Outlier Robust Extreme Learning Machine Research Articles

Application of machine learning models in predicting discharge coefficient of side B-type piano key weir

Side weir is a hydraulic structure within a channel which is usually used to discharge excess water, to divert the flow, and to regulate water surface levels in rivers and irrigation and drainage networks. In general, piano key weirs (PKW) have been used as weirs perpendicular to the flow direction in straight channels. However, the use of the PKW as a side weir in the outer arch of the channels is a new approach to enhance the weir's performance. In this study, 289 tests were first performed on the B-type rectangular side piano key weir (RSPKW) at two arc angles of 30 and 120°. Then, Fuzzy Inference System (FIS), Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS and Teaching Learning Based Optimization (TLBO), ANFIS and Grasshopper Optimization Algorithm (GOA), Extreme Learning Machine (ELM) and Outlier Robust ELM (ORELM) models were used to predict the weir discharge coefficient. The results showed that two optimization models of TLBO and GOA increased the accuracy of the ANFIS model. The results showed that the ANFIS-GOA model has accuracy of Root Mean Squared Error (RMSE) = 0.0361, Coefficient of determination (R2) = 0.9772, and Kling Gupta coefficient (KGE) = 0.9858. The ANFIS-TLBO, ANFIS, and FIS models were ranked, respectively. Also, the results showed that ELM and ORELM models have accuracy close to ANFIS-GOA and can be a suitable alternative for complex fuzzy models. According to the statistical analysis, it was found that the parameters of the ratio of weir height to flow depth at the upstream edge of weir (P/h1), arc angle (α), and the ratio of height of the foundation to the main channel width (pd/B) had the greatest role in the development of the models, respectively.

Advancing Spatial Drought Forecasts by Integrating an Improved Outlier Robust Extreme Learning Machine with Gridded Data: A Case Study of the Lower Mainland Basin, British Columbia, Canada

Droughts have extensive consequences, affecting the natural environment, water quality, public health, and exacerbating economic losses. Precise drought forecasting is essential for promoting sustainable development and mitigating risks, especially given the frequent drought occurrences in recent decades. This study introduces the Improved Outlier Robust Extreme Learning Machine (IORELM) for forecasting drought using the Multivariate Standardized Drought Index (MSDI). For this purpose, four observation stations across British Columbia, Canada, were selected. Precipitation and soil moisture data with one up to six lags are utilized as inputs, resulting in 12 variables for the model. An exhaustive analysis of all potential input combinations is conducted using IORELM to identify the best one. The study outcomes emphasize the importance of incorporating precipitation and soil moisture data for accurate drought prediction. IORELM shows promising results in drought classification, and the best input combination was found for each station based on its results. While high Area Under Curve (AUC) values across stations, a Precision/Recall trade-off indicates variable prediction tendencies. Moreover, the F1-score is moderate, meaning the balance between Precision, Recall, and Classification Accuracy (CA) is notably high at specific stations. The results show that stations near the ocean, like Pitt Meadows, have higher predictability up to 10% in AUC and CA compared to inland stations, such as Langley, which exhibit lower values. These highlight geographic influence on model performance.

Optimization of Signal Detection Using Deep CNN in Ultra-Massive MIMO

This paper addresses the evolving landscape of communication technology, emphasizing the pivotal role of 5G and the emerging 6G networks in accommodating the increasing demand for high-speed and accurate data transmission. We delve into the advancements in 5G technology, particularly the implementation of millimeter wave (mmWave) frequencies ranging from 30 to 300 GHz. These advancements are instrumental in enhancing applications requiring massive data transmission and reception, facilitated by massive MIMO (multiple input multiple output) systems. Looking towards the future, this paper forecasts the necessity for faster data transmission technologies, shifting the focus toward the development of 6G networks. These future networks are projected to employ ultra-massive MIMO systems in the terahertz band, operating within 0.1–10 THz frequency ranges. A significant part of our research is dedicated to exploring advanced signal detection techniques, helping to mitigate the impact of interference and improve accuracy in data transmission and enabling more efficient communication, even in environments with high levels of noise, and including zero forcing (ZF) and minimum mean square error (MMSE) methods, which form the cornerstone of our proposed approach. Additionally, signal detection contributes to the development of new communication technologies such as 5G and 6G, which require a high data transmission efficiency and rapid response speeds. The core contribution of this study lies in the application of deep learning to signal detection in ultra-massive MIMO systems, a critical component of 6G technology. We compare this approach with existing ELMx-based machine learning methods, focusing on algorithmic efficiency and computational performance. Our comparative analysis included the regularized extreme learning machine (RELM) and the outlier robust extreme learning machine (ORELM), juxtaposed with ZF and MMSE methods. Simulation results indicated the superiority of our convolutional neural network for signal detection (CNN-SD) over the traditional ELMx-based, ZF, and MMSE methods, particularly in terms of channel capacity and bit error rate. Furthermore, we demonstrate the computational efficiency and reduced complexity of the CNN-SD method, underscoring its suitability for future expansive MIMO systems.

A novel machine learning tool for current and future flood susceptibility mapping by integrating remote sensing and geographic information systems

Flood mapping is essential for managing and mitigating the risks associated with flood events. This study integrates weighted overlay analysis and analytical network process to create a flood susceptibility map. Twelve factors were selected to assess flood risk in the region, and an analytical network process was used to derive weights of factors. Weighted overlay analysis was then used to apply weights to the flood conditioning factors to prepare the flood susceptibility map. The most prominent historical flood extent was derived by using Landsat 8, Sentinel-2 and Sentinel-1 satellite imageries, spectral indices and decision tree model to generate a flood inventory map. The flood susceptibility map was assessed for accuracy using the flood inventory map, achieving an overall accuracy rate of 88.3 %. The primary factors affecting flood risk were elevation, slope, and distance from the stream, with high-risk areas mainly located downstream. To develop the flood risk assessment model, the essential factors were classified into four main categories: topographical, environmental, hydrological, and anthropological. All possible input combinations were checked using the outlier robust extreme learning machine for one to twelve input variables, and the best model was selected using the outlier robust extreme learning machine with the input combination of five variables (i.e., normalizes difference vegetation index, geology, precipitation, elevation, and slope). Based on the Sixth Intergovernmental Panel on climate change report, the developed outlier robust extreme learning machine was used to project potential flood areas in the next 78 years. Based on the different scenarios, the results indicated that 10.93 %, 8.55 %, 8.09 %, 11.99 %, and 16.28 % of all areas are projected to be highly and very highly flood susceptible. The tools and methods outlined in this study can assist decision-makers in preparing for and responding to floods. Moreover, the method developed in this study can be implemented in watersheds and urban areas and help manage flood risk in urban drainage systems.

An evolutionary robust soft measurement technique via enhanced atom search optimization and outlier robust extreme learning machine for wastewater treatment process

Accurate and prompt measurement of certain key variables occurring during wastewater treatment, especially effluent ammonia nitrogen (NH4-N) and biological oxygen demand (BOD), is of great importance. In this study, a soft measurement model combining random forest (RF), enhanced atomic search optimization (EASO) and online sequential outlier robust extreme learning machine (OSORELM) is proposed for wastewater treatment. First, RF is used to select auxiliary variables with high correlation of NH4-N and BOD as model inputs. Second, a dynamic perturbation strategy and a generalized opposition-based learning are added to ASO to improve the algorithm performance. And EASO is used for model hyperparameter optimization. Then, the optimized OSORELM model is used for soft measurements of NH4-N and BOD. Finally, to verify the stability of the model, 5 %, 10 % and 15 % noise were added for further experiments. The results show that the proposed model has better prediction and stronger robustness in soft measurements of NH4-N and BOD.

A New Insight for Daily Solar Radiation Prediction by Meteorological Data Using an Advanced Artificial Intelligence Algorithm: Deep Extreme Learning Machine Integrated with Variational Mode Decomposition Technique

Reliable and precise estimation of solar energy as one of the green, clean, renewable and inexhaustible types of energies can play a vital role in energy management, especially in developing countries. Also, solar energy has less impact on the earth’s atmosphere and environment and can help to lessen the negative effects of climate change by lowering the level of emissions of greenhouse gas. This study developed thirteen different artificial intelligence models, including multivariate adaptive regression splines (MARS), extreme learning machine (ELM), Kernel extreme learning machine (KELM), online sequential extreme learning machine (OSELM), optimally pruned extreme learning machine (OPELM), outlier robust extreme learning machine (ORELM), deep extreme learning machine (DELM), and their versions combined with variational mode decomposition (VMD) as integrated models (VMD-DELM, VMD-ORELM, VMD-OPELM, VMD-OSELM, VMD-KELM, and VMD-ELM), for solar radiation estimation in Kurdistan region, Iraq. The daily meteorological data from 2017 to 2018 were used to implement suggested artificial models at Darbandikhan and Dukan stations, Iraq. The input parameters included daily data for maximum temperature (MAXTEMP), minimum temperature (MINTEMP), maximum relative humidity (MAXRH), minimum relative humidity (MINRH), sunshine duration (SUNDUR), wind speed (WINSPD), evaporation (EVAP), and cloud cover (CLOUDCOV). The results show that the proposed VMD-DELM algorithm considerably enhanced the simulation accuracy of standalone models’ daily solar radiation prediction, with average improvement in terms of RMSE of 13.3%, 20.36%, 25.1%, 27.1%, 34.17%, 38.64%, and 48.25% for Darbandikhan station and 5.22%, 10.01%, 10.26%, 21.01%, 29.7%, 35.8%, and 40.33% for Dukan station, respectively. The outcomes of this study reveal that the VMD-DELM two-stage model performed superiorly to the other approaches in predicting daily solar radiation by considering climatic predictors at both stations.

Modelling coagulant dosage in drinking water treatment plant using advance machine learning model: Hybrid extreme learning machine optimized by Bat algorithm.

Despite the high importance of coagulation process in drinking water treatment plant (DWTP), challenge remains in effectively linking raw water quality measured at the inlet of the DWTP with coagulant dosage rate. This study proposes an integral modelling framework using hybrid extreme learning machine and Bat metaheuristic algorithm (ELM-Bat) for modelling coagulant dosage rate using water temperature, pH, specific conductance, dissolved oxygen, and water turbidity. The aluminum sulphate (Al2 (SO4)3.18H2O) coagulant is determined using conventional Jar-Test procedure. Results obtained using the hybrid ELM-Bat were compared to those obtained using standalone ELM, outlier robust extreme learning machine (ORELM), online sequential extreme learning machine (OSELM), optimally pruned extreme learning machine (OPELM), and kernel extreme learning machine (KELM). First, the models have been calibrated during the training stage and in a second stage; they are validated using various statistical metrics, i.e., RMSE, MAE, the correlation coefficient (R), and the Nash-Sutcliffe model efficiency (NSE). We found that the hybrid ELM-Bat was significantly more accurate and it has yielded accuracy higher than all other models. During the validation stage, the R and NSE values calculated using the ELM-Bat were ≈0.959 and ≈0.918 exhibiting an improvement rates of approximately (≈15.26% and ≈33.82%), (≈10.35% and ≈21.92%), (≈14.98% and ≈31.89%), (≈7.63% and ≈16.35%), (≈10.99% and ≈23.05%), compared to the values obtained using the ELM, OPELM, OSELM, KELM and ORELM, respectively. Besides, the new ELM-Bat model has shown to have high predictive capabilities, which can be used optimally for calculating the optimal coagulant dosage with high accuracy.

A novel hybrid prediction model for PM2.5 concentration based on decomposition ensemble and error correction.

PM2.5 concentration is an important index to measure the degree of air pollution. It is necessary to establish an accurate PM2.5 concentration prediction system for urban air monitoring and control. Due to the nonlinear characteristics of PM2.5 concentration, it is difficult to predict it directly. Therefore, a novel hybrid model for PM2.5 concentration based on improved variational mode decomposition (IVMD), outlier-robust extreme learning machine (ORELM) optimized by hybrid cuckoo search (CS), and chimp optimization algorithm (ChOA), error correction (EC) is proposed named IVMD-ChOACS-ORELM-EC. First of all, an improved VMD based on energy loss coefficient, named IVMD, is proposed. IVMD decomposes the original data to obtain K IMF components. Then, a hybrid optimization algorithm based on ChOA improved by CS is proposed, named ChOACS. The hybrid optimization algorithm is used to optimize ORELM. On this basis, the prediction model ChOACS-ORELM is proposed, and the K IMF components are predicted by ChOACS-ORELM. Finally, the EC model based on decomposition ensemble is established to further improve the prediction accuracy. The PM2.5 concentration data collected at hourly intervals in Beijing, Shanghai, Shenyang, and Qingdao in China are used as experimental data. The experimental results show that the correlation coefficients between the prediction results and the actual values of the four cities are 0.9999, and the prediction performance of the proposed model is better than that of all comparison models.

Online sequential, outlier robust, and parallel layer perceptron extreme learning machine models for sediment transport in sewer pipes.

Sediment transport is a noteworthy task in the design and operation of sewer pipes. Decreasing sewer pipe hydraulic capacity and transport of pollution are the main consequences of continuous sedimentation. Among different design approaches, the non-deposition with deposited bed (NDB) method can be used for the design of large sewer pipes; however, existing models are established on limited data ranges and mostly applied conventional regression methods. The current study improves the NDB sediment transport modeling by utilizing wide data ranges, and furthermore, applying robust machine learning techniques. In the present study, the conventional extreme learning machine (ELM) technique and its advanced versions, namely the online sequential-extreme learning machine (OS-ELM), outlier robust-extreme learning machine (OR-ELM), and parallel layer perceptron-extreme learning machine (PLP-ELM) are used for the modeling. In the studies conducted in the literature, sediment deposited bed thickness (ts) or deposited bed width (Wb) was used in the model structure as a deposited sediment variable, and therefore, different parameters in terms of ts and Wb can be incorporated into the model structure. However, an uncertainty arises in the selection of the appropriate parameter among Wb/Y, ts/Y, Wb/D, and ts/D (Y is flow depth and D circular pipe diameter). In order to define the most appropriate parameter to best describe the impact of deposited sediment at the channel bottom in the modeling procedure, four various scenarios using four different parameters that incorporate deposited sediment variables at their structures as Wb/Y, ts/Y, W/D, and ts/D are considered for model development. It is found that models that incorporate sediment bed thickness (ts) provide better results than those whichuse deposited bed width (Wb) in their structures. Among four different scenarios, models that utilized ts/D dimensionless parameter, give superior results in contrast to their alternatives. Based on the outcomes, the OR-ELM approach outperformed ELM, OS-ELM, and PLP-ELM techniques. The results obtained from applied methods are compared to their corresponding models in the literature, indicating the superiority of the OR-ELM model. It is figured out that the thickness of the deposited bed is an effective variable in modeling NDB sediment transport in sewer pipes.

Noise-resistant state of charge estimation of Li-ion battery using the outlier robust extreme learning machine

The State of Charge (SOC) indicates the amount of charge remaining in the battery, which is a critical parameter in the battery management system (BMS). A precise SOC estimation can effectively protect the battery and extend its service life. Recently, a leading-edge machine learning model, namely the extreme learning machine (ELM), has been applied for SOC estimation due to its powerful fitting and fast training capabilities. However, as BMS is required to operate in more and more complex environments, it is inevitable to encounter the effects of non-Gaussian noises caused by system errors, human causes, and other factors. These noises are random, sparse, and far from the targets, mainly referring to the outliers. The classical extreme learning machine (ELM) is susceptible to noise, leading to poor performance in outlier-contaminated datasets. To overcome this problem, we developed a new robust SOC estimation method through the outlier robust ELM (OR-ELM) in this paper. Additionally, a powerful iterative algorithm, namely the alternating direction method of multipliers (ADMM), was utilized for training OR-ELM. Experiments were carried out on a dataset of Panasonic 18650 cells, and the results show the applicability and robustness of OR-ELM in the SOC estimation.

A reliable hybrid outlier robust non-tuned rapid machine learning model for multi-step ahead flood forecasting in Quebec, Canada

Reliable and accurate flood forecasting is a complex and challenging problem that is essential for the creation of disaster preparedness plans to protect life and reduce economic losses. This study suggests a novel hybrid model for real-time multi-steps-ahead flood forecasting within the Saint-Lawrence River in Quebec by integrating the discrete wavelet transform (DWT) and improved outlier-robust extreme learning machine (IORELM) models. The DWTIORELM model was constructed with three main novelties: (i) Consider the sparsity characteristics of the outliers to enhance the performance of the ELM-based model in the presence of outliers, (ii) Introduce an iterative process to overcome the random definition of the two main matrices in the ELM-based approaches, (iii) Integrate IORELM with DWT as a preprocessing technique to decompose the main input signals to high-scale and low-frequency signals. The performance of the individual IORELM is compared with the original version of ELM, Regularized ELM (RELM), and Weighted RELM (WRELM) in terms of global accuracy and accuracy in peak flow forecasting. The results indicated that the IORELM outperformed other models. However, there was a need for a model that could perform better for peak flow detection. IORELM, as the best individual model, was integrated with DWT, and the DWTIORELM model was developed to overcome this limitation. In addition, the comparison results of the hybrid DWTIORELM and individual IORELM models in terms of accuracy and simplicity as well as peak flow forecasting indicate that the introduced hybrid model (R = 0.99, NSE = 0.99; RMSE = 0.234; NRMSE = 0.021; MARE = 0.02) in the current study not only overcomes all limitations of the existing ELM-based methods but also could be applied in multi-steps-ahead flood forecasting. The optimum values of the number of hidden neurons, decomposition level, and iteration number were found to be 200, 1, and 500, respectively. Furthermore, the Sigmoid function and Discrete Meyer (DM) were selected as the best activation function and mother wavelet, respectively. The developed hybrid model was applied to check its performance in multi-steps-ahead flood forecasting for one to nine hours ahead. The results showed that it could forecast peak flows with an average relative error of less than 5 %.

An evolutionary robust solar radiation prediction model based on WT-CEEMDAN and IASO-optimized outlier robust extreme learning machine

As a kind of clean energy, solar energy occupies a pivotal position in energy applications. Accurate and reliable solar radiation prediction is critical to the application of solar energy. In particular, a novel solar radiation prediction based on wavelet transform (WT), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), improved atom search optimization (IASO) and outlier-robust extreme learning machine (ORELM) is proposed for solar radiation prediction. First, WT is used to denoise the original solar radiation time series, and CEEMDAN method is used to decompose the denoised sequence into intrinsic mode function (IMF) components with different distributions according to the fluctuation scale. Then the IASO algorithm is used to optimize the weights and thresholds of the ORELM to improve the performance of the ORELM model. Levy flight is added to the ASO to enhance the local and global search capability while the chaos population initialization based on piecewise linear chaotic map (PWLCM) is taken to improve the randomness and ergodicity of the initial population within the feasible region. Finally, the comparison with other benchmark models verifies the robustness and accuracy of the proposed solar radiation prediction model.

Estimating discharge coefficient of side weirs in trapezoidal and rectangular flumes using outlier robust extreme learning machine

Using the outlier robust extreme learning machine (ORELM) method, the discharge coefficient of side weirs placed on rectangular and trapezoidal canals was simulated for the first time in this study. The parameters governing the discharge coefficient of side weirs including Froude number (Fr), the ratio of the weir length to the main channel length (L/b), the ratio of the flow depth at the upstream of the side weir to the main channel width (y1/b) and the ratio of the crest height of the side weir to the flow depth at the upstream of the side weir (W/y1), the ratio of the weir length to the main channel width (L/y1), and the side wall slope parameter (m) were initially detected. Using the parameters governing, eight different input combinations were defined. By randomly selection approach, 65% of the data were considered to train the ORELM models and the rest of samples were applied to test them. The correlation coefficient, Nash–Sutcliffe efficiency coefficient, and Scatter Index for this model were calculated to be 0.937, 0.869 and 0.092, respectively. The results of sensitivity analysis indicated the ORELM model was more sensitive to the W/y1 and L/b than Fr and y1/b. The results of the ORELM model were also compared with the support vector machine optimized with genetic algorithm (SVM-GA) and extreme learning machine (ELM)) and four multiple linear regression models, with a better performance of the ORELM model. The ORELM models demonstrated a higher precision and correlation with experimental values.

Prognostication of scour around twin and three piers using efficient outlier robust extreme learning machine.

One of the most essential difficulties in the design and management of bridge piers is the estimation and modeling of scouring around the piers. The scour depth downstream of twin and three piers were simulated using a new outlier robust extreme learning machine (ORELM) model in this study. Furthermore, k-fold cross-validation with k = 4 was employed to validate the outcomes of numerical models. Four ORELM models with effective scouring parameters were first created to simulate scour depth. After then, the number of hidden layer neurons increased from two to thirty. The number of ideal hidden neurons was determined by examining the modeling results. The sigmoid activation function was also introduced as the best function. Furthermore, a sensitivity analysis was used to identify the superior model. The best model predicted scour depth as a function of the Froude number (Fr), the pier diameter to flow depth ratio (D/h), and the distance between the piers to flow depth ratio (d/h). The values of the objective function were accurately approximated by this model. As a result, using the ORELM model, the R2, scatter index, and Nash-Sutcliffe efficiency coefficient were calculated to be 0.953, 0.146, and 0.949, respectively. The most efficient parameters for simulating the scour depth were Fr and D/h, according to the modeling results. It is worth noting that nearly half of the superior model's simulated outputs had an inaccuracy of less than 10%. The superior model's performance has been underestimated, according to uncertainty analysis. After that, a simple and practical equation for calculating the scour depth was established for the superior model. Additionally, the influence of each input parameter on the objective function was assessed using a partial derivative sensitivity analysis.

Outlier robust extreme learning machine to simulate discharge coefficient of side slots

As the first time, this paper attempts to recreate the discharge coefficient (DC) of side slots by another artificial intelligence procedure named "Outlier Robust Extreme Learning Machine (ORELM)". Accordingly, at first, the variables affecting the DC comprising the ratios of the flow depth to the side slot length (Ym/L), the side slot crest elevation to the side slot length (W/L), the main channel width to the side slot length (B/L), as well as the Froude number (Fr) are determined and subsequently five ORELM models (ORELM 1 to ORELM 5) are created utilizing these variables. From that point forward, laboratory measurements are arranged into two datasets comprising training (70%) and testing (30%). At the subsequent stage, the best model alongside the most affecting input variables is presented by executing a sensitivity examination. The most impressive model (i.e., ORELM 3) reproduces DC values as far as B/L, W/L and Fr. It is worth focusing on that ORELM 3 forecasts DC values with worthy precision. For instance, the correlation coefficient (R), the scatter index (SI) and the Nash–Sutcliffe effectiveness (NSC) for ORELM 3 are acquired in the examination state to be 0.936, 0.049 and 0.852, independently. Examining the outcomes yielded from the simulation demonstrates that W/L and Fr are the most impacting factors to reproduce the DC. Besides, the findings of the sensitivity examination uncover that ORELM 3 acts in an underestimated way. Finally, a computer code is put forward to compute the DC of side slots.

Big multi-step ship motion forecasting using a novel hybrid model based on real-time decomposition, boosting algorithm and error correction framework

Big multi-step ship motion forecasting plays an essential role as ship safety warning in maritime operations. However, big multi-step prediction will weaken the correlation of time series and introduce large error accumulation. Real-time prediction also requires a simple prediction model structure, data input-output relationship in line with the actual application, and a high prediction accuracy. To realize the above requirements, a hybrid big multi-step forecasting model is proposed based on real-time wavelet packet decomposition (RTWPD), outlier robust extreme learning machine (ORELM), boosting algorithm, and least squares support vector machine (LSSVM)-based error correction method. Taking 10-step, 20-step, and 30-step as the research objects of big multi-step prediction, two sets of ship roll and pitch motion data obtained by practical experiment are provided to complete four comparison experiments, including the comparison of different decomposition algorithms, the comparison of different classical forecasting models, the comparison of different error correction methods and the comparison of the proposed model with different benchmark models. Taking the 10-step, 20-step, and 30-step prediction results of the pitch of dataset #2 as an example, the mean absolute errors (MAEs) of the proposed model are 0.1619°, 0.1742°, and 0.1808°, respectively; and the minimum Diebold-Mariano (DM) value is 4.88, which is greater than the upper limit of the 1 % confidence level, indicating that the prediction results of the proposed model differ significantly from those of the other models. And the root mean square error (RMSE) of the proposed model is about 0.20° for different data sets and different ship motions. The experimental results indicate that the proposed RTWPD-ORELM-AdaBoost.MRT-LSSVM (RWOALS) model is stable and feasible in practical applications, and it can provide reliable guidance for maritime operations.

Optimization of Channel Estimation Using ELMx-based in Massive MIMO

In communication channel estimation, the Least Square (LS) technique has long been a widely accepted and commonly used principle. This is because the simple calculation method is compared with other channel estimation methods. The Minimum Mean Squares Error (MMSE), which is developed later, is devised as the next step because the goal is to reduce the error rate in the communication system from the conventional LS technique which still has a higher error rate. These channel estimations are very important to modern communication systems, especially massive MIMO. Evaluating the massive MIMO channel is one of the most researched and debated topics today. This is essential in technology to overcome traditional performance barriers. The better the channel estimation, the more accurate it is. This paper investigated machine learning (ML) for channel estimation. ML channel estimations based on the Extreme Learning Machine (ELMx) group are also implemented. These estimations, known as the ELMx group, include Regularized Extreme Learning Machine (RELM) and Outlier Robust Extreme Learning Machine (ORELM). Then, it was compared with LS and MMSE. The simulation results reveal that the ELMx group outperforms LS and MMSE in channel capacity and bit error rate. Additionally, this paper has proven complexity for verified computational times. The RELM method is less time consuming and has low complexity which is suitable for future use in large MIMO systems.

Air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction

Performing scientific and accurate forecasting and realizing the quantitative description of uncertainties in air quality remain challenging prospects. Because of the strong volatility and uncertainty of air pollutant concentrations, this problem increases in difficulty when multiple requirements are considered. In this study, a novel air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction was proposed to realize air quality early warning. The proposed system solves the non-stochastic non-deterministic problem in air quality forecasting considering a novel hesitant fuzzy time series forecasting model wherein the intervals are partitioned by different approaches with optimal weights determined by the multi-objective JAYA algorithm. The forecasting performance is further enhanced with the introduction of a new nonlinear error correction model based on an outlier robust extreme learning machine and multi-objective JAYA algorithm, and the quality of the solution obtained is verified by sensitivity analysis. However, point forecast information alone is not sufficient to facilitate the rational integration of pollution control measures. Therefore, this study conducts probabilistic forecasting and constructs proper prediction intervals based on the optimal distribution of the forecasting residuals. By comparing the results with typical counterparts and comparison models considering multiple metrics, the experimental results confirmed the improvement scheme proposed in this study on the traditional fuzzy time series forecasting method while the effectiveness of applying the proposed system to air quality early warning was confirmed as well.

Short-term wind speed forecasting using deep reinforcement learning with improved multiple error correction approach

The safe and stable operation of wind power systems requires the support of wind speed prediction. To ensure the controllability and stability of smart grid dispatching, a novel hybrid model consisting of data-adaptive decomposition, reinforcement learning ensemble, and improved error correction is established for short-term wind speed forecasting. In decomposition module, empirical wavelet transform algorithm is used to adaptively disassemble and reconstruct the wind speed series. In ensemble module, Q-learning is utilized to integrate gated recurrent unit, bidirectional long short-term memory, and deep belief network. In error correction module, wavelet packet decomposition and outlier-robust extreme learning machine are combined to developing predictable components. An appropriate correction shrinkage rate is used to obtain the best correction effect. Ljung-Box Q-Test is utilized to judge the termination of the error correction iteration. Four real data are utilized to validate model performance in the case study. Experimental results show that: (a) The proposed hybrid model can accurately capture the changes of wind data. Taking 1-step prediction results as an example, the mean absolute errors for site #1, #2, #3, and #4 are 0.0829 m/s, 0.0661 m/s, 0.0906 m/s, and 0.0803 m/s, respectively; (b) Compared with several state-of-the-art models, the proposed model has the best prediction performance.

A spatial multi-resolution multi-objective data-driven ensemble model for multi-step air quality index forecasting based on real-time decomposition

In recent years, the problem of urban air pollution has become more serious. Effective Air Quality Index (AQI) forecasting can provide a reliable guarantee for pollution control and air quality warnings. In this research background, a spatial multi-resolution data-driven ensemble AQI forecasting model based on real-time decomposition is proposed. The model uses spatial correlation analysis to screen out the auxiliary sites that are most relevant to the target site. Wavelet Packet Decomposition (WPD) decomposes the original AQI data into multiple subseries. The iterative refresh mechanism of real-time decomposition makes the decomposition method more valuable in engineering applications. The classic averaging method and deep learning-based Stacked Auto-Encoder (SAE) are used to obtain low-resolution data and high-resolution data, respectively. Subseries containing fluctuation information and depth features are input into Outlier Robust Extreme Learning Machine (ORELM) for forecasting. Multi-Objective Wolf Colony Algorithm (MOWCA) is utilized for the ensemble of multiple resolution predictors. Then, the high-correlation auxiliary sites tested by the Pearson method are input into the model where the target site is located. After the optimized ensemble of the new meta-heuristic bat algorithm, the final AQI forecasting result is produced. To comprehensively evaluate the proposed model, historical air quality data from 26 city monitoring stations in China is used for experimental comparison. Experimental results show that each component of the proposed model has a positive effect on the forecasting performance of the model. The proposed model has excellent forecasting performance, and its performance is superior to other comparative models. Reasonable consideration of multi-resolution and space-time data provides more ideas for the enrichment of the air pollution forecasting model library.