Dynamic monitoring and analysis method for deformation degree of tennis racket frame

Abstract

The invention provides a dynamic monitoring and analysis method for the deformation degree of a tennis racket frame, and the method comprises the steps: carrying out the real-time vibration signal capturing of the tennis racket frame through a piezoelectric vibration collection unit, obtaining the original vibration data of different orders of inherent frequencies of the frame, recording the modal amplitude distribution of each order of vibration mode, and obtaining an initial vibration signal set; according to the frame vibration analysis result, the drift distance from the inherent frequency of each order to a low frequency band is identified, the drift distance is identified as a high drift distance or a low drift distance through a drift distance threshold value, and a frequency drift level is obtained; the plastic deformation evaluation conclusion and the brittleness deformation evaluation conclusion are combined, the frequency drift level is combined, the frame damage is recognized as light damage, medium damage or heavy damage through a deformation severity threshold value, and the frame damage level is obtained; and according to the frame damage level, in combination with a plastic deformation evaluation conclusion or a brittleness deformation evaluation conclusion, outputting a classification result of a frame deformation type and a damage degree, and completing frame deformation dynamic monitoring and analysis processing.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame. Background Technology

[0002] Tennis racket frames are subjected to repeated impacts during high-intensity matches, leading to gradual deformation and even damage. This directly affects the transfer of hitting power, the sweet spot position, and the overall lifespan. Therefore, the dynamic monitoring and analysis of frame deformation has become an important research area for ensuring equipment reliability and athlete performance. Current monitoring methods mainly assess the degree of deformation by observing changes in the frame's vibration frequency, generally assuming that a greater shift in the fundamental frequency to lower frequencies indicates more severe deformation. However, this method has significant flaws because frequency reduction can originate from different damage mechanisms, yet they are treated uniformly, easily leading to misjudgments. Especially in actual use, it is impossible to distinguish the true cause behind the deformation, resulting in a large deviation between the assessment results and the actual condition of the frame. A deeper problem lies in the fact that changes in frame vibration frequency are affected by the damping ratio, which changes in the opposite direction depending on the type of damage. When the frame undergoes plastic deformation due to relaxation of the internal material structure, the damping ratio tends to increase, and vibration energy dissipates faster; conversely, when the frame undergoes brittle deformation due to localized cracking, the damping ratio decreases, and the vibration duration prolongs. When the frequency decreases by the same amount, a large damping ratio reflects overall material softening, while a small damping ratio indicates structural integrity failure. The severity of deformation and subsequent risks in these two scenarios are completely different, yet they are difficult to distinguish accurately by focusing solely on frequency. For example, in a long match, as the frame's fundamental frequency gradually decreases, if the monitoring system judges severe deformation based solely on the drift amplitude, ignoring the simultaneous decrease in damping ratio, it may misjudge brittle damage that has already shown localized cracking as minor plastic deformation, thus delaying timely replacement or repair of the racket and increasing the risk of breakage. Therefore, how to dynamically adjust the criteria for judging the type and degree of deformation based on frequency changes combined with the direction of damping ratio changes becomes a key issue for accurately classifying frame damage. Summary of the Invention

[0003] This invention provides a method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame, comprising: The tennis racket frame is captured in real time by a piezoelectric vibration acquisition unit to obtain the original vibration data of different natural frequencies of the frame, and the modal amplitude distribution of each vibration mode is recorded to obtain the initial vibration signal set. Frequency domain decomposition is performed on the initial vibration signal set to extract the specific frequency values ​​of different natural frequencies and vibration damping ratios. At the same time, the direction of rise and fall of the vibration damping ratio is identified to obtain the frame vibration analysis results. Based on the frame vibration analysis results, the drift of each natural frequency to the lower frequency band is identified, and the drift is divided into high drift or low drift according to the magnitude of the drift to obtain the frequency drift level. For the frequency drift level, when it is identified as a high drift, the deformation type is analyzed in conjunction with the rising and falling direction of the vibration damping ratio. When the vibration damping ratio is rising, the degree of relaxation of the internal structure of the frame material is evaluated, and it is identified as plastic deformation, thus obtaining a plastic deformation assessment conclusion. When the vibration damping ratio is decreasing, the local amplitude concentration area in the amplitude distribution of each mode is analyzed, the location of the concentrated stress point in the frame is identified, and when local amplitude concentration is detected, the degree of local cracking of the frame is evaluated and identified as brittle deformation, thus obtaining the brittle deformation assessment conclusion. Based on the combined conclusions of the plastic deformation assessment and the brittle deformation assessment, and in conjunction with the frequency drift level, the frame damage is classified into mild, moderate, or severe damage according to the deformation severity grading rules, thus obtaining the frame damage level. Based on the damage level of the frame, combined with the plastic deformation assessment conclusion or the brittle deformation assessment conclusion, the classification results of the frame deformation type and damage degree are output, and the dynamic monitoring and analysis of frame deformation are completed.

[0004] Furthermore, the piezoelectric vibration acquisition unit captures the vibration signals of the tennis racket frame in real time, obtains the original vibration data of different natural frequencies of the frame, and records the modal amplitude distribution of each vibration mode to obtain an initial vibration signal set, including: A piezoelectric sensor array is used to monitor the vibration at different locations of the tennis racket frame. The charge signal is converted into a voltage signal by a charge amplifier and the voltage signal is acquired at a sampling frequency higher than the preset sampling frequency to obtain the frame's time-domain vibration response data. The time-domain vibration response data of the frame is converted to time frequency to identify the natural frequency values ​​of the first bending mode, the second torsional mode and the third composite mode, and the damping ratio of each mode is determined. At the same time, the peak amplitude at each position is recorded to construct the modal amplitude distribution. Based on the relative ratios of amplitudes at different positions in the modal amplitude distribution and the phase relationship, the current vibration mode category is determined. By combining the time-domain vibration response data, natural frequency values ​​of each order, damping ratio, and modal amplitude distribution, an initial set of vibration signals is obtained.

[0005] Furthermore, frequency domain decomposition is performed on the initial vibration signal set to extract the specific frequency values ​​of different natural frequencies and the vibration damping ratio. Simultaneously, the direction of increase or decrease of the vibration damping ratio is identified to obtain the frame vibration analysis results, including: After windowing the time-domain data in the initial vibration signal set, a time-frequency transformation is performed to obtain the frequency domain spectral distribution, from which the natural frequency value, amplitude and phase information of each mode are extracted; The damping ratio of each mode is calculated based on the frequency domain spectral line distribution, and the damping ratio values ​​before and after use are compared to identify the direction of increase or decrease of the damping ratio and obtain the damping change trend. By combining the natural frequency values, damping ratio, damping variation trend, and correlation characteristics between different modes, a multidimensional vibration feature matrix is ​​constructed to obtain the analytical results of frame vibration.

[0006] Furthermore, based on the frame vibration analysis results, the drift amount of each natural frequency to the lower frequency band is identified, and the drift amount is divided into high drift amount or low drift amount according to the magnitude of the drift amount to obtain the frequency drift level, including: Extract the reference frequencies of each mode in the initial state of the frame, compare the current natural frequency with the reference frequency, and calculate the frequency drift of each mode. The frequency drift is classified according to a preset drift classification rule. When the absolute value of the drift exceeds the corresponding threshold, it is determined to be a high drift; otherwise, it is determined to be a low drift. By further combining the relative proportions of the drift amounts of each mode and the differences between low-order and high-order drift amounts, the classification results are corrected to obtain the frequency drift levels.

[0007] Furthermore, regarding the frequency drift level, when a high drift is identified, deformation type analysis is performed in conjunction with the rising and falling direction of the vibration damping ratio. When the vibration damping ratio is rising, the degree of relaxation of the internal structure of the frame material is evaluated, and it is identified as plastic deformation. A plastic deformation assessment conclusion is obtained, including: When the frequency drift level is high, read the time sequence of vibration damping ratio, calculate the damping ratio difference between adjacent measurement points, and determine that the damping ratio is rising when the consecutive positive difference value reaches the set number. When the damping ratio is increasing, the strain accumulation characteristics of the frame material under cyclic loading are extracted. When the accumulated strain exceeds the material yield strain range but does not reach the fracture strain range, it is determined that fiber-matrix interface slippage and structural relaxation have occurred inside the frame material. Based on the structural relaxation characteristics and the presence of irreversible permanent deformation, the frame deformation type is identified as plastic deformation, and a plastic deformation assessment conclusion is obtained.

[0008] Furthermore, when the vibration damping ratio decreases, the local amplitude concentration regions in the amplitude distribution of each mode shape are analyzed to identify the location of concentrated stress points in the frame. When local amplitude concentration is detected, the degree of local cracking in the frame is assessed and identified as brittle deformation, resulting in a brittle deformation assessment conclusion, including: When the vibration damping ratio is decreasing, the ratio of the amplitude of each measuring point to the overall average amplitude is calculated from the amplitude distribution of each mode. When the amplitude ratio of a certain area exceeds the set level and the amplitude gradient of adjacent measuring points changes drastically, the area is determined to be an amplitude concentration area and located as a stress concentration location. For the stress concentration location, the high-frequency component variation characteristics of the corresponding vibration signal are analyzed. When the energy of the high-frequency harmonic components increases significantly and the fundamental frequency energy shifts to the high frequency, the nonlinear vibration response caused by microcracks inside the material is determined, and the proportion of high-frequency energy is determined. Based on the trend of continuously decreasing high-frequency energy ratio and damping ratio, the degree of local cracking is assessed, and the frame damage type is identified as brittle deformation, thus obtaining the brittle deformation assessment conclusion.

[0009] Furthermore, combining the plastic deformation assessment conclusions and the brittle deformation assessment conclusions, and in conjunction with the frequency drift level, the frame damage is classified into mild, moderate, or severe damage according to the deformation severity grading rules, resulting in the frame damage level, including: Based on the existence status of the plastic deformation assessment conclusions and the brittle deformation assessment conclusions, the damage type identifier is determined, including single plastic damage, single brittle damage, or combined damage. The frequency drift level and damage type identifier are numerically combined. High drift combined with brittle damage is assigned a higher comprehensive damage index, while low drift combined with ductile damage is assigned a lower comprehensive damage index. The frame damage level is determined as mild, moderate, or severe by comparing the comprehensive damage index with the preset multi-level deformation severity threshold.

[0010] Furthermore, based on the frame damage level and combined with the plastic deformation assessment conclusion or the brittle deformation assessment conclusion, a classification result of the frame deformation type and damage degree is output to complete the dynamic monitoring and analysis of frame deformation, including: Based on the damage level of the frame and the corresponding plastic deformation assessment conclusion or brittle deformation assessment conclusion, a comprehensive status identifier containing damage level and deformation type is formed. Output the classification results corresponding to the comprehensive state identifier. The classification results include the specific categories of mild plastic damage, moderate plastic damage, severe plastic damage, mild brittle damage, moderate brittle damage, severe brittle damage, and composite damage, thus completing the dynamic monitoring and analysis of frame deformation.

[0011] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: This invention discloses a dynamic monitoring and analysis method for the deformation degree of a tennis racket frame. It uses a piezoelectric vibration acquisition unit to capture vibration signals of the tennis racket frame in real time, obtaining initial data on the distribution of natural frequencies and modal amplitudes. A modal analysis processing unit performs frequency domain decomposition to accurately extract the natural frequency values ​​and vibration damping ratio, and identifies the trend of damping ratio increases and decreases. This allows for the determination and classification of the degree of frequency drift towards lower frequencies. When a high drift occurs, the deformation type is intelligently determined based on the direction of damping ratio change: an increase in damping ratio corresponds to plastic deformation due to relaxation within the material, while a decrease in damping ratio is identified through concentrated analysis of local amplitudes to detect the risk of brittle cracking. Finally, by combining the frequency drift level and deformation type conclusions, and based on a severity threshold, accurate classification of mild, moderate, and severe damage is achieved. This completes the entire process of dynamic monitoring and evaluation of the tennis racket frame, from vibration signal acquisition to damage type and degree. This invention solves the technical problem of traditional methods being unable to identify the two damage modes of plastic relaxation and brittle cracking during tennis racket use in real time, non-destructively, and accurately, and to determine their severity. It provides an efficient and reliable technical means for athlete equipment safety management and performance degradation early warning. Attached Figure Description

[0012] Figure 1 This is a flowchart of a method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to the present invention.

[0013] Figure 2 This is a schematic diagram of a method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to the present invention.

[0014] Figure 3 This is another schematic diagram of a dynamic monitoring and analysis method for the degree of deformation of a tennis racket frame according to the present invention. Detailed Implementation

[0015] To further understand the content of this invention, a detailed description of the invention is provided in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. It should also be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0016] like Figures 1-3 This embodiment of a method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame may specifically include: S101. Real-time vibration signal capture of the tennis racket frame is performed through the piezoelectric vibration acquisition unit to obtain the original vibration data of different natural frequencies of the frame, and the modal amplitude distribution of each vibration mode is recorded to obtain the initial vibration signal set.

[0017] A piezoelectric vibration acquisition unit is used to monitor the vibration of a tennis racket frame in real time. This unit includes a piezoelectric sensor array, a charge amplifier, and a signal acquisition module. The piezoelectric sensor array is positioned at different locations on the racket frame. The charge amplifier converts the charge signals output by the piezoelectric sensors into voltage signals. The signal acquisition module samples the voltage signals at a frequency exceeding a preset sampling frequency threshold. When the frame is subjected to a ball impact, the piezoelectric material generates a charge signal proportional to its deformation. This charge signal is converted into a voltage signal by the charge amplifier, and high-frequency vibration components are captured at a frequency exceeding the preset sampling frequency threshold to obtain the frame's time-domain vibration response data. Based on this time-domain vibration response data, the signal is converted from the time domain to the frequency domain to identify the natural frequencies of the frame's first bending mode, second torsional mode, and third composite mode. The damping ratio of each mode is determined by calculating the frequency difference between the half-power points on both sides of the spectral peak. Simultaneously, the amplitude peak values ​​at each sensor location are recorded to construct a modal amplitude distribution map. For the modal amplitude distribution spectrum, the relative ratio of amplitudes at different positions is calculated. If the ratio of amplitude at the top of the frame to amplitude at the handle exceeds a preset threshold, the current vibration mode is determined to be a bending mode. If the amplitudes at the 3 o'clock and 9 o'clock positions are in opposite phase, the current vibration mode is determined to be a torsional mode. By combining the frame time-domain vibration response data, natural frequency values, damping ratio data, and modal amplitude distribution spectrum, an initial vibration signal set is obtained.

[0018] In one embodiment, the piezoelectric sensor array is positioned at key vibration nodes of the tennis racket frame. The throat, as the connection area between the frame and the grip, bears the main transmission path of the impact of the shot, and the vibration signal at this location can reflect the overall response characteristics of the frame. The 3 o'clock and 9 o'clock positions correspond to the lateral symmetry points of the frame, and the vibration difference between these two positions can effectively capture the torsional modal characteristics of the frame.

[0019] Specifically, when the tennis ball impacts the racket face, the frame structure undergoes transient deformation. The electric dipole moments within the piezoelectric material rearrange under mechanical stress, resulting in charge accumulation proportional to the deformation. This charge signal undergoes impedance transformation via a high-input-impedance charge amplifier, converting the high-impedance charge signal into a low-impedance voltage signal. The gain coefficient during this transformation is calibrated based on the charge sensitivity of the piezoelectric material. The sampling frequency must satisfy the Nyquist sampling theorem. Considering that the higher-order modal frequencies of the tennis racket frame can reach several kilohertz, the sampling frequency threshold is set to at least 2.5 times the highest frequency of interest in the frame to ensure that high-frequency vibration components do not produce spectral aliasing.

[0020] It should be noted that the time-domain to frequency-domain conversion is achieved using Discrete Fourier Transform, and the acquired time-domain vibration signal is windowed to reduce spectral leakage. In the spectral analysis results, each mode exhibits distinct peaks. The first-order bending mode typically appears in the lower frequency band, manifesting as overall bending deformation of the frame; the second-order torsional mode has a relatively high frequency, corresponding to torsional vibration of the frame around its central axis; the third-order composite mode contains both bending and torsional components. The half-power bandwidth method determines the damping ratio by identifying the two frequency points corresponding to a 3 dB drop in the spectral peak and calculating the ratio of their frequency difference to the center frequency.

[0021] In one possible implementation, mode shape determination is achieved by analyzing the amplitude relationship at different measuring points. The amplitude ratio between the top of the frame and the handle reflects the degree of participation of the bending mode; when this ratio exceeds a preset threshold, it indicates that the frame is mainly undergoing bending vibration. The amplitude-phase relationship between the 3 o'clock and 9 o'clock positions is used to identify the torsional mode; when the vibrations at the two positions show a 180-degree phase difference, the presence of a torsional mode component is confirmed.

[0022] Preferably, the initial vibration signal set integrates the original waveform data of the time-domain vibration response, the values ​​of each natural frequency, the corresponding damping ratio parameters, and the spatially distributed modal amplitude spectrum to form a complete characterization of the frame vibration state.

[0023] S102. For the initial vibration signal set, the modal analysis processing unit is used to perform frequency domain decomposition, extract the specific frequency values ​​of different natural frequencies and vibration damping ratios, and identify the rising and falling directions of the vibration damping ratios to obtain the frame vibration analysis results.

[0024] For the time-domain data in the initial vibration signal set, windowing is used to suppress spectral leakage. The processed signal undergoes time-frequency transformation to obtain the frequency-domain spectral distribution. The natural frequencies corresponding to the peak positions are identified in the spectrum. Simultaneously, the amplitude and phase information of each mode are extracted, constructing a frequency-domain feature dataset containing frequency, amplitude, and phase. Based on this frequency-domain feature dataset, frequency-domain analysis methods are used to calculate the damping ratio of each mode. By determining the frequency points corresponding to the power drop on both sides of the peak frequency, the relationship between the frequency bandwidth and the center frequency is calculated to obtain the damping ratio value. Simultaneously, the change in damping ratio before and after frame use is compared. If the later damping ratio is greater than the initial damping ratio, it is identified as an upward direction; if the later damping ratio is less than the initial damping ratio, it is identified as a downward direction, thus obtaining the damping change trend. Based on the damping change trend and the frequency-domain feature dataset, the interaction relationship between different modes is analyzed. By calculating the correlation of the modal responses, modal coupling is determined when the correlation exceeds a preset threshold. The phase difference and amplitude ratio between coupled modes are recorded to determine the distribution characteristics of vibration energy among each mode. By combining the natural frequency values, damping ratio values, damping variation trends, and vibration energy distribution characteristics, a multidimensional vibration feature matrix containing frequency data of each order, damping evolution information, and modal coupling relationships is constructed to obtain the frame vibration analysis results.

[0025] In one implementation, when windowing the time-domain data of the initial vibration signal set, the Hanning window function is used to modulate the signal. This window function smoothly transitions to zero at both ends of the window, which can effectively reduce spectral leakage caused by signal truncation.

[0026] Specifically, the time-frequency transformation process employs the Fast Fourier Transform (FFT) algorithm to convert the windowed discrete-time signal into a frequency-domain representation. In the vibration analysis of the tennis racket frame, the spectrum exhibits multiple distinct peaks, each corresponding to a vibration mode. The first-order bending mode represents the overall bending deformation of the frame, the second-order torsional mode reflects the torsional characteristics of the frame around its longitudinal axis, and the third-order composite mode contains both bending and torsional components. A peak-finding algorithm is used to identify the center frequencies of each mode. This algorithm takes spectral data and amplitude thresholds as input and outputs the center frequency, amplitude, and phase information of each mode. These parameters collectively constitute the frequency-domain feature dataset.

[0027] It should be noted that the damping ratio is calculated using the half-power bandwidth method. In the spectrum diagram, after locating the peak power of a certain mode, the frequency points where the power drops to half of the peak power are searched on both sides. The frequency difference between these two frequency points is the half-power bandwidth. The formula for calculating the damping ratio is ζ=Δf / (2fn), where Δf is the half-power bandwidth and fn is the center frequency. When internal damage occurs in the frame material, the friction at the microcrack interface enhances energy dissipation, leading to an increase in the damping ratio; conversely, when the integrity of the frame structure is compromised, changes in constraint conditions may actually decrease the damping ratio. Preferably, the identification of the damping change trend is based on multiple measurement data during the frame's service life. After several games, vibration data are re-acquired under the same test conditions, and the damping ratio is calculated. The direction of change is determined by comparing the damping ratio values ​​before and after use.

[0028] In one possible implementation, modal coupling is identified by calculating the cross-correlation coefficients of different modal responses. The cross-correlation coefficients are normalized and range from -1 to 1; the closer the absolute value is to 1, the stronger the coupling. The phase difference between coupled modes is determined through cross-spectral analysis. First, the time-domain signals of the low-order and high-order modes are acquired as inputs and subjected to Fourier transforms to obtain their frequency-domain representations. Then, the cross-spectral function Cxy(f) = X(f)Y*(f) is calculated, where X(f) and Y(f) are the Fourier transforms of the two signals, and Y*(f) is their conjugate. Finally, the phase information arg(Cxy(f)) is extracted as the output.

[0029] Understandably, the distribution characteristics of vibration energy among different modes are obtained by calculating the power spectral density integral of each mode. Changes in the energy distribution ratio can reflect the evolution of the frame structure characteristics, providing a quantitative indicator for assessing the frame's health status. Furthermore, the construction of a multidimensional vibration characteristic matrix integrates information from multiple dimensions, including frequency, damping, coupling, and energy distribution. The rows of the matrix correspond to different measurement times, and the columns contain various vibration parameters. Through this structured data organization, a comprehensive characterization of the frame's vibration state is achieved. The frame vibration analysis results not only include the static parameters of the current state but also record the evolution trajectory of the parameters over time, providing a complete data description.

[0030] S103. Based on the frame vibration analysis results, identify the drift amount of each natural frequency to the lower frequency band, and identify the drift amount as high drift amount or low drift amount through the drift amount threshold to obtain the frequency drift level.

[0031] Based on the natural frequency values ​​from the frame vibration analysis results, the reference frequencies of each mode in the initial state of the frame are extracted. The currently measured natural frequency is compared with the reference frequencies, and the difference between the current frequency and the reference frequency is calculated as the drift. The magnitude of the drift is recorded to determine the frequency offset characteristic data. For the frequency offset characteristic data, a drift threshold is set according to the frame material properties and the usage environment. The threshold is determined based on the damage critical value of similar frames. If the absolute value of the current drift exceeds the threshold, it is identified as a high drift; if the absolute value of the drift does not exceed the threshold, it is identified as a low drift, thus obtaining a preliminary classification result. Based on the preliminary classification results, the relative relationship between different modal drift values ​​is analyzed. At the same time, the influence of ambient temperature changes on frequency measurement is considered, and temperature compensation correction is applied to the drift values. If the ratio of low-order modal drift values ​​to high-order modal drift values ​​exceeds a preset ratio threshold, it indicates that the overall stiffness of the frame has decreased, and the frequency drift level is determined to be high. If the drift values ​​of each modality remain in a similar ratio, it indicates that there is local damage to the frame, and the frequency drift level is determined to be low. Thus, the frequency drift level is obtained.

[0032] In one implementation, the reference frequency is obtained before the tennis racket frame is used for the first time. Initial natural frequency values ​​for each mode are obtained through standard excitation testing. These values ​​serve as a reference for the frame's health status and are stored in a monitoring database for subsequent comparison. The input to the frequency drift identification algorithm is the currently measured set of natural frequencies {f1}. current f2 current f3 current} and reference frequency set {f1 base f2 base f3 base}, calculate the drift set {Δf1, Δf2, Δf3}, where Δfi = fi current -fi base Negative values ​​indicate a frequency drift towards lower frequencies. The output shows the drift amount and drift level for each mode.

[0033] It should be noted that the frequency drift is calculated by subtracting the reference frequency from the current frequency. A negative value indicates a frequency drift towards lower frequencies, which usually means a decrease in frame stiffness. During the use of a tennis racket, repeated impacts cause micro-damage to the carbon fiber matrix interface, reducing the overall elastic modulus of the material and thus causing a change in the natural frequency.

[0034] Specifically, the setting of the drift threshold needs to comprehensively consider the frame material properties and usage environment. For carbon fiber composite frames, according to material fatigue test data, when the frequency drift reaches a certain percentage of the initial frequency, detectable structural damage begins to appear in the frame. The threshold is adjusted based on the frame's design safety factor and usage level. For ordinary-grade rackets, the threshold is set at 4% of the initial frequency, while for professional-grade rackets, due to higher usage intensity and stricter safety requirements, the threshold is set at 2% of the initial frequency to detect potential damage in advance. Changes in ambient temperature also affect frequency measurement. The temperature compensation coefficient is determined based on the material's thermal expansion characteristics, with approximately 0.5% frequency correction corresponding to every 10 degrees Celsius temperature difference. When the absolute value of the measured drift exceeds the compensated threshold, it is considered a high drift, indicating that the frame has undergone significant deformation.

[0035] In one possible implementation, the relative relationship between the drift amounts of different modes reflects the damage distribution characteristics. Lower-order modes mainly reflect the overall stiffness characteristics of the frame, while higher-order modes are more sensitive to local damage. When the ratio of the drift amount of lower-order modes to that of higher-order modes is greater than 1.5, it indicates a uniform decrease in the overall stiffness of the frame, which is often seen in overall performance degradation caused by material fatigue. Conversely, if the ratio is less than 0.7, it means that there is localized concentrated damage, such as cracks or delamination at specific locations. Preferably, the final determination of the frequency drift level comprehensively considers both the magnitude of the drift and the relationship between modes. A two-dimensional judgment matrix is ​​constructed. The row index of this matrix represents the drift level, including low drift (drift less than 50% of the threshold), medium drift (drift between 50% and 100% of the threshold), and high drift (drift exceeding the threshold). The column index represents the modal relationship level, determined by calculating the ratio of low-order to high-order modal drift. A ratio greater than 1.5 indicates overall damage, a ratio between 0.7 and 1.5 indicates uniform damage, and a ratio less than 0.7 indicates local damage. Each cell in the matrix corresponds to a comprehensive level. The input is the quantized drift amount and the modal relationship ratio, and the output is the final frequency drift level, which can be low, medium, or high.

[0036] S104. Regarding the frequency drift level, when a high drift is identified, the deformation type analysis is performed in conjunction with the rising and falling direction of the vibration damping ratio. When the damping ratio is rising, the degree of relaxation of the internal structure of the frame material is evaluated, and it is identified as plastic deformation, thus obtaining the plastic deformation assessment conclusion.

[0037] For cases with high frequency drift, the time-series variation data of the vibration damping ratio is read, and the difference in damping ratio between adjacent measurement times is calculated. If the difference is positive and consecutive measurements show a positive value, the damping ratio is determined to be increasing, and a damping change trend indicator is obtained. When the damping change trend indicator shows an increasing direction, the viscoelastic response of the frame material is obtained through dynamic mechanical analysis, and the change in the loss factor between the current state and the initial state is calculated. The loss factor is the ratio of the loss modulus to the storage modulus. When the loss factor increases beyond a preset threshold, it is determined that slippage has occurred at the fiber-matrix interface within the material, identifying structural relaxation characteristics. Based on these structural relaxation characteristics, the cumulative strain data of the frame under cyclic loading is extracted. By comparing the cumulative strain value with the material yield strain threshold, when the cumulative strain exceeds the yield threshold but does not reach the fracture strain threshold, irreversible permanent deformation of the frame is identified, and it is determined to be plastic deformation, resulting in a plastic deformation assessment conclusion.

[0038] In one implementation, the time-series variation data of the damping ratio is obtained through periodic testing. Starting from the first use of the frame, a test is conducted every 10 hours, and data from at least 5 measurement points are continuously recorded to form a curve showing the change of the damping ratio over time.

[0039] It is important to note that dynamic mechanical analysis is a key method for evaluating the viscoelastic response of materials. When a frame material is subjected to periodic stress, the strain response exhibits phase hysteresis, which reflects the material's energy dissipation characteristics. The storage modulus represents the material's ability to store elastic energy during deformation, reflecting its stiffness characteristics; the loss modulus characterizes the material's ability to convert mechanical energy into heat energy under cyclic loading, reflecting its damping characteristics. In the actual use of tennis racket frames, the interface between carbon fiber and the epoxy resin matrix is ​​the primary site of energy dissipation. When microslippage begins to occur at the interface, frictional energy loss increases, leading to an increase in the loss modulus. The loss factor, as the ratio of the loss modulus to the storage modulus, can sensitively reflect changes in the material's internal structure. Under normal conditions, the frame's loss factor is typically in the range of 0.01-0.02. When this value increases by more than 50% of its initial value, it indicates that significant structural relaxation has occurred within the material.

[0040] Specifically, the structural relaxation characteristics are characterized by the degree of relative slippage at the fiber-matrix interface. Under repeated impact loads, debonding occurs when the interfacial shear stress exceeds the interfacial strength, allowing the fibers to generate minute relative displacements within the matrix. This displacement macroscopically manifests as a decrease in frame stiffness and an increase in damping. The cumulative effect of interfacial slippage leads to greater deformation of the frame under the same load.

[0041] Preferably, the accumulated strain data is acquired through non-contact optical measurement methods, such as using a laser vibrometer or a high-speed camera to record the peak strain and residual strain at key locations on the frame at each impact. The yield strain threshold of the material is determined based on tensile tests of carbon fiber composites, typically ranging from 0.3% to 0.5%.

[0042] In one possible implementation, the determination of plastic deformation combines two indicators: cumulative strain and recovery rate. The recovery rate R is defined as the ratio of the elastically recovered strain after unloading to the total strain, calculated as R = (εe / εt) × 100%, where εe represents the elastically recovered strain after unloading, εt represents the total strain, εe = εt - εp, and εp is the permanent plastic strain. Plastic deformation of the frame is confirmed when the cumulative strain exceeds the yield threshold and the recovery rate after unloading is less than 90%.

[0043] S105. When the damping ratio is decreasing, analyze the local amplitude concentration areas in the amplitude distribution of each mode, identify the location of the concentrated stress points in the frame, and when local amplitude concentration is detected, assess the degree of local cracking in the frame, identify it as brittle deformation, and obtain the brittle deformation assessment conclusion.

[0044] When the damping ratio decreases, the amplitude distribution data of each mode shape are extracted, and the ratio of the amplitude at each measuring point to the average amplitude of the entire frame is calculated. If the amplitude ratio in a certain area exceeds a preset threshold and the amplitude gradient between adjacent measuring points changes drastically, then that area is identified as an amplitude concentration area, and the stress concentration location is determined. For the stress concentration location, based on the relationship between the peak amplitude and the Young's modulus of the frame material, the dynamic stress level at that location is determined using the vibration stress calculation formula. The dynamic stress is a function of amplitude, frequency, and material density. When the dynamic stress exceeds a preset percentage of the material's fatigue strength, a high stress concentration point is identified. Based on the high stress concentration point, the high-frequency component changes of the vibration signal at that location are analyzed. When an increase in high-frequency harmonic components and a shift of fundamental frequency energy to the high-frequency band are detected, it indicates that a nonlinear vibration response caused by microcracks has appeared inside the material. The degree of local cracking is assessed based on the energy proportion of the high-frequency components. Based on the degree of local cracking and the nonlinear characteristics of vibration, when the proportion of high-frequency energy exceeds the preset threshold and the damping ratio continues to decrease, it indicates that the friction at the crack interface is reduced and the material exhibits brittle characteristics. The damage type is identified as brittle deformation, and a brittle deformation assessment conclusion is obtained.

[0045] In one implementation, a decrease in the damping ratio indicates an alteration in the energy dissipation mechanism of the frame material, typically associated with brittle damage within the material. Amplitude distribution data is obtained by spatially mapping the vibration response at each measuring point; the amplitude value at each point reflects the vibration intensity at that location. When localized damage exists in the frame, the decreased stiffness of the damaged area causes it to become a focal point for vibrational energy, manifesting as an abnormal increase in amplitude. The amplitude ratio is calculated using normalization, with the average amplitude of the entire frame as a benchmark to eliminate the influence of the overall vibration level.

[0046] It should be noted that the rate of change of amplitude gradient is a key indicator for identifying stress concentration. In a healthy frame, the amplitude is relatively uniformly distributed along the frame, and the gradient changes gently; however, near the damaged area, the amplitude changes drastically, forming a distinct peak.

[0047] Specifically, the calculation of vibration stress is based on the stress-strain relationship and vibration theory in materials mechanics. When a frame vibrates in a certain mode, the dynamic stress at each point is closely related to the amplitude, vibration frequency, and material properties at that point. The formula for calculating dynamic stress is σ=E·ε, where σ is the dynamic stress, E is the Young's modulus, and ε is the dynamic strain. The dynamic strain is calculated using ε=A·(2πf)² / L, where A is the amplitude, f is the vibration frequency, and L is the characteristic length. In tennis racket frames, carbon fiber composites have a high Young's modulus and a moderate density. When the calculated dynamic stress approaches or exceeds the fatigue strength limit of the material, fatigue cracks are highly likely to occur at that location, and the fatigue strength is usually lower than the static strength of the material. The fatigue strength is typically 30%-50% of the static strength of the material, and this percentage depends on the loading frequency and the number of cycles.

[0048] In one possible implementation, the generation mechanism of nonlinear vibration response is closely related to the presence of cracks. When microcracks appear inside the frame material, the two surfaces of the crack undergo periodic changes of contact and separation during vibration; this phenomenon is called the crack breathing effect. During the compression half-cycle, the crack closes, and the frame stiffness is close to its intact state; during the tension half-cycle, the crack opens, and the stiffness decreases significantly. This periodic change in stiffness leads to the nonlinearity of the system, resulting in high-order harmonic components in the vibration response. The phenomenon of fundamental frequency energy shifting to higher frequencies can be clearly observed through spectral analysis; energy originally concentrated at the fundamental frequency is dispersed to the second, third, or even higher harmonics. The degree of nonlinearity is positively correlated with the crack size; the larger the crack, the more pronounced the high-frequency components.

[0049] For example, high-frequency components are detected by performing a Fast Fourier Transform on the vibration signal to analyze the energy distribution of each frequency component in the spectrum. In a healthy framework, energy is mainly concentrated at the natural frequencies, with very little energy in the high-frequency region. When a crack appears, significant energy peaks appear in the high-frequency band. The frequencies of these peaks are typically integer multiples of the fundamental frequency, where the fundamental frequency refers to the first natural frequency of the structure. The high-frequency energy proportion is calculated as the ratio of the total energy of the frequency bands above twice the fundamental frequency to the total energy of the entire frequency band.

[0050] Preferably, the assessment of the degree of local cracking comprehensively considers the proportion of high-frequency energy, the number and distribution characteristics of spectral peaks. In cases of slight cracking, high-frequency components are mainly concentrated in the 2nd to 3rd harmonics; in cases of severe cracking, high-frequency components can extend to more than the 10th harmonic, with obvious energy peaks at each harmonic. The crack propagation rate also affects the spectral characteristics; rapidly propagating cracks will generate broadband noise signals.

[0051] Understandably, determining brittle deformation requires considering multiple indicators. A continuous decrease in the damping ratio indicates a weakening of the energy dissipation mechanism within the material, which is the opposite of the increasing trend in the damping ratio during plastic deformation. Brittle materials exhibit almost no plastic deformation before fracture, and cracks propagate rapidly, displaying typical brittle fracture characteristics. When the proportion of high-frequency energy exceeds 15% of the total energy, it usually indicates the presence of macroscopic cracks, severely threatening the safety of the frame.

[0052] S106. Based on the combined conclusions of plastic deformation assessment and brittle deformation assessment, and in conjunction with the frequency drift level, the frame damage is identified as mild, moderate, or severe damage using the deformation severity threshold, thus obtaining the frame damage level.

[0053] Based on the combined assessment results of plastic deformation and brittle deformation, a damage type identifier is constructed according to the presence of both types of deformation. If only plastic deformation exists, it is identified as plastic damage; if only brittle deformation exists, it is identified as brittle damage; if both types of deformation exist simultaneously, it is identified as composite damage. Based on the damage type identifier and frequency drift level, the frequency drift level is numerically processed. High drift is assigned a preset high score, and low drift is assigned a preset low score. Simultaneously, a corresponding score is assigned according to the damage type, with brittle damage assigned a higher score than plastic damage. The two scores are added together to obtain a comprehensive damage index. The comprehensive damage index is compared with a preset deformation severity threshold, which is determined based on the allowable stress and fatigue life of the frame material. If the comprehensive damage index is below the first threshold, it is identified as mild damage; if the comprehensive damage index is between the first and second thresholds, it is identified as moderate damage; and if the comprehensive damage index exceeds the second threshold, it is identified as severe damage. This yields the frame damage level.

[0054] In one implementation, the damage type identifier is constructed based on independent assessments of plastic and brittle deformation. Plastic damage manifests as permanent deformation of the frame material while maintaining continuity, while brittle damage is accompanied by localized fracture of the material. The presence of combined damage indicates that the frame has simultaneously experienced two distinct failure mechanisms.

[0055] It should be noted that the numerical processing of frequency drift levels adopts a segmented assignment method. High drift amounts typically correspond to frequency drops exceeding a threshold, and are assigned a score of 10 points according to engineering practices in structural damage assessment; low drift amounts, with frequency drops below the threshold, are assigned 5 points. Damage type scoring follows the principle of severity: brittle damage, due to its suddenness and unpredictability, is assigned 15 points, referencing the risk level of brittle failure in fracture mechanics; plastic damage, with its progressive characteristics, is assigned 8 points; and combined damage, integrating both characteristics, is assigned 20 points. This differentiated scoring reflects the degree of impact of different damage types on frame safety. The high score for brittle damage is based on the risk of sudden frame fracture, while plastic damage, although affecting performance, usually has a warning time.

[0056] Specifically, the comprehensive damage index is obtained through simple addition, with a value ranging from 5 to 30 points. While this linear superposition method simplifies the calculation process, it effectively distinguishes different damage states. When the frame only exhibits low-frequency drift and ductile damage, the comprehensive index is 13 points; while when high-frequency drift is combined with brittle damage, the index reaches 25 points, clearly reflecting the difference in the severity of the damage.

[0057] Preferably, the deformation severity thresholds are set with reference to fatigue test data of carbon fiber composite materials. The first threshold is set at 12 points, corresponding to the state when the material reaches 30% of its fatigue life; the second threshold is set at 20 points, corresponding to the critical point of 70% of the fatigue life. The determination of these thresholds takes into account both the design safety factor and service life requirements of the frame.

[0058] In one possible implementation, frames with minor damage can continue to be used but require increased monitoring frequency, frames with moderate damage are advised to reduce their usage intensity, and frames with severe damage should be stopped immediately to avoid safety accidents.

[0059] S107. Based on the frame damage level and combined with the plastic deformation assessment conclusion or brittle deformation assessment conclusion, output the classification results of frame deformation type and damage degree, and complete the dynamic monitoring and analysis of frame deformation.

[0060] Based on the frame damage level, combined with the plastic deformation assessment conclusions or brittle deformation assessment conclusions, damage degree information and deformation type characteristics are integrated to construct comprehensive assessment data containing damage level identifiers and deformation type identifiers, thus obtaining frame state classification information. Based on the frame state classification information, the classification results of frame deformation type and damage degree are output. The classification results include specific category identifiers for mild plastic damage, moderate plastic damage, severe plastic damage, mild brittle damage, moderate brittle damage, severe brittle damage, or combined damage, completing the dynamic monitoring and analysis of frame deformation.

[0061] In one implementation, the frame state classification information is constructed by combining the damage level and deformation type using a Cartesian product. The damage level includes three levels: mild, moderate, and severe, and the deformation type includes three types: plastic damage, brittle damage, and combined damage, theoretically forming nine possible combined states.

[0062] It should be noted that specific category labels are defined using a coding system. Mild-plastic damage indicates the frame is still usable but requires regular monitoring; moderate-plastic damage suggests reducing hitting power; severe-plastic damage indicates the frame is nearing the end of its service life. Brittle damage is labeled mild brittle, moderate brittle, and severe brittle, with severely brittle frames at risk of sudden fracture and requiring immediate discontinuation. Combined damage is labeled moderate-combined and severe-combined, indicating the frame exhibits both failure modes simultaneously.

[0063] Preferably, the classification results are output in two formats: text reports and visualization charts. The text reports record detailed information such as the type of damage, the location of the damage, and the degree of deformation; the visualization charts use color coding to visually display the health status of each part of the frame, with green indicating normal, yellow indicating mild damage, and red indicating severe damage.

[0064] If the technical solution of this application involves the collection, processing, or application of personal information, the relevant products have strictly complied with the requirements of the "Personal Information Protection Law of the People's Republic of China" and other laws and regulations before implementing any personal information processing activities, clearly and explicitly informing individuals of the rules for personal information processing and obtaining their independent and voluntary authorization and consent. Specifically, if the information involved is sensitive personal information, the product has not only obtained the individual's separate consent before processing, but this consent is also an explicit consent made on the basis of full knowledge. For example, in areas where personal information collection devices such as cameras are deployed, prominent and eye-catching signs have been set up to clearly inform users that entering the area is considered as consenting to the collection of their personal information; or, on the personal information processing interface (such as applications, web pages, etc.), through pop-ups, checkboxes, or active uploads, the user is required to actively authorize the process after clearly displaying key rules such as the identity of the personal information processor, the purpose of processing, the processing method, and the types of information involved.

[0065] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame, characterized in that, include: The tennis racket frame is captured in real time by a piezoelectric vibration acquisition unit to obtain the original vibration data of different natural frequencies of the frame, and the modal amplitude distribution of each vibration mode is recorded to obtain the initial vibration signal set. Frequency domain decomposition is performed on the initial vibration signal set to extract the specific frequency values ​​of different natural frequencies and vibration damping ratios. At the same time, the direction of rise and fall of the vibration damping ratio is identified to obtain the frame vibration analysis results. Based on the frame vibration analysis results, the drift of each natural frequency to the lower frequency band is identified, and the drift is divided into high drift or low drift according to the magnitude of the drift to obtain the frequency drift level. For the frequency drift level, when it is identified as a high drift, the deformation type is analyzed in conjunction with the rising and falling direction of the vibration damping ratio. When the vibration damping ratio is rising, the degree of relaxation of the internal structure of the frame material is evaluated, and it is identified as plastic deformation, thus obtaining a plastic deformation assessment conclusion. When the vibration damping ratio is decreasing, the local amplitude concentration area in the amplitude distribution of each mode is analyzed, the location of the concentrated stress point in the frame is identified, and when local amplitude concentration is detected, the degree of local cracking of the frame is evaluated and identified as brittle deformation, thus obtaining the brittle deformation assessment conclusion. Based on the combined conclusions of the plastic deformation assessment and the brittle deformation assessment, and in conjunction with the frequency drift level, the frame damage is classified into mild, moderate, or severe damage according to the deformation severity grading rules, thus obtaining the frame damage level. Based on the damage level of the frame, combined with the plastic deformation assessment conclusion or the brittle deformation assessment conclusion, the classification results of the frame deformation type and damage degree are output, and the dynamic monitoring and analysis of frame deformation are completed.

2. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, The process involves capturing real-time vibration signals of the tennis racket frame using a piezoelectric vibration acquisition unit, obtaining raw vibration data of different natural frequencies of the frame, and recording the modal amplitude distribution of each vibration mode to obtain an initial vibration signal set, including: A piezoelectric sensor array is used to monitor the vibration at different locations of the tennis racket frame. The charge signal is converted into a voltage signal by a charge amplifier and the voltage signal is acquired at a sampling frequency higher than the preset sampling frequency to obtain the frame's time-domain vibration response data. The time-domain vibration response data of the frame is converted to time frequency to identify the natural frequency values ​​of the first bending mode, the second torsional mode and the third composite mode, and the damping ratio of each mode is determined. At the same time, the peak amplitude at each position is recorded to construct the modal amplitude distribution. Based on the relative ratios of amplitudes at different positions in the modal amplitude distribution and the phase relationship, the current vibration mode category is determined. By combining the time-domain vibration response data, natural frequency values ​​of each order, damping ratio, and modal amplitude distribution, an initial set of vibration signals is obtained.

3. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, Frequency domain decomposition is performed on the initial vibration signal set to extract the specific frequency values ​​of different natural frequencies and the vibration damping ratio. Simultaneously, the direction of increase or decrease of the vibration damping ratio is identified to obtain the frame vibration analysis results, including: After windowing the time-domain data in the initial vibration signal set, a time-frequency transformation is performed to obtain the frequency domain spectral distribution, from which the natural frequency value, amplitude and phase information of each mode are extracted; The damping ratio of each mode is calculated based on the frequency domain spectral line distribution, and the damping ratio values ​​before and after use are compared to identify the direction of increase or decrease of the damping ratio and obtain the damping change trend. By combining the natural frequency values, damping ratio, damping variation trend, and correlation characteristics between different modes, a multidimensional vibration feature matrix is ​​constructed to obtain the analytical results of frame vibration.

4. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, Based on the frame vibration analysis results, the drift of each natural frequency to the lower frequency band is identified, and the drift is classified into high drift or low drift according to the magnitude of the drift to obtain the frequency drift level, including: Extract the reference frequencies of each mode in the initial state of the frame, compare the current natural frequency with the reference frequency, and calculate the frequency drift of each mode. The frequency drift is classified according to a preset drift classification rule. When the absolute value of the drift exceeds the corresponding threshold, it is determined to be a high drift; otherwise, it is determined to be a low drift. By further combining the relative proportions of the drift amounts of each mode and the differences between low-order and high-order drift amounts, the classification results are corrected to obtain the frequency drift levels.

5. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, Regarding the frequency drift level, when a high drift is identified, deformation type analysis is performed based on the rising and falling direction of the vibration damping ratio. When the vibration damping ratio is rising, the degree of relaxation of the internal structure of the frame material is assessed, and plastic deformation is identified, resulting in a plastic deformation assessment conclusion, including: When the frequency drift level is high, read the time sequence of vibration damping ratio, calculate the damping ratio difference between adjacent measurement points, and determine that the damping ratio is rising when the consecutive positive difference value reaches the set number. When the damping ratio is increasing, the strain accumulation characteristics of the frame material under cyclic loading are extracted. When the accumulated strain exceeds the material yield strain range but does not reach the fracture strain range, it is determined that fiber-matrix interface slippage and structural relaxation have occurred inside the frame material. Based on the structural relaxation characteristics and the presence of irreversible permanent deformation, the frame deformation type is identified as plastic deformation, and a plastic deformation assessment conclusion is obtained.

6. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, When the vibration damping ratio is decreasing, the local amplitude concentration areas in the amplitude distribution of each mode shape are analyzed to identify the location of the concentrated stress points in the frame. When local amplitude concentration is detected, the degree of local cracking in the frame is assessed and identified as brittle deformation. The brittle deformation assessment conclusion is obtained, including: When the vibration damping ratio is decreasing, the ratio of the amplitude of each measuring point to the overall average amplitude is calculated from the amplitude distribution of each mode. When the amplitude ratio of a certain area exceeds the set level and the amplitude gradient of adjacent measuring points changes drastically, the area is determined to be an amplitude concentration area and located as a stress concentration location. For the stress concentration location, the high-frequency component variation characteristics of the corresponding vibration signal are analyzed. When the energy of the high-frequency harmonic components increases significantly and the fundamental frequency energy shifts to the high frequency, the nonlinear vibration response caused by microcracks inside the material is determined, and the proportion of high-frequency energy is determined. Based on the trend of continuously decreasing high-frequency energy ratio and damping ratio, the degree of local cracking is assessed, and the frame damage type is identified as brittle deformation, thus obtaining the brittle deformation assessment conclusion.

7. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, Based on the combined conclusions of the plastic deformation assessment and the brittle deformation assessment, and in conjunction with the frequency drift level, the frame damage is classified into mild, moderate, or severe damage according to the deformation severity grading rules, resulting in the frame damage level, including: Based on the existence status of the plastic deformation assessment conclusions and the brittle deformation assessment conclusions, the damage type identifier is determined, including single plastic damage, single brittle damage, or combined damage. The frequency drift level and damage type identifier are numerically combined. High drift combined with brittle damage is assigned a higher comprehensive damage index, while low drift combined with ductile damage is assigned a lower comprehensive damage index. The frame damage level is determined as mild, moderate, or severe by comparing the comprehensive damage index with the preset multi-level deformation severity threshold.

8. The method for dynamic monitoring and analysis of the deformation degree of a tennis racket frame according to claim 1, characterized in that, Based on the frame damage level, combined with the plastic deformation assessment conclusion or the brittle deformation assessment conclusion, the classification results of frame deformation type and damage degree are output, completing the dynamic monitoring and analysis of frame deformation, including: Based on the damage level of the frame and the corresponding plastic deformation assessment conclusion or brittle deformation assessment conclusion, a comprehensive status identifier containing damage level and deformation type is formed. Output the classification results corresponding to the comprehensive state identifier. The classification results include the specific categories of mild plastic damage, moderate plastic damage, severe plastic damage, mild brittle damage, moderate brittle damage, severe brittle damage, and composite damage, thus completing the dynamic monitoring and analysis of frame deformation.

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