CN114971013A - Wavelet denoising-based earth surface settlement prediction method for gray BP neural network model - Google Patents

Abstract

The invention discloses a ground surface subsidence prediction method of a grey BP neural network model based on wavelet denoising, which particularly belongs to the technical field of goaf residual subsidence prediction and comprises the following steps of optimizing measured data by adopting a wavelet threshold denoising method; generating a calculation sequence of the data after wavelet preprocessing to establish a grey GM (1, 1) prediction model to obtain a prediction result and an error sequence; carrying out neural network training on the prediction result of the GM (1, 1) model for multiple times, processing to obtain an error sequence corrected by the BP neural network prediction model, and adding the error sequence to the prediction sequence of the GM (1, 1) model to obtain the prediction value of the gray BP neural network model; and finally, calculating the prediction precision of the combined model, and evaluating the prediction result. The method realizes the organic combination of the advantages of various prediction methods, further improves the accuracy and reliability of the prediction result of the tandem model, and has good theoretical significance and application prospect in the aspect of settlement prediction.

Description

Wavelet denoising-based earth surface settlement prediction method for gray BP neural network model

Technical Field

The invention relates to the technical field of goaf residual settlement prediction, in particular to a goaf surface settlement prediction method based on a gray BP neural network model with wavelet denoising.

Background

In order to improve the novel urbanization strategy and accelerate the urbanization development, the ground goaf site becomes an important measure for solving the problem of land shortage at present as a building foundation. Therefore, research for predicting the residual settlement of the earth surface of the old goaf by establishing a relevant prediction model so as to ensure the safety and stability of a newly-built building on the earth surface of the goaf is necessary.

The intelligent algorithm has better performance in the aspects of automatic control, data prediction, optimization solution and the like, wherein the grey model prediction method and the BP neural network model prediction method have wider application to prediction of the surface subsidence of the underground coal mining area. The grey system theory is a set of mathematical method which integrates automatic control and operation research and is proposed by professor Duncong of China and deeply excavates grey color problems, can effectively predict unknown information beneficial to development of objects through partial information of known objects, and is widely applied to numerous fields of engineering technology. The BP neural network concept is provided by American scientists Rumelhart, McCelland and the like on the basis of an artificial neural network algorithm, the algorithm utilizes a nonlinear neuron processing function, has the advantages of simple structure, flexibility, convenience and the like, and is suitable for researching the nonlinear problems of surface subsidence and the like caused by coal mining. In summary, the gray model and the BP neural network model have good applicability to the prediction of the array variation, but have respective limitations. For example: the gray model has the disadvantages that the mathematical model capability for processing errors and nonlinear fitting is not ideal, the BP neural network model has low convergence rate, and the requirement on data samples is high. With the continuous expansion of the application range, the defects and shortcomings of a single prediction model are gradually shown.

Therefore, on the basis of the research of wavelet theory, grey theory and BP neural network prediction mechanism, the actual engineering is used as the research background, the residual settlement of the old goaf is predicted and analyzed by adopting various theories and combination forms thereof, and a new basis is provided for the theoretical exploration and practical application of the mining area ground surface deformation monitoring and forecasting engineering by combining the actual engineering.

Disclosure of Invention

The invention aims to overcome the defects of the technical problems and provide a goaf surface subsidence prediction method based on a gray BP neural network model with wavelet denoising, mainly aims to develop a combined prediction model with high integrity and strong stability, effectively improves the prediction precision, and can be widely applied to monitoring subsidence deformation of a mining area.

The technical scheme is as follows to solve the technical problems:

the invention relates to a goaf surface subsidence prediction method based on a gray BP neural network model with wavelet denoising, which comprises the following steps:

firstly, introducing a wavelet function by using a wavelet analysis tool kit of MATLAB software to preprocess measured data, selecting different threshold modes by a controlled variable method to perform white noise denoising on the original data at unknown scale, comparing different denoising effects, finally performing denoising processing on the accumulated settlement amount of a monitoring point by selecting a Daubechies3 wavelet, a Rigrsure threshold mode and a soft threshold principle through one-layer decomposition, and reconstructing to obtain a data sequence of wavelet threshold denoising;

step two, generating a calculation sequence by the denoised data sequence through a first-order cumulative method, solving a development coefficient a and a gray acting quantity b by establishing a first-order linear differential equation, substituting an original differential equation to obtain a gray GM (1, 1) prediction model equation, and comparing the gray GM (1, 1) prediction model equation with a denoised value to obtain a prediction result and an error sequence of a GM (1, 1) model;

step three, taking the fitting prediction result of the GM (1, 1) model as an input value to train a neural network, inputting an error sequence obtained by the GM (1, 1) model into a trained BP neural network prediction model, and adding the obtained corrected error sequence and the prediction sequence of the GM (1, 1) model to obtain a prediction value of a gray BP neural network model;

and step four, evaluating the prediction accuracy of the combined model through two reference indexes of Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE).

The first step specifically comprises: the wavelet threshold denoising method is a process for reducing or removing noise distributed in a high-frequency wavelet coefficient, and a one-dimensional signal model of the method is as follows:

s(n)＝f(n)+σe(i)，i＝1，2，…，n-1

where s (n) is the monitor signal, f (n) is the true signal, σ is the noise level, and e (i) is the noise signal.

The second step specifically comprises: the grey GM (1, 1) prediction model adopts a single-sequence first-order linear model, and the modeling process is as follows:

(1) establishing an original data sequence for the wavelet de-noising value:

x ⁽⁰⁾ ＝[x ⁽⁰⁾ (1)，x ⁽⁰⁾ (2)，…，x ⁽⁰⁾ (n)]

progressive addition (1-AGO) generates a new prediction sequence:

x ⁽¹⁾ ＝[x ⁽¹⁾ (1)，x ⁽¹⁾ (2)，…，x ⁽¹⁾ (n)]

(2) for cumulative sequence x: ( ¹ ) Establishing a gray differential equation:

x ⁽⁰⁾ (t)+az ⁽¹⁾ (t)＝b，t＝2，3，…，n

wherein z is: ( ¹ ) Is x: ( ¹ ) Generated close-proximity mean number series:

z ⁽¹⁾ ＝[z ⁽¹⁾ (2)，z ⁽¹⁾ (3)，…，z ⁽¹⁾ (n)]

z ⁽¹⁾ (t)＝0.5x ⁽¹⁾ (t)+0.5x ⁽¹⁾ (t-1)

the corresponding whitening differential equation:

wherein a is a development coefficient and b is a gray effect amount.

(3) Constructing a coefficient matrix B and a constant term Y, and calculating a and B by a least square method:

u＝(a，b) ^T ＝(B ^T B) ^-1 B ^T Y

(4) and (3) the values obtained by a and b are substituted back into the original differential equation and a time response formula of gray differential is deduced:

and (3) reducing according to the following formula to obtain a prediction model of the original sequence:

the third step specifically comprises: the grey BP neural network prediction model realizes multiple times of training of the BP neural network on a sample by using an MATLAB software programming method so as to reduce the error of a predicted value, and the modeling process is as follows:

(1) prediction sequence x obtained by GM (1, 1) model ⁰ As input samples, the error sequence ε ⁽⁰⁾ As an output sample, training a BP neural network model to obtain a corresponding weight V and a threshold value W;

(2) error sequence epsilon ⁽⁰⁾ Inputting the error sequence into a trained BP neural network model for continuous prediction to obtain a new error sequence epsilon' ⁽⁰⁾ ；

(3) Will predict sequence x ⁰ With a new error sequence of epsilon' ⁽⁰⁾ Adding to obtain a predicted value Z of the gray BP neural network model ⁽⁰⁾ ＝ x ⁽⁰⁾ +ε′ ⁽⁰⁾ 。

The fourth step specifically comprises: the smaller the two reference index values are, the smaller the actual predicted value error is, and the calculation formulas are respectively as follows:

in the formula, X _t In order to accumulate the measured values of the sink points,

n is the number of sample data for accumulating the predicted value of the sinking point.

In conclusion, the beneficial effects of the invention are as follows:

1. data monitored by the goaf surface subsidence can be interfered by a plurality of influence factors, errors usually exist when original data are directly used for prediction, wavelet threshold denoising processing is carried out by selecting the accumulated subsidence amount of a certain monitoring point, a reconstructed subsidence curve after denoising is smoother and more stable, and the phenomena of obvious oscillation and fold lines do not exist. The wavelet denoising well reserves an original signal, decomposes a noise signal, achieves the purpose of denoising the monitoring data, and is closer to the real sinking data.

2. The single GM (1, 1) prediction model has high overall fitting degree, but the residual error and the relative error of individual prediction values are large, which shows that the non-linear problem in reality is difficult to solve by the prediction model established only by the grey theory. The gray BP neural network combined prediction model integrates the advantages of the GM (1, 1) model and the BP neural network model, a prediction curve is closer to an original data curve, the fitting degree is higher, and in comparison, the gray BP neural network combined prediction model is mild and stable, the dispersion degree is small, and the gray BP neural network combined prediction model is more accurate and applicable to data prediction.

3. The noise in an original monitoring sequence is processed by a wavelet threshold denoising method, nonlinear settlement data is linearized, the capability of effectively processing small samples and less data by combining a gray theory and the advantage that a BP neural network is good at solving the nonlinear problem are combined, and the two are connected in series to form a gray BP neural network model for prediction. The calculation result shows that the average absolute percentage error (MAPE) and the Root Mean Square Error (RMSE) are only 1.78% and 16.05 respectively, the prediction precision is greatly improved, the prediction effect of the method meets the requirements of engineering practice, and the method has good theoretical significance and application prospect in the aspect of subsidence prediction.

Drawings

FIG. 1 is a schematic flow chart of the operation of the combined prediction model of the present invention;

FIG. 2 is a schematic diagram of a wavelet threshold denoising process in the present invention;

FIG. 3 is a schematic flow chart of the gray GM (1, 1) model programming in the present invention;

FIG. 4 is a schematic diagram of a training process of a BP neural network model in the present invention;

FIG. 5 is a residual error comparison diagram of a gray BP neural network model before and after wavelet de-noising in the present invention;

FIG. 6 is a graph comparing the original values with the predicted results of each model.

Detailed description of the invention

For the purpose of illustrating the technical solutions and technical objects of the present invention, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments:

as shown in fig. 1, a goaf surface subsidence prediction method based on a gray BP neural network model with wavelet denoising includes the following steps:

firstly, introducing a wavelet function by using a wavelet analysis tool kit of MATLAB software to preprocess measured data, selecting different threshold modes by a controlled variable method to perform white noise denoising on the original data at unknown scale, comparing different denoising effects, finally performing denoising processing on the accumulated settlement amount of a monitoring point by selecting a Daubechies3 wavelet, a Rigrsure threshold mode and a soft threshold principle through one-layer decomposition, and reconstructing to obtain a data sequence of wavelet threshold denoising;

step two, generating a calculation sequence by the denoised data sequence through a first-order cumulative method, solving a development coefficient a and a gray acting quantity b by establishing a first-order linear differential equation, substituting an original differential equation to obtain a gray GM (1, 1) prediction model equation, and comparing the gray GM (1, 1) prediction model equation with a denoised value to obtain a prediction result and an error sequence of a GM (1, 1) model;

step three, taking the fitting prediction result of the GM (1, 1) model as an input value to train a neural network, inputting an error sequence obtained by the GM (1, 1) model into the trained BP neural network prediction model, and adding the corrected error sequence and the prediction sequence of the GM (1, 1) model to obtain a prediction value of the gray BP neural network model;

and step four, evaluating the prediction accuracy of the combined model through two reference indexes of Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE).

As shown in fig. 2, the wavelet threshold denoising method in the first step is a process of reducing or removing noise distributed in a high-frequency wavelet coefficient, and a one-dimensional signal model thereof is as follows:

s(n)＝f(n)+σe(i),i＝1,2,…,n-1

where s (n) is the monitor signal, f (n) is the true signal, σ is the noise level, and e (i) is the noise signal.

As a more preferred embodiment, the method adopts Daubechies3 wavelet, Rigrsure threshold mode and soft threshold principle to perform denoising processing on the accumulated settlement amount of the monitoring point through one-layer decomposition, and each layer sequence after denoising decomposition is shown in FIG. 5.

As shown in fig. 3, the gray GM (1, 1) prediction model in step two is a single-sequence first-order linear model, and the modeling process is as follows:

(1) establishing an original data sequence for the wavelet de-noising value:

x ⁽⁰⁾ ＝[x ⁽⁰⁾ (1)，x ⁽⁰⁾ (2)，…，x ⁽⁰⁾ (n)]

progressive addition (1-AGO) generates a new prediction sequence:

x ⁽¹⁾ ＝[x ⁽¹⁾ (1)，x ⁽¹⁾ (2)，…，x ⁽¹⁾ (n)]

(2) for cumulative sequence x ⁽¹⁾ Establishing a gray differential equation:

x ⁽⁰⁾ (t)+az ⁽¹⁾ (t)＝b，t＝2，3，…，n

in the formula, z ⁽¹⁾ Is x ⁽¹⁾ Generated close-proximity mean number series:

z ⁽¹⁾ ＝[z ⁽¹⁾ (2)，z ⁽¹⁾ (3)，…，z ⁽¹⁾ (n)]

z ⁽¹⁾ (t)＝0.5x ⁽¹⁾ (t)+0.5x ⁽¹⁾ (t-1)

the corresponding whitening differential equation:

wherein a is a development coefficient and b is a gray effect amount.

(3) Constructing a coefficient matrix B and a constant term Y, and calculating a and B by a least square method:

u＝(a，b) ^T ＝(B ^T B) ^-1 B ^T Y

(4) and (3) the values obtained by a and b are substituted back into the original differential equation and a time response formula of gray differential is deduced:

and (3) reducing according to the following formula to obtain a prediction model of the original sequence:

as a more preferable embodiment, the GM (1, 1) prediction model has a higher precision level and a better overall fitting degree, but the residual error and the relative error of individual predicted values are larger, and the prediction result has non-uniformity. The results of model construction, comparison of predicted values and original values are shown in tables 1 and 2.

Table 1 results of model construction

TABLE 2 original vs. predicted values for two models TABLE-)

As shown in fig. 4, the gray BP neural network prediction model described in step three implements multiple training of the BP neural network on the sample by using an MATLAB software programming method to reduce the error of the prediction value, and the modeling process is as follows:

(1) prediction sequence x obtained by GM (1, 1) model ⁰ As input samples, the error sequence ε ⁽⁰⁾ As an output sample, training a BP neural network model to obtain a corresponding weight V and a threshold value W;

(2) error sequence epsilon ⁽⁰⁾ Inputting the error sequence into a trained BP neural network model for continuous prediction to obtain a new error sequence epsilon' ⁽⁰⁾ ；

(3) Will predict the sequence x ⁰ With a new error sequence of epsilon' ⁽⁰⁾ Adding to obtain a predicted value Z of the gray BP neural network model ⁽⁰⁾ ＝ x ⁽⁰⁾ +ε′ ⁽⁰⁾ 。

As a more preferred embodiment, the predicted value subjected to error compensation by the BP neural network is closer to the original value, the nonuniformity of the prediction error of the GM (1, 1) model is reduced, the residual error is controlled to be smaller, and the comparison results of the original value and the predicted value of the two models are shown in Table 2 and FIG. 5.

As shown in FIG. 6, the comparative development trends of the predicted values and the original values of several different models are intuitively compared, the model prediction trends substantially similar to the original values, and although the model prediction trends have small fluctuation, the model prediction always floats above and below the original values, and both the two prediction models can better reflect the accumulated sinking condition. However, from a macroscopic perspective, the prediction curve of the gray BP neural network model after wavelet denoising is closer to the original data curve, the fitting degree is higher, and in comparison, the prediction curve is more moderate and stable, and the dispersion degree is small.

As a more preferred embodiment, the Mean Absolute Percentage Error (MAPE) and the Root Mean Square Error (RMSE) of each prediction model are calculated respectively, and the smaller the two reference index values are, the smaller the actual predicted value error is, and the calculation formulas are respectively:

in the formula, X _t In order to accumulate the measured values of the sink points,

n is the number of sample data for accumulating the predicted value of the sinking point.

The calculation result shows that the average absolute percentage error (MAPE) and the Root Mean Square Error (RMSE) of the grey BP neural network model after wavelet denoising are only 1.78% and 16.05 respectively, and the error change of the grey BP neural network model prediction result performed by the cumulative settling volume after wavelet denoising is smaller and more stable, and the grey BP neural network model prediction method accords with the actually measured data change rule.

In summary, the invention processes the noise in the original monitoring sequence by the wavelet threshold denoising method, linearizes the nonlinear settlement data, and reconstructs the obtained denoising value. The method has the advantages that the capability of effectively processing small samples and less data by combining a gray theory and the advantage that a BP neural network is good at solving the nonlinear problem are combined, the gray BP neural network model and the small samples and less data are connected in series to predict a denoising value, and the statistical indexes of the Mean Absolute Percentage Error (MAPE) and the Root Mean Square Error (RMSE) of the combined model are evaluated and found, so that the effect of the optimization error of the combined model is remarkable, the combined model is closer to the variation trend of original data, and the goaf surface subsidence process is accurately reflected. The method has strong generalization capability aiming at the variation analysis with volatility, randomness and nonlinearity, provides a new idea for researching the settlement prediction problem of the coal mine goaf or other similar projects, and can be effectively applied to deformation monitoring according to the theoretical basis.

The above description is only a preferred embodiment of the present invention, and is not limited to the above examples, therefore, on the premise of some technical principles described in the present invention, changes and modifications can be made, and shall fall within the scope of the present invention.

Claims (5)

1. A method for predicting surface subsidence of a gray BP neural network model based on wavelet denoising is characterized by comprising the following steps:

step one, introducing a wavelet function by using a wavelet analysis tool kit of MATLAB software to preprocess measured data, selecting different threshold modes by a controlled variable method to perform white noise denoising on the original data at unknown scale, comparing different denoising effects, finally performing denoising processing on the accumulated settlement amount of a monitoring point by selecting a Daubechies3 wavelet, a Rigrsure threshold mode and a soft threshold principle through one-layer decomposition, and reconstructing to obtain a data sequence of wavelet threshold denoising;

step two, generating a calculation sequence by the denoised data sequence through a first-order addition method, solving a development coefficient a and a gray acting quantity b by establishing a first-order linear differential equation, substituting an original differential equation to obtain a gray GM (1, 1) prediction model equation, and comparing the gray GM (1, 1) prediction model equation with a denoising value to obtain a prediction result and an error sequence of a GM (1, 1) model;

step three, taking the fitting prediction result of the GM (1, 1) model as an input value to train a neural network, inputting an error sequence obtained by the GM (1, 1) model into the trained BP neural network prediction model, and adding the corrected error sequence and the prediction sequence of the GM (1, 1) model to obtain a prediction value of the gray BP neural network model;

and step four, evaluating the prediction accuracy of the combined model by calculating two reference indexes of Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE).

2. The wavelet denoising-based surface subsidence prediction method of the gray BP neural network model according to claim 1, characterized in that: the wavelet threshold denoising method in the first step is a process of reducing or removing noise distributed in a high-frequency wavelet coefficient, and a one-dimensional signal model of the method is as follows:

s(n)＝f(n)+σe(i)，i＝1，2，…，n-1 (1)

where s (n) is the monitor signal, f (n) is the true signal, σ is the noise level, and e (i) is the noise signal.

3. The wavelet denoising-based surface subsidence prediction method of the gray BP neural network model according to claim 1, characterized in that: the grey GM (1, 1) prediction model in the step two adopts a single-sequence first-order linear model, and the modeling process is as follows:

(1) establishing an original data sequence for the wavelet de-noising value:

x ⁽⁰⁾ ＝[x ⁽⁰⁾ (1)，x ⁽⁰⁾ (2)，…，x ⁽⁰⁾ (n)] (2)

progressive addition (1-AGO) generates a new prediction sequence:

x ⁽¹⁾ ＝[x ⁽¹⁾ (1)，x ⁽¹⁾ (2)，…，x ⁽¹⁾ (n)] (3)

(2) for cumulative sequence x ⁽¹⁾ Establishing a gray differential equation:

x ⁽⁰⁾ (t)+az ⁽¹⁾ (t)＝b，t＝2，3，…，n (5)

in the formula, z ⁽¹⁾ Is x ⁽¹⁾ Generated close-proximity mean number series:

z ⁽¹⁾ ＝[z ⁽¹⁾ (2)，z ⁽¹⁾ (3)，…，z ⁽¹⁾ (n)] (6)

z ⁽¹⁾ (t)＝0.5x ⁽¹⁾ (t)+0.5x ⁽¹⁾ (t-1) (7)

the corresponding whitening differential equation:

wherein a is a development coefficient and b is a gray effect amount.

(3) Constructing a coefficient matrix B and a constant term Y, and calculating a and B by a least square method:

u＝(a，b) ^T ＝(B ^T B) ^-1 B ^T Y (10)

(4) and (3) the values obtained by a and b are substituted back into the original differential equation and a time response formula of gray differential is deduced:

and (3) reducing according to the following formula to obtain a prediction model of the original sequence:

4. the wavelet denoising-based surface subsidence prediction method of the gray BP neural network model according to claim 1, characterized in that: the grey BP neural network prediction model in the third step realizes multiple training of the BP neural network on the sample by using an MATLAB software programming method so as to reduce the error of the predicted value, and the modeling process is as follows:

(1) mixing GM (1, 1)Model derived predicted sequence x ⁰ As input samples, the error sequence ε ⁽⁰⁾ As an output sample, training a BP neural network model to obtain a corresponding weight V and a threshold value W;

(2) error sequence epsilon ⁽⁰⁾ Inputting the error sequence into a trained BP neural network model for continuous prediction to obtain a new error sequence epsilon' ⁽⁰⁾ ；

(3) Will predict the sequence x ⁰ With new error sequence epsilon' ⁽⁰⁾ Adding to obtain a predicted value Z of the gray BP neural network model ⁽⁰⁾ ＝x ⁽⁰⁾ +ε′ ⁽⁰⁾ 。

5. The wavelet denoising-based surface subsidence prediction method of the gray BP neural network model according to claim 1, characterized in that: the smaller the two reference index values in the step four are, the smaller the actual predicted value error is, and the calculation formulas are respectively as follows:

in the formula, X _t In order to accumulate the measured values of the sink points,

n is the number of sample data for accumulating the predicted value of the sinking point.

Images