A new method for the rapid identification of external water types in rainwater pipeline networks using UV-Vis absorption spectroscopy.

Ultraviolet-visible (UV-Vis) absorption spectroscopy, due to its high sensitivity and capability for real-time online monitoring, is one of the most promising tools for the rapid identification of external water in rainwater pipe networks. However, difficulties in obtaining actual samples lead to insufficient real samples, and the complex composition of wastewater can affect the accurate traceability analysis of external water in rainwater pipe networks. In this study, a new method for identifying external water in rainwater pipe networks with a small number of samples is proposed. In this method, the Generative Adversarial Network (GAN) algorithm was initially used to generate spectral data from the absorption spectra of water samples; subsequently, the multiplicative scatter correction (MSC) algorithm was applied to process the UV-Vis absorption spectra of different types of water samples; following this, the Variational Mode Decomposition (VMD) algorithm was employed to decompose and recombine the spectra after MSC; and finally, the long short-term memory (LSTM) algorithm was used to establish the identification model between the recombined spectra and the water source types, and to determine the optimal number of decomposed spectra K. The research results show that when the number of decomposed spectra K is 5, the identification accuracy for different sources of domestic sewage, surface water, and industrial wastewater is the highest, with an overall accuracy of 98.81%. Additionally, the performance of this method was validated by mixed water samples (combinations of rainwater and domestic sewage, rainwater and surface water, and rainwater and industrial wastewater). The results indicate that the accuracy of the proposed method in identifying the source of external water in rainwater reaches 98.99%, with detection time within 10 s. Therefore, the proposed method can become a potential approach for rapid identification and traceability analysis of external water in rainwater pipe networks.

Variational Mode Decomposition Analysis of Electroencephalograms during General Anesthesia: Using the Grey Wolf Optimizer to Determine Hyperparameters.

Frequency analysis via electroencephalography (EEG) during general anesthesia is used to develop techniques for measuring anesthesia depth. Variational mode decomposition (VMD) enables mathematical optimization methods to decompose EEG signals into natural number intrinsic mode functions with distinct narrow bands. However, the analysis requires the a priori determination of hyperparameters, including the decomposition number (K) and the penalty factor (PF). In the VMD analysis of EEGs derived from a noninterventional and noninvasive retrospective observational study, we adapted the grey wolf optimizer (GWO) to determine the K and PF hyperparameters of the VMD. As a metric for optimization, we calculated the envelope function of the IMF decomposed via the VMD method and used its envelope entropy as the fitness function. The K and PF values varied in each epoch, with one epoch being the analytical unit of EEG; however, the fitness values showed convergence at an early stage in the GWO algorithm. The K value was set to 2 to capture the α wave enhancement observed during the maintenance phase of general anesthesia in intrinsic mode function 2 (IMF-2). This study suggests that using the GWO to optimize VMD hyperparameters enables the construction of a robust analytical model for examining the EEG frequency characteristics involved in the effects of general anesthesia.

Scientific preparation for JRT: Wind pressure prediction model for large radio telescope based on real data from multi-sensors.

Jingdong 120-meter radio telescope (JRT) is poised to become the world's largest single-aperture fully steerable medium-low frequency radio telescope. However, like other large-aperture radio telescopes, the JRT is vulnerable to wind loads, which can cause structural deformation and pointing errors. Addressing this challenge requires the ability to predict dynamic winds in real-time. This study developed a wind pressure preprocessing and prediction model using sensor data collected from the Kunming 40-meter radio telescope (KRT), enabling real-time prediction of wind pressure on the telescope. The model employs adaptive noise and Variational Mode Decomposition (VMD) techniques to eliminate random noise from the original wind pressure data. Subsequently, wind pressure predictions are made using a Bidirectional Long Short-term Memory (BiLSTM) model. By conducting predictions under various stabilization conditions and conducting a thorough analysis of measurement data from five sensors, the study has achieved impressive results in predicting wind pressure on the KRT reflector surface. The proposed model demonstrates the lowest MAE, RMSE, and MAPE, while achieving the highest R 2 across various data sets. Where the average R 2 of the proposed model is 0.9392 at 45° pitch angle attitude and the RMSE, MAE and MAPE values are 1.4923, 1.2377 and 1.82% respectively. This model helps wind load monitoring of real-time wind pressure monitoring of the telescope surface, to study the effects of wind load on pointing accuracy. By adjusting the control parameters to reduce wind load interference, to ensure the high-precision work of a large radio telescope, such as JRT.

A hybrid approach for power quality event identification in power systems: Elasticnet Regression decomposition and optimized probabilistic neural networks.

The transformation of traditional grid networks towards smart-grid and microgrid concepts raises many critical issues, and quality in the power supply is one of the prominent ones that needs further research. Developing and applying power quality (PQ) recognition methods with efficient and reliable analysis are essential to the fast-growing issues related to modern smart power distribution systems. In this regard, a hybrid algorithm is proposed for PQ events detection and classification using Elasticnet Regression-based Variational Mode Decomposition (ER-VMD) and Salp Swarm Algorithm optimized Probabilistic Neural Network (SSA-PNN). The Elasticnet Regression (ER) process is suggested to modify the conventional VMD approach instead of the Tikhonov Regularization (TR) method to enhance performance and obtain better band-limited intrinsic mode functions. This idea results in robust and effective reconstruction features and helps to obtain accurate classification using the classifier. In the classification stage, a Salp Swarm Algorithm (SSA) based PNN is used for the PQ event, considering the relevant features obtained from ER-VMD. The system parameters often influence PNN performance, and SSA is used to determine the ideal values to improve the PNN's capacity for more accurate classification. The numerical values of the accuracy percentage, percentage of sensitivity, and percentage of specificity in the case of real-time data are found as 98.58, 100, and 98.46, respectively. The acquired comparison findings demonstrate the effectiveness and robustness of the proposed technique in terms of rapid learning speed, smaller computational complexity, robust performance for anti-noise conditions, and accurate identification and categorization.

Identification of exon regions in eukaryotes using fine-tuned variational mode decomposition based on kurtosis and short-time discrete Fourier transform.

In genomic research, identifying the exon regions in eukaryotes is the most cumbersome task. This article introduces a new promising model-independent method based on short-time discrete Fourier transform (ST-DFT) and fine-tuned variational mode decomposition (FTVMD) for identifying exon regions. The proposed method uses the N/3 periodicity property of the eukaryotic genes to detect the exon regions using the ST-DFT. However, background noise is present in the spectrum of ST-DFT since the sliding rectangular window produces spectral leakage. To overcome this, FTVMD is proposed in this work. VMD is more resilient to noise and sampling errors than other decomposition techniques because it utilizes the generalization of the Wiener filter into several adaptive bands. The performance of VMD is affected due to the improper selection of the penalty factor (α), and the number of modes (K). Therefore, in fine-tuned VMD, the parameters of VMD (K and α) are optimized by maximum kurtosis value. The main objective of this article is to enhance the accuracy in the identification of exon regions in a DNA sequence. At last, a comparative study demonstrates that the proposed technique is superior to its counterparts.

Degradation prediction of fuel cell systems based on different operating conditions in dynamic cycling condition.

In this paper, the degradation of PEMFC under different operating conditions in dynamic cycle condition is studied. Firstly, according to the failure mechanism of PEMFC, various operating conditions in dynamic cycle condition are classified, and the health indexes are established. Simultaneously, the rates and degrees of the output voltage decline of the PEMFC under different operating conditions during the dynamic cycling process were compared. Then, a model based on variational mode decomposition and long short-term memory with attention mechanism (VMD-LSTM-ATT) is proposed. Aiming at the performance of PEMFC is affected by the external operation, VMD is used to capture the global information and details, and filter out interference information. To improve the prediction accuracy, ATT is used to assign weight to the features. Finally, in order to verify the effectiveness and superiority of VMD-LSTM-ATT, we respectively apply it to three current conditions under dynamic cycle conditions. The experimental results show that under the same test conditions, RMSE of VMD-LSTM-ATT is increased by 56.11 % and MAE is increased by 28.26 % compared with GRU attention. Compared with SVM, RNN, LSTM and LSTM-ATT, RMSE of VMD-LSTM-ATT is at least 17.26 % higher and MAE is at least 5.65 % higher.

Rolling Bearing Fault Diagnosis Based on SABO-VMD and WMH-KNN.

To improve the performance of roller bearing fault diagnosis, this paper proposes an algorithm based on subtraction average-based optimizer (SABO), variational mode decomposition (VMD), and weighted Manhattan-K nearest neighbor (WMH-KNN). Initially, the SABO algorithm uses a composite objective function, including permutation entropy and mutual information entropy, to optimize the input parameters of VMD. Subsequently, the optimized VMD is used to decompose the signal to obtain the optimal decomposition characteristics and the corresponding intrinsic mode function (IMF). Finally, the weighted Manhattan function (WMH) is used to enhance the classification distance of the KNN algorithm, and WMH-KNN is used for fault diagnosis based on the optimized IMF features. The performance of the SABO-VMD and WMH-KNN models is verified through two experimental cases and compared with traditional methods. The results show that the accuracy of motor-bearing fault diagnosis is significantly improved, reaching 97.22% in Dataset 1, 98.33% in Dataset 2, and 99.2% in Dataset 3. Compared with traditional methods, the proposed method significantly reduces the false positive rate.

Air quality forecasting using a spatiotemporal hybrid deep learning model based on VMD-GAT-BiLSTM.

The precise forecasting of air quality is of great significance as an integral component of early warning systems. This remains a formidable challenge owing to the limited information of emission source and the considerable uncertainties inherent in dynamic processes. To improve the accuracy of air quality forecasting, this work proposes a new spatiotemporal hybrid deep learning model based on variational mode decomposition (VMD), graph attention networks (GAT) and bi-directional long short-term memory (BiLSTM), referred to as VMD-GAT-BiLSTM, for air quality forecasting. The proposed model initially employ a VMD to decompose original PM2.5 data into a series of relatively stable sub-sequences, thus reducing the influence of unknown factors on model prediction capabilities. For each sub-sequence, a GAT is then designed to explore deep spatial relationships among different monitoring stations. Next, a BiLSTM is utilized to learn the temporal features of each decomposed sub-sequence. Finally, the forecasting results of each decomposed sub-sequence are aggregated and summed as the final air quality prediction results. Experiment results on the collected Beijing air quality dataset show that the proposed model presents superior performance to other used methods on both short-term and long-term air quality forecasting tasks.

Enhanced Air Quality Prediction Using a Coupled DVMD Informer-CNN-LSTM Model Optimized with Dung Beetle Algorithm.

Accurate prediction of air quality is crucial for assessing the state of the atmospheric environment, especially considering the nonlinearity, volatility, and abrupt changes in air quality data. This paper introduces an air quality index (AQI) prediction model based on the Dung Beetle Algorithm (DBO) aimed at overcoming limitations in traditional prediction models, such as inadequate access to data features, challenges in parameter setting, and accuracy constraints. The proposed model optimizes the parameters of Variational Mode Decomposition (VMD) and integrates the Informer adaptive sequential prediction model with the Convolutional Neural Network-Long Short Term Memory (CNN-LSTM). Initially, the correlation coefficient method is utilized to identify key impact features from multivariate weather and meteorological data. Subsequently, penalty factors and the number of variational modes in the VMD are optimized using DBO. The optimized parameters are utilized to develop a variationally constrained model to decompose the air quality sequence. The data are categorized based on approximate entropy, and high-frequency data are fed into the Informer model, while low-frequency data are fed into the CNN-LSTM model. The predicted values of the subsystems are then combined and reconstructed to obtain the AQI prediction results. Evaluation using actual monitoring data from Beijing demonstrates that the proposed coupling prediction model of the air quality index in this paper is superior to other parameter optimization models. The Mean Absolute Error (MAE) decreases by 13.59%, the Root-Mean-Square Error (RMSE) decreases by 7.04%, and the R-square (R2) increases by 1.39%. This model surpasses 11 other models in terms of lower error rates and enhances prediction accuracy. Compared with the mainstream swarm intelligence optimization algorithm, DBO, as an optimization algorithm, demonstrates higher computational efficiency and is closer to the actual value. The proposed coupling model provides a new method for air quality index prediction.

A Water Environment-Based Simulated Method for Ultrasonic Testing of Slag Inclusion Weld Defects Based on Improved VMD.

The identification of slag inclusion defects in welds is of the utmost importance in guaranteeing the integrity, safety, and prolonged service life of welded structures. Most research focuses on different kinds of weld defects, but branch research on categories of slag inclusion material is limited and critical for safeguarding the quality of engineering and the well-being of personnel. To address this issue, we design a simulated method using ultrasonic testing to identify the inclusion of material categories in austenitic stainless steel. It is based on a simulated experiment in a water environment, and six categories of cubic specimens, including four metallic and two non-metallic materials, are selected to simulate the slag materials of the inclusion defects. Variational mode decomposition optimized by particle swarm optimization is employed for ultrasonic signals denoising. Moreover, the phase spectrum of the denoised signal is utilized to extract the phase characteristic of the echo signal from the water-slag specimen interface. The experimental results show that our method has the characteristics of appropriate decomposition and good denoising performance. Compared with famous signal denoising algorithms, the proposed method extracted the lowest number of intrinsic mode functions from the echo signal with the highest signal-to-noise ratio and lowest normalized cross-correlation among all of the comparative algorithms in signal denoising of weld slag inclusion defects. Finally, the phase spectrum can ascertain whether the slag inclusion is a thicker or thinner medium compared with the weld base material based on the half-wave loss existing or not in the echo signal phase.

Detection of virtual reality motion sickness based on EEG using asymmetry of entropy and cross-frequency coupling.

The existence of Virtual Reality Motion Sickness (VRMS) is a key factor restricting the further development of the VR industry, and the premise to solve this problem is to be able to accurately and effectively detect its occurrence. In view of the current lack of high-accuracy and effective detection methods, this paper proposes a VRMS detection method based on entropy asymmetry and cross-frequency coupling value asymmetry of EEG. First of all, the EEG of the four selected pairs of electrodes on the bilateral brain are subjected to Multivariate Variational Mode Decomposition (MVMD) respectively, and three types of entropy values on the low-frequency and high-frequency components are calculated, namely approximate entropy, fuzzy entropy and permutation entropy, as well as three types of phase-amplitude coupling features between the low-frequency and high-frequency components, namely the mean value, standard deviation and correlation coefficient; Secondly, the difference of the entropies and the cross-frequency coupling features between the left electrodes and the right electrodes are calculated; Finally, the final feature set are selected via t-test and fed into the SVM for classification, thus realizing the automatic detection of VRMS. The results show that the three classification indexes under this method, i.e., accuracy, sensitivity and specificity, reach 99.5 %, 99.3 % and 99.7 %, respectively, and the value of the area under the ROC curve reached 1, which proves that this method can be an effective indicator for detecting the occurrence of VRMS.

Research on a Fault Feature Extraction Method for an Electric Multiple Unit Axle-Box Bearing Based on a Resonance-Based Sparse Signal Decomposition and Variational Mode Decomposition Method Based on the Sparrow Search Algorithm.

In light of the issue that the vibration signal from an axle-box bearing collected during the operation of an electric multiple unit (EMU) is seriously polluted by background noise, which leads to difficulty in identifying fault characteristic frequency, this paper proposes a resonance-based sparse signal decomposition (RSSD) and variational mode decomposition (VMD) method based on sparrow search algorithm (SSA) optimization to extract the fault characteristic frequency of the bearing. Firstly, the RSSD method is utilized to decompose the signal based on the obtained optimal combination of quality factors, resulting in the optimal low-resonance component with periodic fault information. Then, the VMD method is performed on this low-resonance component. The parameter combinations for both methods are optimized utilizing the SSA method. Subsequently, envelope demodulation is applied to the intrinsic mode function (IMF) with maximum kurtosis, and fault diagnosis is achieved by comparing it with the theoretical fault characteristic frequency. Finally, experimental validation and comparison are conducted by utilizing simulated signals and example signals. The results demonstrate that the proposed method extracts more obvious periodic fault impact components. It effectively filters out the interference of complex noise and reduces the blindness of setting weights on parameters due to human experience, indicating excellent adaptability and robustness.

The Piston Slap Force Reconstruction of Diesel Engine Using WOA-VMD and Deconvolution.

In a diesel engine, piston slap commonly occurs concurrently with fuel combustion and serves as the main source of excitation. Although combustion pressure can be measured using sensors, determining the slap force is difficult without conducting tests. In this study, we propose a method to identify the slap force of the piston to solve this difficult problem. The traditional VMD algorithm easily receives noise interference, which affects the value of parameter combination [k, α] and thus affects the extraction accuracy of the algorithm. First, we obtain the transfer function between the incentive and vibration response through percussion tests. Secondly, a variational modal decomposition method based on whale algorithm optimization is used to separate the slap response from the surface acceleration of the block. Finally, we calculated the slap force using the deconvolution method. Deconvolution is a typical inverse problem of mathematics, often prone to ill-conditioning, and the singular value decomposition and regularization method is used to overcome this flaw and improve accuracy. The proposed method provides an important means to evaluate the angular distribution of the slap force, identify the shock positions on the piston liner, and determine the peak value of the waveform which helps us analyze the vibration characteristics of the piston and optimize the structural design of the engine.

Application of observed data denoising based on variational mode decomposition in groundwater pollution source recognition.

Groundwater pollution source recognition (GPSR) is a prerequisite for subsequent pollution remediation and risk assessment work. The actual observed data are the most important known condition in GPSR, but the observed data can be contaminated with noise in real cases. This may directly affect the recognition results. Therefore, denoising is important. However, in different practical situations, the noise attribute (e.g., noise level) and observed data attribute (e.g., observed frequency) may be different. Therefore, it is necessary to study the applicability of denoising. Current studies have two deficiencies. First, when dealing with complex nonlinear and non-stationary situations, the effect of previous denoising methods needs to be improved. Second, previous attempts to analyze the applicability of denoising in GPSR have not been comprehensive enough because they only consider the influence of the noise attribute, while overlooking the observed data attribute. To resolve these issues, this study adopted the variational mode decomposition (VMD) to perform denoising on the noisy observed data in GPSR for the first time. It further explored the influence of different factors on the denoising effect. The tests were conducted under 12 different scenarios. Then, we expanded the study to include not only the noise attribute (noise level) but also the observed data attribute (observed frequency), thus providing a more comprehensive analysis of the applicability of denoising in GPSR. Additionally, we used a new heuristic optimization algorithm, the collective decision optimization algorithm, to improve the recognition accuracy. Four representative scenarios were adopted to test the ideas. The results showed that the VMD performed well under various scenarios, and the denoising effect diminished as the noise level increased and the observed frequency decreased. The denoising was more effective for GPSR with high noise levels and multiple observed frequencies. The collective decision optimization algorithm had a good inversion accuracy and strong robustness.

Short-term wind speed prediction of wind farm based on TSO-VMD-BiLSTM.

Aiming at the random and intermittent characteristics of wind speed, a short-term wind speed prediction (SWSP) method based on TSO-VMD-BiLSTM is proposed in this article. Firstly, open-source historical data from a certain region in 2022, including wind speed, direction, pressure, and temperature is analyzed. The data is processed through variational mode decomposition (VMD) to fully extract feature data from historical wind speed records. Secondly, taking historical wind speed, direction, pressure, and temperature as inputs and wind speed as output, a SWSP model based on long short-term memory (LSTM) network is constructed. Thirdly, the tuna swarm optimization (TSO) algorithm is utilized for parameters optimization, and a bi-directional long short-term memory (BiLSTM) network is incorporated to enhance prediction accuracy for micrometeorological parameters. The proposed TSO-VMD-BiLSTM model is validated through comparison with other models, demonstrating its higher accuracy with the maximum absolute error of only 2.52 m/s, the maximum root mean square error of 0.81, the maximum mean absolute error of only 0.54, and the maximum mean absolute percentage error of 6.89%.

Breaking through the limitation of carbon price forecasting: A novel hybrid model based on secondary decomposition and nonlinear integration.

Carbon trading is one of the pivotal means of carbon emission reduction. Accurate prediction of carbon prices can stabilize the carbon market, mitigate investment risks, and promote green development. In this study, firstly, the IVMD and ICEEMDAN are used to decompose carbon price quadratically; secondly, the Dispersion entropy is used to identify the sequence frequency, and then the SOA-LSSVM model and TCN model are used to predict the high-frequency and low-frequency sequences, respectively; finally, the prediction results are integrated by SOA-GRU. As a result, the hybrid IVMD-ICEEMDAN-SOALSSVM/TCN-SOAGRU model was constructed. This framework consistently performs best under two carbon markets, the CEEX Guangzhou and the EU ETS, compared with 21 comparative models, with MAPEs of 0.42% and 0.83%, respectively. The main contributions are as follows: (1) A novel IVMD-ICEEMDAN secondary decomposition method is proposed, which improves the problem of poorly determining the value of the decomposition modal number K in the traditional VMD method and improves the efficiency of the carbon price sequence decomposition. (2) A hybrid forecasting model of LSSVM and TCN is proposed, effectively capturing the features of different sequences. (3) Optimization for LSSVM and GRU using SOA improves the stability and adaptability of the model. The article provides governments, enterprises, and investors with novel and effective carbon price forecasting tool.

Research on Deformation Prediction of VMD-GRU Deep Foundation Pit Based on PSO Optimization Parameters.

As a key guarantee and cornerstone of building quality, the importance of deformation prediction for deep foundation pits cannot be ignored. However, the deformation data of deep foundation pits have the characteristics of nonlinearity and instability, which will increase the difficulty of deformation prediction. In response to this characteristic and the difficulty of traditional deformation prediction methods to excavate the correlation between data of different time spans, the advantages of variational mode decomposition (VMD) in processing non-stationary series and a gated cycle unit (GRU) in processing complex time series data are considered. A predictive model combining particle swarm optimization (PSO), variational mode decomposition, and a gated cyclic unit is proposed. Firstly, the VMD optimized by the PSO algorithm was used to decompose the original data and obtain the Internet Message Format (IMF). Secondly, the GRU model optimized by PSO was used to predict each IMF. Finally, the predicted value of each component was summed with equal weight to obtain the final predicted value. The case study results show that the average absolute errors of the PSO-GRU prediction model on the original sequence, EMD decomposition, and VMD decomposition data are 0.502 mm, 0.462 mm, and 0.127 mm, respectively. Compared with the prediction mean square errors of the LSTM, GRU, and PSO-LSTM prediction models, the PSO-GRU on the PTB0 data of VMD decomposition decreased by 62.76%, 75.99%, and 53.14%, respectively. The PTB04 data decreased by 70%, 85.17%, and 69.36%, respectively. In addition, compared to the PSO-LSTM model, it decreased by 8.57% in terms of the model time. When the prediction step size increased from three stages to five stages, the mean errors of the four prediction models on the original data, EMD decomposed data, and VMD decomposed data increased by 28.17%, 3.44%, and 14.24%, respectively. The data decomposed by VMD are more conducive to model prediction and can effectively improve the accuracy of model prediction. An increase in the prediction step size will reduce the accuracy of the deformation prediction. The PSO-VMD-GRU model constructed has the advantages of reliable accuracy and a wide application range, and can effectively guide the construction of foundation pit engineering.

A risk warning method for steady-state power quality based on VMD-LSTM and fuzzy model.

The risk warning for steady-state power quality in the power grid is essential for its prevention and management. However, current risk warning methods fall short in predicting the power quality trend while accounting for potential risks. Consequently, this study introduces a novel steady-state power quality risk warning method utilizing VMD-LSTM and a fuzzy model. Firstly, a power quality index prediction method based on variational mode decomposition (VMD) and long short-term memory (LSTM) is proposed. This approach significantly enhances prediction accuracy. Secondly, a power quality risk warning method incorporating kernel density estimation (KDE) and a fuzzy model is proposed, which systematically addresses the uncertainty associated with power quality risks. To validate the effectiveness and practicality of the proposed method, experiments are conducted using field monitoring data from a residential load in southern China. The results affirm the reliability and applicability of the proposed method. The simulation results show that the median error of prediction of power quality indexes by the proposed method is 5.03 % during the evaluated time period, and the prediction accuracy is mostly maintained above 90 %.

A novel coupled rainfall prediction model based on stepwise decomposition technique.

The traditional decomposed ensemble prediction model decomposes the entire rainfall sequence into several sub-sequences, dividing them into training and testing periods for modeling. During sample construction, future information is erroneously mixed into the training data, making it challenging to apply in practical rainfall forecasting. This paper proposes a novel stepwise decomposed ensemble coupling model, realized through variational mode decomposition (VMD) and bidirectional long short-term memory neural network (BiLSTM) models. Model parameters are optimized using an improved particle swarm optimization (IPSO). The performance of the model was evaluated using rainfall data from the Southern Four Lakes basin. The results indicate that: (1) Compared to the PSO algorithm, the IPSO algorithm-coupled model shows a minimum decrease of 2.70% in MAE and at least 2.62% in RMSE across the four cities in the Southern Four Lakes basin; the IPSO algorithm results in a minimum decrease of 25.58% in MAE and at least 28.19% in RMSE for the VMD-BiLSTM model. (2) When compared to IPSO-BiLSTM, the VMD-IPSO-BiLSTM based on the stepwise decomposition technique exhibits a minimum decrease of 26.54% in MAE and at least 34.16% in RMSE. (3) The NSE for the testing period of the VMD-IPSO-BiLSTM model in each city surpasses 0.88, indicating higher prediction accuracy and providing new insights for optimizing rainfall forecasting.

Surface water quality index forecasting using multivariate complementing approach reinforced with locally weighted linear regression model.

River water quality management and monitoring are essential responsibilities for communities near rivers. Government decision-makers should monitor important quality factors like temperature, dissolved oxygen (DO), pH, and biochemical oxygen demand (BOD). Among water quality parameters, the BOD throughout 5 days is an important index that must be detected by devoting a significant amount of time and effort, which is a source of significant concern in both academic and commercial settings. The traditional experimental and statistical methods cannot give enough accuracy or solve the problem for a long time to detect something. This study used a unique hybrid model called MVMD-LWLR, which introduced an innovative method for forecasting BOD in the Klang River, Malaysia. The hybrid model combines a locally weighted linear regression (LWLR) model with a wavelet-based kernel function, along with multivariate variational mode decomposition (MVMD) for the decomposition of input variables. In addition, categorical boosting (Catboost) feature selection was used to discover and extract significant input variables. This combination of MVMD-LWLR and Catboost is the first use of such a complete model for predicting BOD levels in the given river environment. In addition, an optimization process was used to improve the performance of the model. This process utilized the gradient-based optimization (GBO) approach to fine-tune the parameters and better the overall accuracy of predicting BOD levels. To assess the robustness of the proposed method, we compared it to other popular models such as kernel ridge (KRidge) regression, LASSO, elastic net, and gaussian process regression (GPR). Several metrics, comprising root-mean-square error (RMSE), R (correlation coefficient), U95% (uncertainty coefficient at 95% level), and NSE (Nash-Sutcliffe efficiency), as well as visual interpretation, were used to evaluate the predictive efficacy of hybrid models. Extensive testing revealed that, in forecasting the BOD parameter, the MVMD-LWLR model outperformed its competitors. Consequently, for BOD forecasting, the suggested MVMD-LWLR optimized with the GBO algorithm yields encouraging and reliable results, with increased forecasting accuracy and minimal error.