Variational mode decomposition based prediction model for cough sounds using Xception-GRU classifier.

ABSTRACT Pathological fractures, especially those classified as incomplete fractures, are a significant global health issue. Ultrasonic guided wave (UGW) technology is increasingly recognised for its pivotal role in the early detection and diagnosis of fracture injuries. This paper proposes a novel method for UGW-based damage detection in cortical bone, leveraging both the complete ensemble empirical mode decomposition (CEEMD) and an improved energy spectrum entropy (IESE). The UGW signals captured from the cortical bone are decomposed into intrinsic mode functions (IMFs) to capture the damage-induced features and improve the signal-to-noise ratio. By calculating the IESE to measure the complexity and irregularity of UGW signal and reflect signal’s changes caused by injuries, the Pauta criterion is used to determine the damage status of cortical bone. To validate the effectiveness of the proposed method, three types of experiments are conducted on cortical bone samples with artificial damages. The results indicate that the proposed method is effective in detecting cortical bone injuries, with a higher detection accuracy rate of over 93% and sensitivity compared to traditional methods. This study provides a new idea and method for clinical bone damage assessment and holds significant theoretical value and clinical application prospects.

Financial time series forecasting faces significant challenges due to inherent nonlinearity, non-stationarity, and high levels of noise. To address these issues, this study proposes VMD-CSA-BiT, an integrated framework that combines variational mode decomposition (VMD), convolutional self-attention (CSA), and bidirectional transformers (BiT) to enhance prediction robustness. The methodology first decomposes raw price series into interpretable intrinsic mode functions via VMD. It then employs the CSA module to refine pointwise representations at individual time steps and applies the BiT network to model bidirectional long-term temporal dependencies. Evaluated on a range of financial assets using a comprehensive set of market features, the proposed framework demonstrates consistent performance improvements over multiple benchmark models, including traditional statistical methods, machine learning models, and advanced deep learning architectures, achieving significant reductions in key error metrics. The results indicate that VMD-CSA-BiT offers superior forecasting accuracy and stability, with visual analyses showing that its predictions generally align with actual market movements. This study shows that VMD-CSA-BiT is a promising and effective approach for financial time series forecasting. Future research will focus on further architectural optimizations and extending the framework to additional financial applications.

Network Traffic Anomaly Detection (NTAD) is essential for proactive cyber defense against increasingly sophisticated threats. This paper presents a data-driven framework that integrates adaptive signal decomposition, a hybrid attention-recurrent architecture, and metaheuristic optimization for timely anomaly prediction. Raw traffic sequences are first preprocessed via Empirical Mode Decomposition (EMD) to mitigate non-stationarity and suppress noise, yielding denoised intrinsic mode functions. The refined signal is then modeled by a hybrid deep network that couples a multi-head self-attention mechanism—capturing global, long-range dependencies—with a Bidirectional Long Short-Term Memory (BiLSTM) network that encodes bidirectional temporal dynamics. To circumvent the sensitivity of deep models to hyperparameter selection, the Firefly Algorithm (FA) is employed for automated, population-based optimization. Extensive evaluations on benchmark datasets demonstrate that the proposed EMD-FA-Transformer-BiLSTM model attains state-of-the-art performance, outperforms baseline and state-of-the-art models across all evaluated metrics, with statistically significant improvements in both regression error and classification F1-score.

As an important part of the internal combustion engine, the piston-liner assembly is subjected to high temperature and pressure and prone to failure during operation. Condition monitoring of the piston-liner is crucial for the normal operation and maintenance of the engine. The key parameters of the variational mode decomposition algorithm were determined based on block vibration characteristics, and the algorithm was then used to decompose the block vibration into six intrinsic mode functions (IMFs). Continuous wavelet transform was employed for the time-frequency analysis of block vibration. Time-frequency results indicated that IMF1 and IMF6 were closely associated with combustion and piston slap, respectively. Based on this, multiple evaluation criteria were utilized to confirm the characterization parameters of IMFs linked to combustion and piston slap. The support vector machine model was developed through input vector selection, training and test set construction, and kernel function choice. Subsequently, a genetic algorithm was employed to optimize the key parameters of the penalty factor and the kernel width parameter. The optimized support vector machine model was trained and tested. The diagnosis model achieved a 96.9% classification accuracy and met the piston-liner monitoring requirements.

While photoplethysmogram (PPG) signals are physiologically linked to cardiac activity and widely used for cuffless blood pressure (BP) estimation, their correlation with BP remains limited in reliability due to inter-individual heterogeneity. This study aims to isolate the PPG components that have a strong causal relationship with BP, and leverage them to construct reliable cuffless BP estimation models. We propose a causal decomposition framework combining ensemble empirical mode decomposition (EEMD) with counterfactual inference to isolate physiologically causal components in PPG signals. First, PPG signals are adaptively decomposed into multi-scale intrinsic mode functions (IMFs) via EEMD. Then counterfactual PPG sequences are generated through sequentially excluding each IMF, and their causal relationships with BP are quantified via structure causal modeling to identify hemodynamically significant components. Subsequently, robust cuffless BP estimation models are constructed by selectively incorporating components demonstrating strong causal effects. To validate the framework, we benchmark our causality-based models against conventional approaches: pulse arrival time (PAT)-based physiological model, gradient-boosted regression tree (GBRT)-based feature model, and convolutional neural network (CNN)-based time-series model. mid-frequency PPG components (IMF4-6) showed strongest BP causality, with CNN model achieving superior estimation performance over PAT and GBRT when utilizing these components. Using IMF45 components, the CNN model achieved BP estimation mean absolute errors of 5.55/3.45 mmHg (systolic/diastolic BP), improving accuracy by 26.39%/17.86% over original PPG. Specific PPG frequency bands exhibit physiologically meaningful causal BP relationships. Our causality-driven approach enhances both accuracy and interpretability in cuffless BP estimation. This work establishes a theoretical framework for causal feature selection in BP estimation, and a novel paradigm for physiological signal analysis through causal decomposition.

Accurate forecasting of PM2.5 concentration is a critical focus in air quality monitoring research. Considering the nonlinearity and non-stationarity of the PM2.5 time series, this paper proposes a forecasting model that combines variational mode decomposition (VMD), deep learning methods such as temporal convolutional networks (TCN), bidirectional long short-term memory (BiLSTM), and an attention mechanism. Initially, VMD is used to decompose the original PM2.5 sequence into a set of intrinsic mode functions (IMFs) that assess distinct physical interpretations. Sample entropy (SE) is calculated to evaluate the complexity of each IMF, followed by the application of K-means clustering to group the components into high-, medium-, and low-frequency components. A TCN-BiLSTM-based forecasting architecture is then established, where separate forecasting models are trained for each frequency band. Finally, an attention mechanism is introduced to adaptively learn the importance weights of different frequency component forecasting models, and a weighted fusion approach is applied to generate the final forecasting results. Experimental evaluations establish that the proposed method achieved the best forecasting accuracy with a lowest RMSE of 16.920µg/m3, a lowest MAE of 11.134µg/m3, and a highest R2 of 0.960, thereby demonstrating improved forecasting capability.

To address the limitations of single-image feature information and the insufficient recognition capability of traditional power quality disturbance (PQD) identification systems, this paper proposes a PQD recognition method based on feature-image combination and an improved ResNet-18, following the concept of feature fusion. First, the PQD signal is subjected to variational mode decomposition (VMD) to obtain a series of intrinsic mode functions (IMFs) and a residual component. Second, the IMFs, residual component, original disturbance signal, and Subtract component are vertically concatenated into a component matrix, from which a color feature-component image is generated via a signal-to-image transformation method. Third, the original disturbance signal is processed using continuous wavelet transform (CWT) to produce a time–frequency scalogram. Finally, the color feature-component image and the wavelet time–frequency image are combined and input into an improved six-channel ResNet-18 for training and disturbance classification. Simulation analyses of the proposed PQD identification method are conducted and compared with commonly used recognition systems. The results demonstrate that the proposed method exhibits strong noise robustness, effectively extracts PQD feature information, and achieves higher recognition accuracy.

In this paper, we propose a multivariate fast iterative filtering (MvFIF) decomposition algorithm, entropy-based features, and a nature-inspired feature selection approach for Alzheimer’s disease (AD) detection using electroencephalogram (EEG) signals. Where, the MvFIF decomposes the multichannel EEG signals into multichannel intrinsic mode functions (MIMFs). The entropy features: dispersion entropy (DispEn) and distribution entropy (DistEn) are extracted from the MIMFs. Afterward, five nature-inspired feature selection algorithms are applied to reduce the feature space by selecting the relevant features for the AD. The selected features are finally used for the binary classification to distinguish AD patients from healthy control (HC) subjects using different classifiers. In addition, lobe-wise analysis is performed to understand the neural activity, diagnose AD, and guide targeted treatments. We show that the binary differential evolution optimization (BDEO) feature selection method with the support vector machine (SVM) classifier achieves the highest accuracy of 90.78% with standard deviation (SD) of 1.96% using 10-fold cross-validation (CV) and 75% with SD of 18.20% using leave-one-subject-out CV (LOSO-CV). In lobe-wise analysis, XGBoost classifier with temporal lobe gives the highest accuracy of 80.06% with SD of 1.53% using 10-fold CV and 70.78% with SD of 23.93% using LOSO-CV. The proposed approach surpasses the current leading techniques in AD detection utilizing EEG signals.

To address the complex noise interference caused by the increasing complexity of distribution network topologies and harsh operating environments, as well as the resulting impacts and challenges to the accuracy of traveling wave fault location, the authors introduce a method for traveling wave front detection, which combines an improved wavelet threshold function denoising, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), and the teager energy operator (TEO). Firstly, to suppress the impact of noise interference on wavefront detection, this paper constructs an improved wavelet threshold function to denoise the fault signals, thereby enhancing the signal-to-noise ratio (SNR) and providing high-fidelity input for subsequent wavefront calibration. Secondly, the ICEEMDAN method is applied for decompose the denoised signals, generating multiple intrinsic mode functions (IMFs) that represent the characteristics of the signal. Finally, the TEO is applied to the high-frequency component IMF1, which best represents the properties of the traveling wave front. The moment corresponding to the peak of its energy spectrum is identified as the arrival time of the initial traveling wave front. Experimental results indicate that at a sampling rate of 10 MHz, the proposed method performs excellently under noisy conditions and complex structures, achieving an average positioning error of 21.54 m, with a maximum error not exceeding 51.80 m. The method remains stable under various fault conditions and sampling rates. Even in a strong noise environment with a SNR as low as 10 dB, it can reliably identify the wavefront, demonstrating outstanding anti-noise performance and robustness.

HighlightsAn intelligent ICEEMDAN-LSTM framework is developed to achieve early-stage anomaly pre-warning for buried natural gas pipelines.A unified data-driven model successfully integrates adaptive signal decomposition and sequential learning to enhance weak transient feature extraction from non-stationary vibrations.A novel two-stage complementary validation paradigm is formulated, effectively bridging unsupervised data-driven field baselines with multi-physics fluid-structure interaction digital twins.The framework delivers physically interpretable pre-warning capabilities, systematically overcoming the critical industry bottleneck of labeled failure data scarcity.What are the main findings?A physically-informed health monitoring framework integrating ICEEMDAN decomposition and LSTM classification effectively extracts multi-scale features and isolates transient precursor anomalies from complex acceleration signals.A two-stage complementary validation, coupling continuous field construction logs with FSI digital twins, rigorously verifies the system’s sensitivity to genuine structural degradation.What are the implications of the main findings?The proposed ICEEMDAN-LSTM framework provides a highly reliable, physically interpretable data-driven methodology for the intelligent structural health monitoring of buried pipelines, particularly in complex operating environments subject to heavy background noise and dynamic disturbances.By introducing a novel two-stage complementary validation strategy and leveraging unsupervised clustering, the “cold-start” problem—the complete lack of destructive labeled data—was successfully addressed, offering a scalable and practical solution for the early anomaly pre-warning of critical infrastructure.Structural health monitoring of buried pipelines is essential due to their exposure to corrosion, impact loads, and geotechnical disturbances, which may induce abnormal vibration responses. Acceleration signals provide direct and sensitive measurements of buried pipeline structural dynamic behavior, and are therefore suitable for early anomaly identification. An acceleration-based intelligent framework integrating Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and a Long Short-Term Memory (LSTM) network is proposed for buried pipeline condition recognition. First, the raw acceleration signals are decomposed into a set of intrinsic mode functions (IMFs) using ICEEMDAN to enhance time–frequency resolution and isolate weak transient impact components associated with buried pipeline structural anomalies. Subsequently, multi-scale features extracted from the IMFs are fused and fed into an LSTM network to capture temporal dependencies and perform supervised health state classification. Experimental results demonstrate that the proposed framework achieves an F1-score of 0.70 and a Precision–Recall AUC of 0.72 for identifying anomalies. Furthermore, cross-validation utilizing multi-source field data (dynamic acceleration and quasi-static strain) confirms the model’s physical interpretability and its stable performance under severe noise interference. The results validate the feasibility of combining advanced signal decomposition with deep learning techniques for buried pipeline anomaly pre-warning, providing a rigorous methodological basis for the safe operation of critical energy infrastructures.

This paper proposes a novel rolling bearing fault diagnosis method to address the difficulty of accurate feature extraction from nonlinear and non-stationary vibration signals. First, a Levy–Cauchy Optimized Sparrow Search Algorithm (LOCSSA) is developed to optimize the two core parameters (decomposition level and penalty factor) of Variational Mode Decomposition (VMD), and the optimized VMD is used to decompose raw vibration signals to obtain optimal intrinsic mode functions (IMFs). Second, the extracted IMF features are fed into a convolutional neural network (CNN) for local pattern extraction, followed by a bidirectional long short-term memory (BiLSTM) network to model temporal dependencies, with the final fault classification completed via a fully connected layer. Comparative experiments and ablation studies with five benchmark models are conducted to verify the effectiveness of the proposed framework. The results show that the proposed method achieves 96.33% accuracy, 96.67% recall, and 96.54% F1-score, outperforming all benchmark models. Ablation analysis confirms that both LOCSSA-optimized VMD and BiLSTM contribute significantly to performance improvement (p < 0.05), validating the rationality of the proposed method.

Aiming at the insufficient prediction accuracy caused by the non-stationary and multi-frequency coupling characteristics of complex multi-source vibration signals, this study proposes a parallel fusion prediction model that takes hyperparameter optimization as the core preprocessing step and integrates multivariate variational mode decomposition (MVMD) with parallel weighted KNN-XGBoost. Firstly, a "training-validation-test" three-set data separation framework is constructed, and a stepwise grid search strategy is adopted to optimize key hyperparameters. With the error validation set as the objective function, the number of neighbors for K-Nearest Neighbors (KNN), the tree depth and learning rate for eXtreme Gradient Boosting (XGBoost), and the optimal fusion weights of KNN and XGBoost are determined sequentially. This fundamentally avoids the subjective bias inherent in manual parameter tuning. Secondly, MVMD is employed to decompose complex multi-source vibration signals into 8 intrinsic mode functions (IMFs) with different frequency scales. This addresses the mode mixing issue of traditional decomposition methods, reduces the complexity of vibration signals, and retains the multi-source coupling features. Thirdly, a parallel weighted KNN-XGBoost structure is built based on the optimized parameters. Through independent prediction and weighted fusion, error propagation in serial structures is avoided, enabling the synergy of "local correction-global fitting". Multiple comparative and ablation experiments demonstrate that, compared with other models, the MVMD-parallel-KNN-XGBoost model achieves the optimal balanced performance. This study provides a parallel fusion technical pathway of "parameter optimization-modal separation-model fusion" for complex multi-source vibration time-series prediction, which can meet the high-precision prediction requirements of complex multi-source vibration in fields such as aerospace, rail transit, and industrial engineering etc.

Accurate short-term photovoltaic (PV) power forecasting is critical for maintaining grid stability and enabling efficient dispatch in modern sustainable power systems, yet the inherent volatility and multi-scale temporal dynamics of PV output remain challenging for existing methods. This paper proposes IFTMC, a novel hybrid framework that synergistically integrates improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), fuzzy C-means (FCM) soft clustering, and dual-backbone deep learning networks-TimesNet and Mamba-coupled through a bidirectional cross-attention fusion mechanism. Specifically, ICEEMDAN decomposes the raw PV power series into intrinsic mode functions of distinct frequency scales, which are subsequently regrouped via FCM clustering to reduce modelling complexity while preserving inter-band transitional information. TimesNet and Mamba then operate as complementary feature extractors, capturing multi-periodic local patterns and long-range temporal dependencies, respectively, with cross-attention adaptively allocating their contributions according to input conditions. Extensive experiments on the DKASC benchmark dataset demonstrate that IFTMC achieves state-of-the-art performance, reducing mean absolute error (MAE) by 4.2%-4.8% relative to the strongest baseline across 2-3-hour prediction horizons. Comprehensive ablation studies, case analyses under diverse weather conditions, and attention weight visualizations further confirm the effectiveness, robustness, and interpretability of each component.

Early identification of unbalance and shaft misalignment is essential for averting unforeseen failures and minimizing maintenance expenses in rotor-bearing systems. This paper delineates an experimental examination succeeded by an intelligent condition monitoring system for the identification of healthy, parallel misalignment, and angular misalignment states. A custom-built Machinery Fault Simulator was utilized to get vibration responses from multi-axis accelerometers at speeds of 1200, 1500, and 1800rpm. First, time- and frequency-domain analysis were done to look at the vibration characteristics that were associated to faults. After the vibration signals were collected in the lab, they were broken down using Variational Mode Decomposition (VMD) to get noise-robust intrinsic mode functions. A convolutional autoencoder and a one-dimensional convolutional neural network were then used to get statistical and deep features. Random Forest and XGBoost classifiers with early stopping were used to avoid overfitting and classify the faults. An ensemble learning technique was then employed to obtain the final fault classification. The suggested framework achieved an overall classification accuracy of 95.25%. The F1-scores for healthy, parallel misalignment, and angular misalignment conditions were 0.99, 0.88, and 0.87, respectively. The experimental findings indicated that parallel misalignment is defined by predominant and speed-invariant 2X harmonic components exhibiting radial energy concentration, while angular misalignment displays impulsive broadband responses characterized by substantial axial energy dominance and increased kurtosis. The results demonstrate that the proposed hybrid technique, which combines experimental and data-driven methods, provides a reliable and scalable solution for intelligent condition monitoring of variable-speed rotor-bearing systems.

To introduce ICEEMDAN-PC, a novel quantitative ultrasound (QUS) approach for accurate and noise-robust estimation of mean scatterer spacing (MSS), enabling refined characterization of liver and breast tissue microstructures in health, disease, and post-treatment states. ICEEMDAN-PC integrates the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and power cepstrum (PC). The intrinsic mode function with the highest energy is extracted, and its cepstrum is analyzed to determine MSS. The method was validated using 30,100 simulated noisy RF signals (semi-periodic/diffuse scatterers) and applied to: (1) 301ex vivo porcine liver signals, (2) 31,488 paired RF signals pre/post microwave ablation (MWA), and (3) RF data from 100 clinical breast lesions (52 malignant, 48 benign). Simulations recovered the theoretical MSS (1.25 mm) with low variance despite high noise. In a healthy liver, MSS was 1.02 mm, with significant shifts post-MWA indicating microstructural disruption. Breast lesion MSS values (0.8736 mm benign, 0.9068 mm malignant) matched literature trends. ICEEMDAN-PC consistently achieved high accuracy and sensitivity across simulated, experimental, and clinical datasets, demonstrating strong potential for non-invasive QUS-based tissue characterization and therapeutic monitoring.

To improve milling tool wear prediction accuracy, which is critical for intelligent manufacturing efficiency and cost reduction, a hybrid model based on empirical mode decomposition (EMD), particle swarm optimization (PSO), and bidirectional gated recurrent unit (BiGRU) is proposed. Raw machining signals are decomposed into intrinsic mode functions (IMFs) via EMD; the Pearson correlation coefficient (PCC) is then used to screen wear-related IMFs to eliminate redundancy. Subsequently, PSO is applied to optimize BiGRU parameters, hidden layer neurons, and learning rate, to reduce the risk of local optima. Validated on the PHM2010 dataset, the model increases R2 by 4.1%, reduces root mean square error (RMSE) by 13.9%, achieves a mean absolute percentage error (MAPE) of 5.915%, and outperforms improved subtraction-average-based optimizer (ISABO)-optimized BiGRU with 2.7% higher R2 and faster convergence. The contributions lie in the EMD–PCC screening strategy and the integrated hybrid model, providing a practical solution for industrial tool wear prediction.

Current load spectrum editing methods based on the Hilbert-Huang Transform (HHT) are limited by modal aliasing and boundary effects, and editing precision is therefore reduced. To overcome these limitations, the use of the Empirical Wavelet Transform (EWT) theory for editing automotive component load spectra is investigated in this study. The proposed methodology comprises three primary steps. First, the load spectrum is decomposed into Intrinsic Mode Functions (IMFs) with distinct frequency characteristics by EWT. Second, the instantaneous amplitude and frequency of load components are extracted from these IMFs by applying the Hilbert Transform, and the instantaneous energy spectrum is constructed. Third, the optimal threshold for the instantaneous energy spectrum is determined by a genetic algorithm, thereby allowing the identification and removal of time segments making minimal contribution to component damage. The remaining segments are then spliced, and a streamlined load spectrum is generated. The load spectrum of an automotive lower control arm bushing is used as a case study, and the editing results of the HHT and EWT methods are compared. It is demonstrated that greater time compression is achieved by the EWT-based approach in the reduced load spectrum, while close alignment with the original is maintained in terms of statistical parameters, power spectral density, cross-level counting, fatigue life, and damage distribution. The potential of the EWT-based method to improve the efficiency of durability bench tests for automotive components is highlighted, and a promising direction for load-spectrum editing in automotive engineering is introduced.

Abstract Rainfall variability in tropical regions such as the Indonesian Maritime Continent is shaped by complex interactions of atmospheric and oceanic phenomena across multiple timescales. This study investigates the temporal structure of rainfall over Bandung from 1981 to 2024 using a combination of Empirical Mode Decomposition (EMD), Finite Impulse Response (FIR) filtering, and the Stockwell Transform (S-transform). Rather than being dominated by a single climate driver, rainfall variability in Bandung emerges from the superposition of multiple intrinsic oscillations operating at intra-seasonal, semi-annual, annual, and interannual scales monthly rainfall data from the CHIRPS dataset were decomposed into Intrinsic Mode Functions (IMFs) using EMD, enabling the identification of oscillatory modes associated with intra-seasonal to interdecadal variability. Subsequent frequency analysis revealed the presence of prominent periodicities, including a ∼6-month cycle attributed to the Semi-Annual Oscillation (SAO). To validate these findings, a band-pass FIR filter targeting the 0.143–0.2 cycle/month range was applied to isolate the semi-annual signal from the original rainfall series. The resulting filtered signal confirmed a coherent SAO signature, particularly evident in specific epochs. The application of the S-transform provided time-frequency localization, capturing the evolution of dominant modes and their intermittent intensification. This semi-annual component was also consistently observed in zonal wind and outgoing longwave radiation (OLR) data, indicating a broader atmospheric influence. While the analysis does not establish causality, it highlights the importance of signal-based approaches in detecting embedded climate signals. These findings offer a basis for future studies exploring the dynamic mechanisms driving tropical rainfall variability, particularly the interaction of SAO with larger-scale phenomena such as monsoons, ENSO, and MJO.

Accurate prediction of rainfall events is vital for agriculture, hydrology, flood preparedness, and climate-adaptive strategies in regions of Pakistan susceptible to monsoons and droughts. Increasing climate variability highlights the need for reliable data-driven forecasting systems capable of precisely representing nonlinear atmospheric dynamics across different forecast intervals. This study introduces an extensive hybrid machine learning-deep learning (ML-DL) framework designed to classify daily rainfall events (rain vs. no rain) and predict several horizons (RainDay0-RainDay5) by utilizing 130,230 daily meteorological data collected from 10 geographically diverse cities in Pakistan between 1990 and 2025. Machine learning models, such as Extra Trees classifier, Histogram Gradient Boosting, Ridge Classifier, and Gaussian Naïve Bayes, underwent evaluation using leakage-free TimeSeriesSplit validation with SMOTE applied only to training folds using various seeds.To improve the quality of sequence representation, Variational Mode Decomposition (VMD) was utilized to extract band-limited intrinsic mode functions from meteorological signals, while Particle Swarm Optimization (PSO) was employed for adaptive hyperparameter tuning and genetic algorithms were used. Experimental findings indicate that ensemble ML models delivered robust baseline classification results across various cities, while VMD-augmented deep learning frameworks enhanced robustness and temporal learning consistency throughout different forecast horizons. Specifically, VMD-LSTM demonstrated robust performance in Hyderabad (Acc = 0.862, F1 = 0.871, AUC = 0.941), whereas VMD-GRU exhibited dependable discrimination ability in Jamshoro (AUC = 0.918), Quetta (AUC = 0.867), and Thatta (AUC = 0.896).The enhanced VMD-PSO-GRU (VPG) framework demonstrated superior rainfall classification performance across various cities, particularly excelling in Hyderabad (AUC = 0.912), Jamshoro (Acc = 0.882), and Thatta (Acc = 0.878). In multi-horizon forecasting, a proposed multi-head VMD-GRU-Attention model, improved by hybrid PSO-GA, provided the most reliable results across forecast lead times RainDay0-RainDay5. In short-term forecasting, the system achieved an Accuracy of 0.872 (RainDay0) in Hyderabad, while maintaining steady medium-term performance at RainDay3 (approximately 0.819 for Hyderabad; about 0.808 for Thatta) and long-term predictions near 0.80 at RainDay5 across Gharo, Thatta, and Mirpur Khas, showcasing resilience despite increasing forecast uncertainty. The proposed hybrid framework demonstrates improved stability in temporal learning, robustness against noise, and capacity to generalize across areas, validating its effectiveness for operational rainfall early-warning systems in various climatic settings of Pakistan.