CN107103398A - Flood discharge based on stochastic transition function method induces place vibration prediction method - Google Patents

Abstract

The invention discloses a method for predicting site vibration induced by flood discharge based on the stochastic transfer function method. After the measured signal is filtered, it is used as the output response signal. Based on the input signal and the output response signal, a transfer function is established. Based on the unbiased estimation method of the transfer function, the prediction result signal is calculated, and the noise sequence is superimposed on the basis of the prediction result signal. , as the final prediction result. The prediction method of the present invention is applicable to the site vibration prediction of multiple excitation source water flow pulsating load joint excitation input system, the prediction result is relatively accurate, and can provide a scientific basis for the prediction and evaluation of site vibration induced by flood discharge.

Description

Prediction Method of Site Vibration Induced by Flood Discharge Based on Stochastic Transfer Function Method

technical field

The invention relates to a method for predicting site vibration induced by flood discharge based on a random transfer function method, and belongs to the technical field of water conservancy and hydropower engineering.

Background technique

The site vibration caused by high dam flood discharge occurs repeatedly and lasts for a long time, which is likely to cause hazards such as foundation liquefaction, uneven settlement of building foundations, and cracking of building walls. It will adversely affect the normal work of precision instruments, cause secondary noise in buildings, and easily induce resonance in buildings. At the same time, the vibration will interfere with the normal life of residents and have a certain degree of physical and mental impact. Therefore, in the actual operation of hydropower stations, predicting the site vibration induced by flood discharge, predicting the site vibration intensity, and evaluating the impact of vibration are effective means to avoid or reduce the above-mentioned hazards.

The site vibration prediction method based on the measured data to calculate the transfer function has become the most important means of site vibration prediction because of its advantages of being able to predict vibration intensity and spectrum characteristics, and fast online prediction. However, the site vibration induced by dam discharge is a multi-factor coupling dynamic problem under the interaction and influence of "dynamic water load-dam body-stilling basin-foundation-site". The prediction of site vibration involves: 1) dynamic water load- Discharge structure interaction system; 2) Discharge structure-dam foundation interaction system; 3) Formation vibration wave propagation system, the three subsystems interact and couple with each other, and there are various vibration transmission processes of each subsystem. Affected by various disturbance factors and uncertain factors, the problem of site vibration induced by high dam flood discharge is extremely complicated.

In the past, the prediction of site vibration and other issues through the transfer function was mostly achieved by establishing the relationship between a single excitation and a single response. There are few studies on the single response output prediction under the excitation of multiple excitation sources such as the site vibration induced by high dam flood discharge. At present, there is no A more reasonable prediction method of site vibration induced by flood discharge can obtain more accurate prediction results.

Contents of the invention

In view of the above-mentioned reasons, the object of the present invention is to provide a method for predicting site vibration induced by flood discharge based on the random transfer function method. After filtering the measured signal of each vibration source, the excitation signal of multiple vibration sources is formed as the input signal, and the output After the measured signal of the measuring point is filtered, it is used as the output response signal, the transfer function is established, the prediction result signal is calculated based on the unbiased estimation of the transfer function, and the noise correction is performed on the basis of the prediction result signal, as the final prediction result, the prediction result It is more accurate and can predict and evaluate the site vibration induced by flood discharge.

To achieve the above object, the present invention adopts the following technical solutions:

A method for predicting site vibration induced by flood discharge based on stochastic transfer function method, including:

After filtering the measured signal of each single vibration source, the multi-vibration source excitation signal is composed as the input signal.

After filtering the measured signal of the output measuring point, it is used as the output response signal,

Based on the input signal and the output response signal, the transfer function is established, and the prediction result signal is calculated based on the unbiased estimation method of the transfer function,

The noise sequence is superimposed on the basis of the prediction result signal as the final prediction result.

The method for filtering the measured signal is as follows:

S1: Construct a white noise signal corresponding to the signal length of the measured signal, perform EEMD decomposition on it, and calculate the noise index value η _j ;

η _j =σ _j /σ ₁ (3)

Among them, σ _j is the standard deviation of the jth IMF component, and σ ₁ is the standard deviation of the first IMF component;

Among them, c _j (k) is the jth IMF component, is the mean value of c _j (k), and N is the signal length;

S2: Perform EEMD decomposition on the measured signal, and calculate the standard deviation σ _j ' of each IMF component;

S3: Calculate the noise standard deviation λ _j of each IMF component of the measured signal decomposed by EEMD;

The formula for calculating the noise standard deviation λ _j is:

λ _j = η _j σ ₁ ` (4)

Wherein, j=2, 3, 4, ..., n, n is an integer;

S4: Discriminate the noise components contained in each IMF component of the measured signal. When λ _j is equal to or greater than the corresponding σ _j ', the jth IMF component is directly filtered out; when λ _j is smaller than the corresponding σ _j ', the The jth IMF component is subjected to wavelet threshold filtering.

The calculation formula of the wavelet threshold filtering is:

The variance of the noise sequence is:

Among them, x is the output response signal before filtering, y is the output response signal after filtering, is the variance of the filtered time series, is the variance of the filtered noise sequence.

The advantages of the present invention are:

1. The improved EEMD combined with wavelet threshold filtering and noise reduction processing is performed on the measured signal of each vibration source and the measured signal of the output measuring point, which can not only effectively filter out white noise, but also accurately retain the useful components in the vibration signal. Improve the accuracy of site vibration prediction;

2. The measured signal of each vibration source is filtered and processed to form a multi-source excitation signal, which is used as the input signal, and the measured signal of the output measuring point is filtered and processed as the output response signal, and the transfer function is established, and the unbiased estimation based on the transfer function The site vibration prediction method can accurately reflect the energy change characteristics in the process of site vibration propagation. Through experimental verification, the predicted site vibration spectrum characteristics are consistent or close to the measured results;

3. On the basis of the prediction result signal output by the transfer function, noise correction is performed, which can accurately reflect the vibration intensity change characteristics during the vibration propagation process of the site;

4. The method of the present invention is applicable to the site vibration prediction of multiple excitation source water flow pulsating load joint excitation input system, the prediction result is relatively accurate, and can provide a scientific basis for the prediction and evaluation of site vibration induced by flood discharge.

Description of drawings

Fig. 1 is a schematic flow chart of the method of the present invention.

Figure 2 is a schematic diagram of the output signal amplitude, the input signal and the output response signal are not processed by filtering.

Figure 3 is a schematic diagram of the calculation results of the coherent transfer function with multi-source excitation signals as input signals, and the input signals and output response signals are not processed by filtering.

Figure 4 is a schematic diagram of the comparison of the time-history results between the vibration prediction of the actual working condition and the actual measurement results by calculating the transfer function with the multi-vibration source excitation signal as the input signal.

Fig. 5A is a schematic diagram of the Fourier spectrum calculation results of the vibration prediction of the actual working condition with multi-source excitation signals as the input signal to calculate the transfer function;

FIG. 5B is a schematic diagram of Fourier spectrum calculation results of actual measurement results in the actual working conditions shown in FIG. 5A .

Fig. 6 is a white noise group with the same energy and different signal lengths constructed in the present invention, a schematic diagram of the relationship between the ratio η _j and the N value.

Fig. 7 is a white noise group with different energies and the same signal length constructed in the present invention, a schematic diagram of the relationship between the ratio η _j and the i value.

Fig. 8 is a schematic diagram of the amplitude of the predicted signal for actual working condition prediction using the method of the present invention, and no noise sequence is added to the predicted result signal.

Fig. 9 is a schematic diagram of the frequency of the predicted signal for actual working condition prediction using the method of the present invention, and no noise sequence is added to the predicted result signal.

Fig. 10 is a schematic diagram of the comparison of the time course results between the prediction results and the actual measurement results for actual working condition prediction using the method of the present invention.

Fig. 11A is a schematic diagram of the Fourier spectrum calculation result of the actual working condition prediction by using the method of the present invention.

FIG. 11B is a schematic diagram of Fourier spectrum calculation results of actual measurement results under the actual working conditions shown in FIG. 11A .

Figures 12 and 13 are schematic diagrams of the results of predicting site vibration at T9 measuring point of Xiangjiaba Hydropower Station using the method of the present invention.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, the flood discharge induced site vibration prediction method based on the stochastic transfer function method disclosed by the present invention includes: using the improved EEMD and wavelet threshold filtering method to filter the measured signal of each single vibration source of the flood discharge induced site After processing, the multi-vibration source excitation signal is composed as the input signal; after filtering the measured signal at any measuring point near the site, it is used as the output response signal, and the transfer function is established based on the input signal and the output response signal. The partial estimation method is used to predict the vibration of the site, and the noise sequence is added to the output signal of the transfer function for noise correction as the final prediction result. Specifically:

1. Taking the multi-source excitation signal of the flood discharge site as the input signal, and the measured signal (vibration signal) at any measuring point near the site as the output response signal, establish a transfer function, and perform site vibration prediction based on the unbiased estimation method of the transfer function.

The entire dam area is used as the input of the transfer function system, the vertical acceleration vibration signals of all excitation sources are combined as the input signal of the transfer function, and any position near the dam area is selected as the output measuring point. Since the acquisition of vibration signals occurs simultaneously, the time-domain superposition method is used to superimpose the vibration signals of all vibration sources as the excitation signals of multiple vibration sources. In a specific embodiment, the multi-vibration source excitation signal under the same flood discharge condition is selected as the input signal for 12 times, and the vertical acceleration vibration signal of the site-specific measuring point is used as the output response signal. According to the unbiased estimation method H _n of the transfer function , get the transfer function H _n1 .

As shown in Figure 2, from the perspective of the amplitude change process in the vibration transmission process, the transfer function H _n1 has a large amplitude in the 0-10.0Hz frequency band, peaks at around 5.0Hz, and peaks at 18.5Hz, 22.0Hz and 29.5Hz. There are also large peaks, indicating that the site vibration has an amplification effect at these frequencies; the transfer function H _n1 always has small energy peaks from 0 to 40.0 Hz, which is related to the greater interference received by the joint input of the multi-vibration source excitation signal. As shown in Figure 3, from the calculation results of the coherent transfer function, in the 0-15.0Hz frequency band, the coherence coefficient of the transfer function H _n1 is between 0.1-0.6, and in the 20.0-40.0Hz frequency band, the overall coherence coefficient decreases , but larger values appear at some frequencies. It can be seen that the signal is greatly affected by noise. Therefore, it is difficult to directly obtain the degree of vibration acceleration of a certain frequency band leakage excitation load transmitted to the ground of the site.

Select a certain flood discharge condition to predict the vertical vibration of a specific measuring point. As shown in Figure 4, it can be seen from the comparison chart of the time-course results that the amplitude of the predicted result is significantly larger than that of the prototype observation results. Compared with low frequency and high frequency, there are many more energy peaks. The measured signal only has a dominant frequency band of 0-6.0Hz, and the peak appears at around 8.0Hz, while the predicted signal has 0-6.0Hz and 8.0- 12.0Hz two dominant frequency bands.

From the data analysis of the above experimental results, it can be seen that from the perspective of the frequency spectrum and amplitude distribution of the transfer function, when the excitation signals of multiple vibration sources are jointly used as the input signal of the transfer function, the noise interference of each single vibration source is relatively large, and the interaction between the transfer systems is relatively large. The impact produces more interference, the vibration caused by non-vibration sources is amplified, and the predicted results are quite different from the measured results. In this case, the predicted results are not ideal. Since the flood discharge excitation is a wide-band random excitation and changes with different flood discharge conditions, that is, the transfer function of the vibration transfer is random, one of the biggest problems in analyzing the random transfer function is the noise problem. Therefore, if the random transfer function can be solved Effectively filtering noise and other influencing factors will effectively improve the prediction results of site vibration.

2. Using the improved EEMD and wavelet threshold filtering method, after filtering the measured signal of each single vibration source, the multi-vibration source excitation signal after the noise reduction filter processing is composed as the input signal; the measured signal of the output measuring point After filter processing, as an output response signal, a transfer function is established based on the input signal and the output response signal.

The measured vibration response of hydraulic structures is often mixed with low-frequency interference and white noise. Through EEMD decomposition of the measured signal, the low-frequency noise generally exists in the last few orders of IMF components, and it is easier to filter out. The white noise will be decomposed together with the useful signal and exists in the first few order IMF components. In order to ensure the integrity of the signal, it is necessary to perform wavelet threshold filtering on the first few order IMF components to retain the useful signal components as much as possible.

Since the noise mixed in the measured signal is unknown, the standard deviation of the noise can only be an estimated value, which seriously affects the accuracy and credibility of wavelet threshold filtering. Therefore, the EEMD decomposition characteristics of white noise can be used to determine the noise standard deviation in the first few orders of noisy IMF components.

Define σ _j as the standard deviation of the jth IMF component, then:

In the formula, c _j (k) is the jth IMF component after the signal is decomposed by EEMD, is the mean value of c _j (k), and N is the length of signal acquisition.

White noise is constructed using a normal distribution random matrix randn(m,n). definition:

s _i =2 ⁱ ×randn(N, 1) (2)

Among them, i=0, 1, 2, 3,..., m, 2 ⁱ represents the intensity of white noise, and N is the length of signal collection. When performing prototype observation of hydraulic structures or site vibration, N is usually 1000-60000. According to formula (2), different N values and i values can be combined to construct white noise signal groups with different lengths and different energies.

1) Construct white noise groups with the same energy but different signal lengths.

Taking i=1 as an example, set i=1, N=1000, 2000, . . . , 10000, 20000, . . . , 60000, and construct a white noise signal group according to formula (2).

Use EEMD to decompose each of the white noise signals, and calculate the ratio η _j :

η _j =σ _j /σ ₁ (3)

Among them, σ _j is the standard deviation of the jth IMF component, and σ ₁ is the standard deviation of the first IMF component. As shown in Fig. 6, when N=1000-10000, the variation range of the ratio η _j is relatively large, and when N>10000, the variation range of the ratio η _j decreases.

2) Construct white noise groups with different energies and the same signal length.

Taking N=20000 as an example, set i=0~9, N=20000, and construct a white noise signal group according to formula (2).

Use EEMD to decompose each of the white noise signals, and use formula (3) to calculate the ratio η _j . As shown in Figure 7, when the signal length is constant, the ratio η _j of white noise signals with different energies is basically constant.

It can be seen that after determining the signal length of white noise, the ratio η _j of white noise signals with different energies decomposed by EEMD is basically stable, or fluctuates within a small range.

Based on the above experimental calculation and analysis results, the process of filtering the collected measured signals (including the measured signals of each single vibration source and the measured signals output by specific measuring points) includes the following steps:

S1: construct the white noise signal corresponding to the signal length of measured signal, carry out EEMD decomposition to the white noise signal of construction, calculate ratio η _j by formula (3), as the noise indicator of the noise level in the evaluation IMF component;

S2: Perform EEMD decomposition on the measured signal, and calculate the standard deviation σ _j ' of each IMF component;

S3: Calculate the noise standard deviation λ _j of each IMF component of the measured signal decomposed by EEMD;

In general, after the measured signal containing white noise is decomposed by EEMD, the first IMF components are all white noise components. Therefore, the noise standard deviation λ _j of each IMF component can be determined as:

λ _j = η _j σ ₁ ` (4)

Wherein, j=2, 3, 4, . . . , n, n is an integer.

S4: According to the relationship between the standard deviation σ _j ' of each IMF component of the measured signal and the noise standard deviation λ _j of each IMF component of the measured signal, determine the noise component contained in each IMF component, and perform corresponding filtering processing.

Specifically, when λ _j is equal to or greater than the corresponding σ _j ', it means that the jth IMF components are all noise components, which can be directly filtered out; when λ _j is smaller than the corresponding σ _j ', it means that the jth IMF If the component contains useful signals, wavelet threshold filtering should be performed on the jth IMF component. The original calculation formula of wavelet threshold filtering is:

Among them, σ is the standard deviation of the noise, the value here is λ _j , N is the signal length, and we get:

After filtering the measured signal of each single vibration source collected by the above-mentioned filtering processing method, the multi-vibration source excitation signal is formed as the input signal, and the measured signal of the collected output measuring point is filtered by the above-mentioned filtering processing method as The response signal is output, and the transfer function is established based on the input signal and the output response signal, and the site vibration is predicted based on the unbiased estimation method of the transfer function. Since both the input signal and the output response signal are filtered to remove noise and environmental factors, the established transfer function is more accurate, and the prediction result is more accurate in terms of vibration mode (reflected by the spectrum angle).

3. Establish the transfer function based on the second item above, calculate the prediction result signal based on the unbiased estimation method of the transfer function, and superimpose the noise sequence on the basis of the prediction result signal as the final prediction result.

For the transfer function established above, the input signal and the output response signal are all filtered to filter out the influence of noise and environmental factors. The spectral characteristics of the predicted results are closer to those of the prototype observations, while the vibration intensity of the prediction results is smaller than that of the prototype observations. the vibration intensity. Therefore, the noise sequence can be constructed according to the signal-to-noise ratio formula and added to the prediction result signal output by the transfer function to reduce the impact of input and output filter processing on the vibration amplitude prediction accuracy. The signal-to-noise ratio of the output response signal after filtering is:

Among them, x is the output response signal before filtering, y is the output response signal after filtering, is the variance of the filtered time series, is the variance of the filtered noise sequence. Therefore, the noise sequence variance can be expressed as:

The constructed noise sequence is added to the prediction result signal output by the transfer function as the final prediction result, so that the prediction result is closer to the prototype observation result in terms of vibration mode and vibration intensity, and the prediction result is more accurate.

4. Validation of the method

For 12 identical working conditions, take the orifice, falling sill, guide wall, stilling floor, and tail sill as the input measuring point, and use the specific measuring point T9 as the output measuring point to collect the vibration of the input measuring point and the output measuring point respectively Signals are filtered using the aforementioned improved EEMD and wavelet threshold filtering methods. After filtering the measured signals of each input measuring point, they are superimposed to form a multi-vibration source excitation source. As the input signal, the measured signal of the output measuring point is processed. After filter processing, it is used as the output response signal, and the transfer function H _n3 is established, and the site vibration is carried out based on the unbiased estimation method of the transfer function.

As shown in Figures 8 and 9, the coherence coefficient of the transfer function H _n3 is the highest at 0 to 8.0 Hz, and reaches a peak at around 3.0 Hz, indicating that energy is less lost in the transmission process of this frequency band, and the coherence coefficient gradually decreases after 10.0 Hz . Judging from the amplitude change process in the vibration transmission process, the transfer function H _n3 has an obvious peak at 2.8 Hz, the main transfer energy is concentrated in the range of 1.0-4.0 Hz, and there is also a small amount of peak distribution at high frequencies. It can be seen that the vibration prediction results are more in line with the measured results through the transfer function established by the filtered input signal and the output response signal.

On the basis of the prediction result signal output by the above transfer function, the standard deviation of the noise sequence is calculated by using formula (8), and the noise sequence is added to the prediction result signal of a specific measuring point T9 to obtain the final time course prediction result (as shown in Figure 10) And spectrum prediction results (shown in Figures 11A and 11B), as shown in the figure, according to the method of the present invention, the main frequency of field vibration can be accurately predicted. The spectrum distribution of site vibration is very similar, and the amplitude prediction results after adding the noise sequence are in good agreement with the actual observation results.

Using the method of the present invention, the site vibration of the T9 measuring point of the Xiangjiaba Hydropower Station from 2013 to 2015 is predicted. As shown in Figures 12 and 13, the predicted results of the T9 measuring point are in good agreement with the measured results: The above increases with the increase of the flow rate of the stilling basin; secondly, the vibration intensity is sensitive to the flood discharge mode, and the vibration intensity of the same discharge condition is different in different flood discharge modes.

The above are the preferred embodiments of the present invention and the technical principles used therefor. For those skilled in the art, without departing from the spirit and scope of the present invention, any technical solution based on the present invention Obvious changes such as equivalent transformation and simple replacement all fall within the protection scope of the present invention.

Claims (4)

1. The site vibration prediction method induced by flood discharge based on stochastic transfer function method, is characterized in that, comprising: After filtering the measured signal of each single vibration source, the multi-vibration source excitation signal is composed as the input signal. After filtering the measured signal of the output measuring point, it is used as the output response signal, Based on the input signal and the output response signal, the transfer function is established, and the prediction result signal is calculated based on the unbiased estimation method of the transfer function, The noise sequence is superimposed on the basis of the prediction result signal as the final prediction result. 2. the site vibration prediction method induced by flood discharge based on the stochastic transfer function method according to claim 1, is characterized in that, the described method for filtering the measured signal is: S1: Construct a white noise signal corresponding to the signal length of the measured signal, perform EEMD decomposition on it, and calculate the noise index value η _j ; η _j =σ _j /σ ₁ (3) Among them, σ _j is the standard deviation of the jth IMF component, and σ ₁ is the standard deviation of the first IMF component; <mrow> <msub> <mi>&amp;sigma;</mi> <mi>j</mi> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>c</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mover> <msub> <mi>c</mi> <mi>j</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> Among them, c _j (k) is the jth IMF component, is the mean value of c _j (k), and N is the signal length; S2: Perform EEMD decomposition on the measured signal, and calculate the standard deviation σ _j ' of each IMF component; S3: Calculate the noise standard deviation λ _j of each IMF component of the measured signal decomposed by EEMD; The formula for calculating the noise standard deviation λ _j is: λ _j = η _j σ ₁ ` (4) Wherein, j=2, 3, 4, ..., n, n is an integer; S4: Discriminate the noise components contained in each IMF component of the measured signal. When λ _j is equal to or greater than the corresponding σ _j ', the jth IMF component is directly filtered out; when λ _j is smaller than the corresponding σ _j ', the The jth IMF component is subjected to wavelet threshold filtering. 3. the site vibration prediction method induced by flood discharge based on stochastic transfer function method according to claim 2, is characterized in that, the computing formula of described wavelet threshold filtering is: <mrow> <mi>T</mi> <mo>=</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <msqrt> <mrow> <mn>2</mn> <mi>l</mi> <mi>n</mi> <mi>N</mi> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> 4. the site vibration prediction method induced by flood discharge based on stochastic transfer function method according to claim 1, is characterized in that, the variance of described noise sequence is: <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>x</mi> <mo>-</mo> <mi>y</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>y</mi> <mn>2</mn> </msubsup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mrow> <mi>S</mi> <mi>N</mi> <mi>R</mi> </mrow> <mn>20</mn> </mfrac> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> Among them, x is the output response signal before filtering, y is the output response signal after filtering, is the variance of the filtered time series, is the variance of the filtered noise sequence.