A block analysis method of a transient strong impact non-stationary response signal, a storage medium and a computer device

Abstract

The application provides a block analysis method for a transient strong impact non-stationary response signal, a storage medium and computer equipment, belongs to the field of non-stationary impact response signal processing, strong impact model test and nonlinear dynamics analysis, and solves the problems that the traditional method cannot objectively identify the stage dynamics evolution of the transient strong impact non-stationary response signal, cannot adaptively extract a local approximate stationary block in the same stage, and finally cannot reveal the system motion evolution law and cannot support subsequent dynamics characteristic extraction analysis. Through signal preprocessing, phase space reconstruction, maximum Lyapunov index stage division, critical time criterion block and stationarity test, the application extracts effective block characteristics, realizes accurate analysis of the transient strong impact non-stationary signal, and has objectivity, adaptivity and universality, and can support subsequent dynamics research.

Description

Technical Field

[0001] This invention relates to the fields of non-stationary impact response signal processing, strong impact model testing, and nonlinear dynamic analysis, and in particular to a block-based analysis method, storage medium, and computer equipment for transient strong impact non-stationary response signals. Background Technology

[0002] Structural dynamic response signals under transient high-impact loads (such as underwater explosions, car collisions, underwater launches, etc.) typically exhibit characteristics such as high frequency, high amplitude, fast response, and chaotic amplitude transformation. The motion evolution of the entire impact response system is random, disordered, and unpredictable, exhibiting strong nonlinear and nonstationary characteristics. This makes it difficult to reveal the motion evolution law of the impact response system, whether by observing the amplitude and frequency of the nonstationary impact response signal, calculating its variance, covariance, kurtosis, skewness, or analyzing the system's motion state through power spectrum analysis. Furthermore, directly performing unified frequency domain / time domain or nonlinear dynamic analysis on the entire nonstationary impact response signal under these circumstances usually faces the following problems: 1) The dynamic characteristics of the impact response signal differ at different stages. Impact response systems under strong impact loads often exhibit different dynamic characteristics. In the early response stage, the impact response signal presents a high-frequency, high-amplitude random and disordered form, exhibiting significant chaotic properties. Subsequently, in the transition stage, both the vibration frequency and amplitude decrease significantly, system uncertainty weakens, and the signal characteristics gradually shift towards quasi-periodicity. In the later response stage, the impact response signal tends towards a stable form with low frequency and low amplitude, and the system response ultimately evolves into a typical periodic motion. Therefore, analyzing the entire signal indiscriminately often yields a mixed average of mechanisms from different stages, which is difficult to interpret and stably reproduce. More importantly, it weakens the "stage difference," the most crucial dynamic characteristic of the impact signal.

[0003] 2) Uncertainty of the impact response signal in the same stage Although the system's motion evolution remains uncertain during the early, transition, and late impact response stages, it is crucial to segment the non-stationary, nonlinear impact response signal to ensure that its motion evolution within each segment exhibits certain regularity and predictability. However, the traditional sliding window method requires manually setting the window length and step size. A window length that is too short leads to statistical instability and high characteristic noise, while a window length that is too long increases the uncertainty of the system's motion evolution. Empirical segmentation methods (such as segmentation based on peak threshold, energy threshold, and envelope attenuation threshold) are difficult to reuse for different measurement points, structures, and impact intensities, and they also fail to reflect the inherent differences in the dynamic state.

[0004] In summary, in the processing of transient strong impact non-stationary response signals, there is an urgent need for a method that can objectively identify the stage-by-stage dynamic evolution of the impact response and adaptively extract locally approximately stationary time blocks within each stage. This would enable the analysis of such strongly nonlinear, non-stationary impact response systems and support subsequent analyses such as extraction of system dynamic behavior features, construction of mapping functions, and parameter fitting. Summary of the Invention

[0005] This invention proposes a block-based analysis method, storage medium, and computer equipment for transient strong impact non-stationary response signals. Based on the dynamic evolution characteristics of the impact response system—namely, chaotic, quasi-periodic, and periodic features—the impact response signal is divided into three stages: early stage, transition stage, and late stage. Simultaneously, within each stage, the signal is divided into several locally approximately stationary blocks, ensuring that each block satisfies the deterministic condition that "the block length does not exceed the predictable critical time." This enables subsequent functions such as studying the dynamic system's motion evolution, feature extraction, and mathematical model construction. To address the shortcomings of existing technologies in processing transient, strong, non-stationary impact response signals, which are unable to objectively identify the phased dynamic evolution of the impact response (direct analysis of the entire signal leads to the mixing and averaging of characteristics from different phases, weakening the key dynamic feature of the impact signal, "phase difference"), and are difficult to adaptively extract local approximate stationary time blocks within the same phase (traditional sliding window methods require manual setting of window length and step size, which easily leads to statistical instability or increased uncertainty in the system's motion evolution), and the threshold of empirical segmentation methods is difficult to reuse under different measurement points, structures, and impact intensities and cannot reflect the differences in the dynamic state itself, ultimately making it difficult to reveal the motion evolution law of the impact response system and unable to support subsequent analysis such as extraction of system dynamic behavior features, construction of mapping functions, and parameter fitting.

[0006] A block-based analysis method for transient strong impact non-stationary response signals includes the following steps: S1. Extract the structural response signal under strong impact load and perform noise reduction and trend removal processing; S2. Determine the optimal delay and embedding dimension of the one-dimensional time series, and map the one-dimensional time series to a multi-dimensional phase space to construct a state space that is topologically equivalent to the original dynamic system. S3. Calculate the maximum Lyapunov exponent based on the evolution characteristics of orbit points in phase space to quantify the chaotic characteristics of the impact response system; S4. Based on the maximum Lyapunov exponent range at different stages, the impact response signal is divided into three response stages: early stage, transition stage, and late stage. S5. Based on the exponential divergence law of the initial disturbance of the system, calculate the critical time for the motion state of the impact response system to remain predictable. S6. Subdivide each impact response stage into several small blocks, and preliminarily determine the stability of the blocks through the critical time to screen out candidate locally approximately stable blocks. S7. Perform stationarity tests on candidate locally approximate stationary blocks and confirm valid locally approximate stationary blocks. At the same time, extract and output the relevant feature values ​​of the valid locally approximate stationary blocks.

[0007] Furthermore, in S2, the autocorrelation function method is used to determine the optimal delay of the one-dimensional time series. t The saturated correlation dimension method is used to determine the embedding dimension in the time series embedding phase space. m By using the phase space reconstruction method, a one-dimensional time series is mapped to a multi-dimensional phase space, thus constructing a state space that is topologically equivalent to the original dynamic system, as shown in formula (1): (1) Furthermore, S3 includes the following process: for each point X i Find its nearest neighbor in the reconstructed phase space. X j The following equation is satisfied: (2) For each pair of points ( X i , X j ), initial distance is d 0, evolve along their respective orbits for a short period of time Δ t The distance between the two becomes d 1. Over time n After the step, the distance between the two is as shown in formula (3).

[0008] (3) If the orbits of two adjacent points in the impact response system are exponentially separated, then d n = d 0· e λ(Δt·n) Taking the logarithm of both sides, we get the Lyapunov exponent. l As shown in formula (4).

[0009] (4) Follow n As the value gradually increases, calculate the average logarithmic distance ln( for all points). d n ), where ln( d n Relative to nThe slope of the curve is the maximum Lyapunov exponent.

[0010] Furthermore, in S4, the standard for dividing the impact response stages based on the numerical range of the maximum Lyapunov exponent is as follows: the maximum Lyapunov exponent in the early response stage... l ∈(0.5,1.0), the maximum Lyapunov exponent of the transition response phase. l ∈(0.2,0.5), the maximum Lyapunov exponent in the later response phase. l ∈(0,0.1).

[0011] Furthermore, S5 includes the following processes: Assume that the shock response system has a small disturbance at the initial moment. e 0, then in t The uncertainty of the motion state of the impact response system at time t is e t As shown in formula (5).

[0012] (5) when e t / e 0 reaches the critical value c When the system's trajectory diverges to the point where its motion becomes unpredictable, the system's evolution is completely random and disordered. The time elapsed at this point is called the critical time. t c ,Right now: (6) Therefore, the predictable critical time of the impact response system t c As shown in formula (7).

[0013] (7).

[0014] Furthermore, S6 includes the following steps: S61. Calculate the time range and corresponding maximum Lyapunov exponent for each stage of the impact response signal. l And the logarithmic magnitude parameter ln c; S62. For a certain impact response stage, the peak point within that stage is taken as the start time of the block, and the delay time is determined by the autocorrelation function. t, After phase space reconstruction, select 6-8 data orbit points, i.e. X (t)=[ x ( t ), x ( t + t ), x (t +2 t ), x ( t +3 t ), …, x ( t + n The initial small block length is determined to be... t b ; S63. Using the initial small block as a candidate block, calculate the Lyapunov index of the candidate block. l 1, and through the critical time formula t c = ln c / l 1. Determine the stability of the candidate blocks, when t c > t b When the initial small block becomes a candidate locally approximately stationary block; when t c ≤ t b When shortening the length of the initial small block t b Then, the initial small block with shortened length is used as a new candidate block, its Lyapunov exponent is recalculated, and its stationarity is determined by the critical time formula.

[0015] Furthermore, following S63, it also includes: S64. Using the peak point near the end of the current candidate locally approximately stationary block as the starting point of the next block, repeat S62-S63 to obtain multiple candidate locally approximately stationary blocks in the same stage.

[0016] Furthermore, in S7, the mean-variance stability test is used to verify the stationarity of candidate locally approximately stationary blocks. Blocks that pass the verification are considered valid locally approximately stationary blocks. The extracted and output feature values ​​of valid locally approximately stationary blocks include at least the block number, the stage label, the start and end times of the block, and the block length. t b and critical time t c .

[0017] A storage medium storing a computer program, which, when executed by a processor, implements the aforementioned block analysis method for transient strong impact non-stationary response signals.

[0018] A computer device, characterized in that it comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method for block analysis of transient strong impact non-stationary response signals.

[0019] Compared with the prior art, the present invention achieves significant beneficial effects through the above technical solution: 1) Based on the dynamic characteristics of the impact response signal itself, the maximum Lyapunov exponent is used as a quantitative indicator of the strength of nonlinearity, which can objectively identify the dynamic evolution characteristics of the impact response at different stages.

[0020] 2) The block length is adaptively determined by the critical predictable time criterion, avoiding the artificial setting of window length and step size. Too short a window length will cause statistical instability and amplify noise, while too long a window length will increase the uncertainty of the system's motion evolution.

[0021] 3) While maintaining the overall non-stationary evolution information, each block satisfies the assumption of local approximate stationarity, thereby supporting subsequent analysis such as extraction of dynamic characteristics of the impact response system, construction of mapping functions, and parameter fitting.

[0022] 4) This nonlinear, non-stationary response signal block method is applicable to various transient strong impact response processes such as underwater explosions, car collisions, and underwater launches, and has strong universality. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a reinforced cylindrical shell model. Figure 2 Diagram of an underwater explosion high-impact model test; Figure 3 This is a diagram showing the layout of the impact response signal measurement points. Figure 4 This is the acceleration response signal of the transient high-impact model structure; Figure 5 A plot of the maximum Lyapunov exponent for a time series; Figure 6 A schematic diagram illustrating the stage division of the impact response based on the maximum Lyapunov exponent; Figure 7 This is a schematic diagram illustrating the segmented results of the impact response in the early, transitional, and late stages. Figure 8 This is a flowchart of a method for block analysis of transient strong impact non-stationary response signals according to the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Reference Figure 8 As shown, a block-based analysis method for transient strong impact non-stationary response signals includes the following steps: S1. Extract the response signal of the model test structure under strong impact load, such as the acceleration response signal, and treat its time series as... x ( t High-pass filtering is applied to the impulse response signal to reduce noise and the influence of the acquired charge signal. If the impulse response signal has a significant trend, EMD or wavelet decomposition can be used to remove the trend. S2. Determine the optimal delay and embedding dimension of the one-dimensional time series, and map the one-dimensional time series to a multi-dimensional phase space to construct a state space that is topologically equivalent to the original dynamic system. S3. Calculate the maximum Lyapunov exponent based on the evolution characteristics of orbit points in phase space to quantify the chaotic characteristics of the impact response system; S4. Based on the maximum Lyapunov exponent range at different stages, the impact response signal is divided into three response stages: early stage, transition stage, and late stage. S5. Based on the exponential divergence law of the initial disturbance of the system, calculate the critical time for the motion state of the impact response system to remain predictable. S6. Subdivide each impact response stage into several small blocks, and preliminarily determine the stability of the blocks through the critical time to screen out candidate locally approximately stable blocks. S7. Perform stationarity tests on candidate locally approximate stationary blocks and confirm valid locally approximate stationary blocks. At the same time, extract and output the relevant feature values ​​of the valid locally approximate stationary blocks.

[0026] Specifically, this invention preprocesses the structural response signal under strong impact loads by denoising and removing trend terms. Then, it reconstructs a state space topologically equivalent to the original dynamic system through phase space reconstruction. Based on the evolution characteristics of the phase space orbit points, it calculates the maximum Lyapunov exponent to quantify the chaotic characteristics of the system. Furthermore, based on the numerical range of this exponent, the impact response signal is objectively divided into three response stages: early, transition, and late. This effectively avoids the problems of traditional methods directly analyzing the entire non-stationary signal, where the dynamic characteristics of different stages are mixed and averaged, and the key dynamic characteristic of the impact signal—"stage difference"—is weakened. On this basis, this invention calculates the critical time based on the exponential divergence law of the initial system disturbance. This is used to preliminarily determine the stationarity of the subdivided small blocks within each stage and screen candidate locally approximate stationary blocks. Finally, stationarity checks confirm the effective locally approximate stationary blocks and extract feature values. The entire process does not require manual setting of window length and step size, solving the problems of traditional sliding window methods, which are prone to statistical instability or increased uncertainty in system motion evolution due to manual parameter setting, and the difficulty in reusing thresholds in empirical segmentation methods under different measurement points, structures, and impact intensities, and which fail to reflect the differences in the dynamic state itself. Meanwhile, while maintaining the overall non-stationary evolution information of the impact response signal, this invention enables each effective local near-stationary block to satisfy the local stationarity assumption, which can provide reliable support for subsequent research on the motion evolution law of dynamic systems, extraction of dynamic features and construction of mathematical models. It is also applicable to various transient strong impact response processes such as underwater explosions, car collisions, and underwater launches, and has strong universality.

[0027] Furthermore, in S2, the optimal delay for the one-dimensional time series is determined using the autocorrelation function method. t The embedding dimension in the time series embedding phase space is determined by the saturated correlation dimension method. m By using the phase space reconstruction method, a one-dimensional time series is mapped to a multi-dimensional phase space, constructing a state space that is topologically equivalent to the original dynamic system, as shown in formula (1). This reconstructed phase space retains the main geometric and dynamic characteristics of the original dynamic system. (1) Specifically, when reconstructing the phase space of a transient strong impact non-stationary response signal, this invention uses the autocorrelation function method to accurately determine the optimal delay of the one-dimensional time series. t By using the saturated correlation dimension method, the embedding dimension in the time series embedding phase space can be reasonably determined. mThis ensures the objectivity and accuracy of key parameters during phase space reconstruction, avoiding the subjective bias that may exist in traditional parameter setting methods. On this basis, the one-dimensional time series is mapped to a multi-dimensional phase space through the phase space reconstruction method, and a state space that is topologically equivalent to the original dynamic system (as shown in the state vector form of formula (1)) is successfully constructed. This state space completely preserves the main geometric features and dynamic characteristics of the original dynamic system, solving the problem that the one-dimensional time series can only reflect the time domain information of the signal and is difficult to fully characterize the overall motion state of the impact response system. This phase space construction that fits the essence of the original system not only provides a reliable analytical carrier for subsequent calculation of the maximum Lyapunov exponent based on the evolution characteristics of the phase space orbit points and quantification of the chaotic characteristics of the system, but also ensures that subsequent operations such as stage division and block processing of the impact response signal are based on the real system dynamic laws, effectively avoiding analytical bias caused by signal morphology distortion, and thus laying a key premise for accurately revealing the motion evolution law of the impact response system and realizing subsequent effective block analysis.

[0028] Furthermore, S3 includes the following process: for each point X i Find its nearest neighbor in the reconstructed phase space. X j The following equation is satisfied: (2) For each pair of points ( X i , X j ), initial distance is d 0, evolve along their respective orbits for a short period of time Δ t The distance between the two becomes d 1. Over time n After the step, the distance between the two is as shown in formula (3).

[0029] (3) If the orbits of two adjacent points in the impact response system are exponentially separated, then d n = d 0· e λ(Δt·n) Taking the logarithm of both sides, we get the Lyapunov exponent. l As shown in formula (4).

[0030] (4) Follow n As the value gradually increases, calculate the average logarithmic distance ln( for all points). d n ), where ln( dn Relative to n The slope of the curve is the maximum Lyapunov exponent, such as Figure 5 As shown.

[0031] Specifically, in the reconstructed phase space, the present invention provides each point... X i Accurately find the nearest neighbor. X j By establishing clear constraints, the rationality and relevance of neighbor point selection are ensured, and point pairs are tracked on this basis. X i , X j The evolution process along their respective orbits, passing through the initial distance in sequence. d 0. Evolution Δ t Distance after time d 1 and n Distance after step evolution d n This establishes a quantitative analysis framework for orbital evolution. (Using...) d n = d 0· e λ(Δt·n) The exponential separation relationship and logarithmic transformation are used to derive the Lyapunov exponent λ, and then the average logarithmic distance ln(λ) of all points is calculated. d n ), relative to the iteration step n The slope of the curve is used to determine the maximum Lyapunov exponent. The entire calculation process strictly follows the laws of dynamic evolution, with the formula derivation and calculation logic progressing step by step, avoiding the subjectivity and ambiguity of traditional methods when quantifying the chaotic characteristics of a system. This precise method of calculating the maximum Lyapunov exponent can objectively and quantitatively characterize the degree of chaos in an impact response system, effectively solving the problem that traditional analysis methods struggle to accurately capture the chaotic characteristics of strongly nonlinear and non-stationary signals. It not only provides a reliable quantitative indicator for subsequently dividing the impact response stages based on the numerical range of this exponent, but also ensures that the entire block-based analysis process is always based on the true dynamic characteristics of the system.

[0032] Furthermore, in S4, the Lyapunov exponents of the response signals in different stages characterize the chaotic properties of the structural response system under strong impact. In the early stage of the impact response, the Lyapunov exponent λ ∈ (0.5, 1.0); in the transition stage, λ ∈ (0.2, 0.5); and in the later stage, λ ∈ (0, 0.1), indicating that the nonlinear characteristics of the early impact response are most significant, and the Lyapunov exponent value is the largest. As the impact energy decays, the nonlinear characteristics of the impact response also weaken, leading to a relative decrease in the Lyapunov exponent in the transition stage. When the impact response enters the later stage, it mainly manifests as free vibration of the structure, at which point the Lyapunov exponent is smallest, the system's motion state tends to be stable, and the nonlinear characteristics are weakest. Based on the above Lyapunov exponent variation law, the impact response process can be divided into stages, as shown in the following figure. Figure 6 As shown.

[0033] Specifically, this invention clarifies the maximum Lyapunov exponent range for different stages of the impact response signal, using λ∈(0.5,1.0) for the early response stage, λ∈(0.2,0.5) for the transition stage, and λ∈(0,0.1) for the late response stage as clear dividing criteria, thus achieving an objective and accurate definition of the impact response signal stages. This stage division method based on quantitative indicators perfectly matches the dynamic evolution law of the impact response system from early strong chaos, quasi-periodic transition stage to late periodicity. It effectively solves the problem of traditional methods that do not distinguish between the entire signal, resulting in the mixing and averaging of characteristics of different stages and the weakening of key dynamic characteristics of "stage differences." This allows the dynamic characteristics of each stage to be clearly presented, making the analysis results easier to interpret and reproducible.

[0034] Furthermore, S5 includes the following processes: Assume that the shock response system has a small disturbance at the initial moment. e 0, then in t The uncertainty of the motion state of the impact response system at time t is e t As shown in formula (5).

[0035] (5) when e t / e 0 reaches the critical value c When the system's trajectory diverges to the point where its motion becomes unpredictable, the system's evolution is completely random and disordered. The time elapsed at this point is called the critical time. t c ,Right now: (6) Therefore, the predictable critical time of the impact response systemt c As shown in formula (7).

[0036] (7).

[0037] Specifically, this invention is based on the dynamic nature of impact response systems, and quantifies the initial small disturbance. e 0 Uncertainty in the evolution over time e t The formula clearly defines the critical boundary between the predictable and completely random state of a system's motion—when... e t / e 0 reaches the critical value c The corresponding elapsed time is the critical time. t c And through the formula Precise derivation t c The calculation method strictly follows the exponential divergence law of the initial system disturbance, ensuring the objectivity and scientific nature of the critical time calculation. This method of determining critical time based on the system dynamics evolution mechanism effectively solves the problem of traditional methods lacking a quantifiable and predictable time standard, providing a precise basis for subsequent block processing and avoiding subjective biases caused by human experience. Simultaneously, the critical time... t c Closely linked to the previously calculated maximum Lyapunov exponent λ, the entire analysis process forms a logical closed loop. As the core constraint condition for block length, it can accurately measure the predictability of system motion within the block, ensuring that the subsequent blocks will not cause state divergence and increased uncertainty due to excessive length, nor will they cause statistical instability due to excessive short length. This lays a key foundation for the adaptive extraction of locally approximately stationary blocks in each stage. At the same time, it allows this judgment criterion to be reused in scenarios with different measurement points, different structures, and different impact intensities, breaking through the limitation that empirical thresholds are difficult to apply universally.

[0038] Furthermore, S6 includes the following steps: S61. Calculate the time range and corresponding maximum Lyapunov exponent for each stage of the impact response signal. l And the logarithmic magnitude parameter ln c; S62. For a certain impact response stage, the peak point within that stage is taken as the start time of the block, and the delay time is determined by the autocorrelation function. t, After phase space reconstruction, select 6-8 data orbit points, i.e. X (t)=[ x ( t ), x (t + t ), x ( t +2 t ), x ( t +3 t ), …, x ( t + n The initial small block length is determined to be... t b ; S63. Using the initial small block as a candidate block, calculate the Lyapunov index of the candidate block. l 1, and through the critical time formula t c = ln c / l 1. Determine the stability of the candidate blocks, when t c > t b When the initial small block becomes a candidate locally approximately stationary block; when t c ≤ t b When shortening the length of the initial small block t b Then, the initial small block with shortened length is used as a new candidate block, its Lyapunov exponent is recalculated, and its stationarity is determined by the critical time formula.

[0039] Specifically, in the block-based processing, this invention first calculates the time range of each impact response stage, the corresponding maximum Lyapunov exponent λ, and the logarithmic amplitude parameter ln c, providing accurate basic data support for subsequent block division and ensuring that the block-based operation always conforms to the dynamic characteristics of each stage. For each impact response stage, the peak point within the stage is used as the starting time of the block, which not only conforms to the amplitude evolution law of transient strong impact signals but also accurately captures the key nodes of signal changes within each stage; simultaneously, the delay time τ is determined through the autocorrelation function, and 6-8 data trajectory points are selected through phase space reconstruction to construct a state vector. X (t), and determine the initial small block length accordingly. t b This block construction method, based on the signal's own dynamic characteristics, avoids the drawbacks of subjectively setting the starting point and block length in traditional methods, ensuring the rationality and relevance of the initial small block. Based on this, the present invention uses the initial small block as a candidate block, calculates its Lyapunov exponent λ1, and utilizes the critical time formula... t c = ln c / l1. Perform a stationarity determination when t c > t b When it is directly identified as a candidate locally approximately stationary block, t c ≤ t b Then shorten the initial small block length. t b The adaptive adjustment mechanism, which recalculates and re-determines, perfectly solves the problems of statistical instability caused by excessively short window lengths and increased uncertainty in system motion evolution caused by excessively long window lengths in the traditional sliding window method. At the same time, it breaks through the limitations of empirical segmentation methods, such as the difficulty in reusing thresholds and the inability to reflect differences in dynamic states. It allows the block length to accurately match the predictable time range of the system, ensuring that each candidate locally approximately stationary block has good local stationarity and predictability.

[0040] Furthermore, following S63, it also includes: S64. Using the peak point near the end of the current candidate locally approximately stationary block as the starting point of the next block, repeat S62-S63 to obtain multiple candidate locally approximately stationary blocks in the same stage.

[0041] Specifically, this invention uses the peak point near the end of the current candidate locally approximate stationary block as the starting point of the next block. This not only conforms to the amplitude variation law of transient strong impact signals but also ensures that the blocks are connected coherently without missing key information, avoiding the subjectivity and arbitrariness in the selection of block starting points in traditional segmentation methods. By repeating the complete process of S62-S63, each newly generated block follows the same objective judgment criteria. The length is determined based on phase space reconstruction, and stationarity is verified through the critical time formula. This ensures that the partitioning logic of all candidate locally approximate stationary blocks within the same stage is consistent and the standards are unified, effectively solving the problem of inconsistent block partitioning quality and difficulty in reflecting the continuity of the system's dynamic state in traditional methods. This iterative block generation method can comprehensively cover the signal evolution process within the same stage, ensuring that each stage obtains a sufficient number of candidate blocks that meet the requirements of local stationarity. This not only fully preserves the differences in the dynamic characteristics of the signal within the stage, but also provides a rich and reliable analysis object for subsequent stationarity testing. At the same time, the same process is used for each impact response stage, which further enhances the universality of the invention in different scenarios, ensuring that accurate and comprehensive block processing can be achieved whether it is the early strong chaos, the quasi-periodic transition phase, or the later periodic phase.

[0042] Furthermore, in S7, the mean-variance stability test is used to verify the stationarity of candidate locally approximately stationary blocks. Blocks that pass the verification are considered valid locally approximately stationary blocks. The extracted and output feature values ​​of valid locally approximately stationary blocks include at least the block number, the stage label, the start and end times of the block, and the block length. t b and critical time t c .

[0043] Specifically, this invention employs a mean-variance stability test to perform secondary stationarity verification on candidate locally approximately stationary blocks. Through rigorous statistical testing standards, it ensures that the finally confirmed effective locally approximately stationary blocks fully satisfy the local stationarity assumption, avoiding potential biases from preliminary judgments based solely on critical times. This makes the block stationarity more reliable and convincing. Furthermore, this invention explicitly extracts and outputs the core feature values ​​of effective locally approximately stationary blocks, including block number, stage label, block start and end times, and block length. t b and critical time t c These eigenvalues ​​comprehensively and accurately characterize the key information of each effective block, forming standardized analysis results output. This not only facilitates subsequent in-depth exploration of the dynamic characteristics of the impact response system, construction of mapping functions, and parameter fitting, but also provides a unified reference for signal analysis in different scenarios. This further enhances the practicality and operability of the invention, allowing the entire block-based analysis process to form a complete closed loop from signal processing to result output, ensuring that the analysis results can directly support relevant research and design in practical engineering applications.

[0044] A storage medium storing a computer program, which, when executed by a processor, implements the aforementioned block analysis method for transient strong impact non-stationary response signals.

[0045] Specifically, the storage medium of this invention, by storing the corresponding computer program, enables the block-based analysis method for transient strong impact non-stationary response signals to be deployed and executed conveniently on various devices that support the storage medium, independent of specific development environments and scenarios. This effectively realizes the preservation, dissemination, and reuse of the analysis method, avoiding the waste of resources caused by repeated development. When the computer program carried by the storage medium is executed by the processor, it can accurately reproduce the complete process of the above method. From signal preprocessing, phase space reconstruction, maximum Lyapunov exponent calculation, response stage division, to critical time solution, block processing, and effective block feature extraction, each step strictly follows objective dynamic laws and judgment criteria, ensuring the consistency, accuracy, and reliability of the analysis process and avoiding deviations that may be introduced by manual operation. At the same time, combined with the universality of the analysis method itself, which is applicable to various transient strong impact response processes such as underwater explosions, car collisions, and underwater launches, this storage medium allows signal processing in these different scenarios to be carried out more efficiently and flexibly, providing a convenient and stable implementation carrier for signal analysis and research in related engineering and technical fields.

[0046] A computer device, characterized in that it comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method for block analysis of transient strong impact non-stationary response signals.

[0047] Specifically, the computer device of this invention stores the corresponding computer program in its memory and uses a processor to run and execute the program. This provides a stable and efficient hardware platform for the block analysis of transient strong impact non-stationary response signals, allowing the complete analysis process of this invention to be accurately implemented on the device. When the processor executes the program, it strictly follows the entire chain logic of signal preprocessing, phase space reconstruction, maximum Lyapunov exponent calculation, response stage division, critical time solution, block processing, and effective block feature extraction. This avoids the errors and inefficiencies that may occur with manual operation, ensuring that each step of the analysis conforms to the laws of system dynamics and objective judgment criteria. At the same time, the hardware architecture of this computer device supports flexible deployment in different application scenarios and can adapt to the signal processing needs of various transient strong impact response processes such as underwater explosions, car collisions, and underwater launches. This further enhances the universality and practicality of the technical solution of this invention, enabling complex block analysis work to be carried out efficiently and reliably, and providing strong equipment support for system dynamics research and impact-resistant structure design in related engineering and technical fields.

[0048] The following is an embodiment of the present invention: Underwater explosion impact tests were conducted on a reinforced cylindrical shell structure. The model structure dimensions were: length 2.46 m, diameter 1.60 m, rib spacing 0.19 m, and rib height 62.8 mm. To reduce the influence of boundary effects, a rib was extended at each end to serve as a ballast chamber, and the end caps were 10 mm thick. The pressure hull thickness was 15.6 mm, and the dimensions of the ribs and longitudinal girder on the pressure hull were as follows: mm. The overall weight is 2332 kg, the material used is Q355B steel, the yield strength is 360 MPa, and the density is 7850 kg / m³. 3 The elastic modulus is 2.06 E11 Pa, and the Poisson's ratio is 0.3. A two-dimensional planar schematic diagram and a physical image of the structure are shown below. Figure 1 As shown.

[0049] The reinforced cylindrical shell model structure was placed 13 m underwater, and impact tests were conducted in an explosion pool. A counterweight was placed below the reinforced cylindrical shell to increase the overall weight and improve the stability of the test system. An impact-resistant buoy structure was designed to provide buoyancy to the target structure. The impact-resistant buoy not only provides additional buoyancy to balance the model but also needs to have a certain impact and blast resistance. Based on the above design concept, the impact-resistant buoy was designed with a diameter of 2 m, a length of 4 m, an ultimate buoyancy of 25.12 t, a rib spacing of 0.4 m, a rib height of 0.2 m, a shell plate thickness of 10 mm, and end caps of 20 mm thickness. Explosives were placed on a steel lifting device welded to the support structure below the buoy end face. The steel lifting device had pre-machined Ф5.0 mm holes in three directions at its lower end to secure the wire rope, ensuring the correct underwater loading attitude through three-directional constraints. The impact test system is as follows: Figure 2 As shown.

[0050] Acceleration measurement points are mainly arranged on the pressure shell. Measurement point A1 is placed at the midpoint of the 0° circumferential grid; measurement point A2 is placed at one rib position of the 0° circumferential grid; measurement point A3 is placed at two rib positions of the 0° circumferential grid; and measurement points A4 and A5 are arranged sequentially. Measurement point A6 is placed at the midpoint of the 45° circumferential grid; measurement point A7 is placed at one rib position of the 45° circumferential grid; measurement point A8 is placed at the midpoint of the 90° circumferential grid; measurement point A9 is placed at the midpoint of the 135° circumferential grid; measurement point A10 is placed at the midpoint of the 180° circumferential grid; measurement point A11 is placed at one rib position of the 180° circumferential grid; measurement point A12 is placed at two rib positions of the 180° circumferential grid; and measurement points A13 and A14 are arranged sequentially. The measurement point arrangement is as follows: Figure 3 As shown. The acceleration response signal at measuring point A1 is as follows: Figure 3 As shown.

[0051] Based on the analysis of the measured signals, the system response under transient strong impact exhibits significant strong nonlinearity and non-stationarity in its time series. From the overall evolution process, the response can be roughly divided into three stages: the early response stage, where the acceleration signal exhibits a high-frequency, high-amplitude random disorder, and the system displays significant chaotic characteristics; the subsequent transition stage, where both the vibration frequency and amplitude decrease significantly, the system uncertainty weakens, and the signal characteristics gradually shift towards quasi-periodicity; and the later response stage, where the acceleration signal tends towards a low-frequency, low-amplitude stable form, and the system response ultimately evolves into a typical periodic motion. The following sections will further elaborate on these three stages and provide further analysis.

[0052] Lyapunov exponents, by quantitatively characterizing the divergence rate of a system's trajectory, can effectively distinguish these dynamic states. Therefore, Lyapunov exponents are introduced to provide a detailed characterization of the time-varying dynamic behavior of the system response, and based on this, the early, transition, and late stages of the impact response are defined. To characterize the average exponential divergence characteristics of the physical system, the maximum Lyapunov exponent of the system is calculated.

[0053] Determining the optimal delay of a one-dimensional time series using the autocorrelation function method t The embedding dimension in the time series embedding phase space is determined by the saturated correlation dimension method. m By using the phase space reconstruction method, a one-dimensional time series is mapped to a multi-dimensional phase space, and a state space that is topologically equivalent to the original dynamic system is constructed, as shown in formula (1). This reconstructed phase space retains the main geometric and dynamic characteristics of the original dynamic system.

[0054] (1) For each point X i Find its nearest neighbor in the reconstructed phase space. X j The following equation is satisfied: (2) For each pair of points ( X i , X j ), initial distance is d 0, evolve along their respective orbits for a short period of time Δ t The distance between the two becomes d 1. Over time n After the step, the distance between the two is as shown in formula (3).

[0055] (3) If the orbits of two adjacent points in the impact response system are exponentially separated, then dn = d 0· e λ(Δt·n) Taking the logarithm of both sides, we get the Lyapunov exponent. l As shown in formula (4).

[0056] (4) Follow n As the value gradually increases, calculate the average logarithmic distance ln( for all points). d n ), where ln( d n Relative to n The slope of the curve is the maximum Lyapunov exponent. The maximum Lyapunov exponent at measurement point A1 is as follows: Figure 5 As shown.

[0057] The chaotic characteristics of the structural response system under strong impact are characterized by the Lyapunov exponents of the response signals in different stages. Table 1 shows the Lyapunov exponents of the acceleration time series of the stiffened cylindrical shell prototype structure in the early stage, transition stage and late stage.

[0058]

[0059] Table 1. Lyapunov exponents of prototype acceleration time series Under strong impact loads, the system's structural response exhibits a high sensitivity to initial conditions. The corresponding Lyapunov exponent for the system... l All values ​​are greater than zero, indicating that it exhibits typical chaotic dynamic characteristics. Numerical analysis results based on the same impact response signal show that... l The response gradually decreases as the process progresses: in the early stages l ∈(0.5,1.0), during the transition phase l ∈(0.2,0.5), while in the later stages l ∈(0,0.1). This variation pattern indicates that the nonlinear characteristics of the impact response are most significant in the early stages, and the dynamic behavior of the system gradually stabilizes over time. Based on the above variation pattern of the Lyapunov exponent, the impact response process can be divided into stages, and the results of the division are as follows: Figure 6 As shown.

[0060] Transient high-impact signals typically exhibit significant non-stationary characteristics across the entire time series, with their amplitude, frequency components, and statistical features all changing significantly over time. Directly analyzing the entire non-stationary signal is not conducive to revealing the dynamic differences between different time blocks and also affects the effectiveness of analytical methods based on the assumption of stationarity. Therefore, this study further subdivides each stage into several smaller blocks of varying time lengths, allowing each block to be approximated as a stationary process within a local range. This improves the accuracy and robustness of subsequent phase space reconstruction and feature extraction while ensuring overall non-stationarity.

[0061] Assume that the shock response system has a small disturbance at the initial moment. e 0, then in t The uncertainty of the motion state of the impact response system at time t is e t As shown in formula (5).

[0062] (5) when e t / e 0 reaches the critical value c When the system's trajectory diverges to the point where its motion becomes unpredictable, the system's evolution is completely random and disordered. The time elapsed at this point is called the critical time. t c ,Right now: (6) Therefore, the predictable critical time of the impact response system t c As shown in formula (7).

[0063] (7) The steps for selecting small blocks based on the Lyapunov index are as follows: (1) Calculate the time range of the early, transition and late response stages of the impact response signal, and calculate the corresponding maximum Lyapunov exponents for each stage. l And the logarithmic magnitude parameter ln c; (2) For a certain impact response stage, the peak point within that stage is taken as the starting time of the block, and the delay time is determined by the autocorrelation function. t Then, using phase space reconstruction, 6-8 data orbit points are selected, namely: X (t)=[ x ( t ), x ( t + t ), x ( t +2 t ), x ( t +3 t ),…, x ( t + n The current small block length is determined as follows: t b ; (3) Calculate the Lyapunov index based on the selected small blocks. l 1, and through the critical time formula t c =ln c / l 1. Determine its stationarity: when t c > t b At that time, candidate blocks are t b It maintains relatively strong determinism and can be considered as a locally approximately stationary block; when t c ≤ t b If the block length exceeds the predictable time, the state within the block is rapidly diverging, making it difficult to meet the requirements for local stability, and the block length should be shortened. t b The validity of the block is confirmed by combining the results of the stationarity test.

[0064] (4) Using the peak point near the end of the current block as the starting point of the next block, repeat the above steps to obtain multiple small blocks within the same stage at once. Similarly, the blockization method for other impact response stages is the same as above, such as... Figure 7 As shown.

[0065] Based on the above analysis steps, an overall flowchart of the present invention is drawn, as follows: Figure 8 As shown in Table 2, the acceleration response signals at different measuring points under strong impact are divided into impact response stages and then segmented based on the critical time, forming a method for processing transient strong impact non-stationary response signals.

[0066]

[0067] Table 2 Blocking of Strong Impact Response Signals The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A block-based analysis method for transient strong impact non-stationary response signals, characterized in that, Includes the following steps: S1. Extract the structural response signal under strong impact load and perform noise reduction and trend removal processing; S2. Determine the optimal delay and embedding dimension of the one-dimensional time series, and map the one-dimensional time series to a multi-dimensional phase space to construct a state space that is topologically equivalent to the original dynamic system. S3. Calculate the maximum Lyapunov exponent based on the evolution characteristics of orbit points in phase space to quantify the chaotic characteristics of the impact response system; S4. Based on the maximum Lyapunov exponent range at different stages, the impact response signal is divided into three response stages: early stage, transition stage, and late stage. S5. Based on the exponential divergence law of the initial disturbance of the system, calculate the critical time for the motion state of the impact response system to remain predictable. S6. Subdivide each impact response stage into several small blocks, and preliminarily determine the stability of the blocks through the critical time to screen out candidate locally approximately stable blocks. S7. Perform stationarity tests on candidate locally approximate stationary blocks and confirm valid locally approximate stationary blocks. At the same time, extract and output the relevant feature values ​​of the valid locally approximate stationary blocks.

2. The block-based analysis method for transient strong impact non-stationary response signals according to claim 1, characterized in that, In S2, the autocorrelation function method is used to determine the optimal delay of the one-dimensional time series. τ The saturated correlation dimension method is used to determine the embedding dimension in the time series embedding phase space. m By using the phase space reconstruction method, a one-dimensional time series is mapped to a multi-dimensional phase space, thus constructing a state space that is topologically equivalent to the original dynamic system, as shown in formula (1): （1）。 3. The block-based analysis method for transient strong impact non-stationary response signals according to claim 2, characterized in that, S3 includes the following processes: For each point X i Find its nearest neighbor in the reconstructed phase space. X j The following equation is satisfied: （2） For each pair of points ( X i , X j ), initial distance is d 0, evolve along their respective orbits for a short period of time Δ t The distance between the two becomes d 1. Over time n After the step, the distance between the two is as shown in formula (3). （3） If the orbits of two adjacent points in the impact response system are exponentially separated, then d n = d 0· e λ(Δt·n) Taking the logarithm of both sides, we get the Lyapunov exponent. λ As shown in formula (4), （4） Follow n As the value gradually increases, calculate the average logarithmic distance ln( for all points). d n ), where ln( d n Relative to n The slope of the curve is the maximum Lyapunov exponent.

4. The block-based analysis method for transient strong impact non-stationary response signals according to claim 3, characterized in that, In S4, the standard for dividing the impact response stages based on the numerical range of the maximum Lyapunov exponent is as follows: the maximum Lyapunov exponent in the early response stage. λ ∈(0.5,1.0), the maximum Lyapunov exponent of the transition response phase. λ ∈(0.2,0.5), the maximum Lyapunov exponent in the later response phase. λ ∈(0,0.1).

5. The block-based analysis method for transient strong impact non-stationary response signals according to claim 4, characterized in that, In S5, The process includes the following steps: Assume that the shock response system has a small disturbance at the initial moment. ε 0, then in t The uncertainty of the motion state of the impact response system at time t is ε t As shown in formula (5), （5） when ε t / ε 0 reaches the critical value c When the system's trajectory diverges to the point where its motion becomes unpredictable, the system's evolution is completely random and disordered. The time elapsed at this point is called the critical time. t c ,Right now: （6） Therefore, the predictable critical time of the impact response system t c As shown in formula (7), （7）。 6. The block-based analysis method for transient strong impact non-stationary response signals according to claim 5, characterized in that, S6 includes the following steps: S61. Calculate the time range and corresponding maximum Lyapunov exponent for each stage of the impact response signal. λ And the logarithmic magnitude parameter ln c; S62. For a certain impact response stage, the peak point within that stage is taken as the start time of the block, and the delay time is determined by the autocorrelation function. τ, After phase space reconstruction, select 6-8 data orbit points, i.e. X (t)=[ x ( t ), x ( t + τ ), x ( t +2 τ ), x ( t +3 τ ), …, x ( t + nτ The initial small block length is determined to be... t b ; S63. Using the initial small block as a candidate block, calculate the Lyapunov index of the candidate block. λ 1, and through the critical time formula t c = ln c / λ 1. Determine the stability of the candidate blocks, when t c > t b When the initial small block becomes a candidate locally approximately stationary block; when t c ≤ t b When shortening the length of the initial small block t b Then, the initial small block with shortened length is used as a new candidate block, its Lyapunov exponent is recalculated, and its stationarity is determined by the critical time formula.

7. The block-based analysis method for transient strong impact non-stationary response signals according to claim 6, characterized in that, Following S63, it also includes: S64. Using the peak point near the end of the current candidate locally approximately stationary block as the starting point of the next block, repeat S62-S63 to obtain multiple candidate locally approximately stationary blocks in the same stage.

8. The block-based analysis method for transient strong impact non-stationary response signals according to claim 7, characterized in that, In S7, the mean-variance stability test is used to verify the stationarity of candidate locally approximately stationary blocks. Blocks that pass the verification are considered valid locally approximately stationary blocks. The extracted and output feature values ​​of valid locally approximately stationary blocks include at least the block number, the stage label, the start and end times of the block, and the block length. t b and critical time t c .

9. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the block analysis method for transient strong impact non-stationary response signals as described in any one of claims 1-8.

10. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the block analysis method for transient strong impact non-stationary response signals according to any one of claims 1-8.

Images