Elastic wave impact echo signal frequency spectrum synthesis method based on Gaussian function

Abstract

The invention provides an elastic wave impact echo signal frequency spectrum synthesis method based on a Gaussian function, and the method comprises the steps: determining a vibration source wavelet frequency spectrum according to an excitation mode, respectively determining main frequencies, amplitudes and half widths of longitudinal wave and transverse wave reflection response signals for a concrete structure, and constructing a corresponding Gaussian function model according to the main frequencies, amplitudes and half widths; calculating spectrum components, superposing and synthesizing a reflection response signal spectrum, simultaneously carrying out Gaussian modeling and spectrum synthesis on the noise signal, and finally combining the reflection response signal spectrum, the noise response signal spectrum and a vibration source wavelet spectrum to obtain a vibration source wavelet spectrum. And synthesizing a complete elastic wave impact echo signal frequency spectrum which can be used for identifying the internal characteristic frequency of the concrete structure. The method provided by the invention aims to improve the recognition capability of the characteristic frequency and the reliability of the detection result under the complex noise background through accurate modeling of the vibration source characteristics, the structure reflection response and the noise components.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of concrete structure detection, and particularly relates to a method for synthesizing elastic wave impact echo signal spectrum based on a Gaussian function. BACKGROUND

[0002] In the nondestructive testing of concrete structures, the elastic wave impact echo method is an important means. Its principle is that when elastic waves encounter wave impedance difference interfaces (such as defects or structural boundaries) during propagation, reflections are generated. Through spectral analysis of the echo signal, characteristic frequencies related to the structure state can be extracted. For example, the thickness of a concrete plate can be calculated based on the spectral fundamental frequency, and the presence of internal defects can be determined by comparing the fundamental frequency variations at different measurement points.

[0003] However, in actual engineering applications, the effectiveness and reliability of this method still face significant challenges. First, the non-uniformity of concrete causes the reflection of multiple waveforms such as longitudinal waves and transverse waves, which are superimposed on the spectrum, making it difficult to identify the characteristic peaks representing structural information. At the same time, various disturbances in the field test environment, such as internal steel bar scattering, environmental vibrations, and instrument electronic noise, further exacerbate spectral mixing, making it difficult to accurately identify and extract characteristic frequencies representing structural thickness or defects.

[0004] In summary, existing spectral synthesis methods are often oversimplified and do not comprehensively consider the scattering mechanisms of source characteristics, multiple waveforms within the structure, and noise, making it difficult to provide effective frequency range and distribution guidance for feature frequency identification. Therefore, there is an urgent need to develop a method that can clearly and controllably synthesize and highlight effective characteristic frequencies in a complex noise background, to improve the identification accuracy of characteristic frequencies in impact echo signals and the reliability of detection results. SUMMARY

[0005] To address the deficiencies in the prior art, the present application provides a method for synthesizing elastic wave impact echo signal spectrum based on a Gaussian function, aiming to improve the identification ability of characteristic frequencies in a complex noise background and the reliability of detection results by accurately modeling the source characteristics, structural reflection response, and noise components.

[0006] According to an embodiment of the present application, a method for synthesizing elastic wave impact echo signal spectrum based on a Gaussian function includes the following steps: S1. Selecting a source wavelet form according to the impact elastic wave source excitation mode, and performing Fourier transform on the source wavelet to obtain the elastic wave source wavelet spectrum; S2. Determining the main frequency of the longitudinal wave reflection response signal spectrum and the main frequency of the transverse wave reflection response signal spectrum based on the form of the concrete structure reflection interface; S3, constructing a Gaussian function model of the longitudinal wave and the transverse wave reflection response signals respectively based on the amplitude and half-width of the longitudinal wave reflection response signal spectrum and the amplitude and half-width of the transverse wave reflection response signal spectrum; S4, calculating the Gaussian function form of the spectrum components of the longitudinal wave and the transverse wave reflection response signals respectively according to the Gaussian function model and the main frequency of the spectrum of the longitudinal wave and the transverse wave reflection response signals; S5, superimposing the Gaussian functions of the spectrum components of the longitudinal wave and the transverse wave reflection response signals to synthesize the spectrum of the reflection response signals; S6, obtaining the main frequency of the spectrum of the noise response signals, and the amplitude and half-width of the spectrum of the noise response signals; S7, constructing a Gaussian function model of the noise response signals based on the amplitude and half-width of the spectrum of the noise response signals, and calculating the Gaussian function form of the spectrum components of the noise response signals according to the Gaussian function model of the noise response signals and the main frequency of the spectrum of the noise response signals; S8, superimposing the Gaussian functions of all the spectrum components of the noise response signals to synthesize the spectrum of the noise response signals; S9, synthesizing the spectrum of the elastic wave impact echo signals for identifying the characteristic frequency of the concrete structure based on the spectrum of the reflection response signals, the spectrum of the noise response signals and the spectrum of the elastic wave source wavelet.

[0007] Further, in step S2, the determination of the main frequency of the spectrum of the longitudinal wave reflection response signals and the main frequency of the spectrum of the transverse wave reflection response signals based on the form of the reflection interface of the concrete structure comprises: S2.1, if both the reflection interfaces of the elastic wave impact echo are free boundaries, the main frequency of the spectrum of the longitudinal wave reflection response signals is , and the main frequency of the spectrum of the transverse wave reflection response signals is ; S2.2, if one of the reflection interfaces of the elastic wave impact echo is a free boundary and the other is a fixed boundary, the main frequency of the spectrum of the longitudinal wave reflection response signals is , and the main frequency of the spectrum of the transverse wave reflection response signals is ; In the formula, 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 reflection layer.

[0008] Further, in step S3, the process of constructing the Gaussian function model of the longitudinal wave and the transverse wave reflection response signals comprises: Step S3.1, calculating the Gaussian function frequency coefficients of the spectrum of the longitudinal wave reflection response signals and the spectrum of the transverse wave reflection response signals respectively based on the half-width of the spectrum of the longitudinal wave reflection response signals and the half-width of the spectrum of the transverse wave reflection response signals; Step S3.2, constructing a Gaussian function model based on the Gaussian function frequency coefficient and the amplitude of the longitudinal wave reflection response signal spectrum or the amplitude of the transverse wave reflection response signal spectrum.

[0009] Further, in step S4, the process of calculating the Gaussian function form of the longitudinal wave and transverse wave reflection response signal spectrum components is as follows: The Gaussian function model of the longitudinal wave and transverse wave reflection response signal is combined with the main frequency of the longitudinal wave reflection response signal spectrum and the main frequency of the transverse wave reflection response signal spectrum, respectively, to generate the Gaussian function form of each spectrum component; wherein, The Gaussian function form of the longitudinal wave reflection response signal spectrum component is: ; The Gaussian function form of the transverse wave reflection response signal spectrum component is: ; In the formula, , and respectively represent the amplitude, main frequency and half-width of the i-th longitudinal wave reflection response signal spectrum; , and respectively represent the amplitude, main frequency and half-width of the j-th transverse wave reflection response signal spectrum.

[0010] Further, the Gaussian function form of the noise response signal spectrum component is: ; In the formula, , and respectively represent the amplitude, main frequency and half-width of the k-th noise response signal spectrum.

[0011] Further, in step S9, the elastic wave impact echo signal spectrum for identifying the characteristic frequency of the concrete structure is synthesized: the reflection response signal spectrum is superimposed with the noise response signal spectrum to obtain a structure response signal spectrum; and the structure response signal spectrum is multiplied with the elastic wave source wavelet spectrum to obtain the final elastic wave impact echo signal spectrum.

[0012] Further, the elastic wave impact echo signal spectrum is calculated by the following formula: ; In the formula, represents the elastic wave source wavelet spectrum, represents the structure response signal spectrum.

[0013] Compared with the prior art, the present application has the following beneficial effects: The present application realizes deep analysis and controllable synthesis of spectrum composition by decomposing complex measured signal spectrum into multiple spectrum components with clear physical meaning, including longitudinal wave reflection, transverse wave reflection and noise component, and accurately modeling each component based on Gaussian function. The method converts the ambiguous and mixed spectrum characteristics in traditional analysis into a series of quantifiable and independently adjustable parameters, significantly improving the understanding ability and explanation effectiveness of the internal structure and formation mechanism of the spectrum.

[0014] The present application also realizes effective separation of structure reflection effective signal and environmental or system noise at the spectrum level by establishing a Gaussian function model of noise response signal. In the spectrum synthesis or subsequent analysis process, the effective signal component can be selectively enhanced and noise interference can be suppressed, so that the characteristic frequency representing the structure thickness or internal defect can still be clearly and accurately identified in a strong noise background. The reliability, repeatability and overall identification accuracy of the impact echo detection method are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 A step flow chart of an elastic wave impact echo signal spectrum synthesis method based on Gaussian function provided for an embodiment of the present application; Figure 2 An elastic wave source wavelet Ricker wavelet spectrum provided for an embodiment of the present application; Figure 3 A synthesized longitudinal wave and transverse wave reflection response signal spectrum provided for an embodiment of the present application; Figure 4 A noise response spectrum provided for an embodiment of the present application; Figure 5 A synthesized elastic wave impact echo signal spectrum provided for an embodiment of the present application. DETAILED DESCRIPTION

[0016] The technical solutions in the present application will be further described below in combination with the drawings and embodiments.

[0017] As described in the above background, the elastic wave impact echo method faces the problems of complex spectrum, strong noise interference and difficulty in extracting characteristic frequency in concrete structure detection. The traditional method is insufficient in modeling the source characteristics, multi-mode wave reflection and noise mechanism, resulting in significant difference between the synthesized spectrum and the measured signal, and unable to effectively guide the identification of characteristic frequency.

[0018] The present embodiment proposes an elastic wave impact echo signal spectrum synthesis method based on Gaussian function, which establishes a parameterized Gaussian model for the source, structure response and noise respectively, realizes controllable synthesis and effective separation of spectrum components, and significantly improves the identifiable of characteristic frequency in strong noise background.

[0019] AsFigure 1 As shown in the figure, a method for synthesizing the spectrum of elastic wave impact echo signals based on Gaussian functions includes the following steps: S1. According to the excitation mode of the elastic wave vibration source, the form of the vibration source wavelet is selected, and Fourier transform is performed on the vibration source wavelet to obtain the spectrum of the elastic wave vibration source wavelet; S2. Based on the form of the reflection interface of the concrete structure, the main frequency of the longitudinal wave reflection response signal spectrum and the main frequency of the transverse wave reflection response signal spectrum are determined; S3. Based on the amplitude and half-width of the longitudinal wave reflection response signal spectrum and the amplitude and half-width of the transverse wave reflection response signal spectrum, Gaussian function models of the longitudinal wave and transverse wave reflection response signals are respectively constructed; S4. According to the Gaussian function models and the main frequencies of the longitudinal wave and transverse wave reflection response signal spectra, the Gaussian function forms of the longitudinal wave and transverse wave reflection response signal spectrum components are respectively calculated; S5. The Gaussian functions of the longitudinal wave and transverse wave reflection response signal spectrum components are superimposed to synthesize the reflection response signal spectrum; S6. The main frequency of the noise response signal spectrum, and the amplitude and half-width of the noise response signal spectrum are obtained; S7. Based on the amplitude and half-width of the noise response signal spectrum, a Gaussian function model of the noise response signal is constructed, and according to the Gaussian function model of the noise response signal and the main frequency of the noise response signal spectrum, the Gaussian function form of the noise response signal spectrum component is calculated; S8. The Gaussian functions of all noise response signal spectrum components are superimposed to synthesize the noise response signal spectrum; S9. Based on the reflection response signal spectrum, the noise response signal spectrum, and the elastic wave vibration source wavelet spectrum, the spectrum of the elastic wave impact echo signal for identifying the characteristic frequency of the concrete structure is synthesized.

[0020] As shown in the figure, Figure 2 , Figure 2 is the spectrum of the Ricker wavelet as the vibration source wavelet form x(t). In this embodiment, the Ricker wavelet widely used in nondestructive testing is selected as the vibration source model, and Fourier transform is performed on the Ricker wavelet as the vibration source wavelet form x(t) to obtain the spectrum of the elastic wave vibration source wavelet : , wherein, represents the main frequency parameter of the Ricker wavelet.

[0021] According to the form of the reflection interface of the concrete structure, the main frequencies of the longitudinal wave and transverse wave reflection response signals are determined. Assuming that for a concrete plate with a thickness of L and two free boundary interfaces: the main frequency of the longitudinal wave reflection response signal spectrum is: , the main frequency of the spectrum of the reflected signal of the transverse wave is: , where n and m represent the number of reflected signals of the longitudinal wave and the transverse wave respectively.

[0022] In this embodiment, we select the main frequencies of the spectrum of two reflected signals of the longitudinal wave and two reflected signals of the transverse wave for analysis: The main frequency of the reflected signal of the longitudinal wave is: ; The main frequency of the reflected signal of the transverse wave is: ; In the formula, vp and vs represent the wave velocities of the longitudinal wave and the transverse wave respectively, and L represents the thickness of the reflected layer.

[0023] If one section of the two reflected interfaces of the elastic wave impact echo is a free boundary and the other section is a fixed boundary: The main frequency of the spectrum of the reflected signal of the longitudinal wave is: ; The main frequency of the spectrum of the reflected signal of the transverse wave is: ; 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 spectrum form of the reflected signal.

[0024] For each main frequency and , the corresponding amplitude A and half-width Hf are selected. The amplitude reflects the reflection intensity, and the half-width reflects the degree of wave attenuation. Specifically, the amplitude and the half-width of the spectrum of the reflected signal of the longitudinal wave are selected, and the amplitude and the half-width of the spectrum of the reflected signal of the transverse wave are selected.

[0025] Construct the Gaussian function model of the reflected signal , , the longitudinal wave, , and for the transverse wave, ; where is the frequency coefficient of the Gaussian function, , for the longitudinal wave, , and for the transverse wave, .

[0026] Combine the Gaussian function model of the reflected signal with the main frequency to generate each spectral component: Construct the Gaussian function Epi(ω) of the spectral component of the reflected signal of the longitudinal wave: ; Construct the Gaussian function Esj(ω) of the spectral component of the reflected signal of the transverse wave: ; The Gaussian functions of the spectral components of all longitudinal and transverse waves are superimposed to synthesize the total reflection response signal spectrum. , ; 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.

[0027] 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.

[0028] 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.

[0029] Construct a Gaussian function model for the noise response signal: ; 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. : Constructing the spectral components of the noise response signal Gaussian function : ; Gaussian function of all noise response spectral components Superimpose the signals to synthesize the noise response signal spectrum. : ; 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.

[0030] 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).

[0031] Specifically, the spectrum of the reflection response signal and noise response signal spectrum Adding them together yields the complete structural response spectrum. , ; Then, the source spectrum of the elastic wave source sub-wavelength is... and structural response signal spectrum multiplication, the elastic wave impact echo signal spectrum for identifying the characteristic frequency of the concrete structure is obtained: ; In the formula, represents the elastic wave source wavelet spectrum, represents the structural response signal spectrum.

[0032] As Figure 5 shown, the synthetic elastic wave impact echo signal spectrum diagram clearly shows the characteristic frequency peak value that can be identified under the noise background, facilitating the subsequent judgment of the structure thickness or defects.

[0033] Through the above steps, the spectrum synthesized by the present application is a parameterized and transparent model. If it is found that the synthesized spectrum and the measured spectrum have differences in a certain frequency band, we can go back to adjust the amplitude, half-width and even the main frequency of the corresponding Gaussian component, so as to better understand the reason for the difference. Through the accurate modeling and synthesis of the source, reflection response and noise components by the Gaussian function, the effective construction of the elastic wave impact echo signal spectrum and the highlighting of the characteristic frequency under complex noise environment are realized, and finally the precise and reliable nondestructive testing of the concrete structure state under complex working conditions is realized, which significantly improves the identification accuracy and reliability of the characteristic frequency in the concrete structure detection.

[0034] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced by equivalents without departing from the purpose and scope of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A method for synthesizing a spectrum of elastic wave impact echo signals based on Gaussian functions, characterized in that, The method comprises the following steps: S1, selecting a subwave form of a vibration source according to an impact elastic wave vibration source excitation mode, and performing Fourier transform on the subwave to obtain a subwave spectrum of the elastic wave vibration source; S2, determining a main frequency of a longitudinal wave reflection response signal spectrum and a main frequency of a transverse wave reflection response signal spectrum based on a form of a reflection interface of the concrete structure; S3, constructing a Gaussian function model of the longitudinal wave and the transverse wave reflection response signals based on a spectrum amplitude and a half-width of the longitudinal wave reflection response signal spectrum and a spectrum amplitude and a half-width of the transverse wave reflection response signal spectrum; S4, calculating a Gaussian function form of a spectrum component of the longitudinal wave and the transverse wave reflection response signals respectively according to the Gaussian function model and the main frequencies of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum; S5, superimposing the Gaussian functions of the spectrum components of the longitudinal wave and the transverse wave reflection response signals to synthesize a reflection response signal spectrum; S6, obtaining a main frequency of a noise response signal spectrum, a spectrum amplitude and a half-width of the noise response signal spectrum; S7, constructing a Gaussian function model of the noise response signal based on the spectrum amplitude and the half-width of the noise response signal spectrum, and calculating a Gaussian function form of a spectrum component of the noise response signal according to the Gaussian function model of the noise response signal and the main frequency of the noise response signal spectrum; S8, superimposing the Gaussian functions of all the spectrum components of the noise response signal to synthesize a noise response signal spectrum; S9, synthesizing an elastic wave impact echo signal spectrum for identifying a characteristic frequency of the concrete structure based on the reflection response signal spectrum, the noise response signal spectrum and the subwave spectrum of the elastic wave vibration source.

2. The method according to claim 1, wherein, In step S2, the determination of the main frequency of the longitudinal wave reflection response signal spectrum and the main frequency of the transverse wave reflection response signal spectrum based on the form of the reflection interface of the concrete structure comprises: 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 Gaussian function is defined as: ###0001### where x is the frequency of the elastic wave impact echo signal, and a, b, and c are constants. In step S3, the process of constructing the Gaussian function model of the longitudinal wave and the transverse wave reflection response signals comprises: Step S3.1, calculating Gaussian function frequency coefficients of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum respectively based on the half-widths of the two; Step S3.2, constructing a basic Gaussian function model based on the Gaussian function frequency coefficients and the spectrum amplitudes of the longitudinal wave reflection response signal spectrum and the transverse wave reflection response signal spectrum.

4. The method according to claim 3, wherein, In step S4, the process of calculating the Gaussian function form of the spectrum component of the longitudinal wave and the transverse wave reflection response signals comprises: combining the Gaussian function models of the longitudinal wave and the transverse wave reflection response signals respectively with the main frequency of the longitudinal wave reflection response signal spectrum and the main frequency of the transverse wave reflection response signal spectrum to generate the Gaussian function form of each spectrum component; wherein, the Gaussian function form of the spectrum component of the longitudinal wave reflection response signal is ； the Gaussian function form of the spectrum component 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.

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

6. The method of claim 1, wherein, In step S9, the elastic wave impact echo signal spectrum for identifying the characteristic frequencies of the concrete structure is synthesized: the reflected response signal spectrum is superimposed with the noise response signal spectrum to obtain a structure response signal spectrum; the structure response signal spectrum is multiplied with the elastic wave vibration source wavelet spectrum to obtain the final elastic wave impact echo signal spectrum.

7. The method of claim 6, 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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