Non-stationarity Of Data Research Articles

Software Reliability Prediction by Adaptive Gated Recurrent Unit‐Based Encoder‐Decoder Model With Ensemble Empirical Mode Decomposition

ABSTRACTAccurate software reliability prediction is significant to software quality assurance. However, the rapid development and evolution of modern software pose more challenges for accurate software quality assessment. With the rapid development of machine learning and intelligent algorithms, data‐driven nonparametric models have gradually attracted increasing attention with outstanding prediction performance. However, we found that there may exist some prediction lags caused by the autocorrelation and nonstationarity of software fault data in the prediction of nonparametric models affecting their performance. To address this problem, we proposed an adaptive gated recurrent unit‐based encoder‐decoder model (ED‐GRU) with ensemble empirical mode decomposition (EEMD), effectively reducing prediction lags and performing accurate software fault number prediction. The autocorrelation and nonstationarity of fault data are first reduced by using first‐order difference and EEMD to clearly characterize the changing trend of the data. The frequency‐specific ED‐GRU networks are then combined to adaptively learn the nonlinear fluctuation trend of fault data under different frequency scales and obtain accurate prediction final results after aggregation. Experiments on eight public datasets showed that the proposed EEMD‐ED‐GRU‐PF model could effectively reduce the prediction lags and achieve the best prediction performance compared with four nonparametric and five parametric baseline methods in all datasets. Therefore, the proposed method can effectively and stably reduce the prediction lag to significantly improve the prediction accuracy. In this way, developers can accurately evaluate the current quality of the software and provide valuable guidance for software development and maintenance.

Application of improved adaptive method of CEEMD and data-drive in fault diagnosis

Purpose The diagnosis and prediction methods used for estimating the health conditions of the bearing are of great significance in modern petrochemical industries. This paper aims to discuss the accuracy and stability of improved empirical mode decomposition (EMD) algorithm in bearing fault diagnosis. Design/methodology/approach This paper adopts the improved adaptive complementary ensemble empirical mode decomposition (ICEEMD) to process the nonlinear and nonstationary signals. Two data sets including a multistage centrifugal fan data set from the laboratory and a motor bearing data set from the Case Western Reserve University are used to perform experiments. Furthermore, the proposed fault diagnosis method, combined with intelligent methods, is evaluated by using two data sets. The proposed method achieved accuracies of 99.62% and 99.17%. Through the experiment of two data, it can be seen that the proposed algorithm has excellent performance in the accuracy and stability of diagnosis. Findings According to the review papers, as one of the effective decomposition methods to deal with nonlinear nonstationary signals, the method based on EMD has been widely used in bearing fault diagnosis. However, EMD is often used to figure out the nonlinear nonstationarity of fault data, but the traditional EMD is prone to modal confusion, and the white noise in signal reconstruction is difficult to eliminate. Research limitations/implications In this paper only the top three optimal intrinsic mode functions (IMFs) are selected, but IMFs with less correlation cannot completely deny their value. Considering the actual working conditions of petrochemical units, the feasibility of this method in compound fault diagnosis needs to be studied. Originality/value Different from traditional methods, ICEEMD not only does not need human intervention and setting but also improves the extraction efficiency of feature information. Then, it is combined with a data-driven approach to complete the data preprocessing, and further carries out the fault identification and classification with the optimized convolutional neural network.

Volatility spillover effect between cryptocurrency and stock market using MGARCH Bekk model

This paper explores the volatility spillover effects between the cryptocurrency market and the Pakistan Stock Exchange (PSX). Utilising data from January 1, 2019, to April 5, 2024, sourced from Investing and Yahoo Finance, the study employs the Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH) BEKK model to assess the dynamic interactions between these markets. Stationarity tests confirmed the non-stationarity of time series data at their levels, which became stationary after first differencing, ensuring robust econometric analysis. The results indicate significant volatility spillovers from major cryptocurrencies, such as Bitcoin and Ethereum, to the PSX, highlighting a solid interconnectedness between these markets. This suggests that digital asset volatility significantly influences traditional financial systems. The study concludes that integrating cryptocurrencies into global financial markets introduces risks and opportunities for investors and policymakers. The findings underscore the need for market participants to account for these volatility interactions in their risk management strategies. Additionally, policymakers must consider these interlinkages to maintain financial stability. This research contributes to the literature on financial market volatility by emphasising the importance of understanding the impact of emerging digital currencies on traditional stock markets.

Exploring spatio-temporal dynamics for enhanced wind turbine condition monitoring

Efficient wind power cluster management and sustainable industry development require an optimized maintenance approach integrating condition monitoring. However, the intricate spatiotemporal correlations and non-stationarity of the data continue to pose significant challenges in extracting valuable insights from the supervisory control and data acquisition (SCADA) system. Hence, this paper proposes a novel approach for Dynamically Fusing Spatio-Temporal information with Difference Excitation (DFST-DE) in wind power systems’ condition monitoring. First, it extracts spatial dependencies by integrating sparse graph structures with Gumbel Softmax regularization and incorporates temporal information using a hybrid adaptive self-attention mechanism. This combined approach effectively captures comprehensive spatiotemporal correlations. Second, it proposes a Spatio-Temporal Difference Excitation module to mitigate non-stationarity in time series data by smoothing trend changes. The proposed DFST-DE approach achieves superior performance by effectively fusing spatial, temporal and excitation information. Finally, it optimizes anomaly detection accuracy and efficiency by dynamically adjusting the threshold based on anomaly score statistics. Experimental results on real-world wind farm datasets demonstrate that the proposed approach outperforms other established methods in detecting early abnormal conditions in wind turbines.

Mid-term electricity demand forecasting using improved multi-mode reconstruction and particle swarm-enhanced support vector regression

Balancing electricity supply and demand is crucial for China's energy transition and the stability of its electricity market. Accurate prediction of mid-term electricity demand plays a vital role in mitigating supply-demand imbalances, enabling policymakers and power plants to make informed decisions. This study proposes a novel hybrid model, EEMD-SE-PSO-SVR, to forecast mid-term electricity demand in China. The model integrates ensemble empirical mode decomposition (EEMD) with sample entropy (SE) for data preprocessing, particle swarm optimization (PSO) for parameter optimization, and support vector regression (SVR) for prediction. Our findings demonstrate that the EEMD-SE-PSO-SVR model outperforms traditional benchmark models, achieving a 54.49 % reduction in mean absolute percentage error (MAPE) compared to the SVR model. The model's performance is significantly enhanced by EEMD-SE, which effectively addresses the non-stationarity of electricity demand data. Moreover, the analysis highlights the strong influence of economic factors, followed by the seasonal factors and energy structure, underscoring their importance in accurately forecasting electricity demand. These findings contribute valuable insights for improving the accuracy of mid-term electricity demand forecasts and support the development of carbon-neutral and peak-carbon policies in China.

Sparse Wasserstein stationary subspace analysis for fault detection and diagnosis of nonstationary industrial processes

Fault detection and diagnosis of nonstationary processes are crucial for ensuring the safety of industrial production systems. However, the nonstationarity of process data poses multifaceted challenges to them. First, conventional stationary fault detection methods encounter difficulties in discerning evolving trends within nonstationary data. Secondly, the majority of current nonstationary fault detection methods directly extract features from all variables, rendering them susceptible to redundant interference. Moreover, nonstationary trends possess the capacity to conceal and modify the correlations among variables. Coupled with the smearing effect of faults, it is challenging to achieve accurate fault diagnosis. To address these challenges, this paper proposes sparse Wasserstein stationary subspace analysis (SWSSA). Specifically, a ℓ2,p-norm constraint is introduced to endow the stationary subspace model with excellent sparse representation capability. Furthermore, recognizing that fault variables within the sparse stationary subspace influence only a limited subset of stationary sources, this paper proposes a novel contribution analysis method based on local dynamic preserving projection (LDPP), termed LDPPBC, which can effectively mitigate the smearing effect on nonstationary fault diagnosis. LDPPBC establishes a LDPP matrix by extracting the latent positional information of fault variables within the stationary subspace. This allows LDPPBC to selectively analyze the contributions of variables within the latent fault subspace to achieve precise fault diagnosis while avoiding the interference of variable contributions from the fault-free subspace. Finally, the superiority of the proposed method is thoroughly validated through a numerical simulation, a continuous stirred tank reactor, and a real industrial roaster.

Addressing the Non-Stationarity and Complexity of Time Series Data for Long-Term Forecasts

Real-life time series datasets exhibit complications that hinder the study of time series forecasting (TSF). These datasets inherently exhibit non-stationarity as their distributions vary over time. Furthermore, the intricate inter- and intra-series relationships among data points pose challenges for modeling. Many existing TSF models overlook one or both of these issues, resulting in inaccurate forecasts. This study proposes a novel TSF model designed to address the challenges posed by real-life data, delivering accurate forecasts in both multivariate and univariate settings. First, we propose methods termed “weak-stationarizing” and “non-stationarity restoring” to mitigate distributional shift. These methods enable the removal and restoration of non-stationary components from individual data points as needed. Second, we utilize the spectral decomposition of weak-stationary time series to extract informative features for forecasting. To learn features from the spectral decomposition of weak-stationary time series, we exploit a mixer architecture to find inter- and intra-series dependencies from the unraveled representation of the overall time series. To ensure the efficacy of our model, we conduct comparative evaluations against state-of-the-art models using six real-world datasets spanning diverse fields. Across each dataset, our model consistently outperforms or yields comparable results to existing models.

Unraveling Financial Markets: Deep Neural Network-Based Models for Stock Price Prediction

This paper delves into the potential and challenges of leveraging deep neural networks (DNNs) in stock price forecasting. Traditional econometric models often grapple with the complexities of financial time series data, leading to the exploration of DNNs, especially architectures like Long Short-Term Memory (LSTM) networks, to capture intricate patterns in such data. While these networks present promising results, challenges such as model interpretability, non-stationarity of data, overfitting, and computational demands remain. The financial sector's increasing digitization and influx of alternative data offer a unique opportunity for DNNs, emphasizing their capability for automatic feature extraction. However, the integration of DNNs necessitates a multi-disciplinary approach, involving financial experts, data scientists, and computational specialists. The paper concludes with an optimistic outlook for the synergy between deep learning and traditional financial theories, aiming for a harmonious blend of modern computational techniques with foundational financial principles.

Short-to-Medium-Term Wind Power Forecasting through Enhanced Transformer and Improved EMD Integration

Accurate wind power forecasting (WPF) is critical in optimizing grid operations and efficiently managing wind energy resources. Challenges arise from the inherent volatility and non-stationarity of wind data, particularly in short-to-medium-term WPF, which extends to longer forecast horizons. To address these challenges, this study introduces a novel model that integrates Improved Empirical Mode Decomposition (IEMD) with an enhanced Transformer called TransIEMD. TransIEMD begins by decomposing the wind speed into Intrinsic Mode Functions (IMFs) using IEMD, transforming the scalar wind speed into a vector form that enriches the input data to reveal hidden temporal dynamics. Each IMF is then processed with channel attention, embedding, and positional encoding to prepare inputs for an enhanced Transformer. The Direct Embedding Module (DEM) provides an alternative viewpoint on the input data. The distinctive perspectives of IEMD and DEM offer interaction through cross-attention within the encoder, significantly enhancing the ability to capture dynamic wind patterns. By combining cross-attention and self-attention within the encoder–decoder structure, TransIEMD demonstrates enhanced proficiency in detecting and leveraging long-range dependencies and dynamic wind patterns, improving the forecasting precision. Extensive evaluations on a publicly available dataset from the National Renewable Energy Laboratory (NREL) demonstrate that TransIEMD significantly improves the forecasting accuracy across multiple horizons of 4, 8, 16, and 24 h. Specifically, at the 24 h forecast horizon, TransIEMD achieves reductions in the normalized mean absolute error and root mean square error of 4.24% and 4.37%, respectively, compared to the traditional Transformer. These results confirm the efficacy of integrating IEMD with attention mechanisms to enhance the accuracy of WPF.

Predicting Cyber Security Threats in The Digital Age: A Systematic Review and Analysis

Insider threats pose a significant challenge in securing today's digital economy, particularly within the convergence of Critical Infrastructure (CI) and Industry 4.0 applications. This study examines current trends, challenges, and algorithms for detecting and predicting insider threats. We analyse key issues such as data non-stationarity and collusion attacks. The paper proposes a model to address these challenges and evaluates its effectiveness. While the initial results show a 66% accuracy in terms of False Positive Rate (FPR), the study recommends doubling the training data size to further enhance the model's prediction accuracy. This research contributes to improved security solutions for safeguarding critical infrastructure in the era of Industry 4.0. In today's digital world, even simple mistakes when using online systems can lead to cyberattacks with serious consequences. These consequences can include damage to an organization's reputation, financial losses, and disruptions to daily operations. This problem is especially concerning in developing countries. Researchers tackled this issue by building a machine learning model that predicts who might fall victim to cyberattacks. The model analyses social and economic data to identify key factors that make someone more susceptible. This model achieved a high level of accuracy by utilizing a sophisticated machine learning technique combined with an algorithm that discovers hidden patterns in data. To train the model, researchers collected information from both victims and those who haven't been attacked. They then employed a special technique to expand the data available for training, ultimately generating valuable insights that can help predict cyberattacks and the associated risks.

MATHEMATICAL MODEL OF RELIABILITY ASSESSMENT FOR DIAGNOSING THE TECHNICAL CONDITION OF ELECTRICAL ENGINEERING COMPLEXES IN DISTRIBUTED WATER SUPPLY SYSTEMS

Distributed water supply systems are high-tech complexes that include a variety of electrical components and control systems. Ensuring their reliable and uninterrupted operation requires continuous monitoring and diagnostics of their technical condition. The diagnosis of distributed water supply systems depends on many factors, which can be both deterministic and random. At present, this is a complex task due to the diversity of processes affecting the parameters of the water supply network's operational state. The non-stationarity of data, caused by cyclic changes in flow rate and pressure over time, also makes their diagnosis challenging. For precise diagnosis of the state of distributed water supply systems, it is necessary to consider not only typical emergency situations but also anomalous water consumption conditions and peculiarities of pressure management system operation. The article proposes a mathematical model for assessing the reliability of electrical engineering complexes in distributed water supply systems for the purpose of their diagnostics. The model is based on the analysis of failure probabilities of various components and subsystems of the complex. The research aims to help identify problematic areas in the water supply system and prevent potential emergency situations. The research results can be used to improve the safety and efficiency of water supply systems, as well as to optimize resource management. The use of the mathematical model in conjunction with modern diagnostic technologies can significantly improve the management of water supply infrastructure and ensure the reliable operation of electrical complexes. A convenient indicator for assessing the diagnosis of the technical condition of electrical engineering complexes in distributed water supply systems is the probability of failure downtime, which reflects both the frequency of failure occurrence and the duration of downtime. For assessing the reliability of the consumer water supply system, it is expedient to use such an indicator: the probability of safe downtime, which takes into account both the frequency of failures and the permissible duration of downtime under safety conditions.

Predicting dust pollution from dry bulk ports in coastal cities: A hybrid approach based on data decomposition and deep learning

Dust pollution from storage and handling of materials in dry bulk ports seriously affects air quality and public health in coastal cities. Accurate prediction of dust pollution helps identify risks early and take preventive measures. However, there remain challenges in solving non-stationary time series and selecting relevant features. Besides, existing studies rarely consider impacts of port operations on dust pollution. Therefore, a hybrid approach based on data decomposition and deep learning is proposed to predict dust pollution from dry bulk ports. Port operational data is specially integrated into input features. A secondary decomposition and recombination (SDR) strategy is presented to reduce data non-stationarity. A dual-stage attention-based sequence-to-sequence (DA-Seq2Seq) model is employed to adaptively select the most relevant features at each time step, as well as capture long-term temporal dependencies. This approach is compared with baseline models on a dataset from a dry bulk port in northern China. The results reveal the advantages of SDR strategy and integrating operational data and show that this approach has higher accuracy than baseline models. The proposed approach can mitigate adverse effects of dust pollution from dry bulk ports on urban residents and help port authorities control dust pollution.

Refined offshore wind speed prediction: Leveraging a two-layer decomposition technique, gated recurrent unit, and kernel density estimation for precise point and interval forecasts

Precise forecasting of offshore wind speeds is paramount for various applications, including offshore wind energy production, disaster prevention and mitigation, and maritime navigation. This study introduces a novel model for point and interval prediction of offshore wind speed, incorporating an innovative two-layer decomposition technique, gated recurrent unit (GRU), and kernel density estimation (KDE). Initially, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is utilized to decompose the raw series into multiple subsequences, thus alleviating the inherent data nonstationarity. Subsequently, we employ the refined composite multiscale fuzzy entropy (RCMFE) to reconstruct the subsequences into multiple components, thereby reducing the computational complexity. Variational mode decomposition (VMD) is utilized to enhance the modeling accuracy to decompose the high-frequency component, thereby generating a set of submodels. The GRU, a specialized recurrent neural network architecture, is leveraged to forecast the remaining components and submodels, producing a series of subresults. The subresults are linearly summed to obtain the final point prediction result. Finally, based on point prediction, employing KDE to gauge the probability density distribution of prediction errors culminates in the derivation of the offshore wind speed prediction interval. The experimental results substantiate the superior predictive performance of the proposed prediction model.

Deep-silicon photon-counting x-ray projection denoising through reinforcement learning.

In recent years, deep reinforcement learning (RL) has been applied to various medical tasks and produced encouraging results. In this paper, we demonstrate the feasibility of deep RL for denoising simulated deep-silicon photon-counting CT (PCCT) data in both full and interior scan modes. PCCT offers higher spatial and spectral resolution than conventional CT, requiring advanced denoising methods to suppress noise increase. In this work, we apply a dueling double deep Q network (DDDQN) to denoise PCCT data for maximum contrast-to-noise ratio (CNR) and a multi-agent approach to handle data non-stationarity. Using our method, we obtained significant image quality improvement for single-channel scans and consistent improvement for all three channels of multichannel scans. For the single-channel interior scans, the PSNR (dB) and SSIM increased from 33.4078 and 0.9165 to 37.4167 and 0.9790 respectively. For the multichannel interior scans, the channel-wise PSNR (dB) increased from 31.2348, 30.7114, and 30.4667 to 31.6182, 30.9783, and 30.8427 respectively. Similarly, the SSIM improved from 0.9415, 0.9445, and 0.9336 to 0.9504, 0.9493, and 0.0326 respectively. Our results show that the RL approach improves image quality effectively, efficiently, and consistently across multiple spectral channels and has great potential in clinical applications.

Enhancing long-term river water quality prediction: Construction and validation of an improved hybrid model

To prevent eutrophication of river caused by excessive inputs of nutrients, accurately predicting these nutrient concentrations is of utmost importance. However, long-term accurate predictions of nutrients concentrations remain a challenge. In this study, an improved hybrid algorithm combining adaptive variational mode decomposition and multi-functional recurrent fuzzy neural network (AVMD-MFRFNN) was proposed. Firstly, whale optimization algorithm (WOA) was developed to identify the optimal number of modes for variational mode decomposition (VMD). Then VMD was employed to decompose input data into intrinsic mode fractions (IMFs), benefiting for reducing the noise effect and non-stationarity of data. Then, MFRFNN with the capability of characterizing complex data was developed to train and test the IMFs. The proposed AVMD-MFRFNN achieved impressive results with the root mean square errors (RMSEs) of 0.036 mg/L, 0.758 mg/L and 1.435 mg/L for predicting total phosphorus (TP), chemical oxygen demand (CODMn) and total nitrogen (TN) after 168 hours. These results signify a decrease of 5.3%, 14.1% and 30.1% compared to the second-best compared method. Moreover, this study demonstrates the potential that integrating the proposed AVMD with other methods can enhance the modeling performance of time series. Furthermore, sensitivity analysis results further validate the effectiveness of WOA in optimizing VMD parameter. Finally, the applicability of AVMD-MFRFNN was confirmed by the data from another river section. These results provide new insights and technical support into the management and preservation of river water environment.

Improving the Machine Learning Stock Trading System: An N‐Period Volatility Labeling and Instance Selection Technique

Financial technology is crucial for the sustainable development of financial systems. Algorithmic trading, a key area in financial technology, involves automated trading based on predefined rules. However, investors cannot manually analyze all market patterns and establish rules, necessitating the development of supervised learning trading systems that can discover market patterns using machine or deep learning techniques. Many studies on supervised learning trading systems rely on up–down labeling based on price differences, which overlooks the issues of nonstationarity, complexity, and noise in stock data. Therefore, this study proposes an N‐period volatility trading system that addresses the limitations of up–down labeling systems. The N‐period volatility trading system measures price volatility to address uncertainty and enables the construction of a stable, long‐term trading system. Additionally, an instance‐selection technique is utilized to address the limitations of stock data, including noise, nonlinearity, and complexity, while effectively reducing the data size. The effectiveness of the proposed model is evaluated through trading simulations of stocks comprising the NASDAQ 100 index and compared with up–down labeling trading systems. The experimental results demonstrate that the proposed N‐period volatility trading system exhibits higher stability and profitability than other trading systems.

Fuzzy Synchronization Likelihood Graph in Deep Neural Networks for Human Motion Time Series Analysis.

Variable interactivity is crucial in biological multivariate time series analysis. This research suggests using graph structures to represent such interactions for more explainable decision-making processes. However, measuring the variable interaction in a graph is an open problem with no unique solution. Existing graph construction methods are either computationally costly, require extensive training, or disregard the inherent data nonlinearities and nonstationarity. We propose using the Fuzzy Synchronization Likelihood (FSL) criterion to address these challenges in constructing a graph and examining the qualitative similarity and dependency among variables. We propose applying this strategy to automated rehabilitation exercise evaluations based on human joint motion data. This multivariate time series application benefits from FSL-constructed graphs by offering further insight into the kinematics of joint interactions. Finally, we extend the convolutional layer in the Deep Mixture Density Neural Network (DMDN) to process the FSL-constructed graph, extracting practical information regarding task-based variable dependencies. An ablation study shows that the proposed FSL Graph-based Deep Neural Network (FSLGDN) outperforms its competitive approaches that use linear correlations and human anatomy for graph construction. Results also indicate that task-based consideration of joint motion data interactions is more beneficial than anatomy. Furthermore, the inherent nonstationarity of motion data leads to the extraction of more information than its linear correlation counterpart. Finally, while the proposed approach ranks competitively with a DMDN, the proposed approach's graph construction and representation of feature dependencies are more intuitive, leading to more explainable decision-making processes.

Impacts of nuclear energy, greener energy, and economic progress on the load capacity factor: What we learn from the leading nuclear power economies?

The worldwide tremor of environmental degradation commonly represents the escalation of emissions levels and ecological footprints that harm the planet's biocapacity. This is because of using gigantic non-renewable energy resources, urbanization stream and massive economic activities in the major industrialized nations. Amid this situation, we investigate the influence of disaggregated energy measures, e.g., renewable, and nuclear energy, income growth and urbanization on the load capacity factor (biocapacity divided by the ecological footprint) of major nuclear power countries, such as France, the USA, Canada, China, and Russia during 1990–2021. To this end, we utilize the CS-ARDL procedure because of the endogeneity, common correlation, non-stationarity in data and heterogeneity in panel units. We contribute to considering the supply side dynamic of environmental degradation parameter, the load capacity, from the perspective of the top nuclear power nations that deviates our analysis from the prevailing scholarly works. However, our findings confirm a significantly positive impact of renewable and nuclear energy on the load capacity factor in improving environmental safety. Besides, economic growth and urbanization negatively affect the load capacity dynamics in spurring environmental degradation. Our findings are robust across an alternative estimation technique, namely the Dumitrescu and Hurlin (DH) causation analysis. Therefore, we recommend formulating pragmatic policies to deter the detrimental effects of income and urbanization by properly utilizing sustainable energy resources to conserve the natural environment.

Deep adaptive temporal network (DAT-Net): an effective deep learning model for parameter estimation of radar multipath interference signals

Accurate parameter estimation in radar systems is critically hindered by multipath interference, a challenge that is amplified in complex and dynamic environments. Traditional methods for parameter estimation, which concentrate on single parameters and rely on statistical assumptions, often struggle in such scenarios. To address this, the deep adaptive temporal network (DAT-Net), an innovative deep learning model designed to handle the inherent complexities and non-stationarity of time series data, is proposed. In more detail, DAT-Net integrates both the pruned exact linear time method for effective time series segmentation and the exponential scaling-based importance evaluation algorithm for dynamic learning of importance weights. These methods enable the model to adapt to shifts in data distribution and provide a robust solution for parameter estimation. In addition, DAT-Net demonstrates the capability to comprehend inherent nonlinearities in radar multipath interference signals, thereby facilitating the modeling of intricate patterns within the data. Extensive validation experiments conducted across parameter estimation tasks and demonstrates the robust applicability and efficiency of the proposed DAT-Net model. The architecture yield root mean squared error scores as low as 0.0051 for single-parameter estimation and 0.0152 for multiple-parameter estimation.

ADAPTIVE DOUBLE NEO-FUZZY NEURON AND ITS COMBINED LEARNING

The subject of the study in the article is the process of data classification under conditions of fuzziness and a limited volume of training sample. The goal is to enhance the double neo-fuzzy neuron within the framework of solving the data classification task with constraints on the training sample volume, processing time, as well as fuzziness and nonstationarity of input data. The tasks include improving the double neo-fuzzy neuron to enhance the system's approximation properties and developing a combined system learning method to ensure fast performance in an online mode. The approaches used are lazy learning, supervised learning, and self-learning. The following results have been obtained: the double neo-fuzzy neuron has been modified by introducing a compressive activation function at the output, creating conditions for building a neo-fuzzy network capable of adapting to non-stationary input data in an online mode and avoiding the vanishing gradient problem. Conclusion. A combined learning method for the double neo-fuzzy neuron has been proposed, involving parallel utilization of lazy learning, supervised learning, and self-learning with the "Winner Takes All" rule, followed by automatic formation of membership functions, enabling fast online classification in the presence of outliers in the input data.