at the neutral axis to prevent the wood beam from moving in the z direction.
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It is assumed that the reduction of the cross-sectional height causes damage to the structure, so the damage is simulated in the finite element by reducing the cell cross-sectional size; the specific operation steps are as follows: at the bottom of the wooden beam along the beam width direction, create a rectangular slot body with length 160 mm, width 40 mm, depth 2 mm, 5 mm, 10 mm, 20 mm, 30 mm, and 40 mm and then carry out the Boolean operation. The FEM model of the wooden beam under different damage conditions is obtained by the command of subtracting the body from the body in the Boolean process. Figure 4(a) shows the finite element model of the wood beam for working condition 6, and Figure 4(b) shows the enlarged view of the damage of the wood beam finite element model for working condition 6. The degree of damage S is defined as the ratio of the depth of the rectangular slots he with the height of the beam h, that is, S = he/h, and the degree of damage is 1%, 2.5%, 5%, 10%, 15%, and 20%. The damage conditions are shown in Table 2.
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3. Results and Discussion
3.1. Comparison of the Inherent Frequency under Different Working Conditions
Based on the abovementioned damage conditions, the intrinsic frequencies of the wood beam before and after damage are shown in Table 3. Table 3 shows that it can be seen that the overall frequency change before and after damage to the wooden beam is small; the maximum relative change in frequency before and after damage is 9.42%. It shows that the frequency change is not sensitive to the slight local damage of the wood beam; working conditions 7–12 compared with the second-order frequency relative change of working conditions 1–6 showed that its amplitude is small, analysis of the reason, the location of the damage occurred in the vicinity of the vibration node, resulting in the relative change of frequency amplitude not apparent, and through this indicator, we can determine the occurrence of damage to the wood beam. However, the location and extent of damage to the wood beam cannot be judged.
3.2. Comparison of Displacement Vibration Patterns under Different Working Conditions
In order to verify whether displacement vibration is sensitive to damage, the displacement vibration data values corresponding to 56 nodes on a line on the middle top surface at the level of the center axis of the wooden beam in different working conditions were extracted in the article, considering that the test measurement points were arranged on the middle axis of the top surface of the wooden beam (Figure 5), and the spacing between each node in the model was 0.04 m. Displacement vibration patterns were converted according to the coordinate relationship between the nodes and the wooden beam model. The displacement vibration pattern is converted to the two-dimensional plane for analysis. In this section, the extracted displacement vibration patterns are normalized to the maximum amplitude of the vibration pattern to facilitate the subsequent analysis.
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Figures 6 and 7 are the first two orders of the displacement vibration pattern of single damage in working conditions 1–6 and working conditions 7–12, respectively, and Figure 8 is the first two orders of the displacement vibration pattern of two damage in working conditions 13–18, where the subpicture part is the magnification of the vibration pattern at the local damage location.
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As can be seen in Figures 6–8, in single damage or in two damage conditions, the difference between the first two orders of displacement vibration curves of the wooden beam structure is minimal and difficult to distinguish through the naked eye; so, it is difficult to identify the damage to the wooden beam structure using displacement vibration.
3.3. Single Location Damage Identification Analysis
In the measured measurements, the higher-order modes of the structure are not easily measured. At the same time, research scholars have found that lower-order methods play a dominant role in structural vibration; the first-order displacement array of the wooden beam is used as the original data for subsequent damage identification studies in this article [20]. In this article, the extracted first-order displacement vibrations are normalized to the maximum magnitude of the pulses to facilitate subsequent analysis.
The normalized first-order displacement mode calculates the first-order curvature modes of each working condition according to equations (3) and (4). Figures 9 and 10 show the first-order curvature modes of the single damage for working conditions 1–6 and working conditions 7–12, respectively.
As can be seen from Figures 9 and 10, when the damage degree is greater than the 5% case, the curvature mode at the damage location produces a sudden change, which can be identified by the peak of the sudden change to identify the location of wood beam damage; when the damage degree is less than the 5% case, the curvature mode at the damage location of the sudden change is not significant, and it is difficult to identify its damage location, indicating that the indicator is not sensitive in the case of minor damage to the structure, cannot remember the site of structural damage, coupled with the interference of external environmental noise, and may lead to the indicator not identifying the location of minor damage to the structure. Also, the wavelet transform has the feature of local amplification of abrupt signals in the time and the frequency domain, which can identify the location and the degree of minor structural damage. Therefore, in this paper, the first-order curvature modal data of wooden beams are subjected to a three-layer discrete wavelet transform using bior6.8 wavelets, and the high-frequency wavelet coefficients are derived and then divided to obtain the difference maps of the wavelet coefficients under each working condition, as shown in Figures 11 and 12. It should be noted that since the damage location is located in the cell between two nodes, the wavelet coefficient difference indicator is taken as the extreme value of one of the two mutation nodes; so, the peak of the mutation point in the wavelet coefficient difference map is located in one of the two nodes of the damaged cell, and it can indicate the existence of damage near this point.
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As can be seen in Figures 11 and 12, compared to the problem that the curvature mode index is not apparent to recognize minor damages to wood beams, the problem is effectively solved using the wavelet coefficient difference index. This indicator can amplify the signal of small abrupt changes in the modal curvature index and, at the same time, effectively reduce the influence of adjacent units, making the recognition effect more significant. In the case of slight damage, the wavelet coefficient difference index also has ups and downs at the undamaged position but its transformation amplitude is smaller than that of the damaged position, which has little influence on the determination of the damaged position; with the increasing damage degree, the wavelet coefficient difference at the undamaged position is almost close to the level, and the sudden change peak of the wavelet coefficient difference at the damaged position is pronounced, and the peak of the wavelet coefficient difference index increases with the increasing damage degree.
3.4. Two Location Damage Identification Analysis
To verify the sensitivity of the wavelet coefficient difference index for the identification of the two location damage, the working conditions (conditions 13–18) were established for the simultaneous presence of damage at positions 520–560 mm and 1040–1080 mm of the wooden beam. Figure 13 shows the first-order curvature modal diagrams of the two damage locations for cases 13–18. As shown in Figure 13, consistent with the single damage results, the indicator is not sensitive in the case of minor damage to the structure. It cannot identify the location of the damage to the wood beam and coupled with the interference of external environmental noise, which may cause the indicator to fail to identify the location of minor damage to the structure. Therefore, in this paper, the first-order curvature modal data of the wood beam are subjected to a three-layer discrete wavelet transform using bior6.8 wavelets, and the high-frequency wavelet coefficients are derived and then differenced to obtain the difference maps of wavelet coefficients under each working condition, as shown in Figure 14.
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As seen in Figure 14, the wavelet coefficient difference index produces a significant abrupt change at two predetermined damage locations of the wood beam. The location of damage to the structure of the wood beam can still be accurately determined in the case of minor damage, which indicates that the wavelet coefficient difference index is more effective than the curvature mode index in locating minor damage to the wood beam, and the maximum value of the wavelet coefficient difference index increases with the increasing damage degree.
3.5. Identification of the Degree of Damage
The wavelet coefficient difference index was found to increase with the increase in the degree of damage when a single damage and two damage localizations were performed on the wooden beam, which indicated that there was a close correlation between the wavelet coefficient difference index and the degree of damage with high sensitivity; so, the degree of the wooden beam could be estimated by fitting the relationship equation between the wavelet coefficient difference index and the degree of damage.
For single damage, this paper analyzes the working conditions 1–6 as an example and adds the simulation of the damage depth of 60 mm at the location of 520 mm–560 mm for single damage of the wooden beam by ANSYS, that is, the damage degree is 30%. The maximum value of the difference in the wavelet coefficient is shown in Table 4 (because the difference in the wavelet coefficient value is negative, and to facilitate analysis, the absolute value is taken).
In order to further obtain the relationship between the wavelet coefficient difference index and the degree of damage, this paper is based on the data in Table 4 and on the principle of least squares and used Origin software to fit the relationship curve between the wavelet coefficient difference and the degree of damage under different working conditions, where the number of polynomials fitted is taken as 3, and the damage fitting curve is shown in Figure 15.
The relationship between the wavelet coefficient difference index and the degree of damage in a single damage location (520 mm–560 mm) is obtained from Figure 15 as follows:where is the level of damage, and is the wavelet coefficient difference damage index.
The applicability of the fitted formula was verified in ANSYS by simulating a damage depth of 50 mm (a damage level of 25%) at the location of 520 mm–560 mm for a single damage to the wood beam.
Figure 16 gives the wavelet coefficient difference plot of 25% of the degree of damage in the single damage position of the wooden beam of 520 mm–560 mm. From Figure 13, the absolute value of the difference in the wavelet coefficient in the position of 520 mm–560 mm is 0.83026. Taking the absolute value of the difference of the wavelet coefficient into equation (8), the degree of damage at the position of 520 mm–560 mm is obtained as 24.63% using the MATLAB solution, which is only a 1.76% error. Therefore, the degree of the wooden beam can be estimated using equation (8).
For the two injuries, ANSYS increased the simulation of the depth of damage of 60 mm at 520 mm–560 mm and 1040 mm–1080 mm for the two injuries of the timber beam, that is, the degree of damage was 30%. The peaks of the wavelet coefficient difference for the two damage locations, 520 mm–560 mm and 1040 mm–1080 mm, are shown in Table 5 (because the peaks of the wavelet coefficient difference is negative, it is taken as an absolute value for the convenience of analysis).
According to the data in Table 5, based on the principle of least squares, Origin software was used to fit the relationship curves between the difference of the wavelet coefficients and the degree of damage under different working conditions, where the number of fitted polynomials was taken as 3. The damage fitting curves for the two damage locations are shown in Figure 17.
The relationship between the wavelet coefficient difference index and the degree of damage at the two damage locations was obtained from Figure 17 as follows:where is the level of damage, is the wavelet coefficient difference damage indicator at 520 mm–560 mm position, and is the wavelet coefficient difference damage indicator at the position 1040 mm–1080 mm.
The applicability of the fitted formula was verified in ANSYS by simulating the damage depth of 50 mm (the damage was 25%) at the locations of 520 mm–560 mm and 1040 mm–1080 mm for the two damage locations of the wood beam.
The wavelet coefficient difference plots of the 25% damage level for the two damage locations, 520 mm–560 mm and 1040 mm–1080 mm, for the wooden beams are given in Figure 18.
In Figure 18, the absolute values of the differences in the wavelet coefficient at the positions 520 mm–560 mm and 1040 mm–1080 mm are 0.59787 and 0.83205, respectively. The absolute values of the wavelet coefficient differences at the two damage positions are brought into equations (9) and (10), and the degree of damage at the 520 mm–560 mm position is obtained by using MATLAB to solve for 24.39%, with only 2.44% error; at the 1040 mm–1080 mm position, the damage degree is 24.61%, with only 1.56% error. Therefore, the degree of the wooden beam can be estimated using equations (9) and (10).
3.6. Experimental Verification
3.6.1. Experimental Program
To further verify the feasibility of the proposed method, wooden beams with the same material and dimensions as the numerical simulation were used as the research object. The wooden beams were divided into 20 parts of 110 mm each, and the damage was simulated by changing the cross-sectional dimensions of the wooden beams. The specific implementation was as follows: rectangular slots of length 160 mm, width 40 mm, and depth 2 mm, 5 mm, 10 mm, 20 mm, 30 mm, and 40 mm were manually cut by an electric planer at the bottom of the wooden beams along the beam width direction (Figure 19). The degree of damage S is defined as the ratio of the rectangular slot depth he to the beam height h, that is, S = he/h. The specific rectangular slot locations are shown in Table 6.
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The test adopted a single-point excitation and a multipoint output measurement method to conduct modal tests on the wooden beam. A force hammer was used to hammer the wooden beam at a preset reference point. The structure’s response was collected in batches by multiple INV9822 accelerometers from the Beijing Oriental Vibration and Noise Technology Research Institute. An average of 19 acceleration sensors must be placed within the clear span of the wooden beam. The magnetic holders are glued to the top surface of the wooden shaft with 502 glue and the acceleration sensors are installed on the magnetic holders. Data were collected and analyzed with a multifunctional data acquisition analyzer (model INV306N2) and DASP (V11) signal analysis software using an impact hammer to strike the eight # acceleration sensor measurement points three times. The field test and the schematic diagram are shown in Figure 20.
3.6.2. Analysis of Experimental Results
The inherent frequencies and vibration patterns of the wooden beam were calculated for different operating conditions by referring to the EMA modal test procedure in the DASP&INV product operation and using the guide. Table 7 compares the first second-order inherent frequencies of the intact wood beam finite element model with the first second-order inherent frequencies of the test. From Table 7, it can be seen that the error between the first-order inherent frequency of the finite element model and the first-order inherent frequency of the tested beam is 1.74%, increases with the increase of the modal order, and the maximum value is 1.41%, which is within the acceptable range. Figure 21 compares the first two orders of displacement modal vibration patterns of the finite element model of the intact wood beam and the intact wood beam test. In Figure 21, it can be seen that the modal vibration pattern of the structure is consistent with the modal vibration pattern characteristics of the supported beam. Through the abovementioned analysis, the finite element model and the test results of the wooden beam can be verified with each other.
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(1) Single Location Damage Identification Analysis. This paper uses DASP (V11) signal analysis software to extract first-order displacement vibration data under different working conditions. Due to noise interference in the measurement process, the wavelet threshold method is used to denoise the measured displacement vibration data. Then, the denoised displacement vibration is normalized to the maximum magnitude. The wavelet coefficient difference diagrams under working conditions 1–6 are obtained by processing the displacement vibration data according to equations (3) to (7), as shown in Figure 22. It should be noted that since the damage location is located in the cell between two nodes, the wavelet coefficient difference indicator is taken as the maximum value of the two mutation nodes; so, the peak value of the mutation point in the wavelet coefficient difference diagram is located in one of the two nodes of the damaged cell, and it can indicate the existence of damage near this point.
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In Figure 22, it can be seen that the use of the wavelet coefficient difference index can effectively overcome the problem that the curvature mode index is not apparent for small damage identification and can accurately determine the location of the damage to the wood beam structure, and the maximum value of the wavelet coefficient difference index increases with the increasing damage degree. For working conditions 1–6, it should be noted that the location of the damage to the wooden beam in the test occurred in unit 5, and the nodes at both ends of unit 5 are 0.44 m and 0.55 m away from the end of the beam, respectively, and the horizontal coordinates in the figure are the beam length, while the wavelet coefficient difference indicators all peak at 0.44 m. This indicates that the wood beam was damaged near this location, and when combined with the actual location of the damage, it is clear that the wood beam was damaged in unit 5.
(2) Two Location Damage Identification Analysis. The wavelet coefficient difference plots for working conditions 7–12 are obtained according to the same processing method for single-site damage, as shown in Figure 23.
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As shown in Figure 23, the wavelet coefficient difference indicator can accurately locate the damage occurring in units 5 and 10 in the case of two damages. Even in the case of minor damage, the damage location can be correctly determined, indicating that the use of the wavelet coefficient difference index is better than the curvature mode index in locating minor damage, and the maximum value of the wavelet coefficient difference index increases with the degree of damage. For cases 7–12, it should be noted that damage to the wooden beam occurred in units 5 and 10, and the nodes of unit 5 were 0.44 and 0.55 m from the end of the beam, and the nodes of unit 10 were 0.99 and 1.1 m from the end of the beam. The peak value at 0.44 m and 1.1 m indicates that the beam is damaged near this location, and when combined with the actual damage location, it is known that the beam is damaged in unit 5 and unit 10.
(3) Analysis of Damage Level Identification. The wavelet coefficient difference index increases with the increase in damage degree when single damage and two damage localization are performed on wooden beams, so the damage degree of wooden beams can be estimated by fitting the relationship equation between the wavelet coefficient difference index and the damage degree.
Due to space limitation, this article analyzes the example of working conditions 1–6 in single damage. Table 8 shows the difference in the peak wavelet coefficient for the simple-supported wooden beam at the single damage location 480 mm–520 mm (unit 5) with different damage levels (because the wavelet coefficient difference value is negative, it is taken as the absolute value for the convenience of analysis).
In order to further obtain the relationship between the wavelet coefficient difference index and the degree of damage, this section based on the data in Table 8, based on the principle of least squares, and using Origin software to fit the relationship curve between the wavelet coefficient difference and the degree of damage under different conditions, where the number of polynomials fitted is taken as 3, the damage fitting curve at the position of 480 mm–520 mm (unit 5) is shown in Figure 24. It should be noted that only the wavelet coefficient difference corresponding to the damage degree of 1%, 2.5%, 5%, 10%, and 20% was fitted under this section, the wavelet coefficient difference under 15% damage degree was not involved in the fitting, and the purpose is to let the wavelet coefficient difference of 15% damage degree as a verification of the applicability of the fitting formula.
The relationship between the wavelet coefficient difference index and the degree of damage in a single damage is obtained from Figure 24 as follows:where x is the level of damage, and y is the wavelet coefficient difference damage indicator at position 480 mm–520 mm (unit 5).
To verify the applicability of the fitting formula, the absolute value of the difference in the wavelet coefficient at the position of 480 mm–520 mm (cell #5) was entered into equation (11) and solved using MATLAB to obtain a damage level of 14.51% at the position of 480 mm–520 mm (cell #5), with an error of only 3.27%; therefore, the damage level of the wooden beam can be estimated using equation (11).
4. Conclusion
This paper takes a simple-supported wooden beam as the research object, performs a three-layer discrete wavelet transform on the first-order curvature mode before and after the damage, proposes the method of using the wavelet coefficient difference damage index to identify the damage location and the damage degree of the wooden beam under different working conditions, and verifies the effectiveness of the method through numerical simulation and the wooden beam test; the conclusions are as follows:(1)In the case of one or two damage, the wavelet coefficient difference index can accurately identify the damage location of the wooden beam structure. It is sensitive to the degree of damage. The degree of the wooden beam at the damage location can be quantitatively estimated by fitting the relationship between the wavelet coefficient difference index and the degree of damage at the damage location.(2)Combined with the results of the damage identification test of the supported timber beams, it was found that the identification results were consistent with the numerical simulation results. The damage index could identify the location of the damage to the timber beam and estimate the extent of damage to the timber beam. The results of the study can provide a reference for future identification of wood beam damage.
Since noise and other effects are inevitable during the wood beam test, the next step can be to apply noise to the damage identification method used in this paper and explore the resistance to noise along the way. In addition, the damaged form of the wooden beam designed in this paper is more regular, and the damaged condition is single. However, in actual engineering, the structure of the wooden beam is complex. The damaged form is irregular, which is more difficult for the identification of the damage to the wooden frame; with the future development of modal test technology, this problem will gradually be improved.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The work was supported by the National Natural Science Foundation of China (52068063), Shandong Province Graduate Natural Science Foundation (ZR2020ME240), Gansu Province Natural Science Foundation Research Program (21JR1RE286), Gansu Province Higher Education Innovation Fund Project (2020B-173), Fuxi Scientific Research Innovation Team Project (FXD2020-13), and the Maijishan Grottoes Art Research Project of Tianshui Normal University (MJS2021-06).