A system for identifying acoustic emission characteristics of laser-induced thermal cracking cutting of glass

Abstract

This application relates to the fields of laser processing and acoustic emission monitoring, and discloses a system for identifying acoustic emission characteristics of laser-induced thermal cracking of glass, which includes an acoustic emission sensor for capturing acoustic emission signals generated during the laser cutting process; a signal processing unit configured to preprocess the acoustic emission signals and generate STFT time-frequency diagrams and Mel time-frequency diagrams; a data fusion module configured to combine the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram; and a neural network processing unit containing a ViT-LSM model for analyzing the comprehensive time-frequency diagram and classifying the crack propagation state. The present invention combines the advantages of STFT and Mel time-frequency diagrams and cooperates with a deep learning model to improve the monitoring and classification accuracy of the crack propagation state during the laser-induced thermal cracking of glass.

Description

Technical Field

[0001] The present invention relates to the technical fields of laser processing and acoustic emission monitoring, and specifically to a system for identifying acoustic emission characteristics of laser-induced thermal crack cutting of glass. Background Art

[0002] In the process of laser-induced thermal crack cutting of glass (LITP), a laser is used to generate high temperatures to induce thermal stresses on the surface and inside of the material, causing the glass to crack along a preset path. Although this technology has advantages in terms of precision and efficiency, the process of monitoring crack formation and propagation is complex, and there is a high demand for real-time monitoring technology.

[0003] In practical applications, acoustic emission (AE) monitoring is an effective non-destructive detection technology that can be used to monitor the dynamic state of cracks during laser cutting. Acoustic emission signals contain rich information about the development state of cracks, but they also pose challenges. First, the operating noise of the laser cutting machine tool may have a negative impact on the quality of the acoustic emission signal, increasing the difficulty of signal processing. Second, the acoustic emission characteristics of cracks at different stages (such as starting to crack, trajectory deviation, fragmentation, and melting) vary in terms of frequency and time, and precise analysis is required to distinguish these states.

[0004] Traditional acoustic emission signal analysis techniques, such as the short-time Fourier transform (STFT), although able to provide the time-frequency distribution of the signal, have limitations in processing complex laser cutting acoustic emission signals. STFT can capture changes in time locality well when analyzing high-frequency signals, but has low resolution for the low-frequency part. While the Mel spectrum transformation can provide clearer low-frequency information, it is insufficient in capturing high-frequency details. Therefore, using STFT or Mel technology alone cannot comprehensively describe the complexity of various crack propagation states during laser cutting. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention provides a system for identifying acoustic emission characteristics of laser-induced thermal crack cutting of glass. By combining the advantages of STFT and Mel time-frequency diagrams and cooperating with a deep learning model, the monitoring and classification accuracy of the crack propagation state during laser-induced thermal crack cutting of glass is improved, thereby overcoming the deficiencies of the prior art.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A system for identifying acoustic emission characteristics of laser-induced thermal crack cutting of glass, comprising:

[0007] An acoustic emission sensor for capturing acoustic emission signals generated during laser cutting;

[0008] A signal processing unit configured to preprocess the acoustic emission signals and generate STFT time-frequency diagrams and Mel time-frequency diagrams;

[0009] A data fusion module, configured to combine the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram;

[0010] A neural network processing unit, including a ViT-LSM model, for analyzing the comprehensive time-frequency diagram and classifying the crack propagation state.

[0011] Preferably, the signal processing unit is further configured to process the acoustic emission signal using a wavelet denoising method.

[0012] Preferably, the wavelet denoising method uses a db6 wavelet.

[0013] Preferably, the ViT-LSM model includes multiple Transformer layers, and each layer is equipped with a local selection module to improve the recognition ability of local features.

[0014] Preferably, the local selection module uses an attention mechanism to select important time-frequency picture segments as inputs.

[0015] Preferably, the comprehensive time-frequency diagram is composed of the 100 - 400 kHz frequency part in the STFT time-frequency diagram and the 0 - 5 kHz frequency part in the Mel time-frequency diagram.

[0016] Preferably, the system further includes a display module for displaying the real-time monitoring results of crack propagation.

[0017] The present invention also provides a method for identifying acoustic emission characteristics of laser-induced thermal crack cutting of glass, including the following steps:

[0018] Capture the acoustic emission signal generated during the laser cutting process;

[0019] Preprocess the acoustic emission signal and generate an STFT time-frequency diagram and a Mel time-frequency diagram;

[0020] Combine the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram;

[0021] Use a neural network processing unit based on the ViT-LSM model to analyze the comprehensive time-frequency diagram and classify the crack propagation state.

[0022] The present invention provides a system for identifying acoustic emission characteristics of laser-induced thermal crack cutting of glass. It has the following beneficial effects:

[0023] 1. The present invention combines the advantages of STFT and Mel time-frequency diagrams and cooperates with a deep learning model to improve the monitoring and classification accuracy of the crack propagation state during the laser-induced thermal cracking of glass, and can timely identify abnormal crack states, such as fragmentation or melting, to avoid excessive damage to the material, thereby reducing material waste. At the same time, the collected and analyzed acoustic emission data can be used to further optimize the cutting process parameters to achieve continuous improvement and optimization based on data.

[0024] 2. The acoustic emission feature recognition system for laser-induced thermal cracking of glass according to the present invention provides a comprehensive and accurate tool for monitoring and controlling the laser cutting process. By combining the advantages of STFT and Mel time-frequency diagrams and through in-depth learning of local features by the ViT-LSM model, this system not only improves the accuracy and safety of operations, but also brings technological innovation to the glass cutting industry, promoting the development of the manufacturing industry towards a more efficient and intelligent direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the laser-induced thermal crack propagation processing process;

[0026] Figure 2 Schematic diagram of the principle of laser-induced thermal crack propagation processing;

[0027] Figure 3 Schematic diagram of the acoustic emission feature recognition system for the laser processing process based on deep learning technology;

[0028] Figure 4 Schematic diagram of the STFT of the AE signal of laser thermal cracking of glass;

[0029] Figure 5 Schematic diagram of the Mel of the AE signal of laser thermal cracking of glass;

[0030] Figure 6 Schematic diagram of the system structure of the present invention;

[0031] Figure 7 Schematic diagram of the STFT-Mel of the AE signal of laser thermal cracking of glass according to the present invention;

[0032] Figure 8 Schematic diagram of the ViT-LSM neural network model of the present invention;

[0033] Figure 9 Schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0035] Laser induced thermal-crack propagation (LITP) is a common method for laser cutting glass. Its processing process is as Figure 1 shown. Its principle is as Figure 2 shown. By irradiating a laser beam with appropriate energy density on the surface of the workpiece, a light spot is formed on the surface of the workpiece. The temperature of this area rises after absorbing energy, volume expansion occurs, and a compressive stress state is formed under the constraint of the surrounding medium. The rear heating area exchanges heat with the medium at a lower temperature, causing the temperature to drop rapidly, resulting in shrinkage. This process generates tensile stress under the action of the surrounding medium. If the tensile stress reaches a certain value, the glass surface will start to crack along the predetermined scribing direction, and finally the cutting of the glass is achieved.

[0036] As Figure 3 shown, it is a system for identifying acoustic emission characteristics of a laser processing process based on deep learning technology, used to monitor the crack propagation state in the process of laser-induced thermal crack cutting of glass in real time. This system uses acoustic emission sensors to capture acoustic emission signals during the processing and establish the mapping relationship between acoustic emission signals and processing phenomena.

[0037] As Figure 4 and Figure 5 shown, by processing the acoustic emission signals, STFT time-frequency diagrams and Mel time-frequency diagrams are obtained, and the crack propagation states are divided into normal cracking, trajectory deviation, fragmentation and melting.

[0038] The processing process of laser-induced thermal cracking for cutting glass is relatively complex. The acoustic emission signal is affected by machine tool noise. The differences in frequency for different crack propagation states are mainly concentrated in two intervals: 0 - 5 kHz and 100 kHz - 400 kHz. In the STFT time-frequency diagram, fragmentation has a relatively obvious difference from other crack propagation states, and the characteristic signals are almost evenly distributed throughout the time-frequency image. However, among the three crack propagation states of normal cracking, trajectory deviation, and melting, the characteristic signals show a duration of 0.005 s and the frequency is mainly distributed around 150 kHz. Just using STFT cannot completely describe the characteristics of the four crack propagation states, and the resolution for the low-frequency part is relatively low. In the Mel time-frequency diagram, clear low-frequency information can be obtained, but a large amount of high-frequency information will be compressed. Therefore, relying on a single STFT or Mel technology does not constitute the best solution.

[0039] Please refer to the attached Figure 6 - attached Figure 8 , embodiments of the present invention provide a system for identifying acoustic emission characteristics of laser-induced thermal cracking for cutting glass. This system aims to combine the advantages of STFT and Mel time-frequency diagrams and cooperate with a deep learning model to improve the monitoring and classification accuracy of crack propagation states during the process of laser-induced thermal cracking for cutting glass, thereby overcoming the deficiencies of the prior art.

[0040] Specifically, the system includes:

[0041] An acoustic emission sensor, which is deployed near the laser cutting machine and is used to capture the acoustic emission signals generated during the laser cutting process. This sensor can detect tiny acoustic wave changes, especially those caused by the propagation of glass cracks, and its sensitivity is sufficient to capture acoustic waves in the frequency range from 0 Hz to 400 kHz.

[0042] A signal processing unit, which is equipped with digital signal processing technology. First, it preprocesses the captured acoustic emission signals, such as filtering and enhancement, to remove environmental noise and non-target signals. Subsequently, short-time Fourier transform (STFT) and Mel spectrum (Mel) conversion are used to generate time-frequency diagrams. STFT is used to capture the time-localized characteristics of high-frequency signals, while Mel conversion optimizes the frequency resolution of low-frequency signals.

[0043] A data fusion module, which combines the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram. This fusion ensures a comprehensive analysis of the signal, retains important time-frequency characteristics, and at the same time eliminates the limitations of each technology.

[0044] A neural network processing unit includes a Vision Transformer-Local Selection Module (ViT-LSM) model, which is specifically designed for time-frequency diagrams. The ViT-LSM partitions the time-frequency diagram through its local selection module, enhancing the model's learning ability for local microscopic details. Through learning and training, this processing unit can distinguish different crack propagation states such as normal cracking, trajectory deviation, fragmentation, and melting.

[0045] When the laser operates on the glass surface, the acoustic emission sensor captures the acoustic wave signals caused by thermal cracking in real time. These signals are preprocessed and feature-extracted by the signal processing unit and converted into time-frequency diagrams containing rich information. The data fusion module ensures the comprehensiveness of signal analysis by fusing the time-frequency diagrams of STFT and Mel, making the comprehensive time-frequency diagram contain the key information of the full frequency band.

[0046] The neural network processing unit analyzes these comprehensive time-frequency diagrams, accurately identifies the specific state of crack propagation, and thus provides immediate feedback to the operator to adjust the laser parameters or stop the operation, preventing over-cutting or damage to the material. This intelligent monitoring system greatly improves the safety and efficiency of the laser cutting process, reduces production costs, and improves product quality. In addition, the implementation of this system contributes to automated control and quality assurance, which is particularly crucial in the field of high-precision manufacturing.

[0047] In the system of the embodiment of the present invention, after preprocessing the acoustic emission signal, the classification accuracy increases by 8.89%. And the effect of using the spliced STFT-Mel time-frequency diagram as the input of the neural network is better than using a single STFT or Mel time-frequency diagram, and the accuracy rate reaches 96.78%, which can achieve the purpose of online monitoring of crack propagation.

[0048] By monitoring and identifying the crack propagation state in real time, the system of the present invention can accurately control the laser cutting process, reduce cutting deviation, and ensure product quality. And it can timely identify abnormal crack states such as fragmentation or melting, avoid excessive damage to the material, and thus reduce material waste. At the same time, the collected and analyzed acoustic emission data can be used to further optimize the cutting process parameters to achieve continuous improvement and optimization based on data.

[0049] The acoustic emission feature recognition system for laser-induced thermal crack cutting of glass in the present invention provides a comprehensive and accurate tool to monitor and control the laser cutting process. By combining the advantages of STFT and Mel time-frequency diagrams and through in-depth learning of local features by the ViT-LSM model, this system not only improves the accuracy and safety of operation, but also brings technological innovation to the glass cutting industry, promoting the development of the manufacturing industry towards a more efficient and intelligent direction.

[0050] The development of such a system reflects the wide applicability and key value of acoustic emission technology in practical industrial applications, especially in high-end manufacturing processes that require extremely high precision and reliability. In the future, the application of this system can be extended to other materials and cutting technologies, further broadening its application scope in the fields of material processing and quality control.

[0051] In a preferred embodiment of the present invention, the signal processing unit is further configured to use the wavelet denoising method to process the acoustic emission signal, so as to improve the signal quality and the overall performance of the system. The following details the wavelet denoising process and its application in the system.

[0052] The wavelet denoising technology is an effective signal denoising method, especially suitable for processing non-stationary signals or signals containing instantaneous spikes, such as the acoustic emission signals generated during the laser cutting process. In this preferred embodiment, the wavelet denoising method used is the "db6" (Daubechies 6) wavelet, which is a wavelet basis with good smoothing characteristics and high resolution and is very suitable for analyzing and processing acoustic emission signals. The denoising process is as follows:

[0053] 1. Wavelet decomposition: The acoustic emission signal is first subjected to wavelet decomposition, which decomposes the signal into wavelet coefficients in multiple frequency bands. These coefficients represent the characteristics of the signal at different scales and positions, enabling specific features of the signal (such as noise or certain parts of the signal itself) to be processed separately.

[0054] 2. Threshold processing: The wavelet coefficients obtained by decomposition are quantified by adopting an appropriate threshold. In this process, the coefficients smaller than the threshold are set to 0. This is mainly to eliminate the wavelet coefficients caused by noise while retaining the larger coefficients, which usually represent important information in the signal.

[0055] 3. Wavelet reconstruction: The wavelet coefficients after threshold processing are then subjected to wavelet reconstruction to construct the denoised signal. The reconstruction process ensures that the main features of the signal are retained while most of the noise is removed, thus clearly reflecting the key information in the acoustic emission signal.

[0056] The advantage of using the db6 wavelet for denoising is that it can effectively balance the local processing of the signal and the frequency resolution, thereby more accurately extracting and retaining the important information about the glass crack propagation in the acoustic emission signal. By processing the acoustic emission signal in this way, the signal processing unit can provide clearer and more accurate data for the feature extraction module, thereby improving the monitoring accuracy and reliability of the entire system.

[0057] By implementing this wavelet denoising technique, the acoustic emission feature recognition system for laser-induced thermal crack cutting of glass in the present invention can more effectively process various complex acoustic emission signals generated during the laser cutting process, greatly improving the signal-to-noise ratio of the signals and providing higher-quality input data for subsequent signal analysis and state recognition. This not only enhances the practicality of the system but also improves the control accuracy of the laser cutting process and the quality of the products.

[0058] In a preferred embodiment of the present invention, the ViT-LSM model includes multiple Transformer layers, and each layer is equipped with a local selection module to improve the recognition ability of local features. The local selection module uses an attention mechanism to select important time-frequency image segments as inputs.

[0059] In a preferred embodiment of the present invention, the neural network processing unit in the acoustic emission feature recognition system for laser-induced thermal crack cutting of glass uses the ViT-LSM model. This model is designed to include multiple Transformer layers, and each layer is equipped with a local selection module (LSM) to enhance the recognition ability of key local features, especially when processing time-frequency images.

[0060] As Figure 8 shown, the structure and functions of the ViT-LSM model are as follows:

[0061] Multi-layer Transformer structure:

[0062] Each Transformer layer is constructed to be able to process and analyze the global and local features of the input time-frequency map, using the self-attention mechanism to learn the dependencies between different parts.

[0063] Local selection module (LSM):

[0064] The LSM is embedded in each Transformer layer and uses the attention mechanism to dynamically select the most informative segments in the time-frequency map. These selected segments usually contain important cues about the crack state and are crucial for the classification accuracy of the final output.

[0065] By introducing the local selection module, the ViT-LSM model not only improves the parsing ability of complex time-frequency maps but also particularly enhances the recognition of subtle local changes, which is crucial for detecting the crack propagation state. This advanced local feature processing technology enables the system to provide highly accurate and reliable results during the real-time monitoring of the laser-induced thermal crack cutting of glass.

[0066] In a preferred embodiment of the present invention, a specific splicing method is adopted for the generation of the comprehensive time-frequency diagram. This method combines the respective advantages of the Short-Time Fourier Transform (STFT) and the Mel spectrogram (Mel), thereby optimizing the frequency characteristic representation of the acoustic emission signal. The comprehensive time-frequency diagram is composed by cropping and splicing specific frequency parts of the STFT and Mel time-frequency diagrams.

[0067] The process of generating the comprehensive time-frequency diagram is as follows:

[0068] 1. Cropping of the STFT time-frequency diagram:

[0069] The part from 100 kHz to 400 kHz is cropped from the STFT time-frequency diagram. This part captures the high-frequency information in the acoustic emission signal, which usually contains important clues about material rupture and rapid crack propagation.

[0070] 2. Cropping of the Mel time-frequency diagram:

[0071] The part from 0 to 5 kHz is cropped from the Mel time-frequency diagram. The Mel diagram is selected because of its better frequency resolution in the low-frequency range and is suitable for capturing and representing the characteristics of initial crack formation and small-scale crack propagation.

[0072] 3. Splicing process:

[0073] The cropped part of the Mel time-frequency diagram is used as the lower half of the comprehensive time-frequency diagram, and the cropped part of the STFT time-frequency diagram is used as the upper half. This up-and-down splicing method ensures that the key information of both low and high frequencies is displayed in one image, facilitating more comprehensive feature analysis.

[0074] This method for generating the comprehensive time-frequency diagram makes full use of the respective advantages of the STFT and Mel. By focusing on the key frequency intervals in the acoustic emission signal, it effectively enhances the system's ability to identify different crack propagation states. Through this method:

[0075] The comprehensive time-frequency diagram can more comprehensively display the information contained in the acoustic emission signal, thereby improving the accuracy of crack state classification.

[0076] Through precise cropping and targeted splicing, the signal processing flow is optimized, the interference of irrelevant frequency parts is reduced, and the processing efficiency and system performance are improved.

[0077] Overall, this strategy for generating the comprehensive time-frequency diagram significantly improves the practicality and effectiveness of the acoustic emission feature recognition system for laser-induced thermal crack cutting of glass, making it a highly effective industrial application tool.

[0078] In a preferred embodiment of the present invention, a display module is further added to the laser-induced thermal crack cutting glass acoustic emission feature recognition system. The main function of this module is to display the monitoring results of crack propagation in real time, so as to provide intuitive feedback to the operator or system monitor, enhancing the interactivity and practicality of the system.

[0079] Please refer to the attached Figure 9 , the present invention also provides a method for recognizing the acoustic emission characteristics of laser-induced thermal crack cutting glass, including the following steps:

[0080] Step S1: Capture acoustic emission signals

[0081] During the laser cutting process, acoustic emission sensors are deployed near the laser cutting machine to capture in real time the acoustic emission signals caused by the thermal cracking of the glass material. These signals contain key information about crack generation and propagation.

[0082] Step S2: Signal preprocessing and generation of time-frequency diagrams

[0083] Preprocessing: Preprocess the captured acoustic emission signals, including but not limited to denoising, amplifying signals in specific frequency bands, filtering, etc., to reduce noise and enhance the key features in the signals.

[0084] Generation of time-frequency diagrams: Use the short-time Fourier transform (STFT) and Mel spectrum analysis (Mel) to generate the STFT time-frequency diagram and the Mel time-frequency diagram respectively. STFT focuses on capturing the time-localized characteristics of high-frequency signals, while the Mel transform optimizes the frequency resolution of low-frequency signals.

[0085] Step S3: Generate a comprehensive time-frequency diagram

[0086] Combining the advantages of STFT and Mel, a comprehensive time-frequency diagram is generated by cropping and splicing their respective time-frequency diagrams. The high-frequency part of 100 - 400 kHz in the STFT time-frequency diagram and the low-frequency part of 0 - 5 kHz in the Mel time-frequency diagram are selected and combined to form a comprehensive time-frequency diagram covering a wide frequency range for a comprehensive analysis of the acoustic emission signals.

[0087] Step S4: Classification of acoustic emission signals

[0088] Use a neural network processing unit based on the ViT-LSM model to analyze the comprehensive time-frequency diagram. The ViT-LSM model enhances the ability to analyze local microscopic details in the time-frequency diagram through its multi-layer Transformer structure and local selection module (LSM).

[0089] The model deeply analyzes the comprehensive time-frequency diagram, identifies and classifies different crack propagation states, such as normal cracking, trajectory deviation, fragmentation and melting, etc.

[0090] In summary, the method of the present invention not only improves the monitoring and classification efficiency of laser-induced thermal crack cutting of glass, but also provides an efficient and reliable technical solution for related industrial applications.

[0091] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A laser-induced thermal cracking glass acoustic emission feature recognition system, characterized in that Including: An acoustic emission sensor for capturing acoustic emission signals generated during the laser cutting process; A signal processing unit configured to preprocess the acoustic emission signals and generate STFT time-frequency diagrams and Mel time-frequency diagrams; A data fusion module configured to combine the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram; A neural network processing unit containing a Vision Transformer-Local Selection Module model for analyzing the comprehensive time-frequency diagram and classifying the crack propagation state; The comprehensive time-frequency diagram consists of the 100 - 400 kHz frequency part in the STFT time-frequency diagram and the 0 - 5 kHz frequency part in the Mel time-frequency diagram; In the comprehensive time-frequency diagram, the cropped part of the Mel time-frequency diagram is used as the lower half of the comprehensive time-frequency diagram, and the cropped part of the STFT time-frequency diagram is used as the upper half.

2. The laser-induced thermal cracking glass acoustic emission feature recognition system according to claim 1, wherein The signal processing unit is further configured to process the acoustic emission signals using a wavelet denoising method.

3. The laser-induced thermal cracking glass acoustic emission feature recognition system according to claim 2, wherein The wavelet denoising method uses the db6 wavelet.

4. The laser-induced thermal cracking glass acoustic emission feature recognition system according to claim 1, wherein The Vision Transformer-Local Selection Module model includes multiple Transformer layers, each layer equipped with a local selection module to improve the recognition ability of local features.

5. The laser-induced thermal crack cutting glass acoustic emission feature recognition system according to claim 4, characterized in that, The local selection module uses an attention mechanism to select important time-frequency picture segments as inputs.

6. The laser-induced thermal cracking glass acoustic emission feature recognition system according to claim 1, characterized in that The system further includes a display module for displaying the real-time monitoring results of crack propagation.

7. A method for identifying the acoustic emission characteristics of laser-induced thermal cracking of glass, using the system according to any one of claims 1-6, characterized in that, Including the following steps: Capturing acoustic emission signals generated during the laser cutting process; Preprocessing the acoustic emission signals and generating STFT time-frequency diagrams and Mel time-frequency diagrams; Combining the high-frequency part of the STFT time-frequency diagram and the low-frequency part of the Mel time-frequency diagram to generate a comprehensive time-frequency diagram; Using a neural network processing unit based on the Vision Transformer-Local Selection Module model to analyze the comprehensive time-frequency diagram and classify the crack propagation state.

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