Underwater explosion hull structure nonlinear dynamics space-time decoupling data analysis method, program, equipment and storage medium

Abstract

The invention belongs to the technical field of ship structure and system damage mechanism analysis under the action of strong impact load, and particularly relates to an underwater explosion hull structure nonlinear dynamics space-time decoupling data analysis method, program and equipment and a storage medium. According to the method, space-time decoupling data analysis is carried out on a large amount of test data by adopting a phase-space reconstruction technology and a single-peak mapping method, and the characterization and description of the nonlinear evolution law and the non-stationary characteristics of the underwater explosion ship are realized. According to the method, a nonlinear dynamic response analysis result can be obtained on the basis of any initial value condition, when system parameters, initial conditions and other factors are changed to a certain degree, track parameters are adjusted through displacement operation in a symbolic dynamic theory, forecasting of the changed test result is achieved, and the method is suitable for large-scale popularization and application. Therefore, system parameter intra-neighborhood forecasting is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of damage mechanism analysis of ship structures and systems under strong impact loads, and specifically relates to a method, program, equipment and storage medium for analyzing nonlinear dynamics time-space decoupling data of underwater explosion hull structures. Background Art

[0002] The dynamic response of the underwater explosion hull structure and system has obvious cross-scale strong nonlinear transient physical processes in time and space. Moreover, the dynamic response process of the underwater explosion hull structure and system is very sensitive to multiple complex factors such as system parameters, initial conditions, boundary conditions, medium conditions and geometric conditions, and has nonlinear and non-stationary characteristics. It is well known that for strong nonlinear dynamic systems, with the change of system parameters, initial conditions and other parameters, the system dynamic response process will produce nonlinear characteristics such as bifurcation and mutation, which will lead to the uncertainty of the system output. This nonlinear dynamic output characteristic is extremely difficult to describe and characterize with dynamic equations or experiments, and its evolution law is also very different from the deterministic theory. The nonlinear response law contained in the dynamic response of the underwater explosion hull structure and system is difficult to describe with classical dynamic equations. The damage mechanism of the underwater explosion hull structure is inseparable from the nonlinear evolution law and non-stationary characteristics of dynamics. Therefore, it is of great engineering application value to carry out time-space decoupling data analysis on the nonlinear and non-stationary impact dynamic response of the underwater explosion hull structure and system.

[0003] Patent document CN117634361A discloses a method for evaluating the damage of ships caused by underwater explosion bubble pulsation loads. In this patent document, based on three-dimensional potential flow theory and hull vibration, the overall dynamic response model of the ship is established by considering the interaction between bubbles and flow field, flow field and structure, and a method for evaluating the damage of the ship is constructed. However, this method characterizes the damage characteristics of the ship by evaluating the damage of the ship through the framework response model, and does not characterize the nonlinear dynamic characteristics of the underwater explosion of the ship. It is difficult to reveal the damage response process of the ship under the action of the underwater explosion load, and has limited contribution in the field of theoretical analysis of the damage mechanism of the ship.

[0004] Patent document CN117592321A discloses a method for rapid assessment of ship breaches under underwater contact explosion loads. In this patent document, based on the existing empirical formula for breaches of plane reinforced plate frames under underwater contact explosion loads, the influence of factors such as surface characteristics at different positions of the hull, reinforcement size and number, charge amount and explosion distance are taken into account. The existing empirical formula for breaches is corrected through dimensional analysis and numerical simulation results to obtain a rapid assessment formula for breaches under underwater explosion loads applicable to the entire ship. However, this method achieves hull breach assessment by correcting the existing empirical formula. The damage to the hull structure caused by underwater explosions has nonlinear and non-stationary characteristics, and there are limitations in using classical dynamic equations to characterize it.

[0005] The existing analysis methods of underwater explosion hull and system dynamic response characteristics have the following limitations: (1) It is impossible to characterize the dynamic evolution law and non-stationary characteristics of nonlinear dynamic response; (2) When the nonlinear dynamic response process bifurcates with system parameters, initial conditions and other factors and produces uncertainty mutations, the classical analysis method cannot accurately predict the experiment with mutation phenomena. Before the test begins, it is extremely important to quickly predict the nonlinear dynamic response characteristics of underwater explosion hulls. Summary of the invention

[0006] The purpose of the present invention is to provide a method, program, device and storage medium for analyzing nonlinear dynamics of underwater explosion hull structure in time and space.

[0007] The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space decoupling includes the following steps:

[0008] Step 1: Obtain the response signal of the hull structure measurement point in the underwater explosion test, and intercept the time period containing a significant peak in the response signal;

[0009] Step 2: Filter and normalize the intercepted signal, calculate the delay time and embedding dimension of the normalized time series, and reconstruct the phase space based on the calculation results;

[0010] Step 3: According to the unimodal mapping function, perform parabolic mapping fitting on the normalized time series in the phase space to obtain the control parameter μ in the unimodal mapping function;

[0011] Step 4: Determine the periodic orbit sequence corresponding to the unimodal mapping function according to the word lifting method in the symbolic dynamics theory, that is, characterize the state and state change of the system by the kneading sequence; calculate the obtained kneading sequence by the word lifting method to obtain the theoretical control parameter μ of the unimodal mapping function corresponding to the periodic orbit sequence k , to realize the digital representation of the strong nonlinear and non-stationary characteristics of the nonlinear dynamic response signal of the underwater explosion hull structure;

[0012] Step 5: Perform a new round of interception on the subsequent signals of the intercepted response signal, and complete steps 2 to 4 to obtain the single-peak mapping function control parameter μ and the theoretical control parameter μ k For the time series that changes with time, a stationarity analysis is performed on the time series. If the analysis result is stationary, the time-space decoupling data analysis of the nonlinear dynamics of the underwater explosion hull structure is completed; otherwise, return to step 1 and re-intercept the response signal.

[0013] Furthermore, in step 1, when intercepting the signal for the first time, preliminary interception is performed based on the natural frequency of the hull structure, the pulse width of the explosion load, and the transmission and reflection law of the bending waves in the structure.

[0014] Furthermore, the filtering process of the intercepted signal in step 2 is specifically: performing high-pass filtering on the signal based on Fourier transform, and the specific filtering frequency for different signals is determined based on the spectrum analysis of wavelet transform;

[0015] W(a,b)=∫f(t)φ(t)[(tb) / a]dt

[0016] Where W(a,b) represents the wavelet coefficient, f(t) represents the signal to be filtered, φ(t) represents the wavelet basis function, and a and b represent the scale factor and translation factor, respectively.

[0017] Furthermore, the normalization process in step 2 is specifically: the response data and the time signal are respectively normalized, wherein the normalization process of the response data is:

[0018]

[0019] Among them, x is the original response data, x * is the normalized response data, x max is the maximum value in the original response data; the normalized time signal is:

[0020]

[0021] Among them, t is the original time signal, t * is the normalized time signal, t f It is the inverse of the first-order natural frequency of the hull structure.

[0022] Furthermore, in the phase space reconstruction process in step 2, abnormal sample points may appear, and the abnormal sample points must be removed according to the error removal criterion;

[0023] The delay time τ and embedding dimension m are calculated for the normalized time series, specifically:

[0024] The autocorrelation function method is used to characterize the correlation degree of the normalized time series before and after a certain period of time (0, t), that is, the degree of regularity of the sequence; the autocorrelation function T (τ) is defined as:

[0025]

[0026] The first time that the T(τ)-τ curve drops to 0 or the first minimum is selected as the delay time of the normalized time series;

[0027] When the state changes over time, the correlation between the state variables before and after represents the degree of sequence regularity. The correlation function is defined as:

[0028]

[0029] Among them, γ-dimensional correlation quantity, C(ε) is the correlation function representing the degree of data correlation in phase space, and ε is the radius of a given ultra-small ball in phase space;

[0030] For different embedding dimensions m, the lnC(ε)-lnε curve is plotted, ignoring the noise region where ε is extremely small and the saturation region where C(ε) is extremely large and remains unchanged. The slope of the middle straight line is the correlation dimension d2. The d2-m curve is plotted, and the saturated part of the slope, that is, the part where the slope no longer increases with the increase of the embedding dimension m, is taken as the embedding dimension of the normalized time series.

[0031] Furthermore, the mathematical expression of the unimodal mapping function in step 3 is:

[0032]

[0033] Among them, x n ∈[-1,1].

[0034] Furthermore, in step 5, the unit root test method is used to compare μ and μ k Perform stationarity analysis on time series that vary over time.

[0035] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space.

[0036] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space.

[0037] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space.

[0038] The beneficial effects of the present invention are:

[0039] The present invention adopts phase space reconstruction technology and unimodal mapping method to perform time-space decoupling data analysis on a large amount of test data, and realizes the characterization and description of the nonlinear evolution law and non-stationary characteristics of underwater explosion ships. The present invention can obtain its nonlinear dynamic response analysis results based on any initial value conditions, and when the system parameters, initial conditions and other factors change to a certain extent, the orbit parameters are adjusted through the shift operation in the symbolic dynamics theory to realize the prediction of the changed test results, that is, the prediction within the neighborhood of the system parameters is realized. The present invention is different from other underwater explosion ship damage mechanism analysis methods. The present invention does not rely on the existing classical dynamics equations, but adopts phase space reconstruction technology to characterize the time series in the phase space based on the unimodal mapping function to characterize the orbital motion characteristics of the time series; at the same time, the time series of the stable orbit is characterized based on the symbolic dynamics theory, and the nonlinear response sequence is described as an irregular symbol sequence through highly generalized and abstract processing. The nonlinear response characteristics of the system are characterized by the numerical values ​​of a group of variables in the phase space, and a motion orbit is given. When the system parameters, initial conditions and other factors change, the prediction of the test results within a certain range can be achieved by adjusting the motion orbit parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The following are sample images of strain, acceleration and velocity response signals. (a) is the impact strain response signal of the hull structure, (b) is the impact acceleration response signal of the hull structure, and (c) is the impact velocity response signal of the hull structure.

[0041] Figure 2 The following is an example of the spectrum analysis of the hull structure response signal. (a) is the original signal, (b) is the first conversion, and (c) is the second conversion.

[0042] Figure 3 It is the autocorrelation function T(τ)-τ graph.

[0043] Figure 4 is the correlation dimension d2-m graph.

[0044] Figure 5 Plot a spider web for a unimodal map.

[0045] Figure 6 Schematic diagram of single peak mapping trajectory, where (a) is the sample trajectory (excluding outliers), and (b) is the sample trajectory (with outliers).

[0046] Figure 7 This is the overall architecture diagram of the present invention.

[0047] Figure 8 It is the overall flow chart of the present invention.

[0048] Fig. 9 This is a graph of original acceleration data in Example 1 of the present invention.

[0049] Fig.10 This is a schematic diagram of the first data capture in Example 1 of the present invention.

[0050] Fig.11 It is the autocorrelation function T(τ)-τ diagram in Example 1 of the present invention.

[0051] Fig.12 It is the correlation dimension d2-m graph in Example 1 of the present invention.

[0052] Fig.13 This is a single-peak mapping function diagram corresponding to the first interception signal in Example 1 of the present invention.

[0053] Fig.14 The analysis result diagram of the second interception signal in Example 1 of the present invention, where μ = 1.3010, μ k =1.2062.

[0054] Fig.15 The analysis result diagram of the third interception signal in Example 1 of the present invention, where μ = 1.5400, μ k =1.2985.

[0055] Fig.16 The analysis result diagram of the fourth interception signal in Example 1 of the present invention, where μ = 1.9720, μ k =1.9408.

[0056] Fig.17 The analysis result diagram of the fifth interception signal in Example 1 of the present invention, where μ = 1.4390, μ k =1.5749.

[0057] Fig.18 The analysis result diagram of the sixth interception signal in Example 1 of the present invention, where μ = 1.6800, μ k =1.7507.

[0058] Fig.19 The seventh interception signal analysis result diagram in Example 1 of the present invention, where μ = 1.9790, μ k =1.9250.

[0059] Fig. 20 The analysis result diagram of the eighth interception signal in Example 1 of the present invention, where μ = 1.3020, μ k =1.2062.

[0060] Fig.21 The analysis result diagram of the ninth interception signal in Example 1 of the present invention, where μ = 1.3950, μ k =1.3229.

[0061] Fig. 22 where μ and μ in Example 1 of the present invention k Line chart over time.

[0062] Fig.23 This is a graph of the original strain data in Example 2 of the present invention.

[0063] Fig.24 This is a schematic diagram of the first data capture in Example 2 of the present invention.

[0064] Fig.25 It is the autocorrelation function T(τ)-τ diagram in Example 2 of the present invention.

[0065] Fig.26 It is the correlation dimension d2-m graph in Example 2 of the present invention.

[0066] Fig. 27 This is a single-peak mapping function diagram corresponding to the first interception signal in Example 2 of the present invention.

[0067] Fig.28 The analysis result diagram of the second interception signal in Example 2 of the present invention, where μ = 1.645, μ k =1.751.

[0068] Fig.29 The analysis result diagram of the third interception signal in Example 2 of the present invention, where μ = 1.896, μ k =1.861.

[0069] Fig.30 The analysis result diagram of the fourth interception signal in Example 2 of the present invention, where μ = 1.594, μ k =1.674.

[0070] Fig.31 The analysis result diagram of the fifth interception signal in Example 2 of the present invention, where μ = 1.183, μ k =1.145.

[0071] Fig.32 The sixth interception signal analysis result diagram in Example 2 of the present invention, where μ = 1.475, μk =1.293.

[0072] Fig.33 The analysis result diagram of the seventh interception signal in Example 2 of the present invention, where μ = 1.205, μ k =1.145.

[0073] Fig.34 The analysis result diagram of the eighth interception signal in Example 2 of the present invention, where μ = 1.208, μ k =1.266.

[0074] Fig.35 The analysis result diagram of the ninth interception signal in Example 2 of the present invention, where μ = 1.399, μ k =1.145.

[0075] Fig.36 The analysis result diagram of the tenth interception signal in Example 2 of the present invention, where μ = 1.229, μ k =1.145.

[0076] Fig.37 where μ and μ in Example 2 of the present invention k Line chart over time. DETAILED DESCRIPTION

[0077] The present invention is further described below in conjunction with the accompanying drawings.

[0078] This paper takes the typical structure of ships as the research object, uses phase space reconstruction technology and single peak mapping method to study the uncertainty characteristics of hull structure dynamics under different underwater explosion load conditions. The distribution characteristics of the control parameter μ of the impact response signal of the hull structure under different impact loads under single peak mapping conditions are discussed. The specific technical steps are as follows:

[0079] Step 1: Obtain the response signal of the hull structure measurement point in the underwater explosion test, and intercept the time period containing a significant peak in the response signal;

[0080] Intercept the time period containing significant peaks in the response signal, and perform preliminary interception of the signal based on the signal change cycle. Figure 1 As shown, when the signal is intercepted for the first time, it is initially intercepted based on the natural frequency of the structure, the pulse width of the explosion load, and the transmission and reflection laws of the bending waves in the structure. At this time, the duration of the intercepted signal needs to be further optimized through symbol sequence analysis in subsequent single-peak mapping.

[0081] Step 2: Filter and normalize the intercepted signal, calculate the delay time and embedding dimension of the normalized time series, and reconstruct the phase space based on the calculation results;

[0082] like Figure 2 As shown in the figure, according to the zero drift phenomenon of the signal and the interference signal contained in the signal, the signal is high-pass filtered based on Fourier transform. According to a large amount of data analysis, the recommended filtering frequency is 100Hz~500Hz. The specific filtering frequency for different signals can be further determined based on the spectrum analysis of wavelet transform.

[0083] W(a,b)=∫f(t)φ(t)[(tb) / a]dt

[0084] Among them, W(a,b) represents the wavelet coefficient, f(t) represents the original signal, φ(t) represents the wavelet basis function, a and b represent the scale factor and translation factor respectively.

[0085] The response data and the time signal are normalized respectively, where the normalization of the response data is:

[0086]

[0087] Among them, x is the original response data, x * is the normalized response data, x max is the maximum value in the original response data;

[0088] According to the law of Peter propagation change in the structure, some scholars use the appearance of standing waves in the structure as the critical stage of response. If the propagation speed of the wave is u, the corresponding vibration frequency is;

[0089]

[0090] In the formula, when n=1, v1 is called the fundamental frequency, and other frequencies v n They are called second, third, and nth harmonics respectively.

[0091] In the process of engineering analysis, the main focus is on the first-order vibration mode of the structure, so the normalization of the time signal is:

[0092]

[0093] Among them, t is the original time signal, t * is the normalized time signal, t f It is the inverse of the first-order natural frequency of the hull structure.

[0094] Reconstruct the phase space of the normalized time series. Calculate the delay time τ and embedding dimension m of the sequence respectively, and reconstruct the phase space of the time series based on the calculation results. Abnormal sample points may appear during the phase space reconstruction process, and the sample points need to be removed according to the error removal criterion. After removing the abnormal sample points, reconstruct the sequence again.

[0095] The autocorrelation function method is used to characterize the correlation degree of the normalized time series before and after a certain period of time (0, t), that is, the degree of regularity of the sequence; the autocorrelation function T (τ) is defined as:

[0096]

[0097] like Figure 3 As shown, the first time that the T(τ)-τ curve drops to 0 or the first minimum is selected as the delay time of the normalized time series; when the T(τ)-τ curve is at the first minimum, the variance of the curve sequence correlation is the smallest, so the τ value here is selected as the optimal delay amount.

[0098] When the state changes over time, the correlation between the state variables before and after represents the degree of sequence regularity. The correlation dimension is defined as:

[0099]

[0100] Among them, the γ-dimensional correlation quantity, C(ε) is the correlation function that represents the degree of data correlation in the phase space, and ε is the radius of a given super-small ball in the phase space; when ε is extremely small, C(ε)→0, so the above formula cannot be taken as an absolute limit. Because the random process is equivalent to the motion of infinite multi-modes, its dimension is infinite, that is, the dimension of the interference signal increases with the increase of the previous entry.

[0101] Therefore, for different embedding dimensions m, we draw the lnC(ε)-lnε curve, ignoring the noise region where ε is extremely small and the saturation region where C(ε) is extremely large and remains unchanged. The slope of the middle straight line is the correlation dimension d2. Figure 4 As shown, the d2-m curve is drawn, where the saturation part of the slope, that is, the slope no longer increases with the increase of the embedding dimension m, is used as the embedding dimension of the normalized time series. The analysis of a large number of experimental data results shows that the embedding dimension m of the response data phase space under the guidance of this method can be 2, and the delay time τ is related to the system motion trajectory.

[0102] The reconstructed sequence is fitted with a parabola mapping in the phase space. According to the unimodal mapping function, the sample points in the phase space are fitted to obtain the control parameter μ in the unimodal mapping function.

[0103] like Figure 5 The figure shows the spider web plot of a unimodal mapping. The parabola mapping is a unimodal mapping of a quadratic polynomial and a discrete mapping with complex dynamic behavior. The mathematical expression of the unimodal mapping is:

[0104]

[0105] Among them, x n ∈[-1,1].

[0106] Step 4: Determine the periodic orbit sequence corresponding to the unimodal mapping function according to the word lifting method in the symbolic dynamics theory, that is, characterize the state and state change of the system by the kneading sequence; calculate the obtained kneading sequence by the word lifting method to obtain the theoretical control parameter μ of the unimodal mapping function corresponding to the periodic orbit sequence k , to realize the digital representation of the strong nonlinear and non-stationary characteristics of the nonlinear dynamic response signal of the underwater explosion hull structure;

[0107] The state of a physical system can be described by the numerical values ​​of a set of variables in the phase space. The state of the system changes with time, and the representative points of the system move in the phase space, giving a motion trajectory.

[0108] The symbolic dynamics system is the simplest type of dynamics system in form. It is a highly generalized and abstract form of the actual dynamics system. Imagine that many infinitely long symbol sequences are constructed from two different letters R and L. For example:

[0109] RRLLRLRL... and RLRLRLRL...

[0110] They are two different sequences. The only way to generate them is to write the letters one by one. There is no shortcut. Unstable periodic orbits and the interaction between their stable and unstable flow patterns play a key role in generating chaotic motion. With the help of a simple dynamic system, the symbolic dynamics system, the nonlinear response sequence can be described as a large number of extremely irregular symbol sequences. By continuously applying the shift operation to the nonlinear response sequence, the nonlinear dynamic response orbit can be obtained, which can achieve a high degree of generalization and abstraction of the dynamic system of the underwater explosion hull structure and system response, and characterize the orbital properties of the underwater explosion hull structure dynamics system.

[0111] Step 5: Perform a new round of interception on the subsequent signals of the intercepted response signal, and complete steps 2 to 4 to obtain the single-peak mapping function control parameter μ and the theoretical control parameter μ k For the time series that changes with time, a stationarity analysis is performed on the time series. If the analysis result is stationary, the time-space decoupling data analysis of the nonlinear dynamics of the underwater explosion hull structure is completed; otherwise, return to step 1 and re-intercept the response signal.

[0112] In the process of analyzing the intercepted response signal, the interception duration is determined by the distribution law of the reconstructed sample points in the phase space. The specific operation is as follows: Figure 6 As shown, when the second half sample points and the first half sample points are not in the same orbit (that is, the second half sample points do not satisfy the single-peak mapping function corresponding to the first half sample points, it can be understood that the second half sample points are internal mappings, which appear as abnormal points in mathematical statistics and can be removed by the error removal criterion.).

[0113] The control parameter μ in the mapping function and the theoretical control parameter μ k The time series that changes over time is analyzed for sequence stationarity. The present invention uses the unit root test method to verify and analyze the stationarity of the time series, and performs sequence stationarity analysis on the control parameter time series of the same signal. The ADF test method assumes that the random process can be passed through the following modified autoregressive model:

[0114]

[0115] Using the ADF-t test statistic or the related standardized deviation statistic To determine whether the unit root hypothesis is established. and β j , j=1,...,PT are ρ and β respectively j , j=1,...,the least squares estimator of PT, yes The least squares standard deviation of .

[0116] The present invention takes the impact dynamic response of the typical structure of underwater explosion ship as the research object, and performs time-space decoupling data analysis on the test data with strong nonlinear and non-stationary characteristics based on phase space reconstruction, single peak mapping and symbolic dynamics theory. The present invention comprehensively considers the time-space characteristics of the strong nonlinear and non-stationary dynamic impact response of the underwater explosion hull structure, and uses phase space reconstruction technology and single peak mapping method to perform time-space decoupling data analysis on a large amount of test data, so as to realize the characterization and description of the nonlinear evolution law and non-stationary characteristics of the underwater explosion ship; the present invention can obtain its nonlinear dynamic response analysis results based on any initial value conditions, and realize the prediction of the strong nonlinear and non-stationary dynamic impact response process of the system in the neighborhood where the system parameters, initial conditions and other factors change.

[0117] Embodiment 1:

[0118] This embodiment takes the acceleration response signal of the explosion point in the ship model test under the action of underwater explosion as an example to analyze the signal. First, the original data of the acceleration signal is intercepted. Fig.10 As shown: There is no obvious zero drift phenomenon and interference signal in the response signal, so the signal is not filtered. The phase space reconstruction technology is directly used to reconstruct the intercepted time series. The calculation results of the phase space delay time τ and the embedding dimension m are as follows Fig.11 and Fig.12As shown in the figure, after reconstructing the phase space of multiple physical quantity parameter time series such as the hull structure strain signal and acceleration signal of a large number of underwater explosion experiments, it is found that the delay time of the signal may not be the same, but the phase space dimension of the signal is 2-dimensional. Then, a single-peak mapping fitting is performed on the reconstructed time series in the phase space, and the single-peak mapping function obtained by fitting is as follows: Fig.13 As shown, the single-peak mapping function corresponding to the first intercepted signal, the control parameter μ obtained by fitting is 2.0460.

[0119] The kneading sequence (RLRC) corresponding to the above periodic orbit is calculated by the word lifting method, and the single peak mapping theoretical control parameter μ corresponding to the periodic orbit is obtained. k =1.9405. Figures 14 to 21 As shown, a new round of interception is performed on the subsequent signals of the intercepted response signal, and the above steps are repeated to analyze the signal in sections to obtain the control parameter μ in the mapping function and the theoretical control parameter μ k The time series that changes with time, sorting out the above data, obtains the control parameter μ and the theoretical control parameter μ k Time series that vary over time, such as Fig. 22 As shown. Finally, the unit root test method is used to test the stability of the time series of the control parameter μ that changes over time:

[0120] Table 1 ADF statistical test of the time series of control parameter μ value of acceleration response signal

[0121]

[0122] Table 2 Acceleration response signal theoretical control parameters μ k ADF statistical test for time series

[0123]

[0124] Note: If the statistic is greater than the critical value, the series is non-stationary.

[0125] The nonlinear and non-stationary characteristics of the acceleration response signal at the underwater explosion ship measuring point are characterized by the time evolution diagram of the ship and system dynamics characteristics. The nonlinear response characteristics and motion trajectory of the system described in the phase space are visualized and digitized based on the control parameter μ obtained by the symbolic dynamics theory. When the system parameters and boundary conditions change to a certain extent, the nonlinear response characteristics of the test after the change are re-characterized through the shift operation in symbolic dynamics, so as to realize the rapid prediction of the test results after the change.

[0126] Embodiment 2:

[0127] This embodiment analyzes the strain response signal, such as Fig.23 Shown are the strain raw data.

[0128] First, the original data of the strain signal is intercepted. After the first interception, the data is as follows Fig.24 As shown in the figure, there is no obvious zero drift phenomenon and interference signal in the response signal, so the signal is not filtered. The phase space reconstruction technology is directly used to reconstruct the intercepted time series. The calculation results of the phase space delay time τ and the embedding dimension m are shown in the figure. Fig.25 and Fig.26 As shown. After reconstructing the phase space of a large number of underwater explosion test ship structure strain response time series, it is found that the signal delay time may not be the same, but the phase space dimension of the signal is 2-dimensional. Then, a single-peak mapping fitting is performed on the reconstructed time series in the phase space, and the fitted single-peak mapping function is as follows Fig. 27 As shown, the single-peak mapping function corresponding to the first intercepted signal, the control parameter μ obtained by fitting is 1.794.

[0129] The kneading sequence (RLRC) corresponding to the above periodic orbit is calculated by the word lifting method, and the single peak mapping theoretical control parameter μ corresponding to the periodic orbit is obtained. k =1.957. Figures 28 to 36 As shown, a new round of interception is performed on the subsequent signals of the intercepted response signal, and the above steps are repeated to analyze the signal in sections to obtain the control parameter μ in the mapping function and the theoretical control parameter μ k Time series that vary over time, such as Fig.37 As shown. Finally, the unit root test method is used to test the stability of the time series of the control parameter μ that changes over time:

[0130] Table 3 ADF statistical test of the time series of μ values ​​of control parameters of strain response signals

[0131]

[0132] Table 4 Theoretical control parameters μ of strain response signal k ADF statistical test for time series

[0133]

[0134] Note: If the statistic is greater than the critical value, the series is non-stationary.

[0135] Similarly, the nonlinear and non-stationary characteristics of the strain response signal at the underwater explosion ship measuring point can be characterized through the time evolution diagram of the ship and system dynamic characteristics. The control parameter μ obtained based on the symbolic dynamics theory can be used to visualize and digitize the system nonlinear response characteristics and motion trajectory depicted in the phase space. When the system parameters and boundary conditions change to a certain extent, the shift operation in symbolic dynamics is used to re-describe the changed experimental nonlinear response characteristics, so as to achieve a rapid prediction of the changed test results.

[0136] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for analyzing the time-space decoupling data of the nonlinear dynamics of underwater explosion hull structures, characterized in that: The following steps are involved: Step 1: Obtain the response signal of the hull structure measurement point in the underwater explosion test, and intercept the time period containing a significant peak in the response signal; Step 2: Filter and normalize the intercepted signal, calculate the delay time and embedding dimension of the normalized time series, and reconstruct the phase space based on the calculation results; Step 3: According to the unimodal mapping function, perform parabolic mapping fitting on the normalized time series in the phase space to obtain the control parameter μ in the unimodal mapping function; Step 4: Determine the periodic orbit sequence corresponding to the unimodal mapping function according to the word lifting method in the symbolic dynamics theory, that is, characterize the state and state change of the system by the kneading sequence; calculate the obtained kneading sequence by the word lifting method to obtain the theoretical control parameter μ of the unimodal mapping function corresponding to the periodic orbit sequence k , to realize the digital representation of the strong nonlinear and non-stationary characteristics of the nonlinear dynamic response signal of the underwater explosion hull structure; Step 5: Perform a new round of interception on the subsequent signals of the intercepted response signal, and complete steps 2 to 4 to obtain the single-peak mapping function control parameter μ and the theoretical control parameter μ k For the time series that changes with time, a stationarity analysis is performed on the time series. If the analysis result is stationary, the time-space decoupling data analysis of the nonlinear dynamics of the underwater explosion hull structure is completed; otherwise, return to step 1 and re-intercept the response signal.

2. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1 is characterized by: In the step 1, when intercepting the signal for the first time, preliminary interception is performed based on the natural frequency of the hull structure, the pulse width of the explosion load, and the transmission and reflection law of the bending wave in the structure.

3. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1, characterized in that: The filtering process of the intercepted signal in step 2 is specifically: performing high-pass filtering on the signal based on Fourier transform, and the specific filtering frequency for different signals is determined based on the spectrum analysis of wavelet transform; W(a,b)=∫f(t)φ(t)[(tb) / a]dt Where W(a,b) represents the wavelet coefficient, f(t) represents the signal to be filtered, φ(t) represents the wavelet basis function, and a and b represent the scale factor and translation factor, respectively.

4. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1, characterized in that: The normalization process in step 2 is specifically: the response data and the time signal are normalized respectively, wherein the normalization process of the response data is: Among them, x is the original response data, x * is the normalized response data, x max is the maximum value in the original response data; The normalization of the time signal is: Among them, t is the original time signal, t * is the normalized time signal, t f It is the inverse of the first-order natural frequency of the hull structure.

5. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1, characterized in that: In the phase space reconstruction process in step 2, abnormal sample points may appear, and the abnormal sample points must be removed according to the error removal criterion; The delay time τ and embedding dimension m are calculated for the normalized time series, specifically: The autocorrelation function method is used to characterize the correlation degree of the normalized time series before and after a certain period of time (0, t), that is, the degree of regularity of the sequence; the autocorrelation function T (τ) is defined as: The first time that the T(τ)-τ curve drops to 0 or the first minimum is selected as the delay time of the normalized time series; When the state changes over time, the correlation between the state variables before and after represents the degree of sequence regularity. The correlation function is defined as: Among them, γ-dimensional correlation quantity, C(ε) is the correlation function representing the degree of data correlation in phase space, and ε is the radius of a given ultra-small ball in phase space; For different embedding dimensions m, the lnC(ε)-lnε curve is plotted, ignoring the noise region where ε is extremely small and the saturation region where C(ε) is extremely large and remains unchanged. The slope of the middle straight line is the correlation dimension d2. The d2-m curve is plotted, and the saturated part of the slope, that is, the part where the slope no longer increases with the increase of the embedding dimension m, is taken as the embedding dimension of the normalized time series.

6. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1, characterized in that: The mathematical expression of the unimodal mapping function in step 3 is: Among them, x n ∈[-1,1].

7. The method for analyzing the nonlinear dynamics of underwater explosion hull structure in time and space according to claim 1, characterized in that: In step 5, the unit root test method is used to compare μ and μ k Perform stationarity analysis on time series that vary over time.

8. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Images