CN114898278B - Non-contact rockfall protection dynamic response signal automatic identification and feedback method - Google Patents

Abstract

The present invention relates to the technical field of slope rockfall disaster protection, and relates to a non-contact rockfall protection dynamic response signal automatic identification and feedback method, which includes the following steps: step (1): camera location arrangement and high-speed video recording during the impact process; step ( 2): Calculation and calibration of the pixel-distance scale factor; Step (3): Automatic recognition of rockfall impact trajectory; Step (4): Time domain noisy signal frequency domain analysis and its energy distribution; Step (5): Gaussian function and Gaussian wavelet family selection; step (6): signal pseudo-frequency determination and scale parameter selection; step (7): convolution operation of time-domain noisy signal and Gaussian wavelet; step (8): rockfall movement displacement, velocity, acceleration signal Feedback and its consistency check. The invention realizes the automatic identification and real-time feedback of the non-contact rockfall protection dynamic response signal.

Description

Non-contact rockfall protection dynamic response signal automatic identification and feedback method

technical field

The invention relates to the technical field of slope rockfall disaster protection, in particular to a non-contact rockfall protection dynamic response signal automatic identification and feedback method.

Background technique

The flexible protective net is a strong nonlinear structure commonly used for protection against landslides and rockfalls, and it is prone to continuous impacts from falling rocks during work. Under a certain impact energy, there will be multiple collisions and rebound processes between the falling rock and the intercepting mesh, and finally stabilize on the flexible mesh surface. When falling rocks interact with the protective net, the deformation of the protective net, protection energy level, impact load and other information can be indirectly obtained by monitoring the movement state of the falling rock in real time, providing key data support for the impact resistance performance evaluation and engineering design of the protective net system. However, the physical characteristics and structural response of the protective net are constantly changing under continuous impact, and the rockfall motion signal is a nonlinear and unsteady transient pulse signal. When traditional contact wired equipment is used to measure the dynamic response signal of rockfall protection, equipment damage and signal instability are prone to occur. In particular, under the condition of noise interference, it is very difficult to realize automatic feedback and information feedback of rockfall motion data signals.

Contents of the invention

The content of the present invention is to provide a non-contact rockfall protection dynamic response signal automatic identification and feedback method based on wavelet transform, which can overcome some or some defects of the prior art.

According to the non-contact rockfall protection dynamic response signal automatic identification and feedback method of the present invention, it comprises the following steps:

Step (1): Camera placement and high-speed video recording during the impact process;

Step (2): Calculation and calibration of pixel-distance scale factor;

Step (3): automatic recognition of rockfall impact trajectory;

Step (4): frequency domain analysis and energy distribution of noisy signal in time domain;

Step (5): Gaussian function and Gaussian wavelet family selection;

Step (6): signal pseudo-frequency determination and scale parameter selection;

Step (7): the convolution operation of the noise-containing signal in the time domain and the Gaussian wavelet;

Step (8): Feedback of rockfall movement displacement, velocity, acceleration signal and its self-consistency check.

As a preference, in step (1), set up 2 high-speed cameras according to the installation position of the flexible protective net, because different distances and different angle requirements are satisfied between the camera position and the recording target; the frame rate of the camera is set, and the whole process of impact is recorded; The minimum frame rate of the camera should meet the requirements of the sampling theorem, and the maximum frame rate should ensure that the recording time can be greater than or equal to the duration of the entire impact process.

As preferably, in step (2), select different target objects in the high-speed video picture, measure the actual characteristic length of each target object respectively; The one-to-one correspondence between the lengths computes the pixel-distance scale factor.

Preferably, in step (3), mark the rockfall outline in the video picture, and select the feature points captured by the rockfall motion by adjusting the picture contrast and brightness; in the whole process of impact, it should be ensured that the rockfall feature points are not completely blocked; combined with motion analysis technology Realize the automatic capture of rockfall feature points and automatic recognition of rockfall trajectory; through the pixel-distance scale factor calculated in step (2), the captured pixel points of rockfall motion process are converted into rockfall displacement time domain signal f _M [t _n ] , where n=1,2,...,N.

Preferably, in step (4), discrete Fourier transform is performed on the rockfall displacement time-domain signal f _M [t _n ] obtained in step (3), to obtain the Fourier transform result F(ω _k ) of the rockfall motion signal :

where ω _k is the frequency value of the signal; according to the discrete Fourier transform result of the rockfall displacement time domain signal, the frequency domain energy E _freq of the signal can be further obtained:

The signal frequency bands with energy ratio of 0-90% and energy ratio of 0-99% are recorded, and the frequencies of the energy bands are denoted as ω ₉₀ and ω ₉₉ .

As preferably, in step (5), the Gaussian function is one of the most important functions in the application of probability statistics and random signal analysis, and the expression of the Gaussian function g(t) is:

仍然为高斯函数：Among them, C and α are constants; the Fourier transform of the Gaussian function

Still Gaussian:

The Gaussian function has a smooth infinite order derivative, and the n-order derivative of the Gaussian function has the characteristics of wavelet function oscillation and limited energy. Through the n-order differential operation of the Gaussian function, n Gaussian mother wavelets can be generated:

A series of wavelet functions can be obtained by stretching and translating the wavelet function g _n (t), which is called the wavelet function family:

Among them, g _u,s (t) is called the Gaussian wavelet function family, s is called the scale parameter, and u is called the translation parameter.

Preferably, in step (6), the wavelet scale parameter is not equal to the Fourier frequency that is easier to understand in engineering; the signal frequency domain feature corresponding to the wavelet scale parameter s is represented by a pseudo-frequency f _s , and the scale parameter and pseudo-frequency The corresponding relationship can be converted by the following formula:

Where Δt=1/f _samp is the sampling time interval of the time domain signal, f _samp is the sampling frequency, f _c =ω _c /2π is the center frequency of the wavelet, for the time domain impact signal, more attention is paid to the frequency components greater than zero, and the selected After the mother wavelet function g _n (t) is adopted in the wavelet transform, the mother wavelet time center t _c and angular frequency center ω _c can be calculated by the following formula:

As preferably, in step (7), convolution operation is performed on the rockfall displacement signal obtained in step (2) and the Gaussian wavelet selected in step (5), to obtain the Gaussian wavelet transform result GWT(u, s):

为g(t)的复共轭；根据卷积运算的微分性质，高斯小波变换最终可以写为以下形式：in

is the complex conjugate of g(t); according to the differential nature of the convolution operation, the Gaussian wavelet transform can finally be written as the following form:

The above formula shows that the expression of choosing Gaussian wavelet for wavelet transform explicitly includes differential operation d ⁿ /du ⁿ and convolution operation f(u)*g _s (u); is the zero property, the convolution operation is interpreted as the weighted average smoothing process of the function f in the kernel function g _s (u), different orders of Gaussian wavelets correspond to different order differential calculations for the original noisy signal; through wavelet transform, at the same time Realize the smoothing of the noisy vibration signal f and its nth order differential on the scale s.

As a preference, in step (8), for the actual time-domain vibration signal, the wavelet transform differential result needs to ensure the accuracy of the differential result amplitude in addition to the accuracy of the curve shape and the peak and valley positions; from step (7), it is found that , the amplitude of the wavelet differential result is related to the s ⁿ of the wavelet scale parameter, and the normalization of the wavelet function family will also affect the amplitude result of the differential operation; in order to eliminate the influence of the Gaussian wavelet transform process on the differential result amplitude, the amplitude The parameter A _mp defines the wavelet differential operation of the noisy signal as:

The numerical differentiation process will amplify the influence of noise interference in the signal, and in reverse, the numerical integration process will inhibit the noise interference in the original signal; The degree of coincidence can be used to measure the accuracy of the wavelet differential results. The higher the degree of coincidence between the integral result and the original signal, the more accurate and reliable the result after differentiation can be. Since the two time series before and after wavelet transformation have the same Euclidean distance is used to evaluate the coincidence degree between the noisy signal and the integral result of wavelet approximate differentiation. The Euclidean distance is calculated as follows:

为小波变换n阶微分结果

的数值积分，t_k为求积节点，A_k为求积系数，亦称伴随节点t_k的权；当n＝0时，

为含噪信号

与高斯函数g₀(t)的卷积平滑结果；Where j represents the equidistant sampling of the wavelet differential results of the original time domain signal, m is the number of discrete points of the sampled signal, and n is the wavelet differential order;

is the nth order differential result of wavelet transform

, t _k is the product node, A _k is the product coefficient, also known as the weight of the accompanying node t _k ; when n=0,

is a noisy signal

Convolution smoothing result with Gaussian function g ₀ (t);

The value of the amplitude parameter A _mp can be obtained by iterative solution. When the Euclidean distance between the first integral of the n-order wavelet differential and the n-1 order wavelet differential reaches the minimum value ED _min , that is, when the coincidence degree of the curves is the highest, the amplitude Finally, the rockfall impact displacement signal is fed back through the convolution operation of the noisy signal and the Gaussian function; the rockfall impact velocity signal is fed back through the noise signal and the first-order Gaussian wavelet convolution operation; the noise-containing signal and the second-order Gaussian The wavelet convolution operation feeds back the rockfall impact acceleration signal.

The signal processing method based on Gaussian wavelet transform of the present invention can be applied to rockfall movement analysis. This method can realize the automatic recognition and automatic capture of impact rockfall in high-speed video. Taking advantage of the characteristic of Gaussian function having infinite order smooth derivative, Gaussian wavelet is used to carry out wavelet transform on rockfall capture signal, which can realize arbitrary order approximate differential calculation of noisy signal, and the order of derivative depends on the nature of wavelet function. The wavelet method effectively solves the problem of high sensitivity to noise interference in the differential information feedback process of rockfall capture signals. The Gaussian wavelet transform is equivalent to the process of smoothing and deriving the signal convolution. Through a convolution operation, the differential result of the noisy rockfall displacement signal can be fed back, and the rockfall velocity and acceleration time history close to the real one can be obtained, realizing non-contact rockfall Automatic identification and real-time feedback of protection dynamic response signals.

Description of drawings

Fig. 1 is the flow chart of a kind of non-contact rockfall protection dynamic response signal automatic identification and feedback method based on wavelet transform in embodiment 1;

Fig. 2 is the schematic diagram of high-speed camera layout and rockfall motion capture in embodiment 1;

Fig. 3 is Gaussian function, first-order Gaussian wavelet, second-order Gaussian wavelet schematic diagram in embodiment 1;

Fig. 4 is the time domain signal and its frequency domain distribution schematic diagram of rockfall motion capture in embodiment 1;

Fig. 5 is the iterative flowchart of Gaussian wavelet transform magnitude parameter in embodiment 1;

Fig. 6 is a graph showing the feedback results of rockfall motion displacement, velocity, and acceleration signals in Embodiment 1.

Among them, 1. Rockfall, 2. Rockfall impact plane, 3. Ruler, 4. No. 1 high-speed camera, 5. No. 2 high-speed camera, 6. Gaussian function, 7. First-order Gaussian wavelet, 8. Second-order Gaussian wavelet, 9 , Rockfall displacement capture signal, 10. Frequency domain distribution of rockfall displacement signal, 11. Frequency domain energy distribution of rockfall displacement signal, 12. Rockfall displacement fed back by wavelet method, 13. Rockfall speed fed back by wavelet method, 14. Rockfall feedback fed by wavelet method acceleration.

detailed description

In order to further understand the content of the present invention, the present invention will be described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the examples are only for explaining the present invention and not for limiting it.

Example 1

As shown in Figures 1-6, this embodiment provides a non-contact rockfall protection dynamic response signal automatic identification and feedback method based on wavelet transform:

1: Camera placement and high-speed video recording of the impact process

Set up two high-speed cameras according to the range of the impact trajectory of the rockfall 1, wherein the recording direction of the No. 1 high-speed camera 4 is perpendicular to the impact plane 2 of the rockfall, and the distance is d1 _; the recording direction of the No. 2 high-speed camera 5 is parallel to the impact plane 2 of the rockfall , the distance is d ₂ . The frame rate of the two cameras is f _sample , recording the whole process of impact.

Two: Calculation and calibration of pixel-distance scale factor

Select the reference targets in the high-speed video screen as rockfall 1 and scale 3 in the impact plane, and measure the diameter l ₁ of rockfall 1 and the length of scale 3 as l ₂ . The number of pixels occupied by the diameter of the falling rock 1 in the recorded high-speed video is m ₁ , and the number of pixels occupied by the length of the scale 3 is m ₂ . Test different reference targets, and calculate the pixel-distance scale factor calculation value λ according to the correspondence between video picture pixels and feature lengths. When the following expression is satisfied, it is considered that the calibration value [λ] of the pixel scale factor is obtained.

Three: Automatic recognition of rockfall impact trajectory

Mark the outline of the rockfall in the video screen, and select the feature points captured by the motion capture of the rockfall by adjusting the contrast and brightness of the screen. During the whole process of impact, it should be ensured that the feature points of falling rocks are not completely blocked. Combined with motion analysis technology, the automatic capture of rockfall feature points and the automatic identification of rockfall motion trajectories are realized. Through the calibration value [λ] of the pixel-distance scale factor, the captured pixel points of the rockfall movement process are converted into the rockfall displacement time domain signal f _M [t _n ], where n is the number of recorded displacement data points, n=1,2,… , N.

Four: Time domain noise signal frequency domain analysis and its energy distribution

Discrete Fourier transform is performed on the rockfall displacement capture signal 9(f _M [t _n ]), and the frequency domain distribution 10 of the rockfall displacement signal is obtained as F(ω _k ):

Where ω _k is the frequency value of the signal. According to the discrete Fourier transform result of the rockfall displacement time domain signal, the frequency domain energy distribution of the rockfall displacement signal can be further obtained as E _freq :

The signal frequency bands with energy ratio of 0-90% and energy ratio of 0-99% are recorded, and the frequencies of the energy bands are denoted as ω ₉₀ and ω ₉₉ .

Five: Gaussian function and Gaussian wavelet family selection

The Gaussian wavelet is a family of functions generated by the infinite derivative of the Gaussian function6. The general expression of the Gaussian function g(t) can be written as:

仍然为高斯函数6：Among them, C and α are constants. Fourier transform of Gaussian function

Still for the Gaussian function 6:

The Gaussian function 6 has a smooth infinite derivative, and the n-order derivative of the Gaussian function 6 (n is a positive integer) has the characteristics of wavelet function oscillation and limited energy. Through the n-order differential operation of the Gaussian function 6, n Gaussian functions can be generated Mother wavelet:

A series of wavelet functions can be obtained by stretching and translating the wavelet function g _n (t), which is called the wavelet function family:

Among them, g _u,s (t) is called the Gaussian wavelet function family, s is called the scale parameter, and u is called the translation parameter.

When solving the smoothing result of the noisy time-domain shock signal, choose the Gaussian function 6; when solving the first-order derivative (velocity) of the noisy time-domain shock signal, choose the first-order Gaussian wavelet 7; when solving the noisy time-domain shock signal When the second-order derivative (acceleration) of , choose the second-order Gaussian wavelet8.

Six: Signal pseudo-frequency determination and scale parameter selection

The wavelet scale parameter is not equivalent to the Fourier frequency which is easier to understand in engineering. The frequency domain characteristics of the signal corresponding to the wavelet scale parameter s can be represented by the pseudo frequency f _s , and the corresponding relationship between the scale parameter and the pseudo frequency can be converted by the following formula:

Where Δt=1/f _samp is the sampling time interval of the time domain signal, f _samp is the sampling frequency, f _c ＝ω _c /2π is the wavelet center frequency, for the time domain impact signal, more attention should be paid to the frequency components greater than zero, and the selected After the mother wavelet function g _n (t) is adopted in the wavelet transform, the mother wavelet time center t _c and angular frequency center ω _c can be calculated by the following formula:

Seven: Convolution operation of noisy signal in time domain and Gaussian wavelet

Convolute the rockfall displacement signal with the Gaussian wavelet to obtain the Gaussian wavelet transform result GWT(u,s) of the noisy signal in the time domain:

为g(t)的复共轭。根据卷积运算的微分性质，高斯小波变换最终可以写为以下形式：in

is the complex conjugate of g(t). According to the differential nature of the convolution operation, the Gaussian wavelet transform can finally be written as the following form:

The expression of Gaussian wavelet transform explicitly includes differential operation d ⁿ / du ⁿ and convolution operation f(u)*g _s (u). Due to the non-zero property of the Gaussian function integral in the real number field, the convolution operation can be interpreted as a weighted average smoothing process of the function f in the kernel function g _s (u), and different orders of Gaussian wavelets correspond to different orders of the original noisy signal Numeral differential calculations. Through the wavelet transform, the smoothing of the noisy vibration signal f and its n-order differential on the scale s can be realized simultaneously.

Eight: Rockfall movement displacement, velocity, acceleration signal feedback and self-consistency inspection.

For the actual time-domain impact signal, the differential result of wavelet transform needs to ensure the accuracy of the amplitude of the differential result in addition to the accuracy of the shape of the curve and the position of the peak and valley. The magnitude of the wavelet differential result is related to the s ⁿ of the wavelet scale parameter, and the normalization of the wavelet function family will also affect the magnitude of the differential operation. In order to eliminate the influence of the Gaussian wavelet transform process on the amplitude of the differential result, the wavelet differential operation of the noisy signal is defined as:

Among them, A _mp is the amplitude parameter. The numerical differentiation process will amplify the influence of noise interference in the signal, and in reverse, the numerical integration process will inhibit the noise interference in the original signal. Therefore, by performing reverse integration on the wavelet differential result and comparing the degree of coincidence with the original signal, it can be used to measure the accuracy of the wavelet differential result. The higher the degree of coincidence between the integration result and the original signal, the differential can be considered The results are more accurate and reliable. Since the two time series before and after the wavelet transform have the same length, it is convenient to use the Euclidean distance to evaluate the degree of coincidence between the noisy signal and the integral result of the wavelet approximate differential. The Euclidean distance is calculated as follows

为小波变换n阶微分结果

的数值积分，t_k为求积节点，A_k为求积系数，亦称伴随节点t_k的权。特别地，当n＝0时，

为含噪信号

与高斯函数g₀(t)的卷积平滑结果。Where j represents the equidistant sampling of the wavelet differential results of the original time domain signal, m is the number of discrete points of the sampled signal, and n is the wavelet differential order.

is the nth order differential result of wavelet transform

The numerical integration of , t _k is the product node, and A _k is the product coefficient, also known as the weight of the accompanying node t _k . In particular, when n=0,

is a noisy signal

Convolution smoothing result with Gaussian function g ₀ (t).

The value of the amplitude parameter A _mp can be obtained by iterative solution, as shown in the flow chart 5, when the Euclidean distance between the first integral of the n-order wavelet differential and the n-1 order wavelet differential reaches the minimum value ED _min , that is, the curve When the degree of coincidence is the highest, the amplitude parameter A _mp gets the optimal value. Finally, the rockfall displacement 12 fed back by the wavelet method, the rockfall velocity 13 fed back by the wavelet method, and the rockfall acceleration 14 fed back by the wavelet method are respectively obtained.

In this embodiment, the Gaussian function has the property of infinite order smoothness and derivability, and the high-speed video capture signal of falling rocks is convolved with the Gaussian wavelet family, and the approximate differential process of wavelet transform and the principle of anti-noise interference are explained. Theoretical non-contact rockfall speed, acceleration information automatic identification and feedback program. The degree of matching between the signal processed by wavelet transform and the real signal is controlled by introducing the amplitude parameter. The wavelet scale parameters are calibrated according to the main frequency bands in which the signal energy distribution is captured in the time domain. The invented method effectively solves the problem of high sensitivity to noise interference in the differential information feedback process of the rockfall capture signal, improves the signal-to-noise ratio level of the impact signal, and avoids the use of traditional contact wired equipment for monitoring and recording the dynamic response of high-speed rockfall protection Signal instability and vulnerability problems.

The above schematically describes the present invention and its implementation, which is not restrictive, and what is shown in the drawings is only one of the implementations of the present invention, and the actual structure is not limited thereto. Therefore, if a person of ordinary skill in the art is inspired by it, without departing from the inventive concept of the present invention, without creatively designing a structural mode and embodiment similar to the technical solution, it shall all belong to the protection scope of the present invention .

Claims (6)

1. The non-contact rockfall protection dynamic response signal automatic identification and feedback method is characterized in that it includes the following steps: Step (1): Camera placement and high-speed video recording during the impact process; Step (2): Calculation and calibration of pixel-distance scale factor; In step (2), select different target objects in the high-speed video picture, and measure the actual characteristic length of each target object respectively; The one-to-one correspondence relationship calculates the pixel-distance scale factor; Step (3): automatic recognition of rockfall impact trajectory; Step (4): frequency domain analysis of rockfall displacement time domain signal and its energy distribution; Step (5): Gaussian function and Gaussian wavelet family selection; In step (5), the Gaussian function is one of the most important functions in the application of probability statistics and random signal analysis. The expression of the Gaussian function g(t) is:

Among them, C and α are constants; the Fourier transform of the Gaussian function

Still Gaussian:

The Gaussian function has a smooth infinite order derivative, and the n-order derivative of the Gaussian function has the characteristics of wavelet function oscillation and limited energy. Through the n-order differential operation of the Gaussian function, n Gaussian mother wavelets are generated:

A series of wavelet functions are obtained by stretching and translating the wavelet function g _n (t), which is called the wavelet function family:

Among them, g _u,s (t) is called the Gaussian wavelet function family, s is called the scale parameter, and u is called the translation parameter; Step (6): signal pseudo-frequency determination and scale parameter selection; In step (6), the wavelet scale parameter is not equal to the Fourier frequency which is easier to understand in engineering; the frequency domain characteristics of the signal corresponding to the wavelet scale parameter s are represented by a pseudo-frequency f _s , and the corresponding relationship between the scale parameter and the pseudo-frequency is given by The following conversion:

Where Δt=1/f _samp is the sampling time interval of the time domain signal, f _samp is the sampling frequency, f _c =ω _c /2π is the center frequency of the wavelet, for the time domain impact signal, more attention is paid to the frequency components greater than zero, and the selected After the mother wavelet function g _n (t) is adopted in the wavelet transform, the mother wavelet time center t _c and angular frequency center ω _c are calculated by the following formula:

Step (7): Convolution operation of rockfall displacement time domain signal and Gaussian wavelet; Step (8): Feedback of rockfall movement displacement, velocity, acceleration signal and its self-consistency check. 2. The non-contact rockfall protection dynamic response signal automatic identification and feedback method according to claim 1, characterized in that: in step (1), 2 high-speed cameras are set up according to the installation position of the flexible protective net, and the camera position and recording Due to different distances and different angles between targets; set the frame rate of the camera to record the whole impact process; the minimum frame rate of the camera should meet the requirements of the sampling theorem, and the maximum frame rate should ensure that the recording time can be greater than or equal to the duration of the entire impact process. 3. The non-contact rockfall protection dynamic response signal automatic identification and feedback method according to claim 1, characterized in that: in step (3), the rockfall contour is marked in the video picture, and the rockfall movement is selected by adjusting the picture contrast and brightness The captured feature points; in the whole process of impact, it should be ensured that the feature points of the rockfall are not completely blocked; combined with motion analysis technology, the automatic capture of the feature points of the rockfall and the automatic identification of the trajectory of the rockfall; through the pixels calculated in step (2)- The distance scale factor converts the captured pixel points in the rockfall movement process into the rockfall displacement time domain signal f _M [t _n ], where n=1,2,...,N. 4. The non-contact rockfall protection dynamic response signal automatic identification and feedback method according to claim 3, characterized in that: in step (4), the rockfall displacement time domain signal f _M [t _n ] to perform discrete Fourier transform to obtain the Fourier transform result F(ω _k ) of the rockfall displacement time domain signal:

Where ω _k is the frequency value of the signal; according to the discrete Fourier transform result of the rockfall displacement time domain signal, the frequency domain energy E _freq of the signal is further obtained:

The signal frequency bands with energy ratio of 0-90% and energy ratio of 0-99% are recorded, and the frequencies of the energy bands are denoted as ω ₉₀ and ω ₉₉ . 5. The non-contact rockfall protection dynamic response signal automatic identification and feedback method according to claim 1, characterized in that: in the step (7), the time domain signal of the rockfall displacement obtained in the step (2) is compared with the step (5 ) to perform convolution operation on the Gaussian wavelet selected in ), and obtain the Gaussian wavelet transform result GWT(u,s) of the rockfall displacement time domain signal:

in

is the complex conjugate of g(t); according to the differential nature of the convolution operation, the Gaussian wavelet transform is finally written as the following form:

The above formula shows that the expression of choosing Gaussian wavelet for wavelet transform explicitly includes differential operation d ⁿ /du ⁿ and convolution operation f(u)*g _s (u); is the zero property, the convolution operation is interpreted as the weighted average smoothing process of the function f in the kernel function g _s (u), different orders of Gaussian wavelets correspond to different order differential calculations of the original rockfall displacement time domain signal; through wavelet transform , and at the same time realize the smoothing of the noisy vibration signal f and its nth order differential on the scale s. 6. The non-contact rockfall protection dynamic response signal automatic identification and feedback method according to claim 1, characterized in that: in the step (8), for the actual time-domain vibration signal, the wavelet transform differential result is in addition to ensuring that the curve shape and The accuracy of the position of the peak and valley also needs to ensure the accuracy of the amplitude of the differential result; from step (7), it is found that the amplitude of the wavelet differential result is related to the s ⁿ of the wavelet scale parameter, and the normalization of the wavelet function family will also affect The amplitude result of the differential operation; in order to eliminate the influence of the Gaussian wavelet transform process on the differential result amplitude, the amplitude parameter A _mp is introduced, and the wavelet differential operation of the rockfall displacement time domain signal is defined as:

The numerical differentiation process will amplify the influence of noise interference in the signal, and in reverse, the numerical integration process will inhibit the noise interference in the original signal; The degree of coincidence is used to measure the accuracy of the wavelet differential results. The higher the degree of coincidence between the integral result and the original signal, the more accurate and reliable the differential result is; since the two time series before and after the wavelet transform have the same length , the Euclidean distance is used to evaluate the coincidence degree between the time domain signal of the rockfall displacement and the integral result of the wavelet approximate differential. The Euclidean distance is calculated as follows:

Where j represents the equidistant sampling of the wavelet differential results of the original time domain signal, m is the number of discrete points of the sampled signal, and n is the wavelet differential order;

is the nth order differential result of wavelet transform

, t _k is the product node, A _k is the product coefficient, also known as the weight of the accompanying node t _k ; when n=0,

is the rockfall displacement time domain signal

Convolution smoothing result with wavelet function g ₀ (t);

The value of the amplitude parameter A _mp is obtained by iterative solution. When the Euclidean distance between the first integral of the n-order wavelet differential and the n-1 order wavelet differential reaches the minimum value ED _min , that is, when the coincidence degree of the curves is the highest, the amplitude parameter The optimal value is obtained; finally, the rockfall impact displacement signal is fed back through the rockfall displacement time domain signal and wavelet function convolution operation; the rockfall impact velocity signal is fed back through the rockfall displacement time domain signal and the first-order Gaussian wavelet convolution operation; the rockfall impact velocity signal is fed back through the rockfall displacement time domain The signal and the second-order Gaussian wavelet convolution operation feed back the rockfall impact acceleration signal.

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