A method for synthesizing spectrum of elastic wave impact echo signal based on Gaussian function

Abstract

The application provides a method for synthesizing elastic wave impact echo signal spectrum based on Gaussian function, which determines the vibration source wavelet spectrum according to the excitation mode, determines the main frequency, amplitude and half-width of the longitudinal wave and transverse wave reflection response signals of the concrete structure respectively, constructs the corresponding Gaussian function model, calculates the spectrum components and superimposes them to synthesize the reflection response signal spectrum, meanwhile, the noise signal is also modeled and synthesized, and finally, the reflection response signal spectrum, the noise response signal spectrum and the vibration source wavelet spectrum are combined to synthesize the complete elastic wave impact echo signal spectrum which can be used to identify the internal characteristic frequency of the concrete structure. The method aims to improve the identification ability of the characteristic frequency in the complex noise background and the reliability of the detection result by accurately modeling the vibration source characteristics, the structure reflection response and the noise component.

Description

Technical Field

[0001] This invention relates to the field of concrete structure testing technology, and in particular to a method for synthesizing the spectrum of elastic wave impact echo signals based on Gaussian functions. Background Technology

[0002] In non-destructive testing of concrete structures, the elastic wave impact-echo method is an important technique. Its principle is that when an elastic wave encounters an interface with a difference in wave impedance (such as a defect or structural boundary) during propagation, it will be reflected. By performing spectral analysis on the echo signal, characteristic frequencies related to the structural condition can be extracted. For example, the thickness of the concrete slab can be calculated based on the fundamental frequency of the spectrum, and the presence of internal defects can be determined by comparing the changes in the fundamental frequency at different measuring points.

[0003] However, in practical engineering applications, the effectiveness and reliability of this method still face significant challenges. First, the non-homogeneity of concrete causes elastic waves to reflect various waveforms, such as longitudinal and transverse waves. These waveforms superimpose on each other in the spectrum, causing the characteristic peaks representing structural information to be submerged and difficult to identify. At the same time, various interferences in the field testing environment, such as scattering from the internal steel reinforcement, environmental vibration, and electronic noise of the instrument itself, further exacerbate the spectral clutter, making it difficult to accurately identify and extract the characteristic frequencies characterizing the structural thickness or defects.

[0004] In summary, existing spectrum synthesis methods are often overly simplistic, failing to comprehensively consider the characteristics of the vibration source, various waveforms within the structure, and the scattering mechanisms of noise. Consequently, they cannot provide effective frequency ranges and distribution patterns for characteristic frequency identification. Therefore, there is an urgent need to develop a method capable of clearly and controllably synthesizing and highlighting effective characteristic frequencies against complex noise backgrounds, thereby improving the accuracy of characteristic frequency identification and the reliability of detection results in impulse echo signals. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for synthesizing the spectrum of elastic wave impact echo signals based on Gaussian functions. The aim is to improve the identification capability of characteristic frequencies and the reliability of detection results in complex noise backgrounds by accurately modeling the characteristics of the vibration source, the structural reflection response, and the noise components.

[0006] According to an embodiment of the present invention, a method for synthesizing the spectrum of an elastic wave impact echo signal based on a Gaussian function includes the following steps:

[0007] S1. Based on the excitation mode of the shock elastic wave source, select the source wavelet form and perform Fourier transform on the source wavelet to obtain the elastic wave source wavelet spectrum.

[0008] S2. Based on the reflective interface form of the concrete structure, determine the dominant frequency of the longitudinal wave reflection response signal spectrum and the dominant frequency of the transverse wave reflection response signal spectrum.

[0009] S3. Based on the spectral amplitude and half-width of the longitudinal wave reflection response signal, and the spectral amplitude and half-width of the transverse wave reflection response signal, construct Gaussian function models for the longitudinal wave and transverse wave reflection response signals, respectively.

[0010] S4. Based on the Gaussian function model and the main frequencies of the spectrum of the longitudinal and transverse wave reflection response signals, calculate the Gaussian function forms of the spectral components of the longitudinal and transverse wave reflection response signals, respectively.

[0011] S5. Superimpose the Gaussian functions of the spectral components of the longitudinal and transverse wave reflection response signals to synthesize the spectrum of the reflection response signal;

[0012] S6. Obtain the dominant frequency of the noise response signal spectrum, as well as the amplitude and half-width of the noise response signal spectrum;

[0013] S7. Based on the amplitude and half-width of the noise response signal spectrum, construct a Gaussian function model of the noise response signal, and calculate the Gaussian function form of the spectral components of the noise response signal according to the Gaussian function model of the noise response signal and the dominant frequency of the noise response signal spectrum.

[0014] S8. Superimpose the Gaussian functions of all noise response signal spectral components to synthesize the noise response signal spectrum;

[0015] S9. Based on the spectrum of the reflection response signal, the spectrum of the noise response signal, and the spectrum of the elastic wave source wavelet, synthesize the spectrum of the elastic wave impact echo signal used to identify the characteristic frequency of the concrete structure.

[0016] Furthermore, in step S2, determining the dominant frequency of the longitudinal wave reflection response signal spectrum and the dominant frequency of the transverse wave reflection response signal spectrum based on the reflective interface form of the concrete structure includes:

[0017] S2.1 If both reflecting interfaces of the elastic wave impact echo are free boundaries, the dominant frequency of the longitudinal wave reflection response signal spectrum is: The dominant frequency of the transverse wave reflection response signal spectrum is ;

[0018] S2.2 If the two reflecting interfaces of the elastic wave impact echo are a free boundary and a fixed boundary respectively, the dominant frequency of the longitudinal wave reflection response signal spectrum is: The dominant frequency of the transverse wave reflection response signal spectrum is ;

[0019] In the formula, For the longitudinal wave velocity of elastic waves, Let L be the transverse wave velocity of the elastic wave, and L be the thickness of the reflective layer.

[0020] Furthermore, in step S3, the process of constructing the Gaussian function model of the longitudinal and transverse wave reflection response signals includes:

[0021] Step S3.1: Based on the half-width of the spectrum of the longitudinal wave reflection response signal and the half-width of the spectrum of the transverse wave reflection response signal, calculate the corresponding Gaussian function frequency coefficients respectively.

[0022] Step S3.2: Construct a Gaussian function model based on the frequency coefficients of the Gaussian function and the amplitude of the spectrum of the longitudinal wave reflection response signal or the amplitude of the spectrum of the transverse wave reflection response signal.

[0023] Furthermore, in step S4, the process of calculating the Gaussian function form of the spectral components of the longitudinal and transverse wave reflection response signals is as follows:

[0024] The Gaussian function models of the longitudinal and transverse wave reflection response signals are combined with the dominant frequencies of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum, respectively, to generate Gaussian function forms for each spectral component; wherein...

[0025] The Gaussian function form of the spectral components of the longitudinal wave reflection response signal is:

[0026] ;

[0027] The Gaussian function form of the spectral components of the transverse wave reflection response signal is:

[0028] ;

[0029] In the formula, , and Let represent the amplitude, dominant frequency, and half-width of the spectrum of the i-th longitudinal wave reflection response signal, respectively; , and Let represent the amplitude, dominant frequency, and half-width of the spectrum of the j-th transverse wave reflection response signal, respectively.

[0030] Furthermore, the Gaussian function form of the spectral components of the noise response signal is:

[0031] ;

[0032] In the formula, , and These represent the amplitude, dominant frequency, and half-width of the spectrum of the k-th noise response signal, respectively.

[0033] Furthermore, in step S9, the synthesis of the elastic wave impact echo signal spectrum for identifying the characteristic frequency of the concrete structure involves: superimposing the reflection response signal spectrum with the noise response signal spectrum to obtain the structural response signal spectrum; and multiplying the structural response signal spectrum with the elastic wave source wavelet spectrum to obtain the final elastic wave impact echo signal spectrum.

[0034] Furthermore, the spectrum of the elastic wave impact echo signal is calculated using the following formula:

[0035] ;

[0036] In the formula, This represents the sub-wavelength spectrum of the elastic wave source. This represents the spectrum of the structural response signal.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention deconstructs the complex measured signal spectrum into multiple spectral components with clear physical meaning, including longitudinal wave reflection, transverse wave reflection, and noise components. Based on a Gaussian function, it performs precise mathematical modeling of each component, achieving in-depth analysis and controllable synthesis of the spectral composition. This method transforms the ambiguous and mixed spectral characteristics of traditional analysis into a series of quantifiable and independently adjustable parameters, significantly improving the understanding and explanatory power of the intrinsic structure and formation mechanism of the spectrum.

[0039] This invention also achieves effective separation of the effective signal from environmental or system noise at the spectral level by establishing a Gaussian function model of the noise response signal. During spectral synthesis or subsequent analysis, the effective signal components can be selectively enhanced while suppressing noise interference, thus enabling clear and accurate identification of characteristic frequencies representing structural thickness or internal defects even in strong noise environments. This effectively improves the reliability, repeatability, and overall identification accuracy of the impact echo detection method. Attached Figure Description

[0040] Figure 1 A flowchart illustrating the steps of a method for synthesizing the spectrum of an elastic wave impact echo signal based on a Gaussian function, as provided in an embodiment of the present invention;

[0041] Figure 2 The elastic wave source sub-wavelet Reck wavelet spectrum provided in the embodiments of the present invention;

[0042] Figure 3 Synthetic longitudinal and transverse wave reflection response signal spectrum diagrams provided for embodiments of the present invention;

[0043] Figure 4 The noise response spectrum diagram provided for the embodiments of the present invention;

[0044] Figure 5 The spectrum diagram of the synthetic elastic wave impact echo signal provided in the embodiment of the present invention. Detailed Implementation

[0045] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0046] As described in the background section, the elastic wave impact echo method faces challenges in concrete structure testing, including complex spectral density, significant noise interference, and difficulty in extracting characteristic frequencies. Traditional methods lack sufficient modeling of vibration source characteristics, multimode wave reflections, and noise mechanisms, resulting in significant differences between the synthesized spectrum and the measured signal, thus failing to effectively guide characteristic frequency identification.

[0047] This embodiment proposes a method for synthesizing the spectrum of elastic wave impact echo signals based on Gaussian functions. By establishing parameterized Gaussian models for the vibration source, structural response, and noise respectively, the method achieves controllable synthesis and effective separation of spectral components, significantly improving the identifiability of characteristic frequencies in strong noise backgrounds.

[0048] like Figure 1 As shown, a method for synthesizing the spectrum of an elastic wave impact echo signal based on a Gaussian function includes the following steps:

[0049] S1. Based on the excitation mode of the shock elastic wave source, select the source wavelet form and perform Fourier transform on the source wavelet to obtain the elastic wave source wavelet spectrum.

[0050] S2. Based on the reflective interface form of the concrete structure, determine the dominant frequency of the longitudinal wave reflection response signal spectrum and the dominant frequency of the transverse wave reflection response signal spectrum.

[0051] S3. Based on the spectral amplitude and half-width of the longitudinal wave reflection response signal, and the spectral amplitude and half-width of the transverse wave reflection response signal, construct Gaussian function models for the longitudinal wave and transverse wave reflection response signals, respectively.

[0052] S4. Based on the Gaussian function model and the main frequencies of the spectrum of the longitudinal and transverse wave reflection response signals, calculate the Gaussian function forms of the spectral components of the longitudinal and transverse wave reflection response signals, respectively.

[0053] S5. Superimpose the Gaussian functions of the spectral components of the longitudinal and transverse wave reflection response signals to synthesize the spectrum of the reflection response signal;

[0054] S6. Obtain the dominant frequency of the noise response signal spectrum, as well as the amplitude and half-width of the noise response signal spectrum;

[0055] S7. Based on the amplitude and half-width of the noise response signal spectrum, construct a Gaussian function model of the noise response signal, and calculate the Gaussian function form of the spectral components of the noise response signal according to the Gaussian function model of the noise response signal and the dominant frequency of the noise response signal spectrum.

[0056] S8. Superimpose the Gaussian functions of all noise response signal spectral components to synthesize the noise response signal spectrum;

[0057] S9. Based on the spectrum of the reflection response signal, the spectrum of the noise response signal, and the spectrum of the elastic wave source wavelet, synthesize the spectrum of the elastic wave impact echo signal used to identify the characteristic frequency of the concrete structure.

[0058] like Figure 2 As shown, Figure 2 The image shows the spectrum of the elastic wave source wavelet, represented by the Ricker wavelet. In this embodiment, the Ricker wavelet, widely used in nondestructive testing, is selected as the source model. A Fourier transform is performed on the Ricker wavelet, which represents the source wavelet form x(t), to obtain the spectrum of the elastic wave source wavelet. :

[0059] ,

[0060] In the formula, This represents the dominant frequency parameter of the Reichschild wavelet.

[0061] Based on the reflective interface morphology of the concrete structure, determine the dominant frequencies of the longitudinal and transverse wave reflection response signals. Assume this is for a concrete slab of thickness L with both interfaces being free boundaries:

[0062] The dominant frequency of the longitudinal wave reflection response signal spectrum is: The dominant frequency of the transverse wave reflection response signal spectrum is: , where n and m represent the number of longitudinal and transverse wave reflection response signals, respectively.

[0063] In this embodiment, we select the dominant frequencies of the spectra of two longitudinal wave reflection response signals and two transverse wave reflection response signals for analysis:

[0064] Longitudinal wave reflection response dominant frequency: ;

[0065] The dominant frequency of the transverse wave reflection response: ;

[0066] In the formula, vp and vs are the longitudinal and transverse wave velocities, respectively, and L represents the thickness of the reflective layer.

[0067] If the two reflecting interfaces of an elastic wave impact echo are a free boundary on one side and a fixed boundary on the other:

[0068] The dominant frequency of the longitudinal wave reflection response signal spectrum is: ;

[0069] The dominant frequency of the transverse wave reflection response signal spectrum is: ;

[0070] In the actual spectrum, each characteristic peak is not an infinitely thin line. By assigning a Gaussian peak to each main frequency, we can realistically simulate the spectral shape of the reflected signal.

[0071] For each main frequency and Choose the corresponding amplitude A and half-width Hf. The amplitude reflects the reflection intensity, and the half-width reflects the degree of wave attenuation. Specifically, select the amplitude of the longitudinal wave reflection response signal spectrum. and half width And the amplitude of the transverse wave reflection response signal spectrum. and half width .

[0072] Construct a Gaussian function model of the reflection response signal , Longitudinal waves For transverse waves, ;in, The frequency coefficients of the Gaussian function, For longitudinal waves, For transverse waves, .

[0073] By combining the Gaussian function model of the reflected response signal with the dominant frequency, various spectral components are generated:

[0074] Construct the Gaussian function Epi(ω) of the spectral components of the longitudinal wave reflection response signal:

[0075] ;

[0076] Construct the Gaussian function Esj(ω) for the spectral components of the transverse wave reflection response signal:

[0077] ;

[0078] The Gaussian functions of the spectral components of all longitudinal and transverse waves are superimposed to synthesize the total reflection response signal spectrum. ,

[0079] ;

[0080] The spectra of the synthesized longitudinal and transverse wave reflection response signals are as follows: Figure 3 As shown, the multiple characteristic peaks that the structural reflection should exhibit in the spectrum under noise-free conditions are clearly demonstrated.

[0081] To test the robustness of the method to noise, or to actively subtract noise in the analysis, we need to add noise components to the synthesized spectrum.

[0082] Assuming there are 99 different sources of noise, such as 50Hz power frequency interference, equipment resonance, random vibration, etc., what is the dominant frequency of the noise response signal spectrum? The amplitude is and half width is , where p is the number of noise response signals.

[0083] Construct a Gaussian function model for the noise response signal: ;

[0084] By combining the Gaussian function model of the noise response signal with the dominant frequency, the spectral components of the noise response signal are generated. :

[0085] Constructing the spectral components of the noise response signal Gaussian function :

[0086] ;

[0087] Gaussian function of all noise response spectral components Superimpose the signals to synthesize the noise response signal spectrum. :

[0088] ;

[0089] The noise response signal spectrum is as follows: Figure 4 As shown, this simulates the complex situation of spectral background noise in a real environment.

[0090] Ultimately, the signal we receive is formed after the source signal has been reflected by the structure and subjected to noise interference. In the frequency domain, this process is approximated by multiplying the source spectrum by the structure response spectrum (including effective reflections and noise).

[0091] Specifically, the spectrum of the reflection response signal and noise response signal spectrum Adding them together yields the complete structural response spectrum. , ;

[0092] Then, the source spectrum of the elastic wave source sub-wavelength is... and the spectrum of structural response signals Multiplying these two components yields the spectrum of the elastic wave impact echo signal used to identify the characteristic frequencies of the concrete structure:

[0093] ;

[0094] In the formula, This represents the sub-wavelength spectrum of the elastic wave source. This represents the spectrum of the structural response signal.

[0095] like Figure 5 As shown, the spectrum of the synthesized elastic wave impact echo signal clearly shows the characteristic frequency peaks that can still be identified in the background of noise, which is convenient for subsequent judgment of structural thickness or defects.

[0096] Through the above steps, the synthesized spectrum of this invention is a parameterized and transparent model. If a difference is found between the synthesized spectrum and the measured spectrum in a certain frequency band, we can adjust the amplitude, half-width, or even the dominant frequency of the corresponding Gaussian component to better understand the cause of this difference. By accurately modeling and synthesizing the vibration source, reflection response, and noise components using Gaussian functions, the effective construction of the spectrum of elastic wave impact echo signals and the prominent display of characteristic frequencies are achieved in complex noise environments. Ultimately, this enables accurate and reliable non-destructive testing of concrete structures under complex conditions, significantly improving the accuracy and reliability of characteristic frequency identification in concrete structure testing.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for synthesizing a spectrum of elastic wave impact echo signals based on Gaussian functions, characterized in that, Includes the following steps: S1. Based on the excitation mode of the shock elastic wave source, select the source wavelet form and perform Fourier transform on the source wavelet to obtain the elastic wave source wavelet spectrum. S2. Based on the reflective interface form of the concrete structure, determine the dominant frequency of the longitudinal wave reflection response signal spectrum and the dominant frequency of the transverse wave reflection response signal spectrum. S3. Based on the spectral amplitude and half-width of the longitudinal wave reflection response signal, and the spectral amplitude and half-width of the transverse wave reflection response signal, construct Gaussian function models for the longitudinal wave and transverse wave reflection response signals, respectively. S4. Based on the Gaussian function model and the main frequencies of the spectrum of the longitudinal and transverse wave reflection response signals, calculate the Gaussian function forms of the spectral components of the longitudinal and transverse wave reflection response signals, respectively. S5. Superimpose the Gaussian functions of the spectral components of the longitudinal and transverse wave reflection response signals to synthesize the spectrum of the reflection response signal; S6. Obtain the dominant frequency of the noise response signal spectrum, as well as the amplitude and half-width of the noise response signal spectrum; S7. Based on the amplitude and half-width of the noise response signal spectrum, construct a Gaussian function model of the noise response signal, and calculate the Gaussian function form of the spectral components of the noise response signal according to the Gaussian function model of the noise response signal and the dominant frequency of the noise response signal spectrum. S8. Superimpose the Gaussian functions of all noise response signal spectral components to synthesize the noise response signal spectrum; S9. Based on the reflection response signal spectrum, the noise response signal spectrum, and the elastic wave source wavelet spectrum, synthesize the elastic wave impact echo signal spectrum for identifying the characteristic frequency of the concrete structure. In step S3, the process of constructing the Gaussian function model of the longitudinal and transverse wave reflection response signals includes: Step S3.1: Based on the half-width of the spectrum of the longitudinal wave reflection response signal and the half-width of the spectrum of the transverse wave reflection response signal, calculate the corresponding Gaussian function frequency coefficients respectively. Step S3.2: Based on the frequency coefficients of the Gaussian function and the amplitude of the spectrum of the longitudinal wave reflection response signal or the amplitude of the spectrum of the transverse wave reflection response signal, construct a basic Gaussian function model; In step S4, the process of calculating the Gaussian function form of the spectral components of the longitudinal and transverse wave reflection response signals is as follows: The Gaussian function models of the longitudinal and transverse wave reflection response signals are combined with the dominant frequencies of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum, respectively, to generate Gaussian function forms for each spectral component; wherein... The Gaussian function form of the spectral components of the longitudinal wave reflection response signal is: The Gaussian function form of the spectral components of the transverse wave reflection response signal is: wherein, , and represent the amplitude, dominant frequency and half-width of the spectrum of the i-th longitudinal wave reflection response signal, respectively; , and represent the amplitude, dominant frequency and half-width of the spectrum of the j-th transverse wave reflection response signal, respectively; In step S9, the synthesis of the elastic wave impact echo signal spectrum for identifying the characteristic frequency of the concrete structure involves: superimposing the reflection response signal spectrum with the noise response signal spectrum to obtain the structural response signal spectrum; and multiplying the structural response signal spectrum with the elastic wave source wavelet spectrum to obtain the final elastic wave impact echo signal spectrum.

2. The method according to claim 1, wherein, In step S2, determining the dominant frequencies of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum based on the reflective interface form of the concrete structure includes: S2.1, if both reflection interfaces of the elastic wave impact echo are free boundaries, the dominant frequency of the longitudinal wave reflection response signal spectrum is , and the dominant frequency of the transverse wave reflection response signal spectrum is ; S2.2, if two reflection interfaces of the elastic wave impact echo are one free boundary and one fixed boundary, the main frequency of the longitudinal wave reflection response signal spectrum is ; and the main frequency of the transverse wave reflection response signal spectrum is ; wherein is the longitudinal wave velocity of the elastic wave, is the transverse wave velocity of the elastic wave, and L is the thickness of the reflector.

3. The method of claim 1, wherein the method is characterized by: The Gaussian function form of the noise response signal spectrum component is: wherein , and represent the amplitude, dominant frequency and half-width of the kth noise response signal spectrum, respectively.

4. The method of claim 1, wherein, The elastic wave impact echo signal spectrum is calculated by the following formula: wherein represents the elastic wave source wavelet spectrum, represents the structure response signal spectrum.

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