Defect local resonant frequency extraction method based on vibration response space clustering analysis

Abstract

The invention discloses a defect local resonant frequency extraction method based on vibration response space clustering analysis, and belongs to the field of nondestructive testing. The method comprises the following steps: processing an ultrasonic detection data set, calculating a difference function between a frequency spectrum of each scanning point and an average frequency spectrum, extracting a local maximum frequency, carrying out frequency statistics, and screening out an abnormal response frequency; in combination with the spatial distribution characteristics of the detection points, identifying a frequency cluster with spatial aggregation by adopting a density clustering algorithm to form a candidate local resonant frequency set; and constructing an intensity matrix under the candidate local resonant frequency, extracting energy attenuation characteristics in each direction by using an equal-angle scanning method, and comparing the energy attenuation characteristics with a preset threshold value to determine the defect local resonant frequency. The method does not need to preset defect positions and geometric features, can realize automatic extraction of the defect local resonant frequency under the condition of unknown defects, has the advantages of high identification precision, strong anti-interference capability, high calculation efficiency and the like, and is suitable for non-destructive testing requirements in an engineering environment.

Description

Technical Field

[0001] The present invention relates to a local resonance frequency extraction method for structural damage detection, in particular to a defect local resonance frequency extraction method based on vibration response space cluster analysis, and belongs to the technical field of non-destructive testing. Background Art

[0002] Local resonance detection technology matches the excitation frequency to the local resonant frequency of the defect area, stimulating a local resonance effect that significantly amplifies the vibration response at the defect. This increases the difference between the defect and background responses, improving detection sensitivity. Compared to traditional methods, this technology offers advantages such as non-contact, low excitation energy, and high sensitivity to tiny defects. It has been widely used for damage detection in metals, composite materials, and honeycomb sandwich structures, demonstrating strong engineering adaptability and significant development potential.

[0003] The accurate extraction of resonant frequency is a key link in local resonance detection technology. For known defects, the local resonant frequency can be extracted by comparing the frequency domain difference between the defect area and the non-defect area, and then the location and size characteristics of the defect can be evaluated. However, in actual engineering, most of the defects are unknown, and the detection process needs to be completed automatically. Manual judgment is difficult to meet the needs of industrial non-destructive testing. To this end, domestic and foreign scholars have conducted a lot of research on the automatic extraction method of the local resonant frequency of defects, which can be mainly divided into the following three categories: The first category is the analysis method based on frequency domain statistical characteristics. This type of method extracts the local resonant frequency by comparing the frequency domain response difference between the defect area and the overall structure. For example, Zdziebko et al. [1] identified the local resonant frequency by performing statistical analysis on the ratio of vibration intensity. This type of method has high computational efficiency, but it is only based on a single detection point and average frequency domain data for analysis. It does not consider the clustering characteristics of the vibration response abnormal points in the spatial distribution. It is easy to misjudge discrete noise as a defect, resulting in low accuracy in its judgment of the local resonant frequency. The second category is the identification method based on defect response characteristics. This type of method identifies the defect area through feature comparison and threshold segmentation, and infers the local resonant frequency. For example, Hettler et al. [2] used the maximum inter-class variance method to analyze the intensity image features corresponding to the local resonant frequency to obtain the resonant frequency. This type of method can simultaneously obtain the local resonant frequency of the defect and the position and geometric features of the defect, but it is easily interfered by the pseudo-response frequency, the stability and accuracy of the identification results are limited, and the computational efficiency is low. The third type is the recognition method based on neural networks. This type of method learns the multi-dimensional features of the defect by constructing a neural network. For example, Zhang et al. [3] constructed a two-dimensional convolutional neural network and used frequency domain information to identify the local resonant mode of the defect and obtain the local resonant frequency. This type of method can integrate multi-dimensional information, but the computational complexity is high and it relies on a large number of training samples. The above-mentioned defect local resonant frequency extraction method has problems such as single data processing dimension, low computational efficiency, and sensitivity to pseudo-response frequency interference, making it difficult to balance detection accuracy and efficiency.

[0004] In order to improve the accuracy and efficiency of the defect local resonance frequency extraction method, domestic and foreign scholars have proposed a variety of improvement schemes. For example, Chang et al. [4], based on the statistical analysis of vibration intensity data, analyzed the spatial distribution characteristics of abnormal vibration points and removed some pseudo-response frequencies generated by non-defects, thereby narrowing the calculation range. This method improves the computational efficiency, but is susceptible to interference from pseudo-response frequencies and has limited accuracy. Segers et al. [5] introduced a threshold iteration and feature comparison mechanism based on the maximum inter-class variance method for image recognition. On the basis of removing the identified defect areas, the preset artifact rules are used for comparison and elimination to achieve the identification of multiple defect areas. This method can effectively reduce artifact interference, but it requires the preset artifact rules based on experience and increases the amount of computation.

[0005] In summary, existing local resonant frequency extraction methods still have significant limitations in terms of accuracy, efficiency, and engineering applicability. Therefore, this paper proposes a method for extracting the local resonant frequency of defects based on spatial cluster analysis of vibration responses. This method improves the accuracy and efficiency of identifying local resonant frequencies of defects, making it particularly suitable for automated detection of unknown defects. Summary of the Invention

[0006] To address the problems of low recognition accuracy, low computational efficiency, and interference from spurious response frequencies in existing defect local resonant frequency extraction methods, this paper proposes a method for extracting the local resonant frequency of defects based on spatial cluster analysis of vibration responses. This method eliminates the need to pre-determine the location and geometric characteristics of the defect and can automatically extract the local resonant frequency of the defect from an ultrasonic inspection dataset, even when the defect is unknown.

[0007] The present invention proposes a method for extracting the local resonant frequency of defects based on spatial cluster analysis of vibration responses. The basic principle is:

[0008] Local defects in a structure can cause local changes in the material's stiffness, mass, or damping, causing the defect area to exhibit vibration characteristics different from those of the overall structure under external excitation. Under broadband acoustic wave excitation, the vibration amplitude at the defect can be expressed as:

[0009]

[0010] Where X is the displacement of the defect area due to forced vibration, m eff is the equivalent mass of the defect area, ξ is the equivalent damping ratio of the defect area, and F is the force generated by ultrasonic excitation.

[0011] Equation 1 shows that as the ultrasonic excitation frequency ω approaches the local resonant frequency ω0 at the defect, the vibration amplitude at the defect increases significantly, reaching a maximum at ω0, forming a distinct resonant peak in the frequency domain. Therefore, the local resonant frequency of the defect can be identified by searching for the resonant peak in the frequency domain. However, in actual inspections, spurious responses caused by interfering factors such as structural boundary reflections and coupled modes can also form resonant peaks in the frequency domain, affecting the accuracy of local resonant frequency identification.

[0012] According to Equation 1, a defect can produce resonant responses of the same or similar frequencies at multiple inspection points around it, manifesting as resonant peaks with similar frequencies in the frequency domain. The corresponding inspection points are spatially clustered, and the local resonances exhibit high consistency in both frequency and spatial dimensions. Therefore, a statistical analysis method can be used to analyze the frequency of resonant peaks at each inspection point, screening out frequencies that recur across multiple inspection points to form a set of abnormal response frequencies. At the same time, spatially isolated or infrequently occurring frequencies are eliminated to narrow the frequency calculation range and improve overall computational efficiency.

[0013] To obtain the abnormal response frequency set, we first need to extract the frequency corresponding to the resonant peak in the spectrum of each detection point. This frequency can be characterized by calculating the difference function between the spectrum of the detection point and the global average spectrum, and extracting the frequency corresponding to the local maximum point. This difference function can be expressed as:

[0014]

[0015] Where A(x,y,f) is the frequency domain amplitude spectrum at the detection point (x,y), and N is the number of scanning points.

[0016] Take the response frequency f corresponding to the first M local maxima in the difference function of each detection point and record it in the response frequency set F resp , count the number of times each frequency appears in the set, recorded as T(f), if the number of occurrences is greater than the threshold τ, then the frequency f is recorded in the abnormal response frequency set F abn :

[0017] F abn ={f∈F|T(f)≥τ} (3)

[0018] After initially narrowing the frequency calculation range, it is still necessary to further eliminate the pseudo-response frequencies caused by interference factors to improve the efficiency and accuracy of local resonant frequency identification. To this end, it is necessary to combine the propagation characteristics of the defect vibration response in space, establish the relationship between the spatial position of the detection point and the abnormal response frequency, construct a spatial response model of the defect in the resonant state, and analyze the spatial distribution of its amplitude. At the resonant frequency, the forced vibration amplitude of the defect and the surrounding area can be expressed as:

[0019] A(r)=A0·e -αr (4)

[0020] Where A0 is the vibration amplitude at the defect center, α is the attenuation coefficient of the material at the defect, and r is the distance between the measurement point and the defect center.

[0021] As shown in Equation 4, the amplitude of the defect is maximum at its center. As the distance between the inspection point and the defect resonance point increases, the vibration amplitude decays exponentially, forming a local high-energy region centered on the defect outline. In the frequency domain, this phenomenon manifests itself as a clearly clustered inspection area in space, with resonance peaks of similar frequencies appearing at each inspection point within this area, reflecting the consistency of the defect's local resonance response in both frequency and spatial dimensions. Therefore, based on the abnormal response frequencies obtained through the above statistical analysis, the spatial distribution characteristics of the resonance peaks are introduced to further identify the abnormal response frequencies and screen out candidate local resonance frequencies.

[0022] In order to identify abnormal response frequencies with spatial clustering characteristics, the DBSCAN density clustering algorithm is used to perform cluster analysis on the spatial distribution of detection points corresponding to abnormal response frequencies:

[0023] Cluster(F abn ,ε f )={C1,C2,...,C K} (5)

[0024] where ε f is the radius threshold for density clustering.

[0025] Each cluster C k It consists of several detection points, which are clustered in space and have similar abnormal response frequencies. f Under the condition of , the larger clusters are formed, and the corresponding detection points are considered to have stable spatial clustering, and their corresponding similar abnormal response frequencies are excited by the same defect. The abnormal response frequencies corresponding to the detection points in each cluster are weighted and merged according to the frequency of occurrence to construct the candidate local resonance frequency set F cand If a cluster cannot be formed, or the cluster does not meet the threshold requirement, it is considered that the corresponding abnormal response frequency may be caused by noise or interference and is eliminated.

[0026] Based on the spatial clustering of the local resonance characteristics of defects, through statistical and spatial clustering analysis of the resonance peaks at different scanning positions, the frequency calculation range can be quickly narrowed from the full frequency domain to the key frequency band, thereby improving the extraction efficiency of the limited resonance frequency.

[0027] To improve the accuracy of identifying the local resonant frequency of a defect, the spatial omnidirectionality of the attenuation of the defect's local vibration response is further utilized to eliminate spurious response frequencies caused by interference factors. According to Equation 4, the amplitude of a detection point near a defect is only related to its distance from the defect outline and not its direction, meaning that the spatial attenuation of the vibration energy is consistent. Based on this characteristic, the spatial attenuation pattern of the vibration energy of the defect corresponding to the candidate local resonant frequency can be analyzed to determine whether it exhibits spatial energy attenuation consistency, thereby distinguishing the defect resonant response from the non-defect interference response and ultimately determining the defect's local resonant frequency.

[0028] In order to characterize the spatial energy attenuation consistency of the defect resonance response at the candidate local resonance frequency, the frequency domain amplitude of each detection point at this frequency is taken as the relative vibration energy, and the normalized intensity distribution matrix B(x,y) is constructed. The point with the maximum amplitude in the matrix B max As the center point of the defect at the candidate resonant frequency, Figure 1 shown.

[0029] According to formula 4, the resonant response of a real defect will form a ring-shaped energy distribution around it that is similar to the defect outline. Its spatial attenuation consistency can be characterized by the attenuation distance between different ring energy bands. Define the amplitude in the matrix B(x,y) to be no less than 0.8B max The area is the high energy area P H , the amplitude is not less than 0.6B max The area is the second highest energy area P L , as shown in Formula 6:

[0030]

[0031] To reduce computational complexity, the percentage of coverage points in high-energy and second-highest-energy regions relative to the total number of sampling points is counted. If the percentage of a region falls below a preset threshold k, it is considered a non-defect interference response and is removed.

[0032] The extension range of the energy ring area in different directions is statistically analyzed to characterize its spatial attenuation consistency. With the defect center as the center of the circle, Figure 1 As shown, the equi-angle scanning method is used, and the high energy area P is counted every 30°. H Boundary and sub-high energy region P L The radial distance difference between the boundaries is taken as the energy attenuation distance d in that direction. The variance δ of the attenuation distance in all directions is calculated as the energy attenuation consistency indicator:

[0033]

[0034] Compare δ with the preset threshold δ th Compare, if it is less than the preset threshold δ th , it is considered that the defect under the candidate local resonant frequency has consistent spatial energy attenuation and is the resonant response of the real defect. The frequency is determined to be the defect local resonant frequency f LDR Otherwise, it is determined to be a pseudo-response frequency caused by interference factors such as structural boundary reflection and coupled modes, and is eliminated.

[0035] The implementation process of the defect local resonance frequency extraction method based on vibration response space cluster analysis proposed in this invention is as follows: Figure 1 As shown, it is achieved by the following steps:

[0036] Step 1: Obtain the ultrasonic detection data set, perform Fourier transform on N scanning points, and obtain the frequency domain amplitude spectrum. Calculate the difference function between the spectrum of each scanning point and the global average spectrum, extract the first M local maximum frequencies, and form the response frequency set F resp .

[0037] Step 2: Perform frequency statistics on the N×M frequencies in the response frequency set and calculate the number of times they appear in all scanning points. Set a frequency threshold τ and filter out frequencies with frequencies greater than the threshold to form the abnormal response frequency set F abn .

[0038] Step 3: Perform DBSCAN density cluster analysis on each frequency and corresponding detection point in the abnormal response frequency set, and set the radius threshold ε f , for each cluster C k The abnormal response frequencies corresponding to the internal detection points are weighted and combined according to the occurrence frequency to obtain the candidate local resonance frequency set F cand .

[0039] Step 4: For each candidate local resonance frequency, take the frequency domain amplitude of each detection point at that frequency as the relative vibration energy and construct the normalized intensity distribution matrix B(x,y). max Defined as the center point, the amplitude is not less than 0.8B max The area is defined as the high energy area P H , the amplitude is not less than 0.6B max The area is defined as the second highest energy area P L The proportion of the coverage points of the high energy area and the second highest energy area to the total sampling points is counted, and the candidate local resonance frequencies corresponding to the areas whose proportion is lower than the preset threshold k are eliminated.

[0040] Step 5: With the defect center as the center of the circle, use the equal angle scanning method to count the number of times the defect passes through the high energy area P every 30°. H Boundary and sub-high energy region P L The radial distance difference between the boundaries is taken as the energy attenuation distance d in that direction.

[0041] Step 6: Calculate the variance δ of the energy attenuation distance d as the energy attenuation consistency indicator and compare it with the preset variance threshold δ th Compare and identify the frequency with a variance less than the threshold as the defect local resonant frequency f LDR .

[0042] The present invention has the following advantages: 1) Through frequency statistical analysis and vibration response spatial cluster analysis, the frequency analysis range is compressed from the full frequency domain to the key frequency band, reducing the amount of calculation. 2) Through energy attenuation consistency analysis, pseudo-response frequencies are eliminated, improving recognition accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of energy decay consistency.

[0044] Figure 2 Flowchart for the implementation of the method of the present invention.

[0045] Figure 3 This is the difference between the spectrum of one scanning point and the average spectrum.

[0046] Figure 4 This is the result of spatial cluster analysis of detection points.

[0047] Figure 5 Attenuation distance diagram at candidate local resonant frequencies. (a) 8.94kHz; (b) 10.44kHz; (c) 12.07kHz; (d) Attenuation distance distribution diagram;

[0048] Figure 6 This is the energy attenuation consistency threshold judgment diagram.

[0049] Figure 7 This is the defect C-scan result diagram at the local resonant frequency. DETAILED DESCRIPTION

[0050] The following is an example of the detection scenario of 0.05mm debonding defects in honeycomb sandwich structures. Figures 2 to 6 , the proposed method for extracting the local resonant frequency of defects based on spatial clustering analysis of vibration responses is further explained:

[0051] The material tested is a honeycomb panel structure composed of 10 carbon fiber composite facesheets with a 5-ply [0° / 90°] layout and a hexagonal aluminum honeycomb core. A 0.05mm thick, 20mm diameter polytetrafluoroethylene disc is embedded at the interface between the facesheet and the honeycomb core to simulate debonding damage. The test range is 60mm x 60mm, with a 2mm increment.

[0052] Step 1: Obtain the ultrasonic testing data set, perform Fourier transform on 30×30 scanning points, and obtain the frequency domain amplitude spectrum. Calculate the difference function between the spectrum of each scanning point and the global average spectrum, such as Figure 3 As shown, the first three local maximum frequencies are extracted to form the response frequency set F resp .

[0053] Step 2: Perform frequency statistics on the 3×900 frequencies in the response frequency set and calculate the number of times they appear in all scanning points. Set the frequency threshold τ to 15, filter out frequencies with frequencies greater than the threshold, and form the abnormal response frequency set F abn ={5.64kHz, 8.94kHz, 9.23kHz, 10.44kHz, 11.89kHz, 12.07kHz, 13.31kHz, 14.66kHz}.

[0054] Step 3: Perform DBSCAN density cluster analysis on each frequency and corresponding detection point in the abnormal response frequency set, and set the radius threshold ε fis 15, the clustering results are as follows Figure 4 As shown. For each cluster C k The abnormal response frequencies corresponding to the internal detection points are weighted and combined according to the occurrence frequency to obtain the candidate local resonance frequency set F cand ={5.64kHz, 8.94kHz, 10.44kHz, 12.07kHz}.

[0055] Step 4: For each candidate local resonance frequency, take the frequency domain amplitude of each detection point at that frequency as the relative vibration energy and construct the normalized intensity distribution matrix B(x,y). max Defined as the center point, the amplitude is not less than 0.8B max The area is defined as the high energy area P H , the amplitude is not less than 0.6B max The area is defined as the second highest energy area P L The percentage of coverage points in high energy area and second high energy area in total sampling points is counted, and the threshold k is set to 1%. When the candidate local resonance frequency is 5.64kHz, the second high energy area P L The proportion is 0.3% and is excluded.

[0056] Step 5: With the defect center as the center of the circle, use the equal angle scanning method to count the number of times the defect passes through the high energy area P every 30°. H Boundary and sub-high energy region P L The radial distance difference between the boundaries is taken as the energy attenuation distance d in that direction, and the result is as follows Figure 5 shown.

[0057] Step 6: Calculate the variance δ of the energy attenuation distance d as the energy attenuation consistency indicator and set the variance threshold δ th The attenuation distance variances corresponding to the candidate local resonance frequencies of 8.94kHz, 10.44kHz, and 12.07kHz are 7.00, 0.489, and 6.09, respectively. Only the threshold is met at 10.44kHz, as shown in the following example: Figure 6 As shown. That is, the defect local resonance frequency f LDR is 10.44kHz, and the imaging results are as follows Figure 7 shown.

[0058] The above is a typical application of the present invention, and the application of the present invention is not limited thereto.

[0059] References

[0060] [1]Zdziebko P,Krzeminski M,Okon M,et al.An approach to the automatedcharacterization of out-of-plane and in-plane local defect resonances[J].Materials,2023,16(8):3084.

[0061] [2]Hettler J,Tabatabaeipour M,Delrue S,et al.Detection andcharacterization of local defect resonances arising from delaminations andflat bottom holes[J].Journal of Nondestructive Evaluation,2017,36(1):2.

[0062] [3]Zhang C Y,HuY J,Deng M X.Deep learning-assisted local resonancestrategy for accurate internal damage imaging in composites[J].AppliedPhysics Letters,2024,125(19):194102.

[0063] [4]C.Chang,K.Long,Z.Li,H.Rai.Classifier guided cluster densityreduction for dataset selection[C] / / IEEE / CVF Conference on Computer Visionand Pattern Recognition Workshops(CVPRW).Seattle,WA,USA:IEEE,2024:7338-7347.

[0064] [5]Segers J,Hedayatrasa S,Verboven E,et al.Efficient automatedextraction of local defect resonance parameters in fiber reinforced polymersusing data compression and iterative amplitude thresholding[J].Journal ofSound and Vibration,2019,463:114958.

Claims

1. A method for extracting local resonant frequency of defects based on spatial cluster analysis of vibration response, characterized in that: The method is implemented by the following steps: Step 1: Obtain the ultrasonic detection data set, perform Fourier transform on N scanning points, and obtain the frequency domain amplitude spectrum; calculate the difference function between the spectrum of each scanning point and the global average spectrum, extract the first M local maximum frequencies, and form the response frequency set F resp ; Step 2: Perform frequency statistics on the N×M frequencies in the response frequency set and calculate the number of times they appear in all scanning points; Set the frequency threshold τ and filter out the frequencies with a frequency greater than the threshold to form the abnormal response frequency set F abn ; Step 3: Perform DBSCAN density cluster analysis on each frequency and corresponding detection point in the abnormal response frequency set, and set the radius threshold ε f , for each cluster C k The abnormal response frequencies corresponding to the internal detection points are weighted and combined according to the occurrence frequency to obtain the candidate local resonance frequency set F cand ; Step 4: For each candidate local resonance frequency, take the frequency domain amplitude of each detection point at that frequency as the relative vibration energy, and construct the normalized intensity distribution matrix B(x,y); take the point with the maximum amplitude B max Defined as the center point, the amplitude is not less than 0.8B max The area is defined as the high energy area P H , the amplitude is not less than 0.6B max The area is defined as the second highest energy area P L ; Count the proportion of the number of coverage points in the high energy area and the second highest energy area to the total sampling points, and eliminate the candidate local resonant frequencies corresponding to the areas whose proportion is lower than the preset threshold k; Step 5: With the defect center as the center of the circle, use the equal angle scanning method to count the number of times the defect passes through the high energy area P every 30°. H Boundary and sub-high energy region P L The radial distance difference between the boundaries is taken as the energy attenuation distance d in that direction; Step 6: Calculate the variance δ of the energy attenuation distance d as the energy attenuation consistency indicator and compare it with the preset variance threshold δ th Compare and identify the frequency with a variance less than the threshold as the defect local resonant frequency f LDR .

2. The method for extracting the local resonance frequency of a defect based on vibration response space cluster analysis according to claim 1, characterized in that: The weighted merging of frequencies within the clusters described in step 3 refers to using the number of times the abnormal response frequency corresponding to each detection point appears in the cluster as a weight.

3. The method for extracting the local resonance frequency of a defect based on vibration response space cluster analysis according to claim 1, characterized in that: The energy attenuation consistency index in step 4 is the high energy area P H Boundary and sub-high energy region P L The variance of the radial distance differences between boundaries.

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