A method for processing acceleration data based on the piezoelectric effect

Abstract

The present invention relates to the technical field of performance characteristic analysis, and particularly to an acceleration data processing method based on the piezoelectric effect. The method includes the following steps: acquiring piezoelectric material signal data; performing signal adjustment according to the piezoelectric material signal data to obtain signal adjustment data; constructing a charge acceleration model according to the signal adjustment data to obtain the charge acceleration model; analyzing according to the charge acceleration model to obtain piezoelectric material characteristic data for assisting the operation of piezoelectric material detection. The present invention provides higher signal quality, detection efficiency and analysis reliability through clear signal adjustment steps, efficient model construction and accurate feature extraction.

Description

Technical Field

[0001] The present invention relates to the technical field of performance feature analysis, and particularly to an acceleration data processing method based on the piezoelectric effect. Background Art

[0002] In the sensors based on the piezoelectric effect and their applications, the acceleration data processing technology of piezoelectric materials has long received extensive attention. Traditional acceleration signal processing methods mainly focus on direct time-domain or frequency-domain analysis, assuming that the signal is stable and the noise is small. However, in practical applications, the acceleration signals detected by piezoelectric sensors often have complex dynamic characteristics, including significant non-stationarity, superposition of multi-frequency components, and high-frequency noise interference. These characteristics make it difficult for traditional simple analysis methods to comprehensively and accurately describe the signal features and reflect the performance changes of the materials. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes an acceleration data processing method based on the piezoelectric effect to solve at least one of the above technical problems.

[0004] The present application provides an acceleration data processing method based on the piezoelectric effect, including the following steps:

[0005] Obtain piezoelectric material signal data;

[0006] Perform signal adjustment according to the piezoelectric material signal data to obtain signal adjustment data;

[0007] Construct a charge acceleration model according to the signal adjustment data to obtain a charge acceleration model;

[0008] Analyze according to the charge acceleration model to obtain piezoelectric material characteristic data for assisting in the detection of piezoelectric materials.

[0009] In the present invention, through the preliminary signal adjustment step, the noise and interference in the signal can be effectively removed, and cleaner and more reliable signal adjustment data can be obtained. The adjusted signal data is used to construct a charge acceleration model to more accurately describe the response behavior of the piezoelectric material, thereby improving the accuracy of the acceleration feature analysis. By establishing a charge acceleration model, key parameters related to the characteristics of the piezoelectric material can be extracted from the original signal to reflect the health status, working stability or potential fault signs of the material, providing strong support for detection and diagnosis. The piezoelectric material characteristic data is directly used for assisting detection operations. During production, use or maintenance, by analyzing the obtained characteristic data, problem points can be discovered in a timely manner, potential risks can be predicted, or the material usage conditions can be optimized.

[0010] Preferably, the obtaining of the piezoelectric material signal data includes:

[0011] The control signal acquisition device acquires signals from the piezoelectric sensor in the acceleration state at a preset sampling frequency to obtain piezoelectric material signal data.

[0012] In the present invention, directly acquiring the output of the piezoelectric sensor in the acceleration state can accurately capture the true response of the material under dynamic conditions. After adopting a fixed sampling frequency, the obtained signal data is more easily matched with subsequent processing steps (such as signal adjustment and feature extraction), ensuring data compatibility and consistency between different links.

[0013] Preferably, the signal adjustment based on the piezoelectric material signal data to obtain signal adjustment data includes:

[0014] Amplify the piezoelectric material signal data to obtain signal amplification data;

[0015] Shape the signal amplification data to obtain signal adjustment data.

[0016] In the present invention, by amplifying the original piezoelectric material signal, the amplitude of the signal can be significantly increased, making weak signals easier to detect and analyze, and enhancing the resolution ability of the signal. Shaping the amplified signal can eliminate distortion or noise in the signal waveform, making the signal smoother and more regular, thereby improving the signal quality. After signal amplification and shaping, the adjusted signal is closer to the ideal waveform, providing high-quality input data for modeling, feature extraction, and analysis.

[0017] Preferably, the construction of the charge acceleration model based on the signal adjustment data to obtain the charge acceleration model includes:

[0018] Calibrate the signal adjustment data to obtain signal calibration data;

[0019] Construct the charge acceleration model based on the signal calibration data to obtain the charge acceleration model.

[0020] In the present invention, calibration is used to eliminate biases and errors in the data, ensuring that the data input into the model is more accurate and real, significantly improving the calculation accuracy of the charge acceleration model, and reducing the model deviation caused by uncalibrated signals. Modeling based on the calibrated signal can reflect the real physical process, making the model more reliable and stable.

[0021] Preferably, the piezoelectric material characteristic data includes first piezoelectric material characteristic data and second piezoelectric material characteristic data. The analysis based on the charge acceleration model to obtain the piezoelectric material characteristic data for assisting in the piezoelectric material detection operation includes:

[0022] Extract the first data feature based on the charge acceleration model to obtain the first piezoelectric material characteristic data;

[0023] Perform the second data feature extraction according to the charge acceleration model to obtain the second piezoelectric material feature data, where the first data feature extraction and the second data feature extraction are different data feature extraction methods.

[0024] In the present invention, the data features extracted by various methods can complement each other, helping to accurately identify the state, health condition or potential faults of the material. For example, the first feature reflects the overall dynamic characteristics of the material, and the second feature reveals the detailed behavior of the material under specific conditions. The combined analysis can greatly improve the accuracy of the detection results. Different feature extraction methods can perform multi-angle verification on the same data source, making the analysis more robust. Even if a certain feature is affected by noise, other features can still provide reliable references, thereby increasing the stability and reliability of the results.

[0025] Preferably, the performing the first data feature extraction according to the charge acceleration model to obtain the first piezoelectric material feature data includes:

[0026] Perform root mean square calculation according to the charge acceleration model to obtain the first signal intensity data, and perform peak amplitude calculation according to the charge acceleration model to obtain the second signal intensity data;

[0027] Perform energy consumption calculation according to the first signal intensity data and the second signal intensity data to obtain the energy consumption data;

[0028] Perform non-stationary - stationary interval division according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively;

[0029] Perform instantaneous amplitude calculation according to the non-stationary signal data to obtain the first fluctuation amplitude data;

[0030] Perform standard deviation calculation according to the stationary signal data to obtain the second fluctuation amplitude data;

[0031] Perform feature generation according to the energy consumption data, the first fluctuation amplitude data and the second fluctuation amplitude data to obtain the first piezoelectric material feature data.

[0032] In the present invention, based on the root mean square calculation and the peak calculation, the signal intensity data can be provided. Through the division of non-stationary and stationary signals, the instantaneous changes and long-term stability of complex signals can be analyzed separately. The non-stationary part reflects the instantaneous response of the material under dynamic conditions, while the stationary part indicates its long-term stable behavior. The energy consumption data provides the performance indicators of the material under different working conditions, and can quantify the energy loss of the material caused by factors such as vibration and loading in actual applications. Using the instantaneous amplitude and the standard deviation to calculate the fluctuation amplitude of the non-stationary and stationary signals respectively can capture the subtle dynamic changes and long-term fluctuation laws in the signals.

[0033] Preferably, the non-stationary - stationary interval division is performed according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively, including:

[0034] Performing peak-valley region division according to the charge acceleration model to obtain peak-valley region data;

[0035] Performing periodic parameter fitting based on the peak-valley region data to obtain periodic parameter fitting data;

[0036] Performing similar parameter interval division on the charge acceleration model according to the periodic parameter fitting data to obtain non-stationary signal data and stationary signal data.

[0037] In the present invention, the non-stationary signal reflects the complex changes of the piezoelectric material during dynamic loading or vibration, while the stationary signal represents the behavior of the material under relatively stable conditions. Through peak-valley region division and periodic parameter fitting, the periodicity and instantaneous change characteristics of the signal can be described more precisely. The present invention can achieve signal processing in special environments, such as separating non-stationary signals in a strong vibration environment to capture dynamic characteristics; or analyzing the long-term performance of the material in a stationary state.

[0038] Preferably, the instantaneous amplitude calculation is performed according to the non-stationary signal data to obtain first fluctuation amplitude data, including:

[0039] Performing adjacent extreme value extraction according to the periodic parameter fitting data to obtain adjacent extreme value data;

[0040] Performing amplitude calculation on the non-stationary signal data according to the adjacent extreme value data to obtain first fluctuation amplitude data.

[0041] In the present invention, by extracting adjacent extreme value points from the periodic parameter fitting data, the local change amplitude of the signal can be accurately located, avoiding the masking of instantaneous characteristics due to the overall trend or changes within a long time window. The non-stationary signal contains rapid changes or irregular fluctuations, and traditional average value or long time window statistical methods will ignore these details. By extracting adjacent extreme values and calculating the amplitude based on these extreme values, short-term mutations or severe fluctuations in the non-stationary signal can be detected more sensitively. Focusing on the extreme value points during amplitude calculation reduces the dependence on the global trend and can exclude the interference of some low-frequency or stationary backgrounds, thereby improving the resolution of the results.

[0042] Preferably, the second data feature extraction is performed according to the charge acceleration model to obtain second piezoelectric material feature data, including:

[0043] Performing frequency domain feature extraction according to the charge acceleration model to obtain frequency domain feature data;

[0044] Calculate the sample entropy based on the frequency-domain feature data to obtain the frequency-domain sample entropy data;

[0045] Calculate the permutation entropy based on the frequency-domain feature data to obtain the frequency-domain permutation entropy data;

[0046] Perform kernel density estimation based on the frequency-domain sample entropy data and the frequency-domain permutation entropy data to obtain the entropy kernel density data;

[0047] Construct a probability cloud map based on the entropy kernel density data to obtain the characteristic data of the second piezoelectric material.

[0048] In the present invention, by calculating the sample entropy and permutation entropy of the frequency-domain feature data and combining kernel density estimation, the density and distribution characteristics of these entropy values in different frequency distributions can be quantified. This precise probability density estimation enables the analysis to no longer rely on a single eigenvalue but be based on comprehensive distribution information, improving the reliability of the analysis. By constructing a probability cloud map, the distribution of multi-dimensional entropy features is presented, making the division of different characteristic states (such as normal and abnormal) more intuitive and clear.

[0049] Preferably, the calculating the sample entropy based on the frequency-domain feature data to obtain the frequency-domain sample entropy data includes:

[0050] Extract the main frequency components from the frequency-domain feature data to obtain the main frequency component data;

[0051] Generate a scale factor based on the main frequency component data to obtain the scale factor data;

[0052] Perform frequency-domain division on the frequency-domain feature data according to the scale factor data to obtain the frequency-domain feature division data;

[0053] Calculate the sample entropy based on the frequency-domain feature division data to obtain the frequency-domain sample entropy data.

[0054] In the present invention, before calculating the sample entropy, extracting the main frequency components of the frequency-domain data can remove the information of irrelevant frequency bands. The scale factor generated from the main frequency data makes the calculation of the sample entropy more accurate, ensuring that the dynamic characteristics of different frequency bands can be captured with finer granularity. By generating different scale factors, this method enables the sample entropy to be calculated in multiple frequency ranges and time scales. Dividing the frequency-domain feature data according to the generated scale factor makes the characteristics of different frequency ranges appear independently, reducing the influence of frequency aliasing on the calculation of the entropy value. Calculating the sample entropy based on the scale division realizes the calculation of the sample entropy in multiple dimensions, thus providing more accurate data support.

[0055] The beneficial effects of the present invention are as follows: During the signal adjustment process, measurement noise and environmental interference are effectively eliminated, and the generated signal adjustment data is more accurate and consistent. The constructed charge acceleration model starts from physical principles, can capture the characteristics of piezoelectric materials under dynamic acceleration conditions, deeply explores the dynamic response behavior of the materials, so that the extracted piezoelectric material characteristic data can characterize the performance of the materials in multiple dimensions. The characteristic data generated by model analysis can be used to track the changes in material performance in the long term, provide a scientific basis for maintenance decision-making, fault prediction and life assessment, and provide higher signal quality, detection efficiency and analysis reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Other features, objects and advantages of the present application will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0057] Figure 1 The flowchart showing the steps of a method for processing acceleration data based on the piezoelectric effect according to an embodiment;

[0058] Figure 2 The flowchart showing the steps of a method for extracting the characteristics of a first piezoelectric material according to an embodiment;

[0059] Figure 3 The flowchart showing the steps of a method for dividing non-stationary - stationary intervals according to an embodiment;

[0060] Figure 4 The flowchart showing the steps of a method for extracting the characteristics of a second piezoelectric material according to an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] The technical method of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0062] In addition, the accompanying drawings are only schematic diagrams of the present invention and are not necessarily drawn to scale. The functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor methods and / or microcontroller methods.

[0063] It should be understood that although terms such as "first", "second", etc. may be used herein to describe various units, these units should not be limited by these terms. These terms are only used to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, the first unit may be referred to as the second unit, and similarly, the second unit may be referred to as the first unit. The term "and / or" used herein includes any and all combinations of one or more of the listed related items.

[0064] Please refer to Figures 1 to 4 , this application provides an acceleration data processing method based on the piezoelectric effect, including the following steps:

[0065] S1. Obtain piezoelectric material signal data;

[0066] In one embodiment, signal data from the piezoelectric material is obtained through a piezoelectric sensor (e.g., a piezoelectric accelerometer). The piezoelectric material generates charges when subjected to mechanical stress or vibration, and the signal data appears as a voltage or current signal proportional to the acceleration. To ensure the quality of the signal, it is converted into a digital signal through a data acquisition system (such as an oscilloscope or a data acquisition card).

[0067] S2. Perform signal adjustment based on the piezoelectric material signal data to obtain signal adjustment data;

[0068] In one embodiment, after obtaining the original signal data, signal adjustment is performed. The original signal is affected by noise, baseline drift, or other interferences. A low-pass filter is selected and the cut-off frequency is set to remove noise components above the cut-off frequency; or a band-pass filter is used to retain the main signal components within the expected frequency band (e.g., 5–100 Hz), or, to remove baseline drift, it can be eliminated by performing a DC removal process on the signal.

[0069] S3. Construct a charge-acceleration model based on the signal adjustment data to obtain a charge-acceleration model;

[0070] In one embodiment, a charge-acceleration model is constructed based on the signal adjustment data. According to the piezoelectric effect, the output charge of the piezoelectric material is proportional to the applied force or acceleration. The stress-charge relationship of the piezoelectric material is: , where is the charge output by the piezoelectric material, is a constant related to the material properties, is the applied acceleration. Or,

[0071] According to the piezoelectric effect formula, the relationship between the output charge and the acceleration is represented by an integral:

[0072] 。

[0073] S4. Analyze according to the charge acceleration model to obtain the characteristic data of the piezoelectric material for assisting the piezoelectric material detection operation.

[0074] In the present invention and , represents the charge output by the piezoelectric material, and the unit is Coulomb C. is the piezoelectric coefficient, representing the amount of charge generated per unit acceleration, and the unit is , and can also be expressed as (where is the gravitational acceleration constant). and , represents the applied acceleration, and the unit is or ( ). This formula directly comes from the basic theory of the piezoelectric effect and has been verified by a large number of experiments. For example, in the static pressure experiment, the measured charge output is proportional to the applied force (or acceleration), and the proportionality coefficient is the known piezoelectric constant of the material. This formula describes the cumulative result of the instantaneous response. In the dynamic loading experiment, an acceleration that changes with time is applied, and the total charge output obtained by integration is consistent with the charge cumulative result measured in the experiment. The accuracy of this integral relationship has been repeatedly proven in the experiments of material mechanics and electrical coupling. For example, a piezoelectric acceleration sensor generally consists of a housing and a spring, a mass block, a piezoelectric element and a fixed base installed in the housing. A mass block is placed on the piezoelectric wafer, and then the mass block is pre-loaded with a hard spring, and then the whole assembly is installed in a metal housing of a base. When the sensor senses vibration, due to the relatively large stiffness of the spring and the relatively small mass of the mass block, it can be considered that the inertia of the mass block is very small. It senses the same vibration as the sensor base and is subjected to an inertial force in the direction opposite to the acceleration direction. In this way, there is a force acting on the piezoelectric wafer that is proportional to the acceleration on the mass block. Through the piezoelectric effect of the piezoelectric wafer, a voltage that changes with the vibration acceleration will be generated on the surface of the piezoelectric wafer. When the vibration frequency is much lower than the natural frequency of the sensor, the voltage output by the sensor is proportional to the acting force, that is, proportional to the acceleration sensed by the sensor.

[0075] In one embodiment, signal analysis is performed through the charge acceleration model, and the characteristic data of the piezoelectric material is extracted. The charge acceleration model establishes the relationship between acceleration and the induced charge signal The functional relationship between them can convert the actually measured acceleration signal into the corresponding charge time series. By analyzing the charge-acceleration model, different acceleration ranges, frequency responses and other characteristics can be identified. For example, the resonance frequencies of the piezoelectric material in different vibration modes are extracted by analyzing the frequency spectrum of the acceleration. Calculate the spectrum of the signal:

[0076] ;

[0077] where is the spectrum of the signal, is the length of the time window, is the base of the natural logarithm, is the imaginary unit, is the constant term of pi, is the frequency variable of the signal, is the time parameter. Identify the significant peaks in the spectrum.

[0078] Since the piezoelectric response signal has non-stationarity and local modulation characteristics, the Hilbert transform can be used to effectively extract its instantaneous energy change and improve the response detection ability for dynamic processes. Perform the Hilbert transform on the induced charge signal to obtain its analytic signal, , where is the analytic signal, is the imaginary unit, is the Hilbert transform of, representing the 90° phase shift part of the signal. Calculate the instantaneous amplitude :

[0079] , to obtain the instantaneous amplitude changing with time, to represent the dynamic intensity change of the acceleration signal. The extracted spectral characteristics (such as resonance frequency) and the instantaneous amplitude change can be used to identify the response performance of the material, judge whether there is performance attenuation, or evaluate its dynamic behavior at a specific frequency, and are used in the discrimination and early warning module of the piezoelectric material detection auxiliary system.

[0080] In the present invention represents the induced charge signal, with the unit of coulomb C, represents the spectrum of the signal, with the unit the same as because the integration result reflects the amplitude of the signal at the frequency , with the unit of coulomb C, represents the length of the time window, with the unit of second s, represents the base of the natural logarithm, dimensionless, is the imaginary unit, dimensionless, is the constant term of pi, dimensionless, is the frequency of the signal, with the unit of Hertz (Hz) or the reciprocal of seconds , is the time parameter, with the unit of seconds (s). Converting the induced charge signal to the frequency domain can obtain the amplitude and phase distributions of the signal at different frequencies. This spectrum analysis method can reveal the response characteristics of the piezoelectric material to specific acceleration frequencies; directly find the resonance frequency of the material from the prominent peak positions in the spectrum, which is an important parameter characterizing the inherent properties of the material. This formula is based on the theoretical basis of the Fourier transform, which is a widely used signal analysis tool. By integrating the time-domain signal to the frequency domain and extracting the amplitude and phase of the frequency components, this is a classic method of signal processing and can be understood physically as the contributions of the signal in different resonance modes;

[0081] In the present invention is the Hilbert transform of, and it is still part of the induced charge signal, with the same unit as which is Coulomb (C), is the analytic signal, which is composed of and its Hilbert transform , with the same unit as which is Coulomb (C), is the instantaneous amplitude, defined as , and its dimension is the same as which is Coulomb (C). The process of generating the analytic signal by the Hilbert transform is to extend the original signal to the complex domain. The real part of the analytic signal is the original signal , and the imaginary part is the quadrature component of the signal . Through the analytic signal, further calculating the instantaneous amplitude can effectively describe the energy change of the signal at different time points. Through the instantaneous amplitude , the changing trend of signal strength over time can be visually observed. Especially at moments when the signal amplitude fluctuates significantly, the change in instantaneous amplitude can reflect the dynamic response characteristics. Non-stationary signals usually contain local amplitude modulation components, which are clearly visible in the instantaneous amplitude. Compared with traditional spectral analysis, instantaneous amplitude can more accurately capture short-time bursts or local changes in time-varying signals. For piezoelectric materials, the stability of their response performance can be judged by the change of instantaneous amplitude. If the instantaneous amplitude decays rapidly at a specific frequency or vibration mode, it indicates a decline in material performance; if the amplitude remains stable over time, it shows that the material has good dynamic performance under the current conditions. The role of the Hilbert transform is to expand a real signal into a complex signal, providing an orthogonal component. This expansion is mathematically complete and can be used for the calculation of instantaneous amplitude and instantaneous phase, and its results can well characterize the time-varying characteristics in non-stationary signals. The parameters in the formula have consistent dimensions, and all addition and subtraction operations, multiplications, and integral operations have no dimensional conflicts and can be directly added.

[0082] Preferably, the obtaining of the piezoelectric material signal data includes:

[0083] Controlling a signal acquisition device to acquire signals from a piezoelectric sensor in an accelerating state at a preset sampling frequency to obtain piezoelectric material signal data.

[0084] In one embodiment, configure the signal acquisition device. The signal acquisition device includes an analog-to-digital converter (ADC) and an acquisition control unit. In the configuration stage, the control system sets the sampling frequency and sampling time. When selecting the sampling frequency, it is adjusted to be at least twice the highest frequency of the signal. The piezoelectric sensor is installed on the object to be tested (such as machine parts, structural surfaces, etc.), and it is ensured that it is closely coupled with the applied acceleration or vibration state. The control device starts sampling according to the change of acceleration or a specific trigger condition (such as a set vibration threshold). After triggering, the system starts to regularly acquire signal data at the set frequency. The sampling device obtains the charge signal output by the sensor at the set time interval. The acquired piezoelectric signal data is stored through a data storage device (such as a hard disk, solid-state drive, etc.). During the storage process, the signal is stored in a database in discrete digital form or directly exported as a file.

[0085] Preferably, the signal adjustment according to the piezoelectric material signal data to obtain signal adjustment data includes:

[0086] Amplifying the piezoelectric material signal data to obtain signal amplification data;

[0087] In one embodiment, the main purpose of signal amplification is to increase the amplitude of the original signal to ensure the detectability of the signal during the processing. Since the signal output by the piezoelectric sensor is usually relatively weak, direct use may affect the analysis effect due to noise or too small signal amplitude. The amplification factor is selected according to the actual amplitude and expected range of the signal. If the signal amplitude is too small, a larger amplification factor (such as 5 - 10 times) can be selected; if the signal amplitude is large, a moderate amplification factor (such as 1.1 - 3 times) is selected to avoid signal distortion caused by excessive amplification. To prevent saturation or distortion caused by too large an amplification factor, an automatic gain control (AGC) mechanism can be set or a limiting device can be introduced to dynamically adjust the amplified signal.

[0088] Perform signal shaping based on the signal amplification data to obtain signal adjustment data.

[0089] In one embodiment, the purpose of signal shaping is to process the amplified signal to meet the requirements of analysis. Since the piezoelectric signal contains high - frequency noise or low - frequency drift, a filter (such as an RC filter) is used to process the signal. The stress - charge relationship of the piezoelectric material is: , where is the charge output by the piezoelectric material, is a constant related to the material properties, is the applied acceleration. Or,

[0090] According to the piezoelectric effect formula, the relationship between the output charge and the acceleration is represented by integration:

[0091] .

[0092] Preferably, constructing a charge - acceleration model based on the signal adjustment data to obtain a charge - acceleration model includes:

[0093] Perform signal calibration based on the signal adjustment data to obtain signal calibration data;

[0094] In one embodiment, a vibration table, an exciter, or a physical environment with a known acceleration is used to generate a vibration signal with a certain amplitude and frequency through these acceleration sources. Under the action of a standard acceleration source, the output signal of the piezoelectric sensor is recorded. Through experimental data, the relationship between the standard acceleration signal and the piezoelectric signal is established and represented by a linear relationship. The relationship between acceleration and signal is: , is the output signal of the piezoelectric sensor, is the calibration constant of the sensor, representing the proportional relationship between the signal and the acceleration, is the standard acceleration signal. The least squares fitting method is used to estimate the above relationship and calculate the calibration constant, which represents the proportionality of the electrical signal response under unit acceleration input and is used for signal back-calculation. The value and the linear relationship established through this process are part of the signal calibration data and are used to convert the original signal data into standard acceleration values.

[0095] In the present invention represents the output signal of the piezoelectric sensor. Its unit depends on the form of the signal. For example, if the signal is voltage, the unit is volt V; if the signal is charge, the unit is coulomb C. is the calibration constant of the sensor. Its dimension is the output signal unit divided by the acceleration unit. For example, if is voltage V, and is acceleration , then has a dimension of . If is coulomb C, and is acceleration , then has a dimension of . Both physical experiments and theories show that the charge output of piezoelectric materials is usually proportional to the applied force, and the force is proportional to the acceleration, making it reasonable for the output signal to have a linear relationship with the standard acceleration. Within the normal operating range of the sensor (without reaching saturation or non-linear failure), using a linear model is not only reasonable but also simplifies calibration and processing. The least squares method is one of the most commonly used methods in parameter estimation, and its core idea is to minimize the sum of the squares of the deviations between the actual measurement data and the fitting model, thereby obtaining the optimal fitting parameters. For the linear model , the least squares method can quickly and stably calculate the proportionality coefficient , and this estimated value has the minimum variance in the case of random white noise, so it is an ideal choice in the calibration process. The calibration constant directly reflects the sensitivity of the sensor, and the unit is the signal output value (such as voltage, charge) divided by acceleration (such as V / g or C / g). By accurately determining , the repeatability and accuracy of the measurement system can be ensured, providing a solid quantitative basis for experimental analysis. Through the value determined by experiments, any original output signal can be converted into a standard acceleration value, facilitating data comparison and result verification. The calibration constant can also be used to evaluate the long-term stability and consistency of the sensor. If it is found that changes significantly after long-term use, it indicates the drift or degradation of the sensor performance, thereby guiding maintenance or recalibration.

[0096] Construct a charge acceleration model based on the signal calibration data to obtain the charge acceleration model.

[0097] In one embodiment, after signal calibration, a charge acceleration model is constructed to establish the relationship between acceleration and charge. Due to the characteristics of piezoelectric materials, the charge generated by acceleration is proportional to the acceleration. A linear relationship model is constructed: , is the induced charge per unit time, is the sensitivity coefficient of the piezoelectric material, is the acceleration data, is the zero drift term or the initial offset. This model derives the relationship between acceleration and charge based on the calibrated signal.

[0098] Preferably, the piezoelectric material characteristic data includes first piezoelectric material characteristic data and second piezoelectric material characteristic data. Analyzing according to the charge acceleration model to obtain the piezoelectric material characteristic data for piezoelectric material detection auxiliary operations, including:

[0099] Extract the first data characteristics according to the charge acceleration model to obtain the first piezoelectric material characteristic data;

[0100] In one embodiment, the first data characteristic extraction is signal time characteristic extraction. By finding the maximum value of the signal, the peak value of the signal is obtained, representing the maximum amplitude of the piezoelectric material response. Calculate the mean value of the signal, representing the average response value of the signal. Calculate the variance of the signal, representing the degree of signal fluctuation. Calculate the duration when the signal is greater than a certain threshold, which is used to describe the pulse characteristic of the signal, to obtain the signal duration. Through the calculation of these characteristics, the first piezoelectric material characteristic data is obtained.

[0101] Extract the second data characteristics according to the charge acceleration model to obtain the second piezoelectric material characteristic data, where the first data characteristic extraction and the second data characteristic extraction are different data characteristic extraction methods.

[0102] In one embodiment, the second data characteristic extraction is signal spectrum characteristic extraction. Perform a fast Fourier transform (FFT) on the charge signal to obtain the frequency domain signal. Find the frequency point with the largest amplitude in the spectrum as the main frequency, that is, the natural frequency or the strongest response frequency of the piezoelectric material. Calculate the frequency bandwidth of the signal, that is, the frequency range where the amplitude is greater than a certain threshold starting from the main frequency. The bandwidth can be defined by analyzing the region where the spectrum amplitude is greater than a certain threshold. Calculate the power density of the spectrum to obtain the energy distribution of the signal in each frequency band. If the signal contains harmonics, analyze the amplitude of each harmonic to obtain the contribution of the higher harmonics to the overall signal as part of the second characteristic. Based on the foregoing frequency domain analysis, the second piezoelectric material characteristic data is obtained.

[0103] Preferably, the first data feature extraction according to the charge acceleration model to obtain the first piezoelectric material feature data includes:

[0104] S41. Calculate the root mean square according to the charge acceleration model to obtain the first signal intensity data, and calculate the peak amplitude according to the charge acceleration model to obtain the second signal intensity data;

[0105] In one embodiment, the root mean square calculation:

[0106] ;

[0107] where is the first signal intensity data, is the number of signal sampling points, is the time point sequence term, is the time point, is the value of the time point corresponding to the charge acceleration model.

[0108] Determine the time interval [tN, tM] for signal analysis, where tN and tM are the starting and ending time points respectively. Use the charge acceleration model to obtain the acceleration signal data at each time point. The peak amplitude is the maximum absolute value of the signal within this time interval, that is, find the maximum value of the acceleration signal within the interval. The peak amplitude represents the maximum response amplitude of the signal, reflecting the ultimate response ability of the piezoelectric material. Use the charge signal to find the maximum value of the signal within the given interval.

[0109] In the present invention is the root mean square value, representing the energy intensity of the signal. The dimension depends on the physical unit of the signal itself. If is charge, with the unit of Coulomb C, then has the dimension of Coulomb as well, is the number of signal sampling points, dimensionless, is the sequence term of the time point, dimensionless, is the time point, with the unit of second s, is the instantaneous value of the charge signal at the time point , with the unit of Coulomb C. Since are the values of the same physical quantity at different time points, the square has the dimension of , while is dimensionless. Therefore, still has the dimension of . After taking the square root, has the dimension of , which is consistent with the dimension of . The parameters in this formula have consistent dimensions and can be directly added and operated on. Represents the overall energy level of the signal, which is a comprehensive indicator of signal strength. By calculating , the average amplitude of the signal within a time interval can be clearly quantified, which is very important for evaluating the continuous response ability of piezoelectric materials under a certain working condition. The root mean square value is less affected by accidental extreme points and can reflect the overall characteristics of the signal rather than the response at a single moment, making it an important reference for judging the stability of material performance. The peak amplitude reflects the maximum response level of the signal within the selected time interval. The calculation of the peak amplitude provides the ultimate response ability of the material, helps identify possible overload states or maximum bearing capacities, and provides a direct basis for the safety assessment and performance debugging of the material. If the peak amplitude exceeds the expected range, it may indicate that the material has experienced abnormal events or is approaching its operating limit. is a standard calculation method widely used in signal analysis. By squaring, averaging, and taking the square root, it can effectively capture the overall energy level of the signal and has a consistent measurement standard for symmetric signals with positive and negative values. RMS is less affected by high-frequency noise in a short time and helps to stably reflect the average intensity of the signal. The peak amplitude is a physically clear quantity that only depends on the extreme points of the signal and does not involve complex mathematical operations, having direct engineering significance. When evaluating the ultimate performance of piezoelectric materials, the maximum value provides a clear reference index and is an important basis for judging the dynamic behavior of the material. Combining the root mean square value and the peak amplitude can obtain the average response level and the ultimate response level of the signal simultaneously. These two characteristics together constitute a comprehensive analysis of the signal strength. RMS focuses more on the overall characteristics, and the peak amplitude focuses more on extreme cases. The two complement each other and provide multi-angle support for evaluating material performance.

[0110] S42. Calculate the energy consumption based on the first signal strength data and the second signal strength data to obtain the energy consumption data;

[0111] In one embodiment, the signal has an approximately periodic oscillation characteristic. By performing a square integral on the signal strength and its value after sine modulation, the energy consumption per unit time can be reflected, and the overall energy dissipation level can be approximately estimated. The energy consumption calculation:

[0112] ;

[0113] where is the energy consumption data, is the data point sequence term, is the data point quantity data, is the first signal strength data corresponding to the initial time to time , is the th frequency factor, is the angular frequency, representing the oscillation frequency of the signal, is the specific time point of signal sampling (the th time point), is the initial phase of the first signal intensity data, used to characterize the phase shift of the signal waveform, is the second signal intensity data corresponding from the initial moment to the moment (corresponding), is the th time parameter item, is the time parameter, is the initial phase of the second signal intensity data, similar to the phase shift of the first signal, affecting the waveform of signal synthesis, is the time step, representing the time interval between data points.

[0114] In the present invention is the energy consumption data, expressed in energy units (such as joule J), is the data point sequence item, dimensionless, is the data point quantity data, dimensionless, is the first signal intensity data corresponding from the initial moment to the moment (corresponding). The unit depends on the specific signal type. If the signal represents voltage, the unit is volt V; if it represents charge, the unit is coulomb C, is the th frequency factor, dimensionless (representing a proportional factor of a certain frequency), is the angular frequency, with the unit of radian per second rad / s, representing the oscillation frequency of the signal, is the specific time point of signal sampling (the th time point), with the unit of second s, is the initial phase of the first signal intensity data, used to characterize the phase shift of the signal waveform, with the unit of radian rad, is the second signal intensity data corresponding from the initial moment to the moment (corresponding). The unit depends on the specific signal type. If the signal represents voltage, the unit is volt V; if it represents charge, the unit is coulomb C, is the th time parameter item, is the time parameter, is the initial phase of the second signal intensity data, similar to the phase shift of the first signal, affecting the waveform of signal synthesis, with the unit of radian rad, is the time step, representing the time interval between data points, with the unit of second s; The dimension of is consistent with (such as or ) Similarly, the dimension of the square of . After summing over all points and multiplying by , it is equivalent to approximate integration. Therefore, the dimension of the result is or . If and are voltages (in volts V), then has the dimension of watt-second , which is joule J. If and are charges (in coulombs C), then the charge is derived to obtain the voltage, such as V = IZ, where V is the voltage, I is the flowing current, and it is obtained through and conversion, and Z is the complex impedance, which is a preset value. Each term in the formula is dimensionally consistent (in energy units) and can be directly added for summation, which is physically reasonable. The formula approximately calculates the total energy consumption of the signal per unit time through the method of square integration, providing a means for quantitative analysis of the signal dissipation level. Different signal intensities , and the frequency factor combination reflects the energy distribution of the signal in different oscillation modes and can describe the dynamic behavior of the piezoelectric material under multi-frequency excitation. The energy consumption data can help identify changes in material properties under different excitation conditions. For example, whether the energy consumption in the high-frequency oscillation mode is significantly higher than that in the low-frequency mode. By adjusting the input parameters (such as the phase shift , or the frequency factor ), the response law of the material in different vibration modes can be studied, thereby optimizing the usage conditions and performance evaluation. By performing square integration on the signal, it can be regarded as a process of calculating the energy density, which conforms to the common methods of energy calculation in physics. The square operation is used to eliminate the cancellation effect of the positive and negative values of the signal, thereby more accurately reflecting the overall strength of the signal, while the integration reflects the cumulative effect of the signal strength over time. The sine modulation and phase shift in the formula reflect the periodicity and modulation characteristics of the signal, and these factors affect the instantaneous energy change of the signal, reasonably incorporating the dynamic characteristics into the energy calculation.

[0115] S43. Divide the non-stationary - stationary interval according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively;

[0116] In one embodiment, the signal intervals are divided by analyzing the statistical characteristics of the signal, especially the changes in the mean and variance. In the range of t1 and t2, the part where the signal has significant changes (the changes in the mean and variance are not within the threshold range) is regarded as the non-stationary interval, while the part with stable changes (the changes in the mean and variance are within the threshold range) is regarded as the stationary interval.

[0117] S44. Calculate the instantaneous amplitude based on the non-stationary signal data to obtain the first fluctuation amplitude data;

[0118] In one embodiment, for the non-stationary signal data , its instantaneous amplitude is obtained by calculation. The instantaneous amplitude is: , where is the time parameter. The instantaneous amplitude is obtained through the change of the instantaneous frequency of the signal.

[0119] In the present invention is the instantaneous amplitude, which is defined according to the formula as the square root of the sum of the squares of the signal and its derivative, so the unit is the same as that of , is the non-stationary signal, and the dimension depends on the physical unit of the signal. If is a charge signal, the unit is Coulomb C; if it is a voltage signal, the unit is Volt V. is the time parameter, with the unit of s, is the time constant or time scale, with the unit of s. Therefore, after taking the square root, the unit of the instantaneous amplitude is still the same as that of , maintaining dimensional consistency. Physically, the operations of the formula are valid, and the parameters can be directly added. The instantaneous amplitude provides the intensity information of the signal at any time point. For non-stationary signals, their intensity may change with time, and the instantaneous amplitude can capture these dynamic change characteristics, enabling us to have a more intuitive understanding of the local energy or fluctuation of the signal. This formula combines the signal value and its time derivative , thus not only reflecting the intensity of the signal itself but also considering the rate of change of the signal. For example, even if the signal value is small at a certain moment, if the signal change rate is high, the instantaneous amplitude will still show a large value. This characteristic enables the instantaneous amplitude to simultaneously characterize the static and dynamic intensities of the signal. For non-stationary signals, traditional root mean square (RMS) values or power spectrum analysis may not accurately describe the changes of the signal at different time points. The instantaneous amplitude formula directly provides the intensity changes at each time point. Especially for signals containing modulation, burst components, or short-term anomalies, the instantaneous amplitude can reveal their time-varying characteristics.

[0120] S45. Calculate the standard deviation based on the stationary signal data to obtain the second fluctuation amplitude data;

[0121] In one embodiment, for the stationary signal data , the standard deviation is calculated (to measure the fluctuation range):

[0122] ;

[0123] where is the second fluctuation amplitude data, is the number of time parameters, is the time parameter sequence item, is the th time parameter, is the th sampling point of the stationary signal data corresponding to the time parameter, is the average value of the stationary signal data.

[0124] In the present invention, in the standard deviation formula, the dimension of is . After summing all points, the dimension of the result is still . Then divide by for normalization, and the dimension of the result is still . Finally, take the square root, and the dimension of the standard deviation becomes

[0125] , which is consistent with the unit of the original signal. Therefore, the dimensions in the formula are self - consistent, and all addition, subtraction, multiplication, and division operations are valid. The standard deviation is a key indicator for measuring the overall fluctuation degree of the signal. A larger standard deviation means that the signal has a larger range of fluctuations, reflecting the discrete degree of the amplitude distribution of the stationary signal. Through calculation, it can quickly judge the stability and consistency of the signal within a given time interval. As an intuitive statistic, the standard deviation can be used to compare the fluctuation amplitudes of different signal data sets, providing a basis for feature extraction and classification. In material testing or performance evaluation, the changing trend of the standard deviation may indicate changes in material response characteristics or environmental conditions. The standard deviation formula is a standard measure of the degree of dispersion in statistics and is widely used in the field of signal processing. Under the assumption of a stationary signal, the fluctuation amplitude of the signal does not change drastically over time, so the calculation result of the standard deviation can stably reflect its fluctuation range. The standard deviation provides quantitative information about signal fluctuations, which is more intuitive than just observing the signal waveform. Through the standard deviation, it is easier to distinguish the stability of different types of signals. For example, if the standard deviation of the signal under a certain working condition increases significantly, it may indicate the occurrence of abnormal fluctuations or deterioration of equipment performance. In material performance testing, the standard deviation can be used to verify whether the test conditions are consistent or to judge the difference in response amplitudes of materials under different excitations.

[0125] S46. Generate features based on the energy consumption data, the first fluctuation amplitude data, and the second fluctuation amplitude data to obtain the first piezoelectric material feature data.

[0126] In one embodiment, the above three types of features can be spliced according to a preset weight to form a feature vector with a length of N, where the energy feature, the first fluctuation feature, and the second fluctuation feature account for proportions of α, β, and γ respectively (α + β + γ = 1), which is used to characterize the comprehensive response characteristics of the first piezoelectric material.

[0127] In one embodiment, according to the energy consumption data, the first fluctuation amplitude data, and the second fluctuation amplitude data, extract their statistical features (such as mean, standard deviation, maximum value, etc.) or generate compressed features through a specific algorithm (such as principal component analysis PCA) to form the first piezoelectric material feature data.

[0128] Preferably, the non-stationary - stationary interval division according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively includes:

[0129] S431. Divide the peak-valley region according to the charge acceleration model to obtain peak-valley region data;

[0130] In one embodiment, by performing a first-order difference on the signal, find the extreme points of the signal (i.e., local maximum and minimum values). Based on the above detection results, use the time period between two consecutive extreme points as the division basis to divide the peak region and the valley region of the signal. The peak region refers to the time interval when the signal value reaches the local maximum, and the valley region is the time interval when the signal value reaches the local minimum.

[0131] S432. Fit the periodic parameters according to the peak-valley region data to obtain the periodic parameter fitting data;

[0132] In one embodiment, according to the peak-valley region data and the corresponding signal interval being expressed as a periodic fluctuation, give the corresponding periodic function for each peak-valley region data and the corresponding signal interval, such as:

[0133] ;

[0134] where is the periodic parameter fitting data, is the amplitude, is the constant term of pi, is the frequency, is the time parameter, is the phase.

[0135] Perform least squares fitting on the signal to find the periodic parameters that best fit the signal. The fitting process minimizes the fitting error through an optimization algorithm (such as gradient descent or Newton's method): , where the parameters are the same as those in the previous formula, is the number of sampling points. The above objective function is iteratively solved by a numerical optimization algorithm (such as the gradient descent method or the Newton method) to obtain the optimal values of the three parameters , which is used to represent the periodic structure within the current peak-valley interval.

[0136] In the present invention has a dimension determined by , is dimensionless. Therefore has the same dimension as . Each term of the objective function is , which has the same dimension as . After summation, the resulting dimension is still the square of the original signal (for example or ). The dimensions in the entire objective function optimization process are self-consistent, and the dimensions involved can be directly added, subtracted, and optimized. Through least squares fitting, the periodic characteristics of the signal, including amplitude, frequency, and phase, can be accurately extracted. This method is applicable to signals with regular fluctuations (such as signals with obvious peak-valley patterns) and can obtain the optimal periodic parameters describing the signal behavior within a certain time interval. The obtained periodic parameters provide intuitive quantitative indicators for signal characteristic analysis. In material detection and dynamic monitoring, these parameters can be used to compare the signal characteristics at different time periods and different working states, and then judge whether the material has changes, aging, or abnormal behaviors.

[0137] S433. Divide the similar parameter intervals of the charge acceleration model according to the data fitted with the periodic parameters to obtain non-stationary signal data and stationary signal data.

[0138] In one embodiment, a certain similarity threshold is set according to the frequency and amplitude obtained by the periodic fitting. When the frequency and amplitude of the signal are relatively consistent, the signal is considered to belong to the stationary interval; when the frequency or amplitude changes significantly, the signal is considered to belong to the non-stationary interval. It is divided by calculating the amplitude change rate and frequency change rate within the signal segment. If the amplitude change rate and frequency change rate within the signal segment exceed the predetermined threshold, it is demarcated as the non-stationary interval, otherwise it is the stationary interval. According to the above interval division rule, the signal is divided into non-stationary signal data and stationary signal data. Non-stationary signal data refers to the time interval with large changes in frequency and amplitude, while stationary signal data is in the time interval with small changes.

[0139] Preferably, the instantaneous amplitude calculation according to the non-stationary signal data to obtain the first fluctuation amplitude data includes:

[0140] Performing adjacent extreme value extraction according to the data fitted with the periodic parameters to obtain adjacent extreme value data;

[0141] In one embodiment, the periodic characteristic parameters of the signal, such as amplitude, frequency, and phase, are obtained through a periodic fitting model. For non-stationary signal data, by solving its first derivative, local extreme points are obtained. Local extrema occur when the first derivative changes from positive to negative or from negative to positive. At the time point where the peak (local maximum) changes from positive to negative, the value corresponding to that time point is a local maximum. At the time point where the trough (local minimum) changes from negative to positive, the value corresponding to that time point is a local minimum. Through these conditions, the extreme points in the signal, that is, adjacent extreme value data, can be extracted. Local extrema (peaks and troughs) are adjacent extreme value data. Specifically, adjacent extreme value data refers to pairs of consecutive local maxima and local minima in the signal, which can be obtained through the aforementioned calculations.

[0142] The amplitude of the non-stationary signal data is calculated based on the adjacent extreme value data to obtain the first fluctuation amplitude data.

[0143] In one embodiment, for non-stationary signals , the amplitude refers to the maximum amplitude between local extrema of the signal. The amplitude between local extrema can be represented by the difference between the maximum value and the minimum value: for each local extreme (peak and trough) of the signal, and then calculate the amplitude between these extrema. The amplitude between each pair of extrema is regarded as the instantaneous amplitude of the signal. For each pair of adjacent extreme points, the instantaneous amplitude can be expressed as the difference between each pair of extrema, representing the change rate of the signal within this time interval. In this way, the instantaneous amplitude of the signal at each moment can be obtained. By calculating the amplitudes between all adjacent extreme values, the first fluctuation amplitude data of the signal within this interval is obtained. This data can reflect the instantaneous change intensity of the non-stationary signal and describe the dynamic volatility of the signal.

[0144] Preferably, the second data feature extraction is performed according to the charge acceleration model to obtain the second piezoelectric material feature data, including:

[0145] S47. Perform frequency domain feature extraction according to the charge acceleration model to obtain frequency domain feature data;

[0146] In one embodiment, according to the charge acceleration model, it is transformed into a frequency domain signal through fast Fourier transform (FFT). From the frequency domain signal, multiple frequency domain features are extracted, such as power spectral density (PSD), which expresses the power distribution of the signal at different frequencies. It is obtained by calculating the square of the amplitude; the main frequency of the signal is obtained by identifying the peak frequency in the power spectrum; the frequency band energy of the signal (such as the energy in the low frequency band, middle frequency band, and high frequency band) is obtained by integrating the power spectrum, and the integration frequency band boundaries are set according to the frequency range of the specific signal. The obtained frequency domain features include data such as power spectral density, main frequency, and frequency band energy.

[0147] S48. Calculate the sample entropy based on the frequency-domain feature data to obtain the frequency-domain sample entropy data;

[0148] In one embodiment, given a time series corresponding to the frequency-domain feature data, select an embedding dimension and a tolerance (set to 0.2 times the standard deviation of the sequence). Calculate all subsequences of length (target subsequence) and (the remaining subsequences) similarity, defined as the distance between the two subsequences. If , then the two subsequences are considered similar. The formula for sample entropy is:

[0149] ;

[0150] where is the number of pairs of subsequences with similarity and embedding dimension , is the number of pairs of subsequences with similarity and embedding dimension . In the present invention, when calculating the distance , and have the same unit and can be directly compared logically. The number of pairs of subsequences A and B are dimensionless integers, and the ratio A / B in the formula is a dimensionless ratio. Taking the logarithm of the ratio A / B, the result is dimensionless, and the sample entropy value is also dimensionless. Therefore, the dimensional consistency of all parameters in the formula is good, and the operations involved (such as addition, subtraction, multiplication, division, logarithm) have no dimensional contradictions. Sample entropy measures the complexity and uncertainty of a time series by counting the similarity of subsequences in the sequence. A higher sample entropy value indicates a higher sequence complexity and stronger uncertainty; a lower sample entropy value indicates that the sequence is relatively more regular and easier to predict. Sample entropy is highly sensitive to the hidden pattern changes and randomness in the signal. Even if there is no significant change in the frequency components of the signal, sample entropy can capture subtle complexity differences. The calculation method of sample entropy can well handle non-stationary signals because it does not rely on fixed periodic assumptions but directly measures complexity based on the similarity between subsequences.

[0151] S49. Calculate the permutation entropy based on the frequency-domain feature data to obtain the frequency-domain permutation entropy data;

[0152] In one embodiment, the input is a frequency-domain feature data sequence within a certain frequency-domain subinterval, and this data can be the power spectrum, main frequency energy sequence, or intensity sequence of a certain characteristic frequency band extracted from the spectrum. Select an embedding dimension such as 3, 4, 5) and a time delay such as 1, 2), the sequence is constructed into a set of embedding vectors, thereby generating an -dimensional time series embedding vector . For each vector sort it according to the magnitude of its elements to obtain its permutation pattern , and then calculate the probability distribution of the permutation pattern. The calculation formula of permutation entropy is:

[0153] ;

[0154] where is the frequency domain permutation entropy data, is the permutation pattern, is the permutation pattern probability, indicating the occurrence frequency of this permutation pattern in the sequence.

[0155] In the present invention, all operations are carried out in a dimensionless probability space, and the dimensions in the formula are consistent, and all parameters can directly participate in the operation. Permutation entropy measures the complexity and randomness of a sequence through the probability distribution of permutation patterns. If the probability distributions of all permutation patterns in the sequence are close to uniform, the permutation entropy value is high, indicating that the sequence is more complex or closer to random. If the probability of some patterns appears much higher than other patterns, the permutation entropy value is low, indicating that the sequence is more regular or structured. Permutation entropy is applicable to analyzing the time series characteristics of frequency domain data and can capture the time dynamic law of the spectral energy distribution. For example, by calculating the permutation entropy of the main frequency energy sequence, it can be quantified whether there are significant periodic modulations or random fluctuations in the signal. Permutation entropy can help discover the dynamic behavior differences in specific frequency bands and reveal the potential patterns and change trends of the sequence. Permutation entropy does not need to assume the stationarity and linear characteristics of the signal and is suitable for analyzing non-stationary time series of frequency domain characteristics. For example, when the signal has modulation characteristics or short-time mutation characteristics, permutation entropy can provide a reliable complexity quantification index.

[0156] S410. Perform kernel density estimation according to the frequency domain sample entropy data and the frequency domain permutation entropy data to obtain entropy kernel density data;

[0157] In one embodiment, the input data is a set of two-dimensional feature point sets , where represents the frequency domain sample entropy value of the th sample, represents the frequency domain permutation entropy value of the th sample, represents the number of samples. The Gaussian kernel function is defined as follows: , is the Gaussian kernel function value, the standardized distance between the sample point and the target point The corresponding kernel function output value, the weighting factor for probability density estimation is the constant term of pi is the base of the natural logarithm is the standardized distance variable, representing the ratio of the difference between the target point and the sample point to the bandwidth parameter The kernel function is used to perform a smooth estimation of the probability density for each sample point. Set the bandwidth parameter of the kernel density estimation , which is used to control the expansion range of the kernel function. The larger the bandwidth, the stronger the smoothing degree; the smaller the bandwidth, the more sensitive the density estimation is between 0.05 and 0.2. For any target point , its estimated joint probability density , can be calculated by the following formula

[0158] ;

[0159] where is the probability density calculated by kernel density estimation (entropy kernel density data), is the total number of sample points in the dataset, is the bandwidth parameter in kernel density estimation, controlling the width of the kernel function, is the index of the sample point, is the total number of sample points, is the Gaussian kernel function, is the target point in the frequency domain sample entropy data / frequency domain permutation entropy data, is the sample point in the frequency domain sample entropy data / frequency domain permutation entropy data.

[0160] All parameters in the formulas of the present invention are dimensionless numerical values, so operations (including subtraction, division, calculation of the kernel function, and final weighted average) can be directly performed without dimensional conflicts. Using kernel density estimation can generate a smooth probability density distribution in the two-dimensional entropy data space (joint distribution of frequency domain sample entropy and frequency domain permutation entropy). represents the joint probability density at , which can reflect the distribution concentration of entropy data near this point. The bandwidth parameter controls the smoothing degree. A smaller can accurately capture the detailed distribution, while a larger A smoother global distribution is then generated. Kernel density estimation can clearly describe the distribution pattern of frequency-domain entropy feature data through a smooth probability density function. For example, through the estimated density peak, the main patterns or typical values in the entropy data can be identified; by observing the extended area of the density, the distribution range and dispersion degree of the data can be found. Entropy kernel density data provides a description of a probability space, which helps subsequent pattern recognition, classification, and anomaly detection. For example, if the density in a certain area is very low, it indicates that the entropy data in this area is abnormal or rare, and can be used for early warning or fault detection.

[0161] S411. Construct a probability cloud map based on the entropy kernel density data to obtain the characteristic data of the second piezoelectric material.

[0162] In one embodiment, the probability cloud map is a three-dimensional map constructed based on the entropy kernel density data, reflecting the probability distribution of the data. The probability cloud map maps the entropy kernel density data to a three-dimensional space and uses the shade of color to represent the probability density. When constructing the probability cloud map, each point (sample entropy data, permutation entropy data) of the entropy kernel density data is used as a coordinate point in the three-dimensional space, and the probability cloud map is formed by adjusting the size, transparency, and color of the points. For example, the entropy kernel density data used consists of sample entropy data and permutation entropy data, and each data point represents the density value of signal complexity at a certain scale or frequency band. This data is obtained from the entropy calculation and kernel density estimation processing of the frequency-domain feature sub-interval. Map each point in the entropy kernel density data to a three-dimensional coordinate system, where the X-axis represents the sample entropy value SE; the Y-axis represents the permutation entropy value PE; the Z-axis represents the corresponding kernel density estimation value of this point , that is, the probability density value of the entropy joint distribution. When constructing the probability cloud map, the shade of color, transparency, and point size are introduced as visual mapping dimensions to assist in expressing the density level. The darker the color, the higher the density; the lower the density, the more transparent the point; the point size is associated with the local gradient or density to highlight significant areas. All points form a three-dimensional probability density map, which is the probability cloud map. This map can be used to visually identify the characteristic density concentration areas of the piezoelectric material in different response states, assisting in anomaly identification, feature clustering, or material state attribution.

[0163] Preferably, the calculation of the sample entropy based on the frequency-domain feature data to obtain the frequency-domain sample entropy data includes:

[0164] Extract the main frequency component from the frequency-domain feature data to obtain the main frequency component data;

[0165] In one embodiment, a frequency-domain signal processed by FFT is obtained to represent the distribution of the signal at different frequencies. For each signal, its power spectral density (PSD) is extracted to reflect the energy distribution of the signal. The main frequency component refers to the frequency component with the most concentrated energy in the signal. The main frequency component is extracted through the following steps: calculate the power spectrum of the frequency-domain signal to obtain the power value at each frequency. Find the frequency with the maximum value in the power spectrum to represent the main frequency component of the signal, that is, the part with the highest energy in the frequency components.

[0166] Generate a scale factor based on the main frequency component data to obtain scale factor data;

[0167] In one embodiment, according to the main frequency component , a scale factor is generated. The scale factor reflects the periodic characteristics of the signal. Set a scale factor related to the main frequency component . For example, set the scale factor as the reciprocal of the main frequency: , the scale factor is used for the detailed decomposition of the signal. For example, use wavelet transform to decompose the signal into components of different scales. Through the scale factor, the frequency-domain signal can be divided into different scales. A larger scale factor corresponds to a lower frequency component, and a smaller scale factor corresponds to a higher frequency component. When selecting the scale factor, set the value of the scale factor according to logarithmic intervals. The high-frequency part of the signal changes faster, while the low-frequency part changes slower. Through logarithmic intervals, ensure that sufficient scale resolution can be obtained in a wide frequency band range, , is the th scale factor, is the minimum scale factor, is the scale factor, is the scale factor order term, taking values of 1, 2...N, and the value is the value term corresponding to the corresponding scale. N is the total number of scale levels. The obtained scale factor data serves as the basis for the frequency-domain division of the signal to control the signal characteristics of different scales.

[0168] In the present invention, since the reciprocal of the main frequency component defines the basic unit of the scale factor and the remaining parameters are dimensionless integers, all parameter dimensions are consistent, enabling reasonable multiplication and division operations. Through the scale factor, the signal spectrum can be divided into different scale levels, and the low-frequency components (representing long-term trends) and high-frequency components (representing short-term variations) can be extracted separately. A larger scale factor corresponds to a lower frequency component, reflecting the slow change or long-term trend of the signal. A smaller scale factor corresponds to a higher frequency component, capturing the rapid changes and detailed features of the signal. When selecting the scale factor, a logarithmic interval is used to ensure sufficient scale resolution across the entire spectrum. The high-frequency part requires finer resolution because these components change rapidly; the low-frequency part changes slowly, and a wider interval can be used to maintain balanced resolution. The generated scale factor data can be used as input parameters for signal decomposition. For example, in wavelet transform, the scale factor determines the stretching and compression degree of the wavelet basis function, thereby affecting the decomposition effect of the spectrum and the time resolution.

[0169] In one embodiment, further, based on the main frequency energy distribution in the frequency domain, construct the main frequency energy point cloud data; construct a persistence diagram for the main frequency energy point cloud based on the persistent homology theory, and calculate the birth time and death time of its topological features; based on the life cycle of all topological structures in the persistence diagram, calculate the topological lifetime value , where is the topological lifetime value, is the birth time of the topological feature, is the death time of the topological feature, is the power weight parameter, set , is the birth-death time pair of the topological structure; generate the scale factor according to the topological lifetime value, specifically: , where is the maximum scale factor, is a constant normalization factor, used to control the smoothness of the scale when the lifetime is small, avoiding division by zero or too small a scale;

[0170] In the present invention is the birth time of the topological feature, is the death time of the topological feature, with the unit of time (such as seconds s), determines the dimension of By calculating, it is consistent with the dimension of , and the dimensions of all terms are consistent. The denominator and numerator have the same dimension. Therefore, the calculation has the correct dimension, and the formula can perform reasonable addition, subtraction, multiplication, and division operations. The formula is based on the persistent homology theory, uses the point cloud data of the main frequency energy distribution, analyzes the birth and death of topological features, and quantifies the topological lifetime value 。 Represents the total life cycle weight of the topological structure in the data. The higher the indicates that there are more significant topological features or more persistent topological structures in the data. By calculating , the topological characteristics in the data can be effectively extracted, providing a quantitative basis at the topological level for signal analysis and data understanding. According to the topological lifetime value , a scale factor is generated, which can dynamically adjust the scale resolution in signal processing. When is small, through the smoothing factor, it is ensured that the scale factor is not too small, thus preventing analysis instability in extreme cases. When increases, the scale factor will gradually approach , providing a larger resolution for identifying more detailed signal features. By dynamically adjusting , analysis can be carried out at different signal frequency bands or resolution levels, facilitating the discovery of long-term trends and local anomalies. A large scale factor corresponds to a lower frequency and is suitable for observing long-term changes; a small scale factor corresponds to a higher frequency and is suitable for capturing details and rapid changes.

[0171] Specifically, by modeling the topological structure of the main frequency component in the signal frequency domain, calculating its structural stability (topological lifetime), and generating a scale factor adaptable to complexity metrics (such as sample entropy, multi-scale entropy, etc.) based on this, it has good anti-noise performance and frequency response consistency. Perform frequency domain transformation processing on the target signal, such as using spectrum analysis methods such as fast Fourier transform (FFT), power spectral density estimation, wavelet transform, etc., to obtain a frequency-energy distribution map. Extract the main frequency interval or main frequency component from it to construct the main frequency energy point cloud data , where is the th frequency point, is the signal energy value or spectral density value corresponding to the frequency point, and the point cloud data serves as the input basis for topological analysis. Based on the persistent homology theory in topological data analysis, apply methods such as Vietoris–Rips complex to the above frequency point cloud to construct a filtered complex and extract features such as 0-dimensional (connected components) and 1-dimensional (holes) in the topological structure. Continuously calculate for all topological structures to obtain their birth time and death time , thus generating a persistence diagram , where each pair represents the life cycle of a topological structure. Non-linearly weighted sum the life cycles of all topological structures in the persistence diagram to obtain the topological lifetime value , and its calculation formula is: , where is the topological lifetime value, representing the weighted sum of the life cycle lengths of all topological structures (such as connected components, holes, etc.), which is used to reflect the stability of the spectral structure. The larger this value is, the more prominent and stable the topological structure in the main frequency point cloud is. is the birth time of the -th topological feature, representing the scale or filtering threshold at which the topological structure first appears in the persistent homology construction. The unit is related to the point cloud filtering radius or energy threshold. death time of the is the birth time of the topological feature. is the death time of the topological feature. is the persistent diagram data set, representing the set of the life cycles of all topological structures, which is the result of persistent homology analysis. is the power weight parameter, set to 2, which controls the degree of weight distribution of different life cycle lengths in the topological lifetime value. In this embodiment, it is set = 2, which is used to enhance the emphasis on long-lived topological structures and suppress short-lived structures. is the birth-death time pair of the topological structure. According to the topological lifetime value , the scale factor is generated using the following formula : , where is the set maximum scale factor (such as the maximum sliding window length, the maximum sample entropy scale), takes values between 30 and 50. is the constant normalization factor, which is used to control when the lifetime is small. The generated scale factor can be used to control the window length, subsequence extraction granularity, or multi-scale analysis level in subsequent complexity analysis. For example, when calculating the frequency domain sample entropy, it can be used as the basis for scale division to achieve self-adjustment of adaptability to different frequency bands.

[0172] Through topological modeling of the main frequency energy distribution of signals, the present invention can capture the stability and density of the main frequency components, and adjust the size of the scale factor accordingly, so that the scale factor changes with the signal spectrum structure, thereby improving the adaptability of the complexity measurement method to non-stationary signals. Compared with the fixed or manually set scale parameters in the existing methods, this method realizes a dynamic scale control mechanism driven by the frequency domain, has strong anti-noise performance, suppresses the influence of abnormal frequency points on scale selection, and uses the topological lifetime value calculated by persistent homology to effectively distinguish the structural main frequency characteristics from high-frequency noise or short-lived perturbations. By adopting the power weight p = 2 in the lifetime accumulation, the importance of the real main frequency structure can be amplified, and the influence of random frequency points can be weakened, thereby improving the robustness and stability of scale selection. The present invention introduces a topological lifetime → scale factor mapping mechanism, which is equivalent to introducing a mathematical means for structurally inducing and evaluating the frequency response, making the scale selection no longer based solely on the main frequency value, but on the persistence information of the spectrum topology structure, effectively solving the problem that the frequency-scale matching relationship in the existing technology lacks a theoretical basis.

[0173] Perform frequency domain partitioning on the frequency domain feature data according to the scale factor data to obtain frequency domain feature partitioning data;

[0174] In one embodiment, extract the main frequency component from the frequency domain signal , and this frequency corresponds to the maximum energy point or local peak point in the signal energy spectrum. Set the basic frequency band width parameter , and this parameter is a fixed constant (such as 5 Hz, 10 Hz) or adaptively determined according to the actual spectrum bandwidth. Based on the scale factor , divide the frequency domain signal into several frequency bands. The division criterion is to distinguish by frequency range. Set a frequency band width , and then divide according to the scale factor . The boundary of each frequency band can be determined by the following formula:

[0175] ;

[0176] ;

[0177] ;

[0178] where is the frequency domain feature partitioning data, is the main frequency component data. According to the divided frequency bands, divide the frequency domain signal into multiple sub-intervals, and each sub-interval contains the signal components within a specific frequency band. The obtained sub-intervals of the frequency domain signal are the frequency domain feature partitioning data, and each sub-interval represents the frequency domain feature of the signal in a certain frequency band.

[0179] In the present invention is the window factor, is 100HZ or half of the maximum frequency, is the scale factor, with the unit of 1 / HZ. The dimensions of all terms in the formula are consistent, and all addition, subtraction, and multiplication operations of the parameters can be carried out reasonably. Therefore, these operations are physically and mathematically reasonable operations. By setting the frequency band width and the scale factor , each frequency band can be symmetrically divided according to the position of the main frequency component. The formula gives clear boundaries (starting frequency and ending frequency), so that the frequency domain signal can be divided into multiple frequency sub-intervals, and each sub-interval contains the signal components within a specific frequency band. Through the obtained sub-intervals after division, the energy distribution, main frequency component change, or modulation characteristics of the signal in different frequency bands can be analyzed. Each sub-interval, as a representative of the frequency domain characteristics, helps to study the characteristic differences of the signal in each frequency band, and is helpful for pattern recognition, feature extraction, and fault diagnosis. Using the scale factor can dynamically adjust the range of frequency band division: a larger corresponds to a wider frequency band, which is suitable for capturing the overall characteristics of the signal; a smaller corresponds to a narrower frequency band, which is suitable for analyzing the detailed changes of the signal.

[0180] Calculate the sample entropy based on the data divided according to the frequency domain characteristics to obtain the frequency domain sample entropy data.

[0181] In one embodiment, the sample entropy is an index used to measure the complexity of the signal. Calculate the sample entropy for each frequency domain sub-interval. The calculation process of the sample entropy is as follows: Set the embedding dimension and the tolerance according to the pre-parameters. When calculating the sample entropy, set the embedding dimension and the tolerance . The tolerance is a proportion of the standard deviation of the signal, for example . For each frequency domain sub-interval, construct subsequences with a length of . Calculate the similarity between each pair of subsequences, using a distance metric such as the maximum difference distance. Repeat the above process to obtain the number of similar pairs when the embedding dimension is ; The calculation formula of the sample entropy is:

[0182] ;

[0183] where is the frequency domain sample entropy data, is the number of subsequence pairs with an embedding dimension of and a similarity less than , is the number of subsequence pairs with an embedding dimension of and a similarity less than The number of subsequence pairs.

[0184] Therefore, from any perspective, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended application documents rather than the above description. Thus, all changes falling within the meaning and scope of the equivalent elements of the application documents are intended to be encompassed within the present invention.

[0185] The above are only specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features invented herein.

Claims

1. A method for processing acceleration data based on the piezoelectric effect, characterized in that, It includes the following steps: Obtain piezoelectric material signal data; Perform signal adjustment according to the piezoelectric material signal data to obtain signal adjustment data; Construct a charge acceleration model according to the signal adjustment data to obtain a charge acceleration model; Analyze according to the charge acceleration model to obtain piezoelectric material characteristic data for assisting in the detection of piezoelectric materials; Wherein the piezoelectric material characteristic data includes first piezoelectric material characteristic data and second piezoelectric material characteristic data. The analysis according to the charge acceleration model to obtain piezoelectric material characteristic data for assisting in the detection of piezoelectric materials includes: Perform first data feature extraction according to the charge acceleration model to obtain first piezoelectric material characteristic data; Perform second data feature extraction according to the charge acceleration model to obtain second piezoelectric material characteristic data, wherein the first data feature extraction and the second data feature extraction are different data feature extraction methods; The performing first data feature extraction according to the charge acceleration model to obtain first piezoelectric material characteristic data includes: Perform root mean square calculation according to the charge acceleration model to obtain first signal intensity data, and perform peak amplitude calculation according to the charge acceleration model to obtain second signal intensity data; Perform energy consumption calculation according to the first signal intensity data and the second signal intensity data to obtain energy consumption data; Perform non-stationary - stationary interval division according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively; Perform instantaneous amplitude calculation according to the non-stationary signal data to obtain first fluctuation amplitude data; Perform standard deviation calculation according to the stationary signal data to obtain second fluctuation amplitude data; Perform feature generation according to the energy consumption data, the first fluctuation amplitude data and the second fluctuation amplitude data to obtain first piezoelectric material characteristic data.

2. The method according to claim 1, characterized in that, The obtaining piezoelectric material signal data includes: Control the signal acquisition device to collect signals from a piezoelectric sensor in an accelerated state at a preset sampling frequency to obtain piezoelectric material signal data.

3. The method according to claim 1, wherein The performing signal adjustment according to the piezoelectric material signal data to obtain signal adjustment data includes: Perform signal amplification according to the piezoelectric material signal data to obtain signal amplification data; Perform signal shaping according to the signal amplification data to obtain signal adjustment data.

4. The method according to claim 1, characterized in that, The constructing a charge acceleration model according to the signal adjustment data to obtain a charge acceleration model includes: Perform signal calibration according to the signal adjustment data to obtain signal calibration data; Construct a charge acceleration model according to the signal calibration data to obtain a charge acceleration model.

5. The method according to claim 1, wherein The performing non-stationary - stationary interval division according to the charge acceleration model to obtain non-stationary signal data and stationary signal data respectively includes: Perform peak-valley region division according to the charge acceleration model to obtain peak-valley region data; Perform periodic parameter fitting according to the peak-valley region data to obtain periodic parameter fitting data; Perform similar parameter interval division on the charge acceleration model according to the periodic parameter fitting data to obtain non-stationary signal data and stationary signal data.

6. The method according to claim 5, characterized in that, The performing instantaneous amplitude calculation according to the non-stationary signal data to obtain first fluctuation amplitude data includes: Proximity extreme value extraction is performed by fitting data according to periodic parameters to obtain proximity extreme value data; The amplitude of the non-stationary signal data is calculated according to the proximity extreme value data to obtain the first fluctuation amplitude data.

7. The method according to claim 1, wherein The second data feature extraction is performed according to the charge acceleration model to obtain the second piezoelectric material feature data, including: Frequency domain feature extraction is performed according to the charge acceleration model to obtain frequency domain feature data; Sample entropy calculation is performed according to the frequency domain feature data to obtain frequency domain sample entropy data; Permutation entropy calculation is performed according to the frequency domain feature data to obtain frequency domain permutation entropy data; Kernel density estimation is performed according to the frequency domain sample entropy data and the frequency domain permutation entropy data to obtain entropy kernel density data; Probability cloud map construction is performed according to the entropy kernel density data to obtain the second piezoelectric material feature data.

8. The method according to claim 7, wherein The sample entropy calculation is performed according to the frequency domain feature data to obtain the frequency domain sample entropy data, including: Main frequency component extraction is performed according to the frequency domain feature data to obtain main frequency component data; Scale factor generation is performed according to the main frequency component data to obtain scale factor data; Frequency domain division of the frequency domain feature data is performed according to the scale factor data to obtain frequency domain feature division data; Sample entropy calculation is performed according to the frequency domain feature division data to obtain frequency domain sample entropy data.

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