A method and system for time-density multi-dimensional characterization for hopkinson test
By employing a multidimensional characterization method and a dynamic adaptive time window algorithm, the problem of unstable energy analysis results in the Hopkinson experiment was solved, enabling multidimensional quantification and intuitive characterization of energy changes, thereby improving the reliability and consistency of the results.
Patent Information
- Application Number
- CN202611204189.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-10
- Publication Date
- 2026-11-06
AI Technical Summary
Existing energy analysis methods in Hopkinson's experiments often rely on fixed time periods or manual selection, resulting in unstable and inconsistent results. These methods fail to fully express the local changes and abrupt changes at different loading stages, and the signals are easily affected by noise and assembly errors.
A multidimensional characterization method is adopted to calculate the dissipated energy time history through incident, reflected and transmitted wave signals. Combined with dynamic adaptive time window algorithm and stress uniformity quantification index, a multivariate energy time density function and tensor are constructed to generate an energy time density spectrum to reflect the multidimensional characteristics of energy change.
It improves the characterization adaptability of energy dissipation processes, reduces the influence of noise and stress imbalance stages, and can quantify impact energy dissipation processes from multiple perspectives, providing intuitive energy density distribution maps.
Smart Images
Figure CN123045828A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rock dynamic mechanics testing and impact signal processing technology, and in particular to a method and system for multidimensional characterization of energy, time, and density for Hopkinson's experiments. Technical Background
[0002] The split Hopkinson bar test is an important method for studying the dynamic mechanical properties of brittle materials such as rock, concrete, and ceramics under impact loading and high strain rate conditions. This test typically involves acquiring stress wave signals using strain gauges on the bar and combining this with one-dimensional stress wave theory to obtain the stress, strain, strain rate, and energy changes during the specimen loading process.
[0003] During impact failure, energy input, reflection, transmission, and absorption are closely related to crack initiation, propagation, and instability. Therefore, energy dissipation characteristics are often used to evaluate a material's impact resistance and degree of failure. Existing analytical methods mostly use total energy absorption, energy absorption rate, or single energy time history curves. Although these can reflect the overall energy level, they are difficult to fully express the local changes, duration, and abrupt changes at different loading stages.
[0004] Meanwhile, test signals are susceptible to the contact state of the end face, assembly errors, sampling noise, and waveform disturbances. If the analysis relies mainly on fixed time periods or manually selected analysis intervals, inconsistencies in the calculation methods used in different tests can easily occur, affecting the stability and comparability of the results. Therefore, current energy analysis still suffers from insufficient characterization dimensions, reliance on experience in interval selection, and inadequate representation of local variations. Summary of the Invention
[0005] In view of this, embodiments of the present invention provide a method and system for multidimensional characterization of energy-time-density for Hopkinson's disease tests, in order to solve or alleviate the technical problems existing in the prior art.
[0006] The technical solution of this invention is implemented as follows: a multidimensional characterization method for energy-time-density in the Hopkinson's test, comprising the following steps:
[0007] S1. Collect the incident wave signal, reflected wave signal and transmitted wave signal recorded by strain gauges in the split Hopkinson bar test, and output a digital stress wave signal sequence after signal conditioning, filtering and analog-to-digital conversion.
[0008] S2. Obtain the incident energy time history, reflection energy time history and transmission energy time history respectively according to the digitized stress wave signal sequence, and obtain the dissipated energy time history by subtracting the reflection energy time history and transmission energy time history from the incident energy time history.
[0009] S3. Perform multi-scale time-frequency decomposition on the incident wave signal, reflected wave signal, and transmitted wave signal to obtain time-varying energy distribution data at each scale;
[0010] S4. Establish a dynamic adaptive time window algorithm, adjust the time window length according to the instantaneous energy change rate of the dissipation energy time history, and combine the time-varying energy distribution data to segment the dissipation energy time history to obtain multiple time domain sub-intervals.
[0011] S5. Based on the stress time history of the front end of the sample obtained by superimposing the incident wave signal and the reflected wave signal, and the stress time history of the rear end of the sample obtained by the transmitted wave signal, a stress uniformity quantification index is constructed, and the sub-intervals that meet the stress equilibrium condition are selected according to the preset stress uniformity threshold to form an effective calculation domain.
[0012] S6. Define the fundamental energy time density function as the rate of change of dissipated energy with respect to time within the effective computational domain, and introduce time scale variables and normalized window functions to construct a multivariate energy time density function.
[0013] S7. Perform tensor extension on the multivariable energy-time density function to generate zero-order, first-order, and second-order energy-time density tensors.
[0014] S8, using the aforementioned multi-element energy time density function Generate the fundamental energy density spectrum, so as to be generated by The calculated first- or second-order energy-time density tensor components generate tensor component energy-time density spectra. The zero-order energy-time density tensor is used as the total energy feature and is jointly output with the energy-time density spectrum. Multidimensional features are extracted, and the time-frequency distribution map is output.
[0015] In the above embodiments: the dynamic adaptive time window algorithm adjusts the time window length according to the instantaneous energy change rate of the dissipated energy time history;
[0016] When the instantaneous energy change rate is higher than the preset upper threshold, the time window length is shortened; when the instantaneous energy change rate is lower than the preset lower threshold, the time window length is increased.
[0017] When the instantaneous rate of change of energy is between the preset upper threshold and the preset lower threshold, the initial time window length is maintained.
[0018] In the above embodiments: the dynamic adaptive time window algorithm includes an initial time window length, a minimum time window length, a maximum time window length, a shortening factor, and a growth factor;
[0019] The time window length is not less than the minimum time window length and not greater than the maximum time window length during the adjustment process. The time-varying energy distribution data is used to characterize the change state of frequency components in each time domain sub-interval and serves as the verification basis for the time window segmentation results.
[0020] In the above embodiments: the stress uniformity quantification index is determined based on the degree of difference between the stress time history at the front end of the sample and the stress time history at the rear end of the sample, and the closer the stress uniformity quantification index is to 1, the closer the stresses at both ends of the sample are in the corresponding time domain sub-interval.
[0021] When the stress uniformity quantification index of a time domain sub-interval meets the preset stress uniformity threshold, that time domain sub-interval is retained as part of the effective computational domain.
[0022] In the above embodiments: the basic energy-time density function is smoothed after being obtained, and the negative values after smoothing are set to zero to reduce the influence of high-frequency noise and non-physical negative values on the energy density characterization results; the basic energy-time density function can also be normalized according to the sample volume to obtain the energy-time density function per unit volume.
[0023] In the above embodiments: the multivariate energy-time density function is obtained by locally weighting the basic energy-time density function at different time scales using a normalized window function; the time scale variable is used to characterize the differences in energy density distribution under different observation time windows.
[0024] In the above embodiments: the zero-order energy-time density tensor is obtained based on the integral result of the multivariate energy-time density function within the effective computational domain and time scale range, and is used to characterize the total energy characteristics;
[0025] The first-order energy-time density tensor is obtained from the gradient results of the multivariate energy-time density function in the time dimension and the time scale dimension, and is used to characterize the gradient features of energy change.
[0026] The second-order energy-time density tensor is obtained based on the second-order transformation results of the multivariate energy-time density function in the time dimension, time-scale dimension, and the intersection of the two, and is used to characterize the distribution structure of energy in the time-scale space.
[0027] In the above embodiments: the second-order energy-time density tensor includes the energy concentration characteristics in the time dimension, the energy concentration characteristics in the time scale dimension, and the coupling strength characteristics between the time dimension and the time scale dimension.
[0028] In the above embodiments: the energy-time density spectrum includes a multivariate energy-time density function. The generated basic energy time density spectrum, and the tensor component energy time density spectrum generated by the first or second order energy time density tensor components; wherein, the frequency variable and the time scale variable have a corresponding mapping relationship, and the time-frequency distribution spectrum is plotted with time as the horizontal axis and frequency as the vertical axis, and the energy density amplitude is mapped by color or grayscale gradient.
[0029] A multidimensional energy-time-density characterization system for Hopkinson's disease testing is used to perform any one of the multidimensional energy-time-density characterization methods for Hopkinson's disease testing, comprising:
[0030] The signal acquisition module is used to acquire incident wave signals, reflected wave signals, and transmitted wave signals, and output a digital stress wave signal sequence.
[0031] An energy time history calculation module, connected to the signal acquisition module, is used to calculate the incident energy time history, reflected energy time history, transmitted energy time history and dissipated energy time history.
[0032] The time-frequency analysis module is used to perform multi-scale time-frequency decomposition on incident wave signals, reflected wave signals, and transmitted wave signals, and output time-varying energy distribution data.
[0033] The dynamic time window calculation module, connected to the energy time history calculation module and the time-frequency analysis module, is used to perform adaptive segmentation based on the dissipated energy time history and time-varying energy distribution data, and to screen the effective calculation domain by combining the stress time history of the front end of the sample and the stress time history of the rear end of the sample.
[0034] The Energy-Time Density Tensor Construction Module is used to construct basic energy-time density functions, multivariate energy-time density functions, and zeroth-order, first-order, and second-order energy-time density tensors within the effective computational domain.
[0035] The feature extraction and visualization module is used to extract features from multi-dimensional energy time density functions. Generate the basic energy-time density spectrum, generate the tensor component energy-time density spectrum from the first-order or second-order energy-time density tensor components, and combine the zero-order energy-time density tensor to output multidimensional features and time-frequency distribution maps.
[0036] Compared with the prior art, the present invention has the following advantages:
[0037] This invention calculates the dissipated energy time history using incident wave signals, reflected wave signals, and transmitted wave signals, and defines the basic energy time density function within the effective calculation domain, so that the energy dissipation process can be characterized in the form of time change rate, which is beneficial for identifying the rapid energy injection stage and the slow energy dissipation stage in the impact process.
[0038] This invention uses a dynamic adaptive time window algorithm to segment the loading process based on the instantaneous energy change rate and frequency component distribution of the dissipated energy time history. The time window is shortened during the rapid energy change phase and lengthened during the slow energy change phase, thereby improving the characterization adaptability of different energy change phases.
[0039] This invention constructs a stress uniformity quantification index, compares the stress time history of the front end and the stress time history of the back end of the sample, and selects the time domain sub-interval that satisfies the stress equilibrium condition as the effective calculation domain, which can reduce the influence of the stress unbalanced stage on the energy density characterization results.
[0040] This invention constructs a multivariate energy time density function by introducing time scale variables and normalized window functions, enabling energy density to be expressed in both the time dimension and the time scale dimension. It can reflect both transient fluctuations at fine time scales and the overall trend of change at coarse time scales.
[0041] This invention uses zero-order, first-order, and second-order energy-time density tensors to characterize the total energy, energy change gradient, and time-scale distribution structure, respectively, enabling multi-order and multi-angle quantitative expression of the impact energy dissipation process.
[0042] This invention utilizes the multi-element energy time density function It generates a basic energy time density spectrum and generates tensor component energy time density spectra through first-order or second-order energy time density tensor components. At the same time, it outputs the zero-order energy time density tensor as a total energy feature. It can extract peak time, full width at half maximum, rising gradient, falling gradient, dominant frequency features and time-frequency clustering, and output the time-frequency distribution map of energy density, making the comparative analysis of material energy action modes under different impact conditions more intuitive and quantitative.
[0043] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description
[0044] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0045] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the module structure of the system of the present invention; Figure 3 Example diagram of the original stress wave signal from the Hopkinson bar test; Figure 4 Example graph of energy time history curve and rate of change of dissipated energy; Figure 5 Example graph of the density function e(t) curve at basic energy; Figure 6 Example plot of the time density function E(t,τ) for multi-element energy; Figure 7 Example of the time-frequency distribution of the energy density spectrum S(t,f); Figure 8 Example diagram of multi-order features of time-density tensor. Detailed Implementation
[0046] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Without departing from the concept of the present invention, those skilled in the art can make conventional substitutions or adjustments to the sample material, sampling frequency, smoothing method, window function type, threshold setting method, and visualization output method.
[0047] Example 1
[0048] This embodiment uses a split Hopkinson bar test of a rock sample as an example to illustrate the energy-time-density multidimensional characterization method of the present invention.
[0049] like Figure 1 As shown, the method in this embodiment includes stress wave signal acquisition, energy time history calculation, multi-scale time-frequency decomposition, dynamic adaptive time window segmentation, stress uniformity screening, basic energy-time density function construction, multivariate energy-time density function construction, energy-time density tensor expansion, energy-time density spectrum generation, multidimensional feature parameter extraction, and time-frequency distribution map output.
[0050] S1, Stress wave signal acquisition
[0051] A split Hopkinson pressure bar testing system was constructed, comprising an air gun, an impact bar, an incident bar, a transmission bar, and an absorbing bar. The test sample was clamped between the incident bar and the transmission bar, and strain gauges were placed on the incident bar and the transmission bar respectively. The incident wave signal was recorded using a hyperdynamic strain gauge and a data acquisition system. , reflected wave signal and transmitted wave signal .
[0052] The signal acquisition module performs signal conditioning, filtering, and analog-to-digital conversion on the incident, reflected, and transmitted wave signals, outputting a digitized stress wave signal sequence. Filtering removes electrical noise and abnormal pulses, while analog-to-digital conversion converts the continuous analog signal into a discrete digital sequence for subsequent calculations by the energy time-history calculation module.
[0053] S2, Energy Time History Calculation
[0054] The energy time history calculation module calculates the incident energy time history based on the digitized stress wave signal sequence and according to the one-dimensional stress wave theory. Time history of reflection energy Transmission energy time history and dissipation energy time history .
[0055] The incident energy time history, reflected energy time history, transmitted energy time history, and dissipated energy time history are calculated using the following formulas:
[0056]
[0057]
[0058]
[0059]
[0060] in, The cross-sectional area of the compression member. The elastic wave velocity in the compression bar. This is the elastic modulus of the compression bar.
[0061] The energy time history calculation module outputs the incident energy time history, reflected energy time history, transmitted energy time history, and dissipated energy time history, among which the dissipated energy time history is used for subsequent dynamic time window division and basic energy time density function calculation.
[0062] S3, Multiscale Time-Frequency Decomposition
[0063] The time-frequency analysis module receives the incident wave signal, reflected wave signal, and transmitted wave signal output by the signal acquisition module, performs multi-scale time-frequency decomposition on the three types of stress wave signals, and obtains time-varying energy distribution data at each scale.
[0064] In practical implementation, multi-scale time-frequency decomposition can be performed using wavelet transform. This step allows us to obtain the energy distribution at different time scales or frequency components, and provide the time-varying energy distribution data to the dynamic time window calculation module. This enables the dynamic time window division to be based not only on the instantaneous energy change rate of the dissipated energy time history, but also on the frequency component distribution of the stress wave signal.
[0065] S4, Dynamic Adaptive Time Window Segmentation
[0066] The dynamic time window calculation module receives time-varying energy distribution data at various scales from the dissipation energy time history and time-frequency analysis module, establishes a dynamic adaptive time window algorithm, adjusts the time window length according to the instantaneous energy change rate of the dissipation energy time history, and performs segmented processing on the dissipation energy time history in combination with the time-varying energy distribution data.
[0067] First, the dynamic time window calculation module obtains the instantaneous energy change rate based on the dissipated energy time history. And set the initial time window length. Minimum time window length Maximum time window length Shortening factor growth factors Upper threshold and lower threshold .
[0068] Time window length Adjustments will be made according to the following rules:
[0069] when ;
[0070] when
[0071] when hour
[0072] When the instantaneous energy change rate is higher than the preset upper threshold, it indicates that the sample is in a rapid energy change stage. At this time, the time window length should be shortened to improve the time domain resolution. When the instantaneous energy change rate is lower than the preset lower threshold, it indicates that the energy change is relatively slow. At this time, the time window length should be increased to improve the overall characterization ability. When the instantaneous energy change rate is between the upper and lower thresholds, the initial time window length should be maintained.
[0073] During the adjustment of the time window length, the dynamic time window calculation module limits the time window length to be no less than the minimum time window length and no more than the maximum time window length, so as to avoid the segmentation results being disturbed by noise due to the time window being too short, or the energy rapid change stage being over-smoothed due to the time window being too long.
[0074] After the initial time window division is completed, the dynamic time window calculation module verifies the segmentation results based on the changes in frequency components within each time domain sub-interval. When the frequency component changes in a certain sub-interval deviate significantly from those of adjacent sub-intervals, the segmentation boundary of that sub-interval can be adjusted so that the final multiple time domain sub-intervals simultaneously reflect the characteristics of the dissipation energy change rate and the frequency component distribution characteristics.
[0075] Through the above processing, the complete loading process is divided into multiple time-domain sub-intervals. Each time-domain sub-interval corresponds to a local energy dissipation stage, providing a computational object for subsequent stress uniformity screening.
[0076] S5. Stress Uniformity Screening and Determination of Effective Calculation Domain
[0077] The effective computational domain filtering module receives the stress wave signal output by the signal acquisition module and the time domain sub-interval division result output by the dynamic time window calculation module, respectively.
[0078] First, based on the incident wave signal With reflected wave signal The stress time history at the front end of the specimen was obtained by superposition. According to the transmitted wave signal Obtain the stress time history at the rear end of the specimen For the first Time domain sub-intervals Construct a quantitative index for stress uniformity :
[0079]
[0080] The closer the value is to 1, the closer the stresses at both ends of the sample are within that time-domain sub-interval, indicating better stress uniformity. A preset stress uniformity threshold is set. The time-domain sub-intervals that meet the stress uniformity threshold requirement are retained, while the time-domain sub-intervals that do not meet the stress uniformity threshold requirement are removed, and the retained sub-intervals constitute the effective computational domain.
[0081] This step prevents signals from entering the energy density calculation process before the sample reaches stress equilibrium, thereby improving the reliability of subsequent energy density characterization results.
[0082] S6. Construction of Basic Energy Time Density Function and Multivariable Energy Time Density Function
[0083] The energy-time density tensor construction module receives the dissipated energy time history output by the energy time history calculation module and the effective computational domain output by the dynamic time window calculation module, and defines the basic energy-time density function within the effective computational domain. :
[0084]
[0085] To reduce the impact of high-frequency noise and non-physical negative values on the energy density characterization results, the fundamental energy time density function was modified. Perform smoothing processing, and then set the smoothed negative values to zero. (Processed) Used for subsequent construction of multi-element energy density functions.
[0086] When comparing energy density results for samples of different sizes, the basic energy-time density function can be normalized based on the sample volume to obtain the basic energy-time density function per unit volume. The normalized basic energy-time density function can then be used to construct a multivariate energy-time density function per unit volume, thereby reducing the impact of sample volume differences on energy density characterization results.
[0087] Density function at fundamental energy Based on this, time scale variables are introduced. and normalized window function Constructing multi-dimensional energy-time density functions :
[0088]
[0089] in, With time as the central variable, For observing time-scale variables, , For a normalized window function, satisfying:
[0090]
[0091] In this embodiment, a smaller time scale Used to characterize drastic fluctuations in energy density over short periods of time, on larger timescales. This is used to characterize the average trend of energy density variation over a longer time window. By introducing a time-scale variable, the multivariable energy-time density function... It can simultaneously reflect the temporal location and scale characteristics of energy density.
[0092] S7, Energy-Time Density Tensor Extension
[0093] The energy-time density tensor construction module for multivariable energy-time density functions Tensor extensions are performed to generate zero-order, first-order, and second-order energy-time density tensors.
[0094] Zero-order energy-time density tensor The double integral of the multivariable energy-time density function over the effective time domain and scale domain:
[0095]
[0096] The zero-order energy-time density tensor is used to characterize the total energy.
[0097] First-order energy-time density tensor The vector field is composed of the partial derivatives of the multivariable energy-time density function in the time dimension and the time scale dimension:
[0098]
[0099] Among them, time gradient Used to characterize the rate of change of energy density over time; scale gradient Used to characterize the degree of difference in energy density as observed on different scales.
[0100] Second-order energy-time density tensor The Hessian matrix is composed of the second-order partial derivatives of the multivariable energy density function:
[0101]
[0102] in, Used to characterize the degree of energy concentration over time; Used to characterize the degree of energy concentration over a time scale; Used to characterize the coupling strength between the time dimension and the time scale dimension.
[0103] Through the tensor extensions described above, energy density analysis can be expanded from a single curve to a multi-level structured data representation, thereby more fully describing the energy interaction laws during the dynamic failure process of the sample.
[0104] S8. Energy-Time Density Spectrum Generation and Multidimensional Feature Parameter Extraction
[0105] The feature extraction and visualization module receives the multivariate energy-time density function output by the energy-time density tensor construction module. and energy-time density tensor data of various orders, including multivariate energy-time density functions. Generate the fundamental energy time density spectrum as the fundamental transformation object. The first-order and second-order energy-time density tensor components are used as... The derived transformation object is used to generate the tensor component energy density spectrum.
[0106]
[0107] in, For frequency variables, and time-scale variables There is a corresponding mapping relationship; This is the complex conjugate of the mother wavelet function. Frequency variable. When the value is large, it corresponds to rapid energy fluctuations over a smaller time scale; frequency variable When it is smaller, it corresponds to the overall energy change over a larger time scale.
[0108] When using the energy-time density tensor components as the transformation objects, time-frequency transformation can be performed by selecting the time gradient component and scale gradient component in the first-order energy-time density tensor, or the second-order time variation component, second-order scale variation component, and time-scale cross-variation component in the second-order energy-time density tensor. This allows us to obtain not only the time-frequency distribution of the energy density itself, but also the distribution characteristics of the energy variation gradient or energy concentration structure in the time-frequency space.
[0109] In practical implementation, the zeroth-order energy-time density tensor is not directly used as the object of time-frequency transformation, but rather as a joint output of the total energy characteristics and the characteristic parameters of the fundamental energy-time density spectrum and the tensor component energy-time density spectra; the first-order and second-order energy-time density tensor components are used as... The derived data obtained by differentiation are used in time-frequency transformation.
[0110] From the energy density spectrum Extracting peak time Half height and width Ascending gradient descent gradient Main frequency characteristics and time-frequency clustering .
[0111] Peak time Obtained using the following formula:
[0112]
[0113] Ascending gradient and descent gradient Obtained using the following formula:
[0114]
[0115]
[0116] Main frequency characteristics Obtained using the following formula:
[0117]
[0118] The above multidimensional feature parameters are combined into a feature vector:
[0119]
[0120] Among them, peak time Reflects the time position where energy injection is most concentrated; half-width at half-maximum. The time span reflecting the concentration of energy; the ascent gradient Reflects the energy injection rate; descent gradient Reflects the rate of energy dissipation and decay; dominant frequency characteristics The dominant timescale reflecting energy interactions; time-frequency clustering. It reflects the degree of concentration of energy distribution on the time-frequency plane.
[0121] S9, Time-Frequency Distribution Map Output
[0122] The feature extraction and visualization module is based on the energy-time density spectrum. Generate a time-frequency distribution map of energy density. The time-frequency distribution map plots energy density amplitude by mapping time on the horizontal axis and frequency on the vertical axis through color or grayscale gradients.
[0123] In the time-frequency distribution spectrum, the energy density accumulation region, diffusion path, and decay process in the time-frequency space can be visually observed. By comparing the time-frequency distribution spectra and multidimensional characteristic parameters under different impact conditions, the differences in energy interaction modes and failure characteristics of materials under different impact conditions can be determined.
[0124] When the peak time is earlier, the half-width at half-maximum (HWHM) is smaller, the ascent gradient is larger, and the time-frequency clustering is higher, it usually indicates that the energy dissipation process of the sample is more concentrated and the failure process is more sudden. When the peak time is later, the HWHM is larger, the dominant frequency is lower, and the time-frequency clustering is lower, it usually indicates that the energy dissipation process of the sample is more dispersed and the failure process is more gradual.
[0125] Example 2
[0126] This embodiment provides an energy-time-density multidimensional characterization system for implementing the above method.
[0127] like Figure 2 As shown, the system includes a signal acquisition module, an energy time history calculation module, a time-frequency analysis module, a dynamic time window calculation module, an energy-time density tensor construction module, and a feature extraction and visualization module.
[0128] The signal acquisition module is used to acquire the incident wave signal, reflected wave signal and transmitted wave signal collected by strain gauges in the split Hopkinson bar test, and to perform signal conditioning, filtering and analog-to-digital conversion on the signal to output a digital stress wave signal sequence.
[0129] The time-frequency analysis module is connected to the signal acquisition module and has a built-in wavelet transform algorithm. It is used to receive digitized stress wave signal sequences and perform multi-scale time-frequency decomposition on incident wave signals, reflected wave signals, and transmitted wave signals, and output time-varying energy distribution data at each scale.
[0130] The dynamic time window calculation module is connected to the time-frequency analysis module. It has a built-in dynamic adaptive time window algorithm and a stress uniformity quantification index calculation unit. It is used to automatically adjust the time window parameters according to the instantaneous energy change rate and frequency component distribution of the dissipation energy time history, segment the dissipation energy time history, obtain multiple time domain sub-intervals, and select sub-intervals that meet the stress equilibrium conditions based on the stress time history of the front end of the sample obtained by superimposing the incident wave signal and the reflected wave signal, and the stress time history of the rear end of the sample obtained by the transmitted wave signal, and output the effective calculation domain.
[0131] The dynamic time window calculation module sets an initial time window length, a minimum time window length, a maximum time window length, a shortening factor, and an increasing factor when adjusting the time window. When the instantaneous energy change rate exceeds a preset upper threshold, the time window length is shortened; when the instantaneous energy change rate falls below a preset lower threshold, the time window length is increased; and when the instantaneous energy change rate is between the preset upper and lower thresholds, the initial time window length is maintained. Time-varying energy distribution data is used to characterize the frequency component changes within each time domain sub-interval and serves as the basis for verifying the time window segmentation results.
[0132] The stress uniformity quantification index calculation unit is used to calculate the degree of difference between the stress time history at the front end of the specimen and the stress time history at the rear end of the specimen, and to select time domain sub-intervals that meet the stress equilibrium conditions according to the preset stress uniformity threshold, so as to form an effective calculation domain.
[0133] The energy-time density tensor construction module is connected to the dynamic time window calculation module. It is used to receive the effective computation domain, and sequentially perform the calculation of the basic energy-time density function, the construction of the multivariate energy-time density function, and the generation of the zeroth, first and second order energy-time density tensors, and output the energy-time density tensor data of each order.
[0134] The energy-time density tensor construction module smooths the basic energy-time density function after obtaining it, and sets the negative values after smoothing to zero. When it is necessary to conduct comparative analysis on samples of different sizes, it can also normalize the basic energy-time density function according to the sample volume to obtain the energy-time density function per unit volume.
[0135] The feature extraction and visualization module is connected to the energy-time density tensor construction module, and is used to construct multivariate energy-time density functions. Generate the fundamental energy time density spectrum, and in the form of... The calculated first- or second-order energy-time density tensor components generate tensor component energy-time density spectra. Combined with the zero-order energy-time density tensor, peak time, full width at half maximum (FWHM), rising gradient, falling gradient, dominant frequency characteristics, and time-frequency clustering are extracted, and the time-frequency distribution map of energy density is output.
[0136] The components in both the first-order and second-order energy-time density tensors are derived from the multivariate energy-time density function. Differentiation yields the derived transformation object; the zeroth-order energy-time density tensor is not directly used as the time-frequency transformation object, but as a joint output of the total energy feature and the energy-time density spectrum feature.
[0137] The system can be implemented using computer equipment, which may include a processor, memory, data acquisition interface, and display output unit. The memory stores program instructions for executing the above-described method steps. When the processor executes the program instructions, it performs stress wave signal processing, energy time history calculation, dynamic time window segmentation, effective computational domain filtering, energy-time density function construction, tensor expansion, energy-time density spectrum generation, and spectrum output.
[0138] In one specific embodiment, the specimen is a granite cylindrical specimen with a diameter of 50 mm and a length of 50 mm; the compression bar has a diameter of 50 mm, is made of high-strength alloy steel, has an elastic modulus of 210 GPa, and has an elastic wave velocity of 5090 m / s.
[0139] During the test, the granite sample was clamped between the incident rod and the transmission rod, and lubricating medium was applied to both ends of the sample to reduce the effect of end friction.
[0140] Strain gauges were placed on the incident and transmitted rods, respectively. Incident, reflected, and transmitted wave signals were recorded using a hyperdynamic strain gauge and a data acquisition system, with a sampling frequency of 1 MHz. Energy time-history calculations showed that, under this specific experimental condition, the total incident energy was 27.08 J, the total reflected energy was 12.67 J, the total transmitted energy was 3.90 J, and the total dissipated energy was 10.51 J.
[0141] In the dynamic adaptive time window algorithm, the initial time window length is set to 50 μs, the minimum time window length is set to 10 μs, the maximum time window length is set to 200 μs, the shortening factor is set to 0.5, and the growth factor is set to 2.0. The upper threshold can be taken as the 75th quantile of the non-zero instantaneous energy change rate, and the lower threshold can be taken as the 25th quantile of the non-zero instantaneous energy change rate. The stress uniformity threshold can be set to 0.7. When the stress uniformity quantification index of a certain time domain sub-interval is not less than 0.7, that time domain sub-interval is retained as part of the effective computational domain.
[0142] In this specific embodiment, the complete loading process is divided into 13 time-domain sub-intervals, of which 8 time-domain sub-intervals meet the stress uniformity threshold requirement and are retained as valid calculation domains. The above parameters are merely exemplary parameters of the present invention under a specific Hopkinson bar test condition. Those skilled in the art can adaptively adjust the above parameters according to the specimen material, specimen size, impact air pressure, sampling frequency, and signal quality.
[0143] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A multidimensional characterization method for energy-time-density in Hopkinson's disease tests, characterized in that, Includes the following steps: S1. Collect the incident wave signal, reflected wave signal and transmitted wave signal recorded by strain gauges in the split Hopkinson bar test, and output a digital stress wave signal sequence after signal conditioning, filtering and analog-to-digital conversion. S2. Obtain the incident energy time history, reflection energy time history and transmission energy time history respectively according to the digitized stress wave signal sequence, and obtain the dissipated energy time history by subtracting the reflection energy time history and transmission energy time history from the incident energy time history. S3. Perform multi-scale time-frequency decomposition on the incident wave signal, reflected wave signal, and transmitted wave signal to obtain time-varying energy distribution data at each scale; S4. Establish a dynamic adaptive time window algorithm, adjust the time window length according to the instantaneous energy change rate of the dissipation energy time history, and combine the time-varying energy distribution data to segment the dissipation energy time history to obtain multiple time domain sub-intervals. S5. Based on the stress time history of the front end of the sample obtained by superimposing the incident wave signal and the reflected wave signal, and the stress time history of the rear end of the sample obtained by the transmitted wave signal, a stress uniformity quantification index is constructed, and the sub-intervals that meet the stress equilibrium condition are selected according to the preset stress uniformity threshold to form an effective calculation domain. S6. Define the fundamental energy time density function as the rate of change of dissipated energy with respect to time within the effective computational domain, and introduce time scale variables and normalized window functions to construct a multivariate energy time density function. S7. Perform tensor extension on the multivariable energy-time density function to generate zero-order, first-order, and second-order energy-time density tensors. S8, using the aforementioned multi-element energy time density function Generate the fundamental energy density spectrum, so as to be derived from The calculated first- or second-order energy-time density tensor components generate tensor component energy-time density spectra. The zero-order energy-time density tensor is used as the total energy feature and is jointly output with the energy-time density spectrum. Multidimensional features are extracted, and the time-frequency distribution map is output.
2. The energy-time-density multidimensional characterization method for the Hopkinson's disease test according to claim 1, characterized in that, The dynamic adaptive time window algorithm adjusts the time window length based on the instantaneous energy change rate of the dissipated energy time history; When the instantaneous energy change rate is higher than the preset upper threshold, the time window length is shortened; when the instantaneous energy change rate is lower than the preset lower threshold, the time window length is increased. When the instantaneous rate of change of energy is between the preset upper threshold and the preset lower threshold, the initial time window length is maintained.
3. The energy-time-density multidimensional characterization method for the Hopkinson's disease test according to claim 2, characterized in that, The dynamic adaptive time window algorithm includes an initial time window length, a minimum time window length, a maximum time window length, a shortening factor, and a growth factor. The time window length is not less than the minimum time window length and not greater than the maximum time window length during the adjustment process. The time-varying energy distribution data is used to characterize the change state of frequency components in each time domain sub-interval and serves as the verification basis for the time window segmentation results.
4. The energy-time-density multidimensional characterization method for Hopkinson's disease test according to claim 1, characterized in that, The stress uniformity quantification index is determined based on the degree of difference between the stress time history at the front end of the sample and the stress time history at the rear end of the sample. The closer the stress uniformity quantification index is to 1, the closer the stresses at both ends of the sample are within the corresponding time domain sub-interval. When the stress uniformity quantification index of a time domain sub-interval meets the preset stress uniformity threshold, that time domain sub-interval is retained as part of the effective computational domain.
5. The energy-time-density multidimensional characterization method for Hopkinson's disease test according to claim 1, characterized in that, The basic energy-time density function is smoothed after being obtained, and the negative values after smoothing are set to zero to reduce the influence of high-frequency noise and non-physical negative values on the energy density characterization results. The basic energy-time density function can also be normalized according to the sample volume to obtain the energy-time density function per unit volume.
6. The energy-time-density multidimensional characterization method for Hopkinson's disease test according to claim 1, characterized in that, The multivariate energy-time density function is obtained by locally weighting the basic energy-time density function at different time scales using a normalized window function; the time scale variable is used to characterize the differences in energy density distribution under different observation time windows.
7. The energy-time-density multidimensional characterization method for the Hopkinson's disease test according to claim 1, characterized in that, The zero-order energy-time density tensor is obtained from the integral results of the multivariate energy-time density function over the effective computational domain and time scale, and is used to characterize the total energy characteristics. The first-order energy-time density tensor is obtained based on the gradient results of the multivariate energy-time density function in the time dimension and the time scale dimension, and is used to characterize the gradient features of energy change. The second-order energy-time density tensor is obtained based on the second-order transformation results of the multivariate energy-time density function in the time dimension, time-scale dimension, and the intersection of the two, and is used to characterize the distribution structure of energy in the time-scale space.
8. The energy-time-density multidimensional characterization method for Hopkinson's disease test according to claim 7, characterized in that, The second-order energy-time density tensor includes the energy concentration characteristics in the time dimension, the energy concentration characteristics in the time scale dimension, and the coupling strength characteristics between the time dimension and the time scale dimension.
9. The energy-time-density multidimensional characterization method for the Hopkinson's disease test according to claim 1, characterized in that, The energy-time density spectrum includes a multivariate energy-time density function. The generated basic energy time density spectrum, and the tensor component energy time density spectrum generated by the first or second order energy time density tensor components; wherein, the frequency variable and the time scale variable have a corresponding mapping relationship, and the time-frequency distribution spectrum is plotted with time as the horizontal axis and frequency as the vertical axis, and the energy density amplitude is mapped by color or grayscale gradient.
10. A multidimensional energy-time-density characterization system for Hopkinson's disease testing, used to perform the multidimensional energy-time-density characterization method for Hopkinson's disease testing as described in any one of claims 1-9, characterized in that, include: The signal acquisition module is used to acquire incident wave signals, reflected wave signals, and transmitted wave signals, and output a digital stress wave signal sequence. An energy time history calculation module, connected to the signal acquisition module, is used to calculate the incident energy time history, reflected energy time history, transmitted energy time history and dissipated energy time history. The time-frequency analysis module is used to perform multi-scale time-frequency decomposition on incident wave signals, reflected wave signals, and transmitted wave signals, and output time-varying energy distribution data. The dynamic time window calculation module, connected to the energy time history calculation module and the time-frequency analysis module, is used to perform adaptive segmentation based on the dissipated energy time history and time-varying energy distribution data, and to screen the effective calculation domain by combining the stress time history of the front end of the sample and the stress time history of the rear end of the sample. The Energy-Time Density Tensor Construction Module is used to construct basic energy-time density functions, multivariate energy-time density functions, and zeroth-order, first-order, and second-order energy-time density tensors within the effective computational domain. The feature extraction and visualization module is used to extract features from multi-dimensional energy time density functions. Generate the basic energy-time density spectrum, generate the tensor component energy-time density spectrum from the first-order or second-order energy-time density tensor components, and combine the zero-order energy-time density tensor to output multidimensional features and time-frequency distribution maps.