Robust Extreme Learning Machine Research Articles

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.

A Novel Hybrid Model Combining Improved VMD and ELM with Extended Maximum Correntropy Criterion for Prediction of Dissolved Gas in Power Transformer Oil

The prediction of dissolved gas change trends in power transformer oil is very important for the diagnosis of transformer faults and ensuring its safe operation. Considering the time series and nonlinear features of the gas change trend, this paper proposes a novel robust extreme learning machine (ELM) model combining an improved data decomposition method for gas content forecasting. Firstly, the original data with nonlinear and sudden change properties will make the forecasting model unstable, and thus an improved variational modal decomposition (IPVMD) method is developed to decompose the original data to obtain the multiple modal dataset, in which the marine predators algorithm (MPA) optimization method is utilized to optimize the free parameters of the VMD. Second, the ELM as an efficient and easily implemented tool is used as the basic model for dissolved gas forecasting. However, the traditional ELM with mean square error (MSE) criterion is sensitive to the non-Gaussian measurement noise (or outliers). In addition, considering the nonlinear non-Gaussian properties of the dissolved gas, a new learning criterion, called extended maximum correntropy criterion (ExMCC), is defined by using an extended kernel function in the correntropy framework, and the ExMCC as a learning criterion is introduced into the ELM to develop a novel robust regression model (called ExMCC-ELM) to improve the ability of ELM to process mutational data. Third, a gas-in-oil prediction scheme is proposed by using the ExMCC-ELM performed on each modal obtained by the proposed IPVMD. Finally, we conducted several simulation studies on the measured data, and the results show that the proposed method has good predictive performance.

Robust Extreme Learning Machine Based on p-order Laplace Kernel-Induced Loss Function

Robust Extreme Learning Machine Based on p-order Laplace Kernel-Induced Loss Function

Prediction and Recognition of Epileptic Seizures Based on Artificial Intelligence

Repetitive seizures caused by abnormal brain activity are the hallmark of the common neurological illness epilepsy, which has a serious impact on the health of those affected. The introduction of artificial intelligence (AI) in recent years has ushered in novel ways of predicting and recognizing epileptic seizures, transforming the discipline of neurology. In particular, Recurrent Neural Networks (RNNs), Long Short-Term Memory networks (LSTMs), Support Vector Machines (SVMs), and Extreme Learning Machines (ELMs) are examined in this research as potential AI approaches for the prediction and identification of epileptic episodes. The underlying working logic of these AI approaches is investigated, emphasizing their distinct strengths and capacities. RNNs and LSTMs are well-known for their ability to describe temporal dependencies in sequential data, whereas SVMs excel in robust classification and ELMs excel at rapid training and real-time prediction. Real-world case studies show how these AI models may be used to analyze electroencephalogram (EEG) data, extract relevant features, and distinguish between seizure and non-seizure states. Furthermore, the essay explores the ramifications of AI in the medical profession, emphasizing the possibility of prompt intervention, improved patient care, and resource optimization. The difficulties and ethical concerns regarding AI in healthcare are also discussed. Finally, this piece highlights AI's promising role in predicting and identifying epileptic seizures, providing a glimpse into the future of personalized, data-driven healthcare. The combination of AI approaches opens the door to more accurate and timely seizure forecasts, increasing the quality of life for those living with epilepsy and revolutionizing the landscape of neurological healthcare.

Research on robust inversion model of soil moisture content based on GF-1 satellite remote sensing

This study aims to improve the accuracy and applicability of traditional linear regression and machine learning algorithms for monitoring soil moisture content by satellite remote sensing. Shahaoqu Experimental Station within Jiefangzha Irrigation District of Hetao Irrigation Area is selected as the study area. The dataset includes GF-1 satellite remote sensing images and measured soil moisture content. The study employs the best subset selection to determine the combination of sensitive variables for soil moisture content at different soil depths. Additionally, robust regression theory is introduced to traditional linear regression and machine learning algorithms to construct soil moisture content inversion models at different soil depths. The results show that all three improved robust algorithms effectively reduce the influence of outliers, improve the accuracy and stability of these inversion models. The improved robust nonlinear algorithm outperforms the improved robust linear algorithm. Compared with the unprocessed algorithm, at the soil depth of 0–20 cm, Robust Extreme Learning Machine (RELM) algorithm is the most optimal, with the validation set's R2adj increasing from 0.555 to 0.696 (approximately 25.33%) and the RMSE decreasing from 0.025 to 0.018 (approximately 26.54%). Robust Least Squares Support Vector Machine (RLSSVM) algorithm is the second best, with the validation set's R2adj increasing from 0.502 to 0.641 (approximately 27.75%) and the RMSE decreasing from 0.026 to 0.020 (approximately 24.59%). Robust Linear Regression (LMS-RLS) algorithm is relatively the worst, with the validation set's R2adj increasing from 0.491 to 0.659 (approximately 34.05%) and the RMSE decreasing from 0.026 to 0.019 (approximately 27.21%). The sensitivity of the five soil depths to soil moisture content follows the order of 0–20 cm, 20–40 cm, 0–60 cm, 0–40 cm, and 40–60 cm. The improved robust regression algorithms can improve the accuracy and applicability of soil moisture content estimation and provide a reference for monitoring soil moisture content using GF-1 satellite.

Mixture extreme learning machine algorithm for robust regression

The extreme learning machine (ELM) is a well-known approach for training single hidden layer feedforward neural networks (SLFNs) in machine learning. However, ELM is most effective when used for regression on datasets with simple Gaussian distributed error because it often employs a squared loss in its objective function. In contrast, real-world data is often collected from unpredictable and diverse contexts, which may contain complex noise that cannot be characterized by a single distribution. To address this challenge, we propose a robust mixture ELM algorithm, called Mixture-ELM, that enhances modeling capability and resilience to both Gaussian and non-Gaussian noise. The Mixture-ELM algorithm uses an adjusted objective function that blends Gaussian and Laplacian distributions to approximate any continuous distribution and match the noise. The Gaussian mixture accurately models the residual distribution, while the inclusion of the Laplacian distribution addresses the limitations of the Gaussian distribution in identifying outliers. We derive a solution to the novel objective function using the expectation maximization (EM) and iteratively reweighted least squares (IRLS) algorithms. We evaluate the effectiveness of the algorithm through numerical simulation and experiments on benchmark datasets, thereby demonstrating its superiority over other state-of-the-art machine learning methods in terms of robustness and generalization.

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.

Elastic-net based robust extreme learning machine for one-class classification

The one-class extreme learning machine (OC-ELM) builds a classification model by learning samples of the known class to detect abnormal samples, and has the advantages of high learning speed and good generalization performance. However, OC-ELM with the square loss function is sensitive to outliers, which leads to poor robustness. To address this issue, an elastic-net based robust extreme learning machine for one-class classification (ER-OCELM) is proposed to achieve both excellent robustness and comparable sparsity. Correntropy loss function is utilized to limit the negative effects of outliers due to its property of bounded. With an elastic-net regularizer, automatic variable selection and continuous shrinkage can be performed simultaneously, and groups of correlated variables can be selected to make the model sparse. The corresponding optimization can be transformed into the linear equation system. We employ an iterative reweighted algorithm to obtain the optimal solution. In each iteration, the solution form of ER-OCELM is similar to that of ELM. Experiments on artificial and benchmark datasets verify that ER-OCELM has superior robustness and sparsity compared to many state-of-the-art methods.

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.

Modeling triangular, rectangular, and parabolic weirs using weighted robust extreme learning machine

In this study, dimensionless parameters influencing the coefficient of discharge (COD) are found and four different WRELM models are developed. After that, a dataset is created for verifying the WRELM models in which 70% of the data are employed to train learning machine models and the remaining 30% to test them. For the mentioned algorithm, the optimal number of hidden layer neurons along with the best activation function is chosen. Additionally, the best value for the regularization parameter of the WRELM algorithm is computed. By analyzing the simulation results, the superior WRELM model and the variables impacting the COD are detected. The superior WRELM model approximates COD values with the minimum error and the highest correlation with laboratory values. For the superior model, the values of the R, MAE and VAF statistical indices are computed to be 0.994, 0.0004 and 98.662, respectively. The analysis of the simulation results indicates that the dimensionless parameters α and T/B are the most influencing input parameters. The superior WRELM model results are compared with the algorithm, and it is concluded that the WRELM model is noticeably more efficient. For the superior WRELM model, a partial derivative sensitivity analysis (PDSA) is conducted in which as the input parameter α increases, the PSDA value increases as well. Finally, an equation is suggested for estimating COD values.

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.

Robust Extreme Learning Machine with Exponential Squared Loss via DC Programming

Robust Extreme Learning Machine with Exponential Squared Loss via DC Programming

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.

Robust Extreme Learning Machine Using New Activation and Loss Functions Based on M-Estimation for Regression and Classification

This paper provides an analysis of the combining effect of novel activation function and loss function based on M-estimation in application to extreme learning machine (ELM), a feed-forward neural network. Due to the computational efficiency and classification/prediction accuracy of ELM and its variants, they have been widely exploited in the development of new technologies and applications. However, in real applications, the performance of classical ELMs deteriorates in the presence of outliers, thus, negatively impacting the precision and accuracy of the system. To further enhance the performance of ELM and its variants, we proposed novel activation functions based on the psi function of M and redescend the M-estimation method along with the smooth l 2-norm weight-loss functions to reduce the negative impact of the outliers. The proposed psi functions of several M and redescending M-estimation methods are more flexible to make more distinct features space. For the first time, the idea of the psi function as an activation function in the neural network is introduced in the literature to ensure accurate prediction. In addition, new robust l 2 norm-loss functions based on M and redescending M-estimation are proposed to deal with outliers efficiently in ELM. To evaluate the performance of the proposed methodology against other state-of-the-art techniques, experiments have been performed in diverse environments, which show promising improvements in application to regression and classification problems.

Robust Extreme Learning Machine for estimation of triangular, rectangular, and parabolic weirs

In this paper, for the first time, the DC of triangular, rectangular, and parabolic weirs is simulated by a new learning machine called “Robust Extreme Learning Machine” (RELM). The used laboratory data are divided into two categories: training (70% data) and testing (30% data). In the next step, the number of neurons inside the hidden layer is examined. For the structure of the proposed RELM algorithm, 10 hidden layer neurons are embedded. For the learning machine used in the present study, six different activation functions are evaluated that the Sigmoid activation function has better performance and is used for the RELM structure. Next, the calibration parameter of the RELM algorithm is discussed. The optimal regularization parameter is selected for the present study equal to 0.0001. Then, using parameters affecting the DC, four RELM models are developed. By performing various analyzes, the superior RELM model and the most effective input parameters are identified. Also, comparing the performance of the RELM model with ELM shows the superiority of the RELM algorithm. For the superior model, a relative derivative sensitivity analysis is performed to investigate the behaviour of the input parameters on the DC. Finally, an equation for estimating the DCs of triangular, rectangular, and parabolic weirs is proposed.

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.