Intelligent ultra-deep gas well tubular column leakage identification method based on time sequence data and time-frequency fusion BiLSTM model

Abstract

The invention relates to an ultra-deep gas well tubular column leakage intelligent identification method based on time series data and a time-frequency fusion BiLSTM model, and belongs to the technical field of petroleum engineering, and the method comprises the steps: 1, obtaining model input physical characteristics, and constructing an experiment data set; 2, constructing and training a multi-module fusion integrated deep learning model; and step 3, intelligent identification of ultra-deep gas well tubular column leakage is carried out through the trained multi-module fusion integrated deep learning model. According to the method, the input physical characteristics can be efficiently learned, and high-precision regression prediction is realized for leakage position and size tasks.

Description

Technical Field

[0001] This invention belongs to the field of petroleum engineering technology, specifically, it relates to an intelligent identification method for leakage in ultra-deep gas well tubing based on a time-series data and time-frequency fusion BiLSTM model. Background Technology

[0002] The increasing depletion of shallow oil and gas resources has prompted a global shift in exploration focus to ultra-deep wells. Simultaneously, the high temperatures, high pressures, and complex geological environments faced by ultra-deep wells significantly exacerbate the harshness of wellbore conditions, making them vulnerable to well seal failure. As the core production channel for formation fluids, production tubing is highly susceptible to structural damage or corrosion failure under multi-physics coupling and long-term dynamic loads, resulting in a leakage risk far exceeding that of other barriers. Once the tubing leaks, it directly leads to continuous annular pressure, potentially inducing casing failure, annular blowouts, and even underground well blowouts, causing severe consequences such as environmental pollution, platform displacement, and well abandonment. Furthermore, gas well leaks can also trigger fires and explosions, posing a significant threat to public safety and the surrounding environment. Therefore, leak identification in ultra-deep gas well tubing is of paramount importance.

[0003] However, due to the complex and diverse phases of fluids in the wellbore and the special physical properties of gases, and the disturbances in the local temperature, sound, and pressure fields induced by leaks in the gas well production tubing, the physical field signal characteristics are unclear and the intensity is weak, making it difficult to identify leaks in the production tubing. Current research has encountered many problems.

[0004] The multiphase flow characteristics of fluids within the wellbore are the physical foundation for understanding leakage mechanisms and their evolution. Currently, the academic community has established a relatively mature theoretical system for the fluid dynamics mechanisms of production tubing leaks, with research focusing primarily on three areas: multiphase flow pattern identification, annular pressure prediction, and numerical simulation of the leakage flow field. However, current research on transient and full-process leakage models is still incomplete, and existing models are insufficient in accurately predicting changes in fluid temperature, pressure, and gas production within the wellbore. This results in existing models being unable to comprehensively capture transient and full-process leakage characteristics, making it difficult to directly provide reliable data support for the construction of leak identification algorithms and limiting the models' generalization ability.

[0005] Leak identification is divided into qualitative identification (determining whether a leak has occurred) and quantitative identification (determining the location and size of the leak). While qualitative identification techniques are widely used in industry, quantitative identification has greater engineering value due to its ability to provide direct guidance for remediation strategies, but it is also more challenging. Early identification methods mainly relied on fluid composition comparisons. With the development of sensing technology, detection based on physical fields (sound waves, temperature, pressure, flow fields) has become mainstream. Although detection methods are becoming increasingly sophisticated, problems still exist in quantitatively identifying the location and size of leaks. Existing acoustic array methods require shutdown and removal of the tubing, which is costly, cumbersome, and lacks real-time capability. Furthermore, current technologies mainly rely on simple parameters such as temperature and pressure for qualitative judgment, lacking corresponding transient full-process physical models and machine learning methods, making it difficult to effectively identify the specific location and size of leaks.

[0006] With the improvement of computing power and the development of big data technology, machine learning and deep learning have become core tools for solving complex nonlinear pattern recognition and parameter prediction. However, current research in this field mainly focuses on pipeline transportation systems, while research on gas well production tubing is relatively scarce. Compared with the rapid development of artificial intelligence frameworks, research on wellbore and production tubing is still in its early stages. Existing research has few results on simultaneously quantitatively detecting the location and size of leaks, and identifying leaks, especially small leaks, is far more difficult than locating them. Traditional single regression models are unable to cope with highly nonlinear downhole signals, and there is a lack of regression inversion strategies using integrated models or time-series data, resulting in limited quantitative prediction accuracy and difficulty in adapting to complex real-world application environments. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes an intelligent identification method for leakage in ultra-deep gas well tubing based on a time-series data and time-frequency fusion BiLSTM model. This invention proposes an intelligent method for identifying leaks in ultra-deep gas well tubing based on a time-series dataset. This method employs a composite deep learning model combining multi-scale CNN, Fast Fourier Transform (FFT), Bidirectional Long Short-Term Memory (BiLSTM), Adaptive Multi-Head Attention (AMA), and Gated Information Fusion Architecture (GRN). Furthermore, the performance of the integrated model is improved using the Optuna hyperparameter optimization method. The model can simultaneously identify both the leak location and size, exhibiting good accuracy and stability. It is adaptable to extreme data conditions and shows significant application potential in the complex actual production environment of ultra-deep gas wells, providing reliable technical support for intelligent well control and wellbore integrity safety prediction.

[0008] The technical solution of this invention is as follows: A smart identification method for leakage in ultra-deep gas well tubing based on a time-series data and time-frequency fusion BiLSTM model includes: Step 1: Obtain the physical features of the model input and construct the experimental dataset; Step 2: Build and train an ensemble deep learning model that integrates multiple modules; Step 3: Intelligent identification of leaks in ultra-deep gas well tubing is performed using an integrated deep learning model that integrates multiple modules after training.

[0009] According to a preferred embodiment of the present invention, obtaining the physical features of the model input and constructing an experimental dataset includes: Nine parameters were selected as the physical features of the model input: annular top pressure, annular top fluid temperature, tubing top pressure, tubing top fluid temperature, reservoir top pressure, reservoir top fluid temperature, total annular water content, annular top porosity, and total tubing top volumetric flow rate. The experimental dataset is the physical features of the model input.

[0010] According to a preferred embodiment of the present invention, the integrated model refers to an integrated deep learning model that fuses multiple modules, and also refers to a BiLSTM model that fuses time-series data and time-frequency data; including a time-frequency dual-stream feature extraction layer, a global time-series evolution modeling layer, an adaptive key feature aggregation layer, and a gated decision regression layer; In the time-frequency dual-stream feature extraction layer, a parallel dual-path structure is used to process the standardized 9-dimensional physical monitoring signal. The parallel dual-path structure includes a time-domain branch and a frequency-domain branch. In the time-domain branch, a multi-scale convolutional network is used to capture high-frequency abrupt changes in small leaks and low-frequency trends in large leaks in parallel through convolutional kernels of different sizes. In the frequency-domain branch, the signal is mapped to the frequency domain using Fast Fourier Transform (FFT) to extract the Top-K principal energy features. The features from the time-domain branch and the frequency-domain branch are concatenated in the channel dimension to form a hybrid feature vector containing local details and global distribution. In the global temporal evolution modeling layer, a bidirectional long short-term memory network (BiLSTM) is used to process mixed feature vectors; through a dual-channel mechanism of forward and reverse directions, a long-range context dependency that leaks the entire lifecycle is established. In the adaptive key feature aggregation layer, an adaptive multi-head attention mechanism (AMA) is introduced to address the transient characteristics of leakage signals. Through a learnable global query vector, steady-state background noise is automatically masked, and the system dynamically focuses on key time steps where pressure drops or oscillations occur, compressing variable-length time-series features into fixed-length, highly discriminative context vectors. In the gated decision regression layer, the gated residual network GRN is used as the regression head. The aggregated features are screened a second time through the GLU gate unit to suppress redundant information and amplify the core leakage features. Finally, the precise leakage location and size are output through linear layer mapping.

[0011] According to a preferred embodiment of the present invention, the specific implementation process in the time-frequency dual-stream feature extraction layer includes: The 9-dimensional physical monitoring signal, preprocessed with Z-score normalization, is input into a multi-scale convolutional network; specifically, assuming the original signal is... ,in T The time series length is given, and each dimension represents a type of physical monitoring indicator. For each dimension... i Perform independent standardization processing to obtain standardized signals. Standardized signal elements Calculated by the following formula: ; in, It is the first i dimensional signal in the first t The original values ​​at each time point; and The first i The mean and standard deviation of the signal on the training set; The multi-scale convolutional network consists of four parallel convolutional branches, with kernel sizes set to [sizes to be filled in]. These correspond to different receptive fields for features from high frequency to low frequency; the number of output channels for all convolutional branches is uniformly set to 32, and a ReLU activation function is used. The final output of the parallel multi-scale CNN module is obtained by concatenating the output tensors H of each branch along the channel dimension. ; in, Indicates the kernel size as k The output feature tensor of the corresponding branch H Ultimately, a 128-dimensional local-global fusion feature vector is formed. The standardized 9-dimensional physical monitoring signal is processed using Real Fast Fourier Transform (RFFT). After calculating the spectral amplitude and the modulus of the complex spectrum, a Top-K selection strategy is employed to retain only the top K components with the largest amplitude for each channel. ; in, Indicates the first p The sparse frequency domain amplitude characteristics ultimately retained by each channel For the input sequence The complete complex spectrum after RFFT This represents the Top-K truncation operation, which sorts the spectral amplitudes and then truncates only the highest-energy values. K One component; Flatten the extracted frequency domain feature vectors and copy them in the time dimension; The time-domain features of the original input With the extended frequency domain characteristics splicing: ; Finally, the output tensor is obtained. Dimension, will With multi-scale CNN output features The data is spliced ​​together to form a highly discriminative input that includes local details in the time domain and global distribution in the frequency domain.

[0012] According to a preferred embodiment of the present invention, the specific implementation process in the global temporal evolution modeling layer includes: A bidirectional long short-term memory network (BiLSTM) is constructed. The BiLSTM network uses two stacked layers of bidirectional LSTM units, each layer including two parallel LSTM chains, one forward and one backward. At the input end, firstly, the 128-dimensional temporal features extracted by the multi-scale CNN are concatenated with the 153-dimensional frequency features output by the FFT module along the channel dimension to form... The first LSTM unit processes the input sequence bidirectionally, forward and backward, concatenating the forward and backward hidden states into a 128-dimensional feature at each time step. The second LSTM unit further models long-range temporal dependencies, ultimately outputting a 128-dimensional deep temporal feature sequence. Specifically, this includes: The received input includes 128-dimensional temporal features extracted by a multi-scale CNN and 153-dimensional frequency features output by an FFT module, where the input dimensions are... Construct a binary mask matrix : ; in, For the first b The true effective length of each sample t Indicates the position index in the current time step or sequence. It is an indicator function; Perform sequence compression transformation to transform the three-dimensional tensor ( Reorganized into a compact two-dimensional tensor sequence , among which, the t The input for each step includes the current time mask. Valid sample data; BiLSTM extracts features using two stacked LSTM units, and employs a bidirectional propagation mechanism to compute the forward hidden state sequence separately. and reverse hidden state sequence : ; Each LSTM layer has 64 hidden cells; the forward and reverse states at the same time step are concatenated as follows: ; in, Indicates at time step t The hidden state incorporates contextual information and has a feature dimension of 128. After two layers of stacked bidirectional computation, for Perform a sequence decomposition operation to restore the compressed hidden state to the original batch structure, and fill invalid positions with zero values. The final output is the feature tensor. .

[0013] According to a preferred embodiment of the present invention, the specific implementation process of the adaptive key feature aggregation layer includes: The Adaptive Multi-Head Attention (AMA) mechanism serves as the temporal aggregation layer, while the Adaptive Key Feature Aggregation layer receives the hidden state sequence output by the BiLSTM. H Introducing learnable global query parameters The input sequence is split to generate key and value matrices. Attention scores are calculated using matrix multiplication with the Key. After masking invalid padding bits and Softmax normalization, adaptive weights are obtained. These weights are then weighted and summed with the Value to generate the output features of each attention head. The outputs of multiple attention heads are concatenated, linearly projected, and normalized layer by layer to finally output a global context vector. Specifically, this includes: First, define a globally learnable query vector. The attention mechanism employs a multi-head design, including h The first parallel processing head; for the first i One processing head, , will input H and global query parameters Project each element onto a lower-dimensional space to generate the corresponding Query, Key, and Value matrices: ; in, For the first i The linear projection matrix of each processing head. For subspace dimension; Within each processing head, the dot product similarity between the Query matrix and the Key matrix is ​​calculated and divided by a scaling factor. Introducing a Key Padding Mask mechanism for time steps t If the data corresponding to that time step belongs to the filled region, then its attention score is... Set it to negative infinity, as shown below: ; ; in, Indicates the first i In each processing head, the time step t The corresponding key vector; This represents the unnormalized attention score calculated from the global query and the key vector at this time step. Subsequently, a normalized attention weight distribution is generated using the Softmax function. The calculated weights are used to perform a weighted summation on the Value matrix to obtain the first... i Context vector of each processing head : ; in, Indicates the first i In each processing head, with time step t The corresponding Value vector; Finally, all h The outputs of each processing head are concatenated and then linearly projected. After layer normalization, the final fixed-length global context vector is obtained. : ; Final output It is related to the sequence length T Irrelevant high-dimensional feature vectors.

[0014] According to a preferred embodiment of the present invention, the specific implementation process of the gated decision regression layer includes: A gated residual network (GRN) is introduced as the final regression and information fusion module; Gated residual networks (GRNs) consist of gated linear units (GLUs), residual connections, and layer normalization, and include two parallel paths: Nonlinear transformation path: First, the input vector is the final fixed-length global context vector. After passing through a linear layer and the ELU activation function, a latent feature representation is generated. z Subsequently, the latent feature representation is split into a data stream and a gated stream; the gated stream generates weight coefficients in the (0,1) interval using the Sigmoid function, and performs element-wise multiplication with the data stream to obtain the transformed feature. As shown below: ; in, It is the Sigmoid activation function. and Let represent the learnable weight matrix and bias vector, respectively, to represent the degree of gate opening. and These represent the learnable weight matrix and bias vector, respectively, for linear transformation of the original data. Residual connection path: The original input is the final fixed-length global context vector. Direct and transformed features The summation and layer normalization yield the final output. : ; Based on high discriminative features, i.e., the final output vector Finally, the leak location is output through two independent linear heads. With size Quantitative predicted values: ; ; in, and This is the weight vector of the regression head, used to map high-dimensional features to scalar output. and This is the bias term for the regression head.

[0015] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described intelligent identification method for ultra-deep gas well tubing leakage based on a time-series data and time-frequency fusion BiLSTM model.

[0016] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described intelligent identification method for leakage in ultra-deep gas well tubing based on a time-series data and time-frequency fusion BiLSTM model.

[0017] The beneficial effects of this invention are as follows: This invention proposes an intelligent method for identifying leaks in ultra-deep gas well tubing based on time-series data and a multi-module fusion deep learning model. This method can efficiently learn input physical features and achieve high-precision regression prediction for leak location and size. Final application examples show that this model achieves high accuracy in predicting leak location and size for small-to-medium-sized leaks (0.1-30 mm). 2All values ​​exceeded 0.99, achieving sub-millimeter-level detection accuracy (MAE = 0.0907 mm) in size prediction tasks, while controlling the RMSE of leak location prediction to around 30 m. Even with reduced input features and sample size, the model still exhibited strong robustness and generalization ability, demonstrating application potential in the complex actual production environment of ultra-deep gas wells. Attached Figure Description

[0018] Figure 1 This is a diagram of the overall architecture of the comprehensive model; Figure 2 This is a schematic diagram of the time-frequency dual-stream feature extraction layer structure; Figure 3 A schematic diagram of the layer structure for modeling global temporal evolution; Figure 4 This is a schematic diagram of the adaptive key feature aggregation layer structure; Figure 5 This is a schematic diagram of the gating decision regression layer structure; Figure 6 This is a diagram showing the final leakage prediction result of the integrated model; Figure 7 A diagram showing the comparison of regression indicators for representative time-series models; Figure 8 This is a diagram illustrating the comparison of regression indicators for small sample validation. Detailed Implementation

[0019] The present invention will be further defined below with reference to the accompanying drawings and embodiments, but is not limited thereto.

[0020] Example 1 A smart identification method for leakage in ultra-deep gas well tubing based on a time-series data and time-frequency fusion BiLSTM model includes: Step 1: Obtain the physical features of the model input and construct the experimental dataset; Step 2: Build and train an ensemble deep learning model that integrates multiple modules; Step 3: Intelligent identification of leaks in ultra-deep gas well tubing is performed using an integrated deep learning model that integrates multiple modules after training.

[0021] Example 2 The difference between the intelligent identification method for ultra-deep gas well tubing leakage based on time-series data and time-frequency fusion BiLSTM model described in Example 1 and the method described in Example 1 is as follows: Obtain the physical features of the model input and construct the experimental dataset; including: Nine parameters were selected as the physical features of the model input: annular top pressure, annular top fluid temperature, tubing top pressure, tubing top fluid temperature, reservoir top pressure, reservoir top fluid temperature, total annular water content, annular top porosity, and total tubing top volumetric flow rate. The experimental dataset is the physical features of the model input.

[0022] The methods for acquiring input physical feature data include, but are not limited to: generating data using multiphase flow models and numerical simulation algorithms in oil and gas wellbore production, deriving data through calculations using commercial multiphase flow software for wellbore production, or collecting data by deploying corresponding measurement sensors in actual wells. Meanwhile, the leak location (depth) and leak size serve as target features of the dataset. To verify the model's effectiveness, this embodiment constructs a time-series dataset covering leak depths of 500-7500m and leak sizes ranging from 0.1-30mm as the basis for model training and testing.

[0023] To address the non-stationarity, strong noise interference, and long-range time-series dependence issues present in ultra-deep gas well leakage signals, this invention proposes an integrated deep learning model (hereinafter referred to as the integrated model) that fuses multiple modules. This model aims to achieve high-precision identification of the location and size of leaks in ultra-deep gas well tubing through a processing flow of "multi-view feature decoupling—temporal correlation modeling—key information aggregation—gated nonlinear regression."

[0024] like Figure 1 As shown, the integrated model refers to an ensemble deep learning model that integrates multiple modules, and also refers to a BiLSTM model that integrates time-series data and time-frequency data; it includes a time-frequency dual-stream feature extraction layer, a global time-series evolution modeling layer, an adaptive key feature aggregation layer, and a gated decision regression layer; In the time-frequency dual-stream feature extraction layer, a parallel dual-path structure is used to process the standardized 9-dimensional physical monitoring signal. This parallel dual-path structure includes a time-domain branch and a frequency-domain branch. In the time-domain branch, a multi-scale convolutional network is used to capture high-frequency abrupt changes in small leaks and low-frequency trends in large leaks through convolutional kernels of different sizes in parallel. In the frequency-domain branch, a Fast Fourier Transform (FFT) is used to map the signal to the frequency domain and extract Top-K principal energy features to supplement the global periodic pattern. The features from the time-domain and frequency-domain branches are concatenated along the channel dimension to form a hybrid feature vector containing both local details and global distribution.

[0025] In the global temporal evolution modeling layer, the bidirectional long short-term memory network BiLSTM is used to process the mixed feature vectors. Through the dual-channel mechanism of forward and reverse, the model can not only utilize the pressure accumulation information of historical moments, but also trace back the balance recovery trend of future moments, thereby establishing long-range contextual dependencies for the entire life cycle of leakage. In the adaptive key feature aggregation layer, an adaptive multi-head attention mechanism (AMA) is introduced to address the transient characteristics of leakage signals. Through a learnable global query vector, steady-state background noise is automatically masked, and the system dynamically focuses on key time steps where pressure drops or oscillations occur, compressing variable-length time-series features into fixed-length, highly discriminative context vectors. In the gated decision regression layer, the gated residual network GRN is used as the regression head. The aggregated features are screened a second time through the GLU gate unit to suppress redundant information and amplify the core leakage features. Finally, the precise leakage location and size are output through linear layer mapping.

[0026] The specific implementation process in the time-frequency dual-stream feature extraction layer includes: While BiLSTM excels in global temporal modeling, its ability to capture local high-frequency abrupt changes is relatively weak. CNNs, with their superior parallel computing capabilities and local feature extraction advantages, have been widely applied in industrial fault diagnosis and noise-resistant feature extraction. In the field of wellbore integrity monitoring, CNNs are gradually replacing the traditional pressure gradient method, taking on the role of "automatic feature engineering." However, existing single-scale convolutional architectures struggle to handle the complex hydrodynamic characteristics of ultra-deep gas wells. Small-sized convolutional kernels are adept at capturing high-frequency noise caused by minor leaks, while large-sized kernels are better suited for extracting low-frequency trends under high-flow-rate leaks. This invention designs a multi-scale convolutional module before the BiLSTM module, aiming to adaptively decouple multi-frequency components in the leak signal through parallel branches with different receptive fields.

[0027] Multi-scale convolutional networks (multi-scale parallel CNN modules) structure as follows Figure 2 As shown in (a), Figure 2 (a) is a structural diagram of a multi-size CNN module.

[0028] The 9-dimensional physical monitoring signal, preprocessed with Z-score normalization, is input into a multi-scale convolutional network; specifically, assuming the original signal is... ,in T The time series length is defined, with each dimension representing a type of physical monitoring indicator (such as annular top pressure, bottom hole temperature, etc.). For each dimension... i Perform independent standardization processing to obtain standardized signals. Standardized signal elements Calculated by the following formula: ; in, It is the first i dimensional signal in the first t The original values ​​at each time point; and The first iThe mean and standard deviation of the signal on the training set; The multi-scale convolutional network consists of four parallel convolutional branches, with kernel sizes set to [sizes to be filled in]. These correspond to different receptive fields for features from high to low frequencies; the number of output channels for all convolutional branches is uniformly set to 32, and a ReLU activation function is used to enhance nonlinear representation. To ensure the output feature tensors of all parallel branches... H Strict alignment in the time dimension facilitates subsequent fusion; the model employs a Same Padding strategy for each branch. The final output of the parallel multi-scale CNN module is obtained by concatenating the output tensors H of each branch in the channel dimension.

[0029] ; in, Indicates the kernel size as k The output feature tensor of the corresponding branch H Ultimately, a 128-dimensional local-global fusion feature vector is formed, which serves as one of the inputs to subsequent BiLSTM layers.

[0030] Furthermore, although multi-scale CNNs excel at extracting local temporal patterns, they are inherently limited by a finite receptive field, making it difficult to capture global periodic patterns and frequency distribution features. In ultra-deep gas well leaks, physical characteristics often manifest as scattered signals spanning hundreds of time steps in the time domain, but are concentrated in a few significant energy peaks in the frequency domain. To compensate for the limitations of a single time-domain perspective, this invention designs a parallel Fast Fourier Transform (FFT) feature enhancement module. This module utilizes the global receptive field of FFT to transform the time-domain signal into the frequency domain, providing the model with complementary information orthogonal to the time-domain features, thereby constructing a more complete description of the leak characteristics.

[0031] The architecture of the FFT enhancement module is as follows: Figure 2 As shown in (b) of the diagram. Considering that the input 9-dimensional physical monitoring signals are all real numbers and their spectra have conjugate symmetry, a real-number Fast Fourier Transform (RFFT) is used to process the standardized 9-dimensional physical monitoring signals to reduce computational redundancy. Abnormal fluctuations caused by leakage are mainly concentrated in specific energy frequency bands. To eliminate high-frequency noise and control the feature dimensions, after calculating the spectral amplitude, and then calculating the modulus (amplitude) of the complex spectrum, a Top-K selection strategy is adopted. For each channel (corresponding to the 9-dimensional physical feature signal), only the top K components with the largest amplitudes are retained (in this invention, the maximum amplitude is taken as K). K =16):

[0032] ; in, Indicates the first pThe sparse frequency domain amplitude characteristics ultimately retained by each channel For the input sequence The complete complex spectrum after RFFT This represents the Top-K truncation operation, which sorts the spectral amplitudes and then truncates only the highest-energy values. K Each component is used to remove environmental noise, retain the leakage principal energy characteristics, and effectively reduce the learning difficulty of subsequent models.

[0033] Since the FFT features obtained after the above processing are global static features, in order to align with the subsequent time-series input of BiLSTM, the extracted frequency domain feature vector (dimension) will be... Flatten and replicate over time; The time-domain features of the original input With the extended frequency domain characteristics splicing: ; Finally, the output tensor is obtained. The feature vector has a total of 153 dimensions (9 original time-domain features + 144 frequency-domain features); it retains both the transient waveform information of the original signal and embeds global resonant frequency features. With multi-scale CNN output features The data is spliced ​​together to form a highly discriminative input that includes local details in the time domain and global distribution in the frequency domain.

[0034] The specific implementation process in the global temporal evolution modeling layer includes: To address the strong time-varying nature, long-term dependence, and signal lag in ultra-deep gas well leakage monitoring data, this invention employs a bidirectional long short-term memory network (BiLSTM) as the basic architecture for temporal feature extraction. Traditional recurrent neural networks (RNNs) suffer from the vanishing gradient problem, making it difficult to capture long-range dependencies. Long short-term memory networks (LSTMs) effectively alleviate this problem by introducing a gating mechanism; however, their unidirectional structure can only utilize historical information and cannot establish a correlation between the current state and the evolution of subsequent physical features. BiLSTM, referencing bidirectional RNNs, introduces a bidirectional mechanism, enabling it to process both forward and backward sequence information simultaneously. It exhibits good robustness in time-series tasks and generally outperforms models such as LSTM and GRU.

[0035] Construct a bidirectional long short-term memory network BiLSTM, with the following structure: Figure 3 As shown. The Bidirectional Long Short-Term Memory (BiLSTM) network uses two stacked layers of bidirectional LSTM units, each layer including two parallel LSTM chains, one forward and one backward, each configured with 64 hidden units;

[0036] At the input end, firstly, the 128-dimensional temporal features extracted by the multi-scale CNN (the 128-dimensional output tensor of the multi-scale CNN module) are processed. ) and the 153-dimensional frequency domain features output by the FFT module (the 153-dimensional output tensor of the FFT module) (Sponged together in the channel dimension to form) The first LSTM unit processes the input sequence bidirectionally, forward and backward, concatenating the forward and backward hidden states into a 128-dimensional feature at each time step. The second LSTM unit further models long-range temporal dependencies, ultimately outputting a 128-dimensional deep temporal feature sequence. Specifically, this includes: First, such as Figure 3 As shown on the left, the received input includes 128-dimensional temporal features extracted by a multi-scale CNN and 153-dimensional frequency features output by an FFT module, where the input dimensions are... (128-dimensional time domain + 153-dimensional frequency domain); Due to the varying durations of different monitoring periods, invalid padding bits inevitably exist in the input data. To eliminate noise interference from these padding bits on long-range gradient propagation, a binary mask matrix is ​​constructed. :

[0037] ; in, For the first b The true effective length of each sample t Indicates the position index in the current time step or sequence. It is an indicator function; To improve computational efficiency, a sequence compression transformation is performed on the three-dimensional tensor ( Reorganized into a compact two-dimensional tensor sequence , among which, the t The input for each step includes the current time mask. The effective sample data ensures that the gradients of subsequent LSTM units propagate only within the effective time steps.

[0038] On the compressed sequence, BiLSTM extracts features through two stacked LSTM units, and BiLSTM employs a bidirectional propagation mechanism to compute the forward hidden state sequence separately. and reverse hidden state sequence : ; Each LSTM layer has 64 hidden units; to integrate historical and future evolutionary information, the forward and reverse states at the same time step are concatenated, as shown below: ; in, Indicates at time step t The hidden state incorporates contextual information and has a feature dimension of 128. After two layers of stacked bidirectional computation, for Perform a sequence decomposition operation to restore the compressed hidden state to the original batch structure, and fill invalid positions with zero values. The final output is the feature tensor. The final output feature tensor It fully preserves the bidirectional temporal characteristics within the effective time step, while mathematically guaranteeing the gradient blocking of invalid padding bits and eliminating the interference of padding noise on long-range gradient propagation.

[0039] The specific implementation process of the adaptive key feature aggregation layer includes: Although the BiLSTM module extracts rich temporal dependency features, its output is still a variable of length 1000. T Variable-length sequences. In ultra-deep gas well leak detection tasks, leaks often manifest as discrete transient events, with key physical features (such as pressure drops and high-frequency oscillations) concentrated in only a few time steps, while the majority of the time is background noise or steady-state signals. Traditional sequence aggregation methods have significant drawbacks; for example, directly taking the state at the last moment leads to severe long-range forgetting, while average pooling dilutes the crucial weak leak signals with a large amount of background noise. To address this, this invention designs an adaptive multi-head attention mechanism as the temporal aggregation layer, aiming to automatically locate and focus on high-value leak feature fragments, achieving an adaptive transformation from variable-length sequences to fixed-length, highly discriminative vectors.

[0040] Adaptive Multi-Head Attention Mechanism (AMA) as a temporal aggregation layer, such as Figure 4 As shown, unlike traditional self-attention mechanisms where the query originates from the input sequence itself, this module introduces a globally learnable query vector. This vector, as an independently optimized global parameter, acts as the model's latent cognitive structure for the "standard template of leaked features." During training, this vector is continuously adjusted, gradually learning typical patterns of leaked signals. During testing, it is used as the query to match and search the sequence (key / value) output by the BiLSTM. This mechanism allows the model to no longer rely on fixed time positions, but rather adaptively search for key information based on the similarity of signal content. Simultaneously, the multi-head design allows the model to capture features from different subspaces in parallel. For example, one head might focus on the overall downward trend of annular pressure, while another head focuses on capturing bursts of high-frequency noise. Furthermore, in conjunction with the Key Padding Mask technique, the attention score at the padding location is set to negative infinity, ensuring that the model completely shields itself from interference from invalid padding data.

[0041] like Figure 4As shown, the adaptive key feature aggregation layer receives the hidden state sequence output by BiLSTM. H (i.e., the output tensor mentioned above) Introducing learnable global query parameters Instead of traditional time-series queries, the input sequence is split to generate key and value matrices. Attention scores are calculated using matrix multiplication with the Key. After masking invalid padding bits and Softmax normalization, adaptive weights are obtained. These weights are then weighted and summed with the Value to generate the output features of each attention head. The outputs of multiple attention heads are concatenated, linearly projected, and layer normalized to finally output a global context vector. This mechanism automatically locates critical moments of leakage through learnable parameters, compressing variable-length sequences into discriminative feature representations of fixed dimensions. Specifically, it includes:

[0042] First, define a globally learnable query vector. It does not depend on specific inputs but is continuously updated during training via backpropagation to learn typical patterns of leaked signals. To capture features across different subspaces, the attention mechanism employs a multi-head design, including... h The first parallel processing head; for the first i One processing head, , will input H and global query parameters Project each element onto a lower-dimensional space to generate the corresponding Query, Key, and Value matrices:

[0043] ; in, For the first i The linear projection matrix of each processing head. For subspace dimension; Within each processing head, the dot product similarity between the Query matrix and the Key matrix is ​​calculated and divided by a scaling factor. To prevent gradient vanishing, a Key Padding Mask mechanism is introduced to eliminate interference from invalid padding bits in variable-length sequences, for each time step. t If the data corresponding to that time step belongs to the filled region (i.e., the mask) Then, its attention score Set it to negative infinity, as shown below:

[0044] ; ; in, Indicates the first i In each processing head, the time step tThe corresponding key vector; This represents the unnormalized attention score calculated from the global query and the key vector at this time step. Subsequently, a normalized attention weight distribution is generated using the Softmax function. This ensures that the model completely masks invalid data and only weights valid physical signals. The calculated weights are then used to perform a weighted summation of the Value matrix to obtain the... i Context vector of each processing head :

[0045] ; in, Indicates the first i In each processing head, with time step t The corresponding Value vector; Finally, all h The outputs of each processing head are concatenated and then linearly projected. After layer normalization, the final fixed-length global context vector is obtained. : ; Final output It is related to the sequence length T Unrelated high-dimensional feature vectors. It adaptively fuses key transient information and global patterns in the leakage process, providing highly discriminative input features for subsequent quantitative leakage inversion.

[0046] The specific implementation process of the gated decision regression layer includes: After feature extraction from the preceding modules, the model obtains a context vector rich in time-frequency information. However, in ultra-deep gas well leak detection tasks, high-dimensional feature spaces are often accompanied by information redundancy. For example, CNNs may extract repetitive local patterns, and FFT transformations may introduce some frequency domain noise. If traditional fully connected layers (MLPs) are directly used for regression, the model is prone to overfitting or suboptimal solutions because it cannot distinguish the importance of features. To address this, a gated residual network (GRN) is introduced as the final regression and information fusion module. Unlike ordinary nonlinear layers, GRN, through the introduction of a learnable gating mechanism, can adaptively filter effective information according to the context, acting as a "soft feature engineering" filter at the model output.

[0047] like Figure 5As shown, the Gated Residual Network (GRN) combines the residual concept of ResNet and the gating concept of LSTM, allowing models to be stacked deeper without performance degradation. This is beneficial for handling highly nonlinear regression problems. The GRN consists of a gated linear unit (GLU), residual connections, and layer normalization, and includes two parallel paths:

[0048] Nonlinear transformation path: First, the input vector is the final fixed-length global context vector. After passing through a linear layer and the ELU activation function, a latent feature representation is generated. z Subsequently, the latent feature representation is split into a data stream and a gated stream; the gated stream generates weight coefficients in the (0,1) interval using the Sigmoid function, and performs element-wise multiplication with the data stream to obtain the transformed feature. As shown below: ; in, It is the Sigmoid activation function. and Let represent the learnable weight matrix and bias vector, respectively, to represent the degree of gate opening. and These represent the learnable weight matrix and bias vector, respectively, for linear transformation of the original data; this mechanism allows the model to automatically suppress noisy features (weights approaching 0) and amplify key leakage features (weights approaching 1). Residual connection path: The original input is the final fixed-length global context vector. Direct and transformed features The summation and layer normalization yield the final output. : ; This design not only preserves the original information of the attention layer, but also provides a low-loss direct path for gradient propagation, enabling the network to be stacked deeper and overcome the degradation problem.

[0049] Based on high discriminative features, i.e., the final output vector Finally, the leak location is output through two independent linear heads. With size Quantitative predicted values: ; ; in, and This is the weight vector of the regression head, used to map high-dimensional features to scalar output. and This is the bias term for the regression head.

[0050] This embodiment performs Optuna hyperparameter optimization and comparative experiments; Optuna hyperparameter optimization and model regression metrics: To fully explore the model's potential and avoid the limitations of manual parameter tuning, this invention employs the Optuna framework with validation set mean squared error (MSE) as the target. It iterative searches are performed on key parameters such as the BiLSTM hidden layer dimension, initial learning rate, and Dropout ratio. The final optimal configuration is shown in Table 1. Optuna uses the TPE algorithm, which, compared to traditional grid search or random search, can construct a probabilistic model based on the historical evaluation of parameters, more intelligently locating high-potential regions in the search space, thus significantly improving search efficiency and convergence speed.

[0051] Table 1. Optimal hyperparameter configuration of the integrated model (retain 6 decimal places). The final prediction results are as follows Figure 6 As shown. Figure 6 In the diagram, (a) shows the error in predicting the leak location, and (b) shows the error in predicting the leak size. The integrated model demonstrates excellent performance in both leak location and size prediction, with high consistency between the predicted and actual values. The vast majority of sample points converge closely within the diagonal and the 5% error confidence band. Particularly for predicting small leak sizes, the model achieves sub-millimeter accuracy (R0). 2 =0.9982, MAE=0.09mm), and no significant outliers were found. This indicates that the integrated model not only has high fitting accuracy, but also successfully captures the nonlinear temporal characteristics in the multiphase flow leakage signal, verifying the effectiveness of the method.

[0052] Comparison of representative time series models: To further compare the models, four representative deep learning models that have become very popular in recent years and are capable of handling raw time series data were introduced for comparative experiments: Bidirectional Recurrent Neural Network (BiRNN), Temporal Convolutional Network (TCN), Bidirectional Long Short-Term Memory Network (BiLSTM), and Transformer. To ensure the reliability of the experiments, five-fold cross-validation was used. The preprocessed dataset was randomly divided into five mutually exclusive subsets. In each round of validation, one subset was selected as the test set, and the other four subsets were selected as the training set. The average result of the five rounds was then taken.

[0053] Experimental results of various time-series models on the prediction of leak location and leak size are as follows: Figure 7 and Figure 8As shown, the integrated model achieved significant advantages in all metrics. The MAE and RMSE for leak location and size predictions were significantly reduced, exceeding 60% compared to the basic BiLSTM module. The size prediction RMSE was ultimately controlled within 0.3 mm. 2 It is also close to 0.999. This result shows that the integrated model makes full use of temporal features, effectively removes background noise through architectural design, and accurately captures the complex changes caused by small and medium leakages.

[0054] Table 2 Comparison of common time series model regression indicators (retain 4 decimal places); Feature ablation and small-sample validation, specifically including the following: In real-world industrial settings, sensor malfunctions or data loss may occur, preventing the model from acquiring a complete training dataset. To verify the robustness of the proposed integrated model under sparse data and to explore the specific contributions of core physical variables to leakage inversion, a feature ablation experiment was designed.

[0055] The experiment selected two important thermo-baric features with high overall contribution from the sensitivity analysis section: annular top pressure and annular top temperature. Two training sets were constructed: Dataset 1, retaining the two-dimensional input features of annular top pressure and annular top temperature, and Dataset 2, retaining only the most critical feature, annular top pressure. Four high-performing models—LightGBM, ResNet, BiLSTM, and Transformer—were used as baselines for comparison with the comprehensive model. Five-fold cross-validation was used in the experiments. The experimental results are shown in Table 3.

[0056] Table 3 Comparison of representative model regression indicators (retain 4 decimal places);

[0057] In real-world oil and gas field production scenarios, obtaining a large number of high-quality leak samples often faces challenges such as high costs and long cycles. A model with practical deployment value should possess the ability to maintain high performance even under conditions of scarce samples. To verify the model's deployment potential in low-resource environments, a stringent small-sample experiment was designed: a logarithmic stratified sampling strategy was adopted, retaining only 20% of the samples in the single-feature dataset (dataset 2) for training. The experimental results are shown in Table 4.

[0058] Table 4 Comparison of regression indicators for small sample models (retain 4 decimal places);

[0059] Small-sample experiments have demonstrated that, even under extreme conditions with limited single-dimensional monitoring data, the comprehensive model proposed in this invention can still achieve high leak detection accuracy. This "small sample, high accuracy" characteristic makes it practically valuable for rapid deployment in ultra-deep gas well sites where data is scarce.

[0060] Example 3 A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the intelligent identification method for leakage in ultra-deep gas well tubing based on time-series data and time-frequency fusion BiLSTM model as described in Embodiment 1 or 2.

[0061] Example 4 A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the intelligent identification method for ultra-deep gas well tubing leakage based on a time-series data and time-frequency fusion BiLSTM model as described in Embodiment 1 or 2.

Claims

1. A method for intelligent identification of leakage in ultra-deep gas well tubing based on time-series data and a time-frequency fusion BiLSTM model, characterized in that, include: Step 1: Obtain the physical features of the model input and construct the experimental dataset; Step 2: Build and train an ensemble deep learning model that integrates multiple modules; Step 3: Intelligent identification of leakage in ultra-deep gas well tubing using a multi-module fusion integrated deep learning model after training; The multi-module integrated deep learning model includes a time-frequency dual-stream feature extraction layer, a global temporal evolution modeling layer, an adaptive key feature aggregation layer, and a gated decision regression layer; In the time-frequency dual-stream feature extraction layer, a parallel dual-path structure is used to process the standardized 9-dimensional physical monitoring signal. The parallel dual-path structure includes a time-domain branch and a frequency-domain branch. In the time-domain branch, a multi-scale convolutional network is used to capture high-frequency abrupt changes in small leaks and low-frequency trends in large leaks in parallel through convolutional kernels of different sizes. In the frequency-domain branch, the signal is mapped to the frequency domain using Fast Fourier Transform (FFT) to extract the Top-K principal energy features. The features from the time-domain branch and the frequency-domain branch are concatenated in the channel dimension to form a hybrid feature vector containing local details and global distribution. In the global temporal evolution modeling layer, a bidirectional long short-term memory network (BiLSTM) is used to process mixed feature vectors; through a dual-channel mechanism of forward and reverse directions, a long-range context dependency that leaks the entire lifecycle is established. In the adaptive key feature aggregation layer, an adaptive multi-head attention mechanism (AMA) is introduced to address the transient characteristics of leakage signals. Through a learnable global query vector, steady-state background noise is automatically masked, and the system dynamically focuses on key time steps where pressure drops or oscillations occur, compressing variable-length time-series features into fixed-length, highly discriminative context vectors. In the gated decision regression layer, the gated residual network GRN is used as the regression head. The aggregated features are screened a second time through the GLU gate unit to suppress redundant information and amplify the core leakage features. Finally, the precise leakage location and size are output through linear layer mapping.

2. The intelligent identification method for ultra-deep gas well tubing leakage based on a time-series data and time-frequency fusion BiLSTM model according to claim 1, characterized in that, Obtain the physical features of the model input and construct the experimental dataset; including: Nine parameters were selected as the physical features of the model input: annular top pressure, annular top fluid temperature, tubing top pressure, tubing top fluid temperature, reservoir top pressure, reservoir top fluid temperature, total annular water content, annular top porosity, and total tubing top volumetric flow rate. The experimental dataset is the physical features of the model input.

3. The intelligent identification method for ultra-deep gas well tubing leakage based on a time-series data and time-frequency fusion BiLSTM model as described in claim 1, characterized in that, The specific implementation process in the time-frequency dual-stream feature extraction layer includes: The 9-dimensional physical monitoring signal, preprocessed with Z-score normalization, is input into a multi-scale convolutional network; specifically, assuming the original signal is... ,in T The time series length is given, and each dimension represents a type of physical monitoring indicator. For each dimension... i Perform independent standardization processing to obtain standardized signals. Standardized signal elements Calculated by the following formula: ； in, It is the first i dimensional signal in the first t The original values ​​at each time point; and The first i The mean and standard deviation of the signal on the training set; The multi-scale convolutional network consists of four parallel convolutional branches, with kernel sizes set to [sizes to be filled in]. These correspond to different receptive fields for features from high frequency to low frequency; the number of output channels for all convolutional branches is uniformly set to 32, and a ReLU activation function is used. The final output of the parallel multi-scale CNN module is obtained by concatenating the output tensors H of each branch along the channel dimension. ； in, Indicates the kernel size as k The output feature tensor of the corresponding branch H Ultimately, a 128-dimensional local-global fusion feature vector is formed. The standardized 9-dimensional physical monitoring signal is processed using Real Fast Fourier Transform (RFFT). After calculating the spectral amplitude and the modulus of the complex spectrum, a Top-K selection strategy is employed to retain only the top K components with the largest amplitude for each channel. ； in, Indicates the first p The sparse frequency domain amplitude characteristics ultimately retained by each channel For the input sequence The complete complex spectrum after RFFT This represents the Top-K truncation operation, which sorts the spectral amplitudes and then truncates only the highest-energy values. K One component; Flatten the extracted frequency domain feature vectors and copy them in the time dimension; The time-domain features of the original input With the extended frequency domain characteristics splicing: ； Finally, the output tensor is obtained. Dimension, will With multi-scale CNN output features The data is spliced ​​together to form a highly discriminative input that includes local details in the time domain and global distribution in the frequency domain.

4. The intelligent identification method for ultra-deep gas well tubing leakage based on time-series data and a time-frequency fusion BiLSTM model according to claim 3, characterized in that, The specific implementation process in the global temporal evolution modeling layer includes: A bidirectional long short-term memory network (BiLSTM) is constructed. The BiLSTM network uses two stacked layers of bidirectional LSTM units, each layer including two parallel LSTM chains, one forward and one backward. At the input end, firstly, the 128-dimensional temporal features extracted by the multi-scale CNN are concatenated with the 153-dimensional frequency features output by the FFT module along the channel dimension to form... The first LSTM unit processes the input sequence bidirectionally, forward and backward, concatenating the forward and backward hidden states into a 128-dimensional feature at each time step. The second LSTM unit further models long-range temporal dependencies, ultimately outputting a 128-dimensional deep temporal feature sequence. Specifically, this includes: The received input includes 128-dimensional temporal features extracted by a multi-scale CNN and 153-dimensional frequency features output by an FFT module, where the input dimensions are... Construct a binary mask matrix : ； in, For the first b The true effective length of each sample t Indicates the position index in the current time step or sequence. It is an indicator function; Perform a sequence compression transformation to reassemble the three-dimensional tensor into a compact two-dimensional tensor sequence. , among which, the t The input for each step includes the current time mask. Valid sample data; BiLSTM extracts features using two stacked LSTM units, and employs a bidirectional propagation mechanism to compute the forward hidden state sequence separately. and reverse hidden state sequence : ； Each LSTM layer has 64 hidden cells; the forward and reverse states at the same time step are concatenated as follows: ； in, Indicates at time step t The hidden state incorporates contextual information and has a feature dimension of 128. After two layers of stacked bidirectional computation, for Perform a sequence decomposition operation to restore the compressed hidden state to the original batch structure, and fill invalid positions with zero values. The final output is the feature tensor. .

5. The intelligent identification method for ultra-deep gas well tubing leakage based on time-series data and a time-frequency fusion BiLSTM model according to claim 4, characterized in that, The specific implementation process of the adaptive key feature aggregation layer includes: The Adaptive Multi-Head Attention (AMA) mechanism serves as the temporal aggregation layer, while the Adaptive Key Feature Aggregation layer receives the hidden state sequence output by the BiLSTM. H Introducing learnable global query parameters The input sequence is split to generate key and value matrices. Attention scores are calculated using matrix multiplication with the Key. After masking invalid padding bits and Softmax normalization, adaptive weights are obtained. These weights are then weighted and summed with the Value to generate the output features of each attention head. The outputs of multiple attention heads are concatenated, linearly projected, and normalized layer by layer to finally output a global context vector. Specifically, this includes: First, define a globally learnable query vector. The attention mechanism employs a multi-head design, including h The first parallel processing head; for the first i One processing head, , will input H and global query parameters Project each element onto a lower-dimensional space to generate the corresponding Query, Key, and Value matrices: ； in, For the first i The linear projection matrix of each processing head. For subspace dimension; Within each processing head, the dot product similarity between the Query matrix and the Key matrix is ​​calculated and divided by a scaling factor. Introducing a Key Padding Mask mechanism for time steps t If the data corresponding to that time step belongs to the filled region, then its attention score is... Set it to negative infinity, as shown below: ； ； in, Indicates the first i In each processing head, the time step t The corresponding key vector; This represents the unnormalized attention score calculated from the global query and the key vector at this time step. Subsequently, a normalized attention weight distribution is generated using the Softmax function. The calculated weights are used to perform a weighted summation on the Value matrix to obtain the first... i Context vector of each processing head : ； in, Indicates the first i In each processing head, with time step t The corresponding Value vector; Finally, all h The outputs of each processing head are concatenated and then linearly projected. After layer normalization, the final fixed-length global context vector is obtained. : ； Final output It is related to the sequence length T Irrelevant high-dimensional feature vectors.

6. The intelligent identification method for ultra-deep gas well tubing leakage based on time-series data and a time-frequency fusion BiLSTM model according to claim 5, characterized in that, The specific implementation process of the gated decision regression layer includes: A gated residual network (GRN) is introduced as the final regression and information fusion module; Gated residual networks (GRNs) consist of gated linear units (GLUs), residual connections, and layer normalization, and include two parallel paths: Nonlinear transformation path: First, the input vector is the final fixed-length global context vector. After passing through a linear layer and the ELU activation function, a latent feature representation is generated. z Subsequently, the latent feature representation is split into a data stream and a gated stream; the gated stream generates weight coefficients in the (0,1) interval using the Sigmoid function, and performs element-wise multiplication with the data stream to obtain the transformed feature. As shown below: ； in, It is the Sigmoid activation function. and Let represent the learnable weight matrix and bias vector, respectively, to represent the degree of gate opening. and These represent the learnable weight matrix and bias vector, respectively, for linear transformation of the original data. Residual connection path: The original input is the final fixed-length global context vector. Direct and transformed features The summation and layer normalization yield the final output. : ； Based on high discriminative features, i.e., the final output vector Finally, the leak location is output through two independent linear heads. With size Quantitative predicted values: ； ； in, and This is the weight vector of the regression head, used to map high-dimensional features to scalar output. and This is the bias term for the regression head.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the intelligent identification method for leakage in ultra-deep gas well tubing based on time-series data and time-frequency fusion BiLSTM model as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the intelligent identification method for leakage in ultra-deep gas well tubing based on time-series data and time-frequency fusion BiLSTM model as described in any one of claims 1-6.

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