Prediction method and system for motion-induced surface wave making of underwater vibration table

Abstract

The invention discloses a prediction method and system for motion-induced surface wave making of an underwater vibration table, and aims to solve the technical problem that accurate time domain reconstruction of multi-frequency waves induced by asymmetric excitation cannot be realized through frequency domain decomposition due to lack of an explicit physical correlation model of motion parameters and wave surface response in an existing underwater vibration table test. According to the method, an explicit prediction equation of underwater vibration table motion parameters and wave surface elevation is established through derivation, and through combination of fast Fourier transform decomposition, effective frequency component screening, dynamic wave number solving and wavelet component time domain superposition technologies of a seismic oscillation time history, accurate prediction of surface wave making under the working conditions of simple harmonic motion, seismic oscillation and the like is realized. The method fills the theoretical blank of quantitative prediction of the waves induced by the underwater vibration table, improves the wave surface prediction precision and test efficiency, and is suitable for the fields of ocean engineering equipment test, subsea pipeline anti-seismic test and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater shaking table test, in particular to a method and system for predicting surface wave induced by underwater shaking table motion. BACKGROUND

[0002] In the technical field of underwater shaking table test, there has been a key scientific problem that has been seriously underestimated and needs to be solved for a long time: the surface wave effect induced by the motion of underwater shaking table and its systematic influence on the test results. The traditional research regards the underwater shaking table as a pure structure loading device, focusing on the mechanical transmission characteristics of the shaking table to the model structure (such as acceleration transmission function and displacement control accuracy), but completely ignoring the disturbance effect on the water body. This cognitive bias leads to:

[0003] At the theoretical research level, there is a lack of explicit mathematical model of shaking table motion parameters (velocity amplitude U, angular frequency ω, table length 2b, water depth h) and induced wave surface η(x, t).

[0004] At the technical method level, the existing methods show polarization - either ignoring the wave effect or incorrectly borrowing the shaking plate wave generator or point source potential flow model, resulting in significant errors due to mismatched boundary conditions

[0005] At the engineering application level, this theoretical lack has caused significant technical obstacles and economic losses. In the scene of submarine pipeline seismic test, wave disturbance leads to systematic deviation of data; in the wave-current coupling test, the parameters need to be adjusted repeatedly, the test efficiency is reduced, and the cost is significantly increased.

[0006] Through bibliometric analysis, in the past 20 years, the research on the wave effect of underwater shaking table is less than 2%, and most of them are limited to phenomenon observation. With the popularization of high-power multi-degree-of-freedom shaking table (such as six-degree-of-freedom shaking table), the wave effect (wave height can reach more than 0.5m) cannot be ignored, and theoretical breakthrough is urgently needed. SUMMARY

[0007] The purpose of the present application is to provide a method and system for predicting surface wave induced by underwater shaking table motion, which is suitable for precise control of wave effect in the scene of ocean engineering equipment test, submarine pipeline seismic research, seismic performance test of marine engineering structures (such as offshore platform foundation, cross-sea bridge pier, immersed tunnel, underwater equipment base), seismic safety verification experiment of submarine structures (such as submarine pipeline, cable anchoring system, breakwater foundation) and the like.

[0008] To achieve the above purpose, the present application provides a method for predicting surface wave induced by underwater shaking table motion, which is suitable for simple harmonic vibration working condition and seismic motion working condition, comprising the following steps:

[0009] S1, acquiring motion parameters and environmental parameters of the underwater vibration table, the motion parameters including vibration velocity amplitude U and angular frequency ω, and the environmental parameters including table surface half-width b and water depth h;

[0010] S2, dynamically solving wave number k based on dispersion equation ω 2 =gktanh(kh), wherein g is gravitational acceleration;

[0011] S3, substituting the motion parameters and environmental parameters of S1 and the wave number k of S2 into the explicit prediction equation to calculate wave surface elevation η(x, t) at any wave surface position x and time t, which is expressed as follows:

[0012]

[0013] Preferably, for the simple harmonic vibration working condition, the implementation process is as follows:

[0014] (1) acquiring vibration parameters U, ω and environmental parameters b, h of the underwater vibration table under the simple harmonic vibration working condition;

[0015] (2) solving the dispersion equation by a numerical iteration method to obtain wave number k, and the iteration accuracy is ≤10 -6 ;

[0016] (3) substituting the vibration parameters, environmental parameters and wave number k into the explicit prediction equation to output full-time-domain wave surface spatial distribution η(x, t).

[0017] Preferably, for the seismic motion working condition, the implementation process is as follows:

[0018] (1) performing windowed fast Fourier transform on seismic motion time history u(t) to decompose the time-domain signal into discrete frequency components to obtain angular frequency ω i , amplitude U i and phase φ i of each component, and the Fourier transform is expressed as:

[0019]

[0020] (2) retaining valid components satisfying the condition by amplitude threshold filtering method, and the amplitude threshold filtering condition is expressed as:

[0021] |U(ω i )|≥∈·max(|U(ω)|)

[0022] wherein the threshold coefficient ∈=0.0001, and components in main frequency band 0.5-10 Hz are retained;

[0023] (3) independently solving the dispersion equation for each ω i to obtain corresponding wave number k i ;

[0024] (4) Generating wavelet components η according to the explicit prediction equation i (x, t) is expressed as:

[0025]

[0026] (5) Superimposing all wavelet components in time domain to output the synthesized wave surface η(x, t) which is expressed as:

[0027]

[0028] A prediction system of surface wave induced by underwater shaking table motion, used to implement a prediction method of surface wave induced by underwater shaking table motion, comprising:

[0029] A parameter input module configured to receive shaking table motion parameters U, ω and environmental parameters b, h and seismic time history u(t);

[0030] A dynamic wave number solving module: built-in numerical iterative algorithm of dispersion equation ω 2 =gktanh(kh), outputting wave number k;

[0031] A signal processing module: containing an FFT decomposition unit and a wavelet generating unit, the FFT decomposition unit is configured to perform windowed fast Fourier transform on the seismic time history u(t), and the wavelet generating unit is configured to generate wavelet components η i (x, t) under seismic motion conditions and generate full-time wave surface elevation η(x, t) under simple harmonic vibration conditions;

[0032] A parallel computing module: configured to perform real-time operation of superimposing all wavelet components in time domain under seismic motion conditions;

[0033] A result output module: generating wave surface elevation spatiotemporal distribution diagram.

[0034] Preferably, the dynamic wave number solving module adopts an adaptive iteration strategy, and the iteration stopping condition is:

[0035] |ω 2 -gktan h(kh)|≤10 -6 .

[0036] According to the specific embodiments provided by the present application, the following technical effects are disclosed:

[0037] In view of the fundamental problem that the traditional method lacks an explicit prediction equation, the present application establishes, for the first time, a quantitative relationship between the motion parameters of an underwater shaking table and induced waves through strict fluid dynamics theory derivation. This theoretical breakthrough enables the wave surface prediction to jump from the traditional empirical estimation to accurate theoretical calculation. Specifically, the established explicit equation not only includes basic parameters such as the shaking table speed amplitude and frequency, but also accurately quantifies the nonlinear effects of the table surface geometry and water depth on the waves through terms such as sin(kb) and sinh(kh), thereby achieving accurate prediction in the full operating range.

[0038] In view of the problem of wave prediction distortion under complex excitations such as ground motion, the present application proposes an innovative "decomposition-reconstruction" technical path. This method realizes accurate frequency domain decomposition of the ground motion signal through windowed FFT technology, ensuring that the energy capture rate of the 0.5-10Hz main frequency band reaches more than 99%; in the time domain reconstruction stage, by strictly preserving the three key information of spatial propagation phase, time evolution phase and original ground motion phase, the waveform interference distortion problem is effectively solved.

[0039] The technical solutions of the present application will be further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments will be briefly introduced. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor under the premise of the accompanying drawings.

[0041] Figure 2 A flow chart of a method for predicting surface excited waves by underwater shaking table motion according to embodiment 1 of the present application;

[0042] Figure 1 A schematic diagram of the underwater shaking table wave according to embodiment 2 of the present application;

[0043] Figure 3 A wave surface time history data graph at the center position of the shaking table according to embodiment 2 of the present application;

[0044] Figure 4 A wave surface time history data graph at a distance of 12m from the shaking table according to embodiment 2 of the present application;

[0045] Figure 5 An original signal graph of the shaking table moving according to the displacement of the predetermined seismic wave according to embodiment 3 of the present application;

[0046] Figure 6 A shaking table displacement decomposition and reconstruction data graph according to embodiment 3 of the present application;

[0047] Figure 7 The predicted wave surface time history diagram is obtained by superimposing the multiple frequency wave components of embodiment 3 of the present application.

[0048] Reference numerals

[0049] 1. An underwater shaking table. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0051] In order to make the above objectives, characteristics and advantages of the present application more apparent, comprehensible and easier to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0052] Embodiment 1

[0053] A prediction system of surface wave induced by underwater shaking table motion, used to implement a prediction method of surface wave induced by underwater shaking table motion as shown in the figure, can realize prediction under simple harmonic vibration working condition and seismic motion working condition. Specifically, the prediction system comprises: Figure 1

[0054] A parameter input module configured to receive shaking table motion parameters U, ω and environmental parameters b, h and seismic motion time history u(t);

[0055] A dynamic wave number solving module, which is internally provided with a numerical iteration algorithm of dispersion equation ω 2 = gk tan h(kh), and outputs wave number k; the dynamic wave number solving module adopts an adaptive iteration strategy, and an iteration stop condition is:

[0056] |ω 2 -gktanh(kh)|≤10 -6

[0057] A signal processing module, which comprises an FFT decomposition unit and a subwave generating unit, the FFT decomposition unit is configured to perform windowed fast Fourier transform on the seismic motion time history u(t), and the subwave generating unit is configured to generate subwave components η i (x, t) under seismic motion working condition, and to generate full time domain wave surface elevation η(x, t) under simple harmonic vibration working condition;

[0058] A parallel computing module configured to perform real-time operation of time domain superposition of all subwave components under seismic motion working condition;

[0059] ​Result output module: generate wave elevation spatiotemporal distribution map.

[0060] Embodiment 2

[0061] Under simple harmonic vibration working condition, a prediction method of surface wave induced by underwater vibration table motion is as follows:

[0062] (1) The structure of the underwater vibration table 1 is shown in Figure 2 . The pool has an underwater vibration table 1 with a platform located at the bottom of the pool and close to the bottom, which moves vertically along the water depth direction, and the generated waves are at z=h free water surface. Wherein: U is the maximum vibration speed of the underwater vibration table 1, and ω is the vibration circular frequency of the underwater vibration table 1. The amplitude of the underwater vibration table 1 is D, so U=Dω. The center of the underwater vibration table 1 is the z-axis along the water depth direction, the static water surface is z=h, and the intersection of the z-axis and the pool bottom plane is the coordinate origin. In the x direction, the underwater vibration table 1 is 2b long. The system needs to input the basic motion parameters of the underwater vibration table 1, including the vibration speed amplitude U and the angular frequency ω, and the test environment parameters such as the half-width b of the platform and the water depth h. These parameters constitute the basic data for wave surface prediction. As shown in Table 1.

[0063] Table 1 Basic motion parameters of the vibration table

[0064]

[0065] (2) After obtaining the above parameters, the system will solve the dispersion equation ω 2 =gktan h(kh) by numerical iteration method to dynamically determine the wave number k matched with the current working condition. This step ensures that the wave number k can accurately reflect the wave propagation characteristics under specific frequency and water depth conditions.

[0066] (3) After completing the wave number solving, the system will substitute all these parameters into the core wave surface equation of the present application for calculation. During the calculation process, the system will output the wave surface elevation η(x, t) at any observation position x at different times t in real time. Due to the use of a strict physical model, the complete wave surface shape can be accurately predicted. The wave surface elevation η(x, t) is represented as follows:

[0067]

[0068] According to the specified working condition, the time history data and wave height of the wave surface at any position can be calculated to realize complete wave surface prediction. The results are shown in Figure 3 and Figure 4 , Figure 3 represent the wave surface time history data at the center position of the vibration table; Figure 4 represent the wave surface time history data at a distance of 12m from the vibration table.

[0069] Embodiment 3

[0070] For more complex seismic motion conditions, this invention proposes an innovative "decomposition-reconstruction" prediction method. This method effectively solves the challenge of wave prediction under non-periodic excitation by combining frequency domain analysis and time domain superposition.

[0071] like Figure 2 As shown, under seismic motion conditions, the underwater shaking table 1 moves according to the displacement of the predetermined seismic wave, and the original signal is as follows: Figure 5 As shown. A method for predicting surface waves induced by underwater shaking table motion, comprising the following steps:

[0072] (1) Perform a windowed Fast Fourier Transform (FFT) on the seismic motion time history u(t) to decompose it into discrete frequency components. The Fourier transform is expressed as:

[0073]

[0074] This transformation decomposes the time-domain signal into discrete frequency components, yielding the angular frequency ω of each component. i Amplitude U i and phase φ i The displacement of the shaking table was disassembled and reconstructed, and the results are as follows: Figure 6 As shown.

[0075] (2) The effective components that meet the conditions are retained by the amplitude threshold filtering method. The amplitude threshold filtering conditions are expressed as follows:

[0076] |U(ω i )|≥∈·max(|U(ω)|)

[0077] The threshold coefficient is ∈=0.0001, which retains the components of the main frequency band from 0.5 to 10 Hz; ensuring that the main frequency components are retained while eliminating noise interference.

[0078] (3) After obtaining the frequency domain decomposition results, the system will process each effective frequency component independently. For each ω i Solve the dispersion equation independently Obtain the corresponding wave number k i This step ensures that wave components of different frequencies can accurately reflect their propagation characteristics, completely avoiding the errors caused by the fixed wave number used in traditional methods.

[0079] (4) Substitute the parameters of each frequency component into the wavefront equation to generate the wavelet component η. i (x, t), represented as:

[0080]

[0081] In this process, special attention is paid to preserving complete phase information, including the phase φ of the original ground motion.i Phase k of wave propagation i |x|-ω i This processing method allows each wavelet component to accurately reflect its evolution in space and time.

[0082] (5) Finally, time-domain reconstruction is performed. The system uses efficient parallel computation to strictly superimpose all wavelet components in the time domain, outputting the synthesized wavefront η(x,t), which is expressed as:

[0083]

[0084] The predicted wavefront is obtained by superimposing multiple frequency wave components, such as... Figure 7 As shown. Unlike the traditional simple amplitude addition, this scheme fully considers the interference effect between different frequency components.

[0085] In summary, the technical advantages of this invention are not only reflected in its groundbreaking theoretical innovations, but also in its practicality and reliability in engineering applications. By establishing a complete predictive theoretical system, developing efficient algorithms, and constructing an intelligent control system, this invention truly achieves a technological leap from "unpredictable" to "precisely controllable" wave prediction on underwater shaking tables, providing a completely new technical solution for marine engineering experiments. These advantages stem from a profound understanding and systematic solution to the shortcomings of existing technologies, demonstrating the dual breakthroughs of this invention in both theoretical and practical value.

[0086] The remaining technical features in the above embodiments can be flexibly selected by those skilled in the art to meet different specific practical needs. However, it is obvious to those skilled in the art that these specific details are not necessary to implement the present invention. In other instances, to avoid obscuring the present invention, well-known components, structures, or parts are not specifically described, and all are within the scope of technical protection defined by the claims of the present invention.

[0087] Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of this invention should be within the protection scope of the appended claims. In the foregoing description, numerous specific details have been set forth to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to implement the invention. In other instances, to avoid obscuring the invention, well-known techniques, such as specific construction details, operating conditions, and other technical conditions, have not been specifically described.

[0088] The principles and implementation manners of the present application are described by using specific examples in the present application, and the above examples are only used to help understand the method of the present application and its core idea; meanwhile, for the general technical personnel in the art, the specific implementation manners and application ranges will be changed according to the idea of the present application. In conclusion, the content of the present specification should not be understood as the limitation of the present application.

Claims

1. A method for predicting the motion-induced surface wave of an underwater shaking table, characterized in that, Suitable for simple harmonic vibration working condition and seismic motion working condition, comprising the following steps: S1, obtaining the motion parameters and environmental parameters of the underwater vibration table, the motion parameters including vibration velocity amplitude U and angular frequency ω, and the environmental parameters including table half-width b and water depth h; S2, based on the dispersion equation ω 2 = gk tan h(kh) dynamically solves the wave number k, where g is the acceleration of gravity; S3, substituting the motion parameters and environmental parameters of S1 and the wave number k of S2 into the explicit prediction equation to calculate the wave surface elevation η(x, t) at any wave surface position x and time t, represented as follows:

2. The method of claim 1, wherein: For the simple harmonic vibration working condition, the specific implementation process is: (1) obtaining the vibration parameters U, ω and environmental parameters b, h of the underwater vibration table under the simple harmonic vibration working condition; (2) Solve the dispersion equation by numerical iteration method to obtain the wave number k, and the iteration accuracy is ≤10 -6 ; (3) substituting the vibration parameters, environmental parameters and wave number k into the explicit prediction equation to output the full-time-domain wave surface spatial distribution η(x, t).

3. The method of claim 1, wherein: For the seismic motion working condition, the specific implementation process is: (1) The time history of ground motion u(t) is subjected to windowed fast Fourier transform to decompose the time domain signal into discrete frequency components, to obtain the angular frequency ω i , amplitude U i and phase φ i of each component, and the Fourier transform is expressed as: (2) retaining the effective components satisfying the condition through the amplitude threshold filtering method, and the amplitude threshold filtering condition is represented as: |U(ω i )|≥∈·max(|U(ω)|) Wherein, the threshold coefficient ∈ = 0.0001, and the components in the main frequency band of 0.5-10 Hz are retained; (3) for each ω i Solving the dispersion equation independently Obtaining the corresponding wave number k i ; (4) The wavelet component η is generated according to the explicit prediction equation i (x, t) is expressed as: (5) time-domain superposition of all sub-wave components is performed to output the synthesized wave surface η(x, t), represented as:

4. A system for predicting surface-generated waves induced by motion of a submerged shaker, for implementing the method for predicting surface-generated waves induced by motion of a submerged shaker according to any one of claims 1 to 3, characterized in that, It comprises: Parameter input module: configured to receive the vibration table motion parameters U, ω and environmental parameters b, h and seismic time history u(t); Dynamic wave number solver module: numerical iterative algorithm for built-in dispersion equation ω 2 = gk tan h(kh) outputs wave number k; Signal processing module: including FFT decomposition unit and wavelet generation unit, the FFT decomposition unit is configured to carry out windowed fast Fourier transform to seismic time history u (t), the wavelet generation unit is configured to generate wavelet component η i (x, t) under seismic working condition, and generate full time domain wave surface elevation η (x, t) under simple harmonic vibration working condition; Parallel computing module: configured to perform real-time operation of time-domain superposition of all sub-wave components under seismic motion working condition; Result output module: generating wave surface elevation space-time distribution diagram.

5. The system for predicting the wave making of a moving surface induced by a shaking table according to claim 4, wherein: The dynamic wave number solving module adopts an adaptive iteration strategy, and the iteration stop condition is: | ω 2 - gk tan h(kh) | < 10 -6 .

Images