Water disaster risk analysis method based on Fourier function prediction model

Abstract

The invention discloses a water disaster risk analysis method based on a Fourier function prediction model. The water disaster risk analysis method comprises the following steps: carrying out moving average smoothing processing on original data; and fitting the smoothed data by using Fourier series so as to obtain a future predicted value. According to existing historical data, when 12 points are input and one point is predicted in the future, the average relative error can reach 2.46%, and the mean square error can reach 0.007. The model has the main advantages that the operation speed of the model is high, and real-time dynamic prediction can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic prediction and analysis of water disasters. Specifically, it is a method for analyzing water disaster risks based on a Fourier function prediction model. Background Technique

[0002] The hydrogeology of coal mine fields in China is complex. It is significantly controlled and influenced by geological conditions such as geological structures, stratigraphic lithologies, and landforms, as well as natural factors such as hydrology and meteorology, forming unique hydrogeological characteristics, increasing the risks of coal mine exploitation, and affecting the safety of coal mine excavation and mining. To reduce the risks of coal mine water disasters, coal mine production enterprises need to strengthen risk monitoring and improve the prevention and control level. The formation and occurrence of coal mine water disasters are complex adaptive phenomena with non-linear dynamics. There are many influencing factors for water disaster risks, resulting in strong subjectivity in existing water disaster risk assessments, little reflection of objective information, and no comprehensive evaluation system for water disaster risks considering multiple factors. Due to the suddenness of water disasters, the factors considered in the prevention and control process are complex, the prevention and control plans are diverse, the prevention and control effectiveness cycle is long, and there is a lack of scientific cost-benefit analysis methods. Currently, domestic coal mine enterprises still lack a perfect water disaster risk monitoring and water disaster prevention and control auxiliary decision-making management system. Therefore, under this background, studying dynamic water disaster risk assessment and early warning methods that reflect subjective and objective information, establishing a water disaster hazard assessment model, and accurately predicting water disaster accidents have become difficult problems to be solved.

[0003] Currently, for the research on mine water disaster evaluation methods, it mainly involves investigating and analyzing the hydrogeological conditions of the mine and conducting qualitative and quantitative analysis of the data. Although these methods have their merits, there are deficiencies in the monitoring and early warning of water disasters. (1) The subjectivity of water disaster risk assessment is strong and it reflects little objective information. (2) The influence of multiple factors on water disaster risk assessment is not considered. Water disaster risk assessment is affected by multiple indicators, and these indicators are interrelated with different degrees of influence.

[0004] Fourier analysis is an important branch gradually formed in analysis. It studies and expands the concepts of Fourier series and Fourier transform, also known as harmonic analysis. Over the past time, it has become a broad topic and has been widely applied in many fields such as signal processing, quantum mechanics, and neuroscience. Fourier series shows that any continuous function with a period of T can be expressed as a superposition of a series of sine waves and cosine waves, and the coefficients of each term are called Fourier coefficients. By converting the Fourier coefficients into complex numbers according to Euler's formula, information such as the amplitude and phase angle at the corresponding frequency position can be obtained. The frequency spectrum is the distribution curve of frequency. The fitting method based on Fourier series is to use Fourier transform for frequency-domain analysis to extract the laws of the main periodic terms, and then use the trigonometric function method to fit the extracted periodic terms respectively, and finally achieve simulation fitting.

[0005] The prediction of the Fourier model is based on the prediction of the grey model with optimized weights through the Fourier transform function. Since the grey model has high requirements for the smoothness of the original sequence, the original data is preprocessed by the three-point smoothing method, which weakens the influence of outliers on the prediction. The parameters of the grey model are optimized by the particle swarm optimization algorithm, which improves the prediction accuracy of the grey model, but the prediction accuracy is still not ideal. If the Fourier transform is used for correction prediction, the prediction accuracy is effectively improved. This model solves the problem of insufficient prediction accuracy of the time series analysis method and the grey model, and improves the problem that the covariance robust fuzzy linear regression analysis method is not ideal enough when dealing with longitudinal data. The application results of this model prediction are somewhat persuasive. However, so far, there is no method for dynamically risk assessing and warning mine water hazards based on the Fourier model. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to provide a water hazard risk analysis method based on a Fourier function prediction model with fast operation speed.

[0007] To solve the above technical problem, the present invention provides the following technical solutions:

[0008] A water hazard risk analysis method based on a Fourier function prediction model includes the following steps:

[0009] (1) Perform smoothing processing of moving average on the original data;

[0010] (2) Fit the smoothed data using Fourier series to obtain future predicted values.

[0011] In the above water hazard risk analysis method based on a Fourier function prediction model, in step (1), the original data is xx, where xx represents any single monitoring index, and the single monitoring index is water level (m), water temperature (°C), water quality (mg / L), rainfall (mm), water inflow (L / (s·m)), wind speed (m / s), humidity (%rh), or temperature (°C).

[0012] In the above water hazard risk analysis method based on a Fourier function prediction model, in step (1),

[0013] The smoothing processing of moving average is to smooth the original input data xx using a moving average filter. Assuming the length of the input data xx is 12, a column vector x of the same length as the original data xx is returned; the window width of the moving average filter is default set to 5, and the calculation method of the elements in the column vector x obtained after smoothing is as follows:

[0014] x(1) = xx(1)

[0015] x(2) = [xx(1) + xx(2) + xx(3)] / 3;

[0016] x(3) = [xx(1) + xx(2) + xx(3) + xx(4) + xx(5)] / 5;

[0017] x(4) = [xx(2) + xx(3) + xx(4) + xx(5) + xx(6)] / 5;

[0018] x(5) = [xx(3) + xx(4) + xx(5) + xx(6) + xx(7)] / 5;

[0019] ……;

[0020] x(10) = [xx(8) + xx(9) + xx(10) + xx(11) + xx(12)] / 5;

[0021] x(11) = [xx(9) + xx(10) + xx(11)] / 3;

[0022] x(12) = xx(12);

[0023] Where xx(i) is the i-th data in the chronological order of the original data; x(i) is the i-th data after moving and smoothing the original data xx.

[0024] For the above water hazard risk analysis method based on the Fourier function prediction model, the number of original data inputs is greater than or equal to 12 points, assumed to be n points.

[0025] For the above water hazard risk analysis method based on the Fourier function prediction model, in step (2), the smoothed data is curve-fitted using the Fourier function; the Fourier function is selected as:

[0026] y = a0 + a1 cos(wt) + a2 sin(wt) + a3 cos(2wt) + a4 sin(2wt);

[0027] Where t is the independent variable of the function, and a0, a1, a2, a3, a4 and w are parameters to be estimated;

[0028] Then the Fourier function value corresponding to the i-th point after translation is:

[0029] y i = a0 + a1 cos(wi) + a2 sin(wi) + a3 cos(2wi) + a4 sin(2wi).

[0030] For the above water hazard risk analysis method based on the Fourier function prediction model, a0, a1, a2, a3, a4 and w are parameters to be estimated. Using the least squares method, find the values that make Parameter estimate value for obtaining the minimum value and That is, by taking the partial derivatives of Q with respect to each parameter and setting them to 0, the estimated values of each parameter can be obtained by solving the following system of equations:

[0031]

[0032] The water damage risk analysis method based on the Fourier function prediction model according to claim 5, wherein t = 13 and t = 14 are substituted into the Fourier function to predict the data of the next two points in the future, that is, the values of the 13th and 14th points.

[0033] The technical solution of the present invention has achieved the following beneficial technical effects:

[0034] According to the existing historical data, when predicting 1 point in the future for every 12 input points, the average relative error can reach 2.46%, and the mean square error can reach 0.007. The main advantages of this model are its fast operation speed and the ability to achieve real-time dynamic prediction.

[0035] As long as there is a fluctuation regularity in the single variable of the water damage risk, then this regularity can definitely be expressed as the superposition of one or more SIN or COS waves with specific energy and fixed periods. As long as the Fourier transform is performed on this single variable to generate its spectrum, and then the high-energy waves in the spectrum are selected for fitting, the original variable sequence can be fitted with several SIN or COS waves.

[0036] When fitting a variable using the Fourier function, the Fourier function can more easily obtain a larger goodness of fit (R 2 ). BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the simulation experiment results of the Fourier function prediction model of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0038] The water damage risk analysis method based on the Fourier function prediction model in this embodiment includes:

[0039] (1) Perform smoothing processing of moving average on the original data;

[0040] (2) Fit the smoothed data using Fourier series to obtain the predicted values in the future.

[0041] In step (1),

[0042] The smoothing process of the moving average uses a moving average filter to smooth the original input data xx. Assuming the length of the input data xx is 12, a column vector x of the same length as the original data xx is returned. The window width of the moving average filter is default set to 5, and the calculation method of the elements in the column vector x obtained after smoothing is as follows:

[0043] x(1) = xx(1)

[0044] x(2) = [xx(1) + xx(2) + xx(3)] / 3;

[0045] x(3) = [xx(1) + xx(2) + xx(3) + xx(4) + xx(5)] / 5;

[0046] x(4) = [xx(2) + xx(3) + xx(4) + xx(5) + xx(6)] / 5;

[0047] x(5) = [xx(3) + xx(4) + xx(5) + xx(6) + xx(7)] / 5;

[0048] ……;

[0049] x(10) = [xx(8) + xx(9) + xx(10) + xx(11) + xx(12)] / 5;

[0050] x(11) = [xx(9) + xx(10) + xx(11)] / 3;

[0051] x(12) = xx(12).

[0052] Where xx(i) is the i-th data of the original data arranged in chronological order; x(i) is the i-th data after the moving smoothing process of the original data xx.

[0053] The original data is xx, and xx represents any single monitoring index. The single monitoring index is water level (m), water temperature (℃), water quality (mg / L), rainfall (mm), water inflow (L / (s·m)), wind speed (m / s), humidity (%rh), or temperature (℃).

[0054] In this embodiment, 12 original data xx need to be input, such as 12 water level data with the unit of meters, xx = [2.17, 2.23, 2.22, 2.23, 2.13, 2.13, 2.23, 2.3, 2.34, 2.38, 2.34, 2.34]. After smoothing, x = [2.1700, 2.2067, 2.1960, 2.1880, 2.1880, 2.2040, 2.2260, 2.2760, 2.3180, 2.3400, 2.3533, 2.3400].

[0055] In step (2),

[0056] The smoothed data is curve-fitted using the Fourier function; the Fourier function is selected as:

[0057] y = a0 + a1 cos(wt) + a2 sin(wt) + a3 cos(2wt) + a4 sin(2wt);

[0058] Then the Fourier function value corresponding to the i-th point after translation is:

[0059] y i = a0 + a1 cos(wi) + a2 sin(wi) + a3 cos(2wi) + a4 sin(2wi).

[0060] Among them, a0, a1, a2, a3, a4 and w are parameters to be estimated. Using the least squares method, find the parameter estimates that make

[0061] obtain the minimum value

[0062] and That is, take the partial derivatives of Q with respect to each parameter and set them to 0. Solving the solutions of the following equations can obtain the parameter estimates:

[0063]

[0064] Using the least squares method to find the parameters to be estimated,

[0065] a0 = 2.0902, a1 = -0.0844, a2 = 0.2458, a3 = 0.1264, a4 = -0.0079 and

[0066] w = 0.2481.

[0067] Substitute \(t = 13\) and \(t = 14\) into the Fourier function respectively, so that the data shifted backward by 2 points in the future can be predicted. That is, the values of the 13th and 14th points are 2.2769 and 2.1844 respectively, with the unit of meter.

[0068] And so on to obtain the prediction results as Figure 1 shown, and compare them with the actual measurement results. The average relative error can reach 2.46%, and the mean square error can reach 0.007. The main advantage of this model is that it runs fast and can achieve real-time dynamic prediction.

[0069] Obviously, the above embodiments are only examples clearly described, rather than limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the claims of this patent application.

Claims

1. A method for analyzing water disaster risk based on a Fourier function prediction model, characterized in that It includes the following steps: (1) Perform a moving average smoothing process on the original data; (2) Fit the smoothed data using Fourier series to obtain future predicted values.

2. The water hazard risk analysis method based on the Fourier function prediction model according to claim 1, wherein In step (1), the original data is xx, where xx represents any single monitoring index, and the single monitoring index is water level, m, water temperature, °C, water quality, mg / L, rainfall, mm, water inflow, L / (s·m), wind speed, m / s, humidity, %rh, or temperature, °C.

3. The water damage risk analysis method based on the Fourier function prediction model according to claim 2, wherein In step (1), The moving average smoothing process is to smooth the original input data xx using a moving average filter. Assuming the length of the input data xx is 12, a column vector x of the same length as the original data xx is returned. The window width of the moving average filter is default set to 5, and the calculation method of the elements in the column vector x after smoothing is as follows: x(1) = xx(1) x(2) = [xx(1) + xx(2) + xx(3)] / 3; x(3) = [xx(1) + xx(2) + xx(3) + xx(4) + xx(5)] / 5; x(4) = [xx(2) + xx(3) + xx(4) + xx(5) + xx(6)] / 5; x(5) = [xx(3) + xx(4) + xx(5) + xx(6) + xx(7)] / 5; ……； x(10) = [xx(8) + xx(9) + xx(10) + xx(11) + xx(12)] / 5; x(11) = [xx(9) + xx(10) + xx(11)] / 3; x(12) = xx(12); where xx(i) is the i-th data in the original data arranged in chronological order; x(i) is the i-th data after moving smoothing of the original data xx.

4. The water hazard risk analysis method based on the Fourier function prediction model according to claim 3, characterized in that The number of input original data points is greater than or equal to 12 points, assumed to be n points.

5. The water hazard risk analysis method based on the Fourier function prediction model according to claim 3, wherein In step (2), curve fitting is performed on the smoothed data using a Fourier function; the Fourier function selected is: y = a0 + a1cos(wt) + a2sin(wt) + a3cos(2wt) + a4sin(2wt); where t is the independent variable of the function, and a0, a1, a2, a3, a4, and w are parameters to be estimated; then the Fourier function value corresponding to the i-th point after translation is: y i = a0 + a1cos(wi) + a2sin(wi) + a3cos(2wi) + a4sin(2wi).

6. The water hazard risk analysis method based on the Fourier function prediction model according to claim 5, wherein a0, a1, a2, a3, a4 and w are parameters to be estimated. Using the least squares method, find the parameter estimates that minimize the parameter estimates that achieve the minimum value and That is, take the partial derivatives of Q with respect to each parameter and set them to 0. Solving the following system of equations will give the estimates of each parameter:

7. The water hazard risk analysis method based on the Fourier function prediction model according to claim 5, characterized in that Substitute t = 13 and t = 14 into the Fourier function to predict the data of the next 2 points in the future, that is, the values of the 13th and 14th points.

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