Fault identification method based on wavelet basis function optimization and DWT-SVM model

Abstract

The invention relates to a coal mine fault intelligent prediction method based on fusion of discrete wavelet transform (DWT) and a support vector machine (SVM). According to the method, selection of the wavelet basis function is optimized, and multi-scale feature extraction and machine learning classification are combined, so that the fault recognition precision in the complex geological environment is remarkably improved. Experiments show that compared with a traditional method, the method improves prediction accuracy and reliability in practical application of a certain coal mine area in Shanxi, and is of great significance to coal mine safety production.

Description

Technical Field

[0001] The present invention relates to a coal mine fault intelligent prediction method, and more specifically, to a fault identification method based on wavelet basis function optimization and DWT-SVM model. Background Art

[0002] In complex geological environments such as coal mines, accurate fault identification is crucial for safe production in mining areas. Traditional fault identification methods usually rely on manual interpretation or traditional signal processing techniques such as Fourier transform (FFT) and short-time Fourier transform (STFT), but these methods have weak recognition capabilities for complex signals and small-scale faults. Due to its excellent time-frequency localization characteristics, wavelet transform has become an important tool in seismic data processing, showing significant advantages in signal denoising, feature extraction and data reconstruction. The choice of wavelet basis function has a decisive influence on the effect of wavelet transform. Existing studies mostly rely on qualitative analysis or empirical selection of specific application scenarios, and lack a universal wavelet basis selection framework. Summary of the Invention

[0003] One of the purposes of the present invention is to address the above-mentioned shortcomings and provide a fault identification method based on wavelet basis function optimization and DWT-SVM model, in order to solve the technical problems in the prior art such as the lack of a wavelet basis selection framework, the subjective problems in wavelet basis selection, and the influence of the final wavelet transform effect.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0005] The present invention provides a fault prediction method and system based on the fusion of discrete wavelet transform (DWT) and support vector machine (SVM), which is suitable for fault identification in complex geological environments such as coal mines. Specifically, the above-mentioned fault identification method based on wavelet basis function optimization and DWT-SVM model includes the following steps:

[0006] Step A: collect seismic data in the target area, and perform noise filtering, normalization and standardization processing.

[0007] Step B: Use multiple wavelet bases to perform discrete wavelet transform, and then use Fourier transform and discrete cosine transform to calculate the energy distribution of the discrete wavelet transformed signal of each wavelet base, as well as the energy difference between the fault signal and the non-fault signal in the frequency domain and time domain of each wavelet base.

[0008] The energy distribution of the signal after discrete wavelet transformation of each wavelet basis is calculated by the following formula:

[0009]

[0010] Where x(n) is the nth sampling point of the time domain signal, N is the total number of sampling points of the signal, and k is the frequency index in the frequency domain. is the kernel function of Fourier transform, X FFT (k) is the kth frequency component of the frequency domain signal.

[0011]

[0012] Where x(n) is the nth sampling point of the time domain signal, N is the total number of sampling points of the signal, and k is the frequency index in the spatial domain. is the kernel function of discrete cosine transform, X DCT (k) is the kth frequency component of the spatial domain signal.

[0013] The energy difference between the fault signal and the non-fault signal in the frequency domain and the time domain of each wavelet basis is calculated by the following formula:

[0014]

[0015] Where |x| k，F is the frequency domain energy value of the fault signal at frequency k, |x| k，NF is the frequency domain energy value of the non-fault signal at frequency k, N is the total number of frequency components, C FFT is the mean energy difference between fault and non-fault signals in the frequency domain.

[0016]

[0017] Where, DCT k，F is the spatial domain energy value of the fault signal at frequency k, DCT k，NF is the spatial domain energy value of the non-fault signal at frequency k, N is the total number of frequency components, C DCT is the mean energy difference between fault and non-fault signals in the spatial domain.

[0018] Step C: Based on the results of energy difference calculation of each wavelet basis, the waveform basis with the largest energy difference is selected as the optimal wavelet basis, and then the seismic data is subjected to wavelet transform using the optimal wavelet basis to extract time-frequency features. These feature data are then input into the support vector machine model to construct a fault prediction model.

[0019] Step D: Build a model for fault prediction and evaluate the model performance using accuracy, precision, recall, and F1 value.

[0020] A further technical solution is: in step C, the support vector machine model classifies and predicts the input feature data through a decision function, and the decision function is as follows:

[0021]

[0022] In the formula, x is the input sample to be predicted, x i is the i-th sample in the training sample, y i is the corresponding training label, α i is the Lagrange multiplier, which represents the weight of each support vector, k(x, x i ) is the kernel function, b s is the bias term, N is the total number of support vectors, and i is the summation term index.

[0023] A further technical solution is: in step C, the support vector machine model uses the kernel function to perform nonlinear mapping, and the kernel function is as follows:

[0024] k(x,x i )=exp(-γ||xx i || 2 )

[0025] In the formula, γ is the parameter of the kernel function, k is the kernel function, x is the input sample to be predicted, and x i is the i-th support vector.

[0026] A further technical solution is: in step C, the support vector machine model finds the optimal hyperplane by the following formula to classify fault and non-fault signals:

[0027] w T x+b s =0

[0028] Where w is the normal vector of the hyperplane, b s is the bias term, T is the transpose operation, and x is the input eigenvector.

[0029] A further technical solution is: in step C, the support vector machine model is trained to find the optimal hyperplane in the high-dimensional feature space by the Lagrange multiplier method, and the optimization objective of the Lagrange multiplier method is to minimize the following function:

[0030]

[0031] Where, ξ i is the slack variable, C is the penalty parameter, W is the normal vector of the hyperplane, and n is the index of the sample.

[0032] A further technical solution is: the accuracy in step D is calculated by the following formula:

[0033]

[0034] The accuracy is calculated by the following formula:

[0035]

[0036] The recall rate is calculated as follows:

[0037]

[0038] The F1 value is calculated by the following formula:

[0039]

[0040] Where TP is actually a fault and is predicted to be a fault; TN is actually not a fault and is predicted to be a non-fault; FP is actually not a fault and is predicted to be a fault; FN is actually a fault and is predicted to be a non-fault.

[0041] A further technical solution is: the method in step D further includes evaluating the model performance by constructing a negative predictive value of the model, wherein the negative predictive value is calculated by the following formula:

[0042]

[0043] Where, TN is actually non-faulted and predicted to be non-faulted; FN is actually faulted and predicted to be non-faulted.

[0044] Compared with existing technologies, one of the benefits of this invention is that it quantitatively evaluates the energy differences of wavelet bases, selects the optimal wavelet basis function, and combines it with a support vector machine to achieve high-precision fault prediction. This method not only solves the subjective issue of wavelet basis selection but also significantly improves the model's generalization ability in complex geological environments, providing reliable technical support for coal mine safety production. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flowchart illustrating a method according to an embodiment of the present invention.

[0046] Figure 2 1 is a diagram for illustrating a comparison between original data (a) and data processed by wavelet transform (b) in one embodiment of the present invention.

[0047] Figure 3 A comparison chart of fault prediction results of the SVM model (a) and the Db4-SVM model (b) is used to illustrate an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The feature of the present invention is that it proposes an innovative coal mine fault prediction method based on the combination of DWT and SVM. By optimizing the wavelet basis selection, a method based on energy difference is adopted to first evaluate the effect of different wavelet bases in enhancing fault characteristics through FFT and discrete cosine transform (DCT) analysis, and then select the best wavelet basis for subsequent prediction. This method uses the multi-scale characteristics of wavelet transform to effectively extract fault characteristics in seismic signals, and realizes high-precision fault prediction through SVM. Compared with traditional methods, the present invention can improve the recognition accuracy of small faults in complex geological environments, significantly improve the accuracy and reliability of coal mine fault prediction, reduce the safety risks brought by unidentified faults, and provide strong technical support for coal mine safety production.

[0049] refer to Figure 1 As shown, in this embodiment, the method of the present invention is operated according to the following steps:

[0050] Step 1: Collect seismic data from the target coal mining area, perform noise filtering, normalization, and standardization to ensure data consistency and comparability.

[0051] S11. Using actual seismic data from a coal mining area in Shanxi Province, we collected a total of 1,831 data points (including both fault and non-fault samples), including known fault and non-fault information. The data covers different seismic profiles in the area (including 140 inline and 200 crossline data).

[0052] S12. The raw seismic data is first subjected to noise filtering to remove high-frequency noise and low-frequency drift. Next, the processed data is normalized and standardized to ensure comparability between different signals. These preprocessing steps lay the foundation for subsequent wavelet transform and fault feature extraction.

[0053] Step 2: A two-step approach is used to select the optimal wavelet basis. First, the energy differences between different wavelet bases in the time and frequency domains are analyzed to quantify the enhancement effect of each wavelet basis on fault characteristics. Second, the waveform basis with the largest energy difference is selected as the optimal basis function.

[0054] S21. The inventors used multiple wavelet bases in their experiments, including Daubechies (Db3 to Db9), Symlets (Sym3 to Sym9), and Coiflets (Coif3 to Coif5). These wavelet bases were used to evaluate their effectiveness in enhancing fault signal characteristics, particularly in the frequency and time domains.

[0055] S22. Perform DWT on each selected wavelet basis, and then use FFT and DCT to analyze the energy distribution of these transformed signals. Extract the frequency domain and time domain of the subband signal and calculate the energy distribution according to formulas (1) and (2). The calculation formula is as follows:

[0056] (1) Fast Fourier transform formula:

[0057]

[0058] Where, x(n): the nth sampling point of the time domain signal; N: the total number of sampling points of the signal; k: the frequency index in the frequency domain; The kernel function of Fourier transform represents the complex exponential component with frequency k; X FFT (k): The kth frequency component of the frequency domain signal, representing the amplitude and phase information of the signal at frequency k.

[0059] (2) Discrete cosine transform formula:

[0060]

[0061] Where, x(n): the nth sampling point of the time domain signal; N: the total number of sampling points of the signal; k: the frequency index in the spatial domain; The kernel function of discrete cosine transform represents the cosine component with frequency k; X DCT (k): The kth frequency component of the spatial domain signal, which represents the energy distribution of the signal at frequency k.

[0062] S221. After FFT and DCT transformation, calculate the energy difference between the fault signal and the non-fault signal. According to formulas (3) and (4), calculate the energy difference between the fault signal and the non-fault signal in the frequency domain and time domain for each wavelet basis, and use this as an indicator to evaluate the ability of the wavelet basis to enhance the fault characteristics. The calculation formula is as follows:

[0063] (3) Fourier transform energy difference formula:

[0064]

[0065] Where |x| k，F : frequency domain energy value of the fault signal at frequency k; |x| k，NF : frequency domain energy value of the non-fault signal at frequency k; N: the total number of frequency components; C FFT : The mean energy difference between fault and non-fault signals in the frequency domain. The larger the value, the better the enhancement effect of the wavelet basis on the frequency domain characteristics.

[0066] (4) Discrete cosine transform energy difference formula:

[0067]

[0068] Where, DCT k,F : The spatial domain energy value of the fault signal at frequency k; DCT k,NF : the spatial domain energy value of the non-fraction signal at frequency k; N: the total number of frequency components; C DCT : The mean energy difference between fault and non-fault signals in the spatial domain. The larger the value, the better the enhancement effect of the wavelet basis on the spatial domain characteristics.

[0069] S23. Based on the energy difference analysis results, the waveform basis with the largest energy difference is selected as the optimal wavelet basis. Wavelet basis with a large energy difference performs best in enhancing fault features because it can more clearly distinguish fault and non-fault signals, especially in complex geological environments, and can effectively highlight weak fault signals.

[0070] In the experiments of this example, the Db4 wavelet basis exhibited significant energy differences in both the frequency and time domains, effectively enhancing fault signals and suppressing noise. Therefore, it was selected as the optimal wavelet basis. Taking Inline209 and Inline153 as examples, the energy differences between fault and non-fault signals for each wavelet basis are shown in Table 1.

[0071] Table 1. Energy difference between fault and non-fault signals after wavelet transform

[0072]

[0073]

[0074] Step 3: Use the optimal wavelet basis to perform wavelet transform on the seismic data, extract time-frequency features, and input these features into the support vector machine model to build a fault prediction model.

[0075] S31. Through energy difference analysis, Db4 is selected as the optimal wavelet basis. A DWT is then performed on the seismic signal using this optimal wavelet basis. After the wavelet transform, the time-frequency characteristics of the seismic signal are extracted. Multiple fault-related time-frequency characteristics include instantaneous frequency, instantaneous phase, variance, root mean square amplitude, and maximum curvature.

[0076] S32. Support vector machines are a supervised learning algorithm widely used in classification and regression problems. They aim to achieve optimal data separation by constructing hyperplanes. The time-frequency features of seismic signals extracted using an optimal wavelet basis serve as input features for the support vector machine. These features can effectively describe local variations in fault signals and enhance the model's ability to identify faults.

[0077] S321, SVM classifies fault and non-fault signals by finding an optimal hyperplane. In a high-dimensional feature space, SVM uses input features to construct a decision boundary. The goal of model training is to maximize the margin, that is, to make the distance between the support vector and the hyperplane as far as possible, thereby improving the classification accuracy of the model. The optimal hyperplane is defined as:

[0078] w T x+b s =0

[0079] Where, w: hyperplane normal vector; b: s : Bias term; T is the transpose operation, and x is the input eigenvector.

[0080] S322, SVM uses kernel function for nonlinear mapping, and the choice of kernel function directly affects the classification performance of the model. In view of the nonlinear feature distribution in the fault identification task, the present invention adopts radial basis function (RBF) as the kernel function. The RBF kernel can effectively capture the complex nonlinear relationship in the fault data by mapping the samples to the high-dimensional feature space, and its local response characteristics are particularly suitable for processing the common local feature changes in seismic data. Compared with the linear kernel function, the RBF kernel significantly improves the recognition accuracy of the fault boundary while maintaining the generalization ability of the model. Improve the generalization ability and classification accuracy of the model. And it performs well in the case of high-dimensional data. The expression of the RBF kernel function is:

[0081] k(x,x i )=exp(-γ||xx i || 2 )

[0082] Where, γ is the parameter of the kernel function, which controls the similarity between data points; k is the total number of support vectors, x is the input sample to be predicted, and x i is the i-th support vector.

[0083] The training process of S323 and SVM involves solving an optimization problem, namely finding an optimal hyperplane in a high-dimensional feature space that maximizes the margin between classes. This optimization problem can be solved using the Lagrange multiplier method, taking into account some misclassification of samples during the training process. The specific optimization goal is to minimize the following objective function:

[0084]

[0085] Where, ξ i : slack variable, allowing some samples to be misclassified; C: penalty parameter, controlling the tolerance of error; W: normal vector of the decision hyperplane; n is the index of the sample.

[0086] The decision function of S324 and SVM is used to classify and predict input data. The decision function comprehensively considers the weight of the support vector, sample labels, and feature similarity, and outputs a score value: a positive value is judged as a fault, and a negative value is judged as a non-fault. Its core function is to achieve high-precision nonlinear classification. It is particularly good at processing small samples and high-dimensional data. It can effectively distinguish fault and non-fault signals under complex geological conditions, providing reliable predictions for safe coal mining. Decision function:

[0087]

[0088] Where, x: input sample to be predicted; x i : the i-th sample in the training sample; y i : corresponding training label; α i : Lagrange multiplier, representing the weight of each support vector; k(x, x i ): kernel function; b s : bias term; N is the total number of support vectors, and i is the summation term index.

[0089] Step 4: Build a model for fault prediction and evaluate model performance using accuracy (overall prediction accuracy), precision (reliability of predictions for faults), recall (rate of detection of true faults), and F1 value (a balance indicator between precision and recall).

[0090] S41. In order to objectively evaluate the performance of the model in fault identification, the present invention uses a confusion matrix as the basic structure to record the relationship between the model prediction and the actual annotation. The confusion matrix of the classification results is shown in Table 2.

[0091] Table 2. Classification result confusion matrix

[0092]

[0093] Among them, TP is actually a fault and is predicted to be a fault, TN is actually not a fault and is predicted to be a non-fault, FP is actually not a fault and is predicted to be a fault, and FN is actually a fault and is predicted to be a non-fault.

[0094] S411. Based on the confusion matrix, the present invention introduces the following five common classification performance indicators to comprehensively evaluate the model:

[0095] (1) Accuracy:

[0096]

[0097] It indicates the correct prediction ratio of the model for all samples and is the basic indicator for evaluating the overall performance.

[0098] (2) Accuracy:

[0099]

[0100] It indicates the proportion of faults predicted by the model that are actually faults, and is used to measure the prediction results.

[0101] (3) Recall rate:

[0102]

[0103] This measure measures the model's ability to detect all true faults. Higher values indicate fewer missed faults. This metric is particularly important in practical applications, as missed faults can pose serious safety risks.

[0104] (4) F1 value:

[0105]

[0106] It is the harmonic average of precision and recall, which comprehensively weighs the performance of the model in both aspects.

[0107] (5) Negative predicted value:

[0108]

[0109] It indicates the proportion of samples predicted to be non-fault that are actually non-fault, and is used to evaluate the credibility.

[0110] S42. To verify the effect of different wavelet bases on SVM classification performance, the present invention uses Db4, Db9, Coif3, and Coif5 to compare with a standard SVM model that does not use wavelet transform. The evaluation results are shown in Table 3:

[0111] Table 3. Comparison of evaluation indicators of DWT-SVM and SVM models

[0112]

[0113]

[0114] The results in Table 3 show that applying wavelet transform to seismic data can significantly improve prediction accuracy. Compared to the SVM, the DWT-SVM model showed significant improvements across all evaluation metrics. Furthermore, the Db4-SVM and Coif3-SVM models achieved better prediction accuracy than the Db9-SVM and Coif5-SVM models. Given that undiscovered faults are more likely to cause safety incidents in actual production scenarios, higher recall rates and NPV values are more meaningful for actual fault prediction. Among the tested models, the Db4-SVM achieved the highest recall rate and NPV.

[0115] S43. Using the posterior to evaluate the probability of predicted faults, the probability of predicted faults in the range of [0.5, 0.6] is classified as "unreliable", the probability in the range of [0.6, 0.85] is classified as "unreliable", and the probability in the range of [0.85, 1] is classified as "reliable". The results are shown in Table 4:

[0116] Table 4. Fault prediction probability statistics of each model

[0117]

[0118] The results show that the Db4-SVM model achieved 14.5% reliable predictions, significantly higher than other wavelet bases. However, the proportion of unreliable predictions was only 16.1%, significantly lower than models like Coif5. This demonstrates that the Db4-SVM model not only has a high recognition rate but also offers stable and reliable predictions. This makes it particularly suitable for scenarios like coal mines, where fault identification accuracy is crucial for safe production and significantly reduces the risk of coal mine accidents.

[0119] Although the present invention has been described herein with reference to a number of illustrative embodiments thereof, it will be understood that numerous other modifications and implementations may be devised by those skilled in the art that fall within the scope and spirit of the principles disclosed herein. More specifically, within the scope of the present disclosure, the drawings, and the claims, numerous variations and modifications may be made to the components and / or layout of the subject combination arrangement. In addition to variations and modifications to the components and / or layout, other uses will also be apparent to those skilled in the art.

Claims

1. A fault identification method based on wavelet basis function optimization and DWT-SVM model, characterized in that The method comprises the following steps: Collect seismic data in the target area and perform noise filtering, normalization and standardization; Using multiple wavelet bases to perform discrete wavelet transform, and then using Fourier transform and discrete cosine transform to calculate the energy distribution of the discrete wavelet transformed signal of each wavelet basis, as well as the energy difference between the fault signal and the non-fault signal in the frequency domain and time domain of each wavelet basis; The energy distribution of the signal after discrete wavelet transformation of each wavelet basis is calculated by the following formula: Where x(n) is the nth sampling point of the time domain signal, N is the total number of sampling points of the signal, and k is the frequency index in the frequency domain. is the kernel function of Fourier transform, X FFT (k) is the kth frequency component of the frequency domain signal; Where x(n) is the nth sampling point of the time domain signal, N is the total number of sampling points of the signal, and k is the frequency index in the spatial domain. is the kernel function of discrete cosine transform, X DCT (k) is the kth frequency component of the spatial domain signal; The energy difference between the fault signal and the non-fault signal in the frequency domain and the time domain of each wavelet basis is calculated by the following formula: Where |x| k,F is the frequency domain energy value of the fault signal at frequency k, |x| k，NF For non-fault signals at frequency The frequency domain energy value at k, N is the total number of frequency components, C FFT is the mean energy difference between fault and non-fault signals in the frequency domain; Where, DCT k，F is the spatial domain energy value of the fault signal at frequency k, DCT k，NF is the spatial domain energy value of the non-fault signal at frequency k, N is the total number of frequency components, C DCT is the mean energy difference between fault and non-fault signals in the spatial domain; According to the results of energy difference calculation of each wavelet basis, the waveform basis with the largest energy difference is selected as the optimal wavelet basis, and then the seismic data is subjected to wavelet transform using the optimal wavelet basis to extract time-frequency features. And these characteristic data are input into the support vector machine model to build a fault prediction model; A model was constructed for fault prediction, and the model performance was evaluated using accuracy, precision, recall, and F1 value.

2. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 1 is characterized in that: The support vector machine model performs classification prediction on the input feature data through a decision function, and the decision function is as follows: In the formula, x is the input sample to be predicted, x i is the i-th sample in the training sample, y i is the corresponding training label, α i is the Lagrange multiplier, which represents the weight of each support vector, k(x, x i ) is the kernel function, b s is the bias term, N is the total number of support vectors, and i is the summation term index.

3. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 2 is characterized in that: The support vector machine model uses the kernel function to perform nonlinear mapping, and the kernel function is as follows: k(x,x i )=exp(-γ||x-x i || 2 ) In the formula, γ is the parameter of the kernel function, k is the kernel function, x is the input sample to be predicted, and x i is the i-th support vector.

4. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 3 is characterized by: The support vector machine model finds the optimal hyperplane to classify fault and non-fault signals using the following formula: w T x+b s =0 Where w is the normal vector of the hyperplane, b s is the bias term, T is the transpose operation, and x is the input eigenvector.

5. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 3 or 4, characterized in that: The support vector machine model is trained to find the optimal hyperplane in the high-dimensional feature space by the Lagrange multiplier method. The optimization objective of the Lagrange multiplier method is to minimize the following function: Where, ξ i is the slack variable, C is the penalty parameter, W is the normal vector of the hyperplane, and n is the index of the sample.

6. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 1 is characterized in that The accuracy is calculated by the following formula: The accuracy is calculated by the following formula: The recall rate is calculated by the following formula: The F1 value is calculated by the following formula: Where, TP is actually a fault and predicted to be a fault; TN is actually not a fault and predicted to be not a fault; FP is actually not a fault but is predicted to be a fault; FN is actually a fault but is predicted to be a non-fault.

7. The fault identification method based on wavelet basis function optimization and DWT-SVM model according to claim 6 is characterized in that The method further includes evaluating model performance by constructing a negative predictive value for the model, wherein the negative predictive value is calculated as follows: Where, TN is actually non-faulted and predicted to be non-faulted; FN is actually faulted and predicted to be non-faulted.

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