Single Extreme Learning Machine Research Articles

An adaptive selective ensemble algorithm for fault classification

With the aim of improving the classification performance of a single extreme learning machine (ELM) for fault diagnosis, an adaptive selective ensemble classification algorithm is proposed based on the idea of ensemble learning. The proposed algorithm achieves better classification performance than a single model and the selected ELM subnetworks are selected adaptively and the ensemble weights of selected ELM subnetworks are calculated adaptively, which avoids the complex process of manually selecting subnetworks and calculating ensemble weights. First, a regularized error weight adjustment ELM is constructed by introducing regularization parameters and error weight adjustment matrix to a standard ELM, where the error weight adjustment matrix is obtained by the method of adaptive Gaussian kernel density estimation. Then, discrepancy subnetworks are constructed using six different activation functionsand the ensemble weights of subnetworks are obtained adaptively according to the normalized ratio of mean and variance of subnetwork F-scores to achieve the ensemble of subnetworks. Finally, the adaptive selective ensemble classification algorithm is validated using the UCI dataset and experimental acoustic emission signals of gearbox faults. The results show that the adaptive selective ensemble method can improve the stability and accuracy of classification algorithms and the achieved classification accuracy for experimental acoustic emission was 0.9773.

Application of novel binary optimized machine learning models for monthly streamflow prediction

Accurate measurements of available water resources play a key role in achieving a sustainable environment of a society. Precise river flow estimation is an essential task for optimal use of hydropower generation, flood forecasting, and best utilization of water resources in river engineering. The current paper presents the development and verification of the prediction abilities of new hybrid extreme learning machine (ELM)-based models coupling with metaheuristic methods, e.g., Particle swarm optimization (PSO), Mayfly optimization algorithm (MOA), Grey wolf optimization (GWO), and simulated annealing (SA) for monthly streamflow prediction. Prediction precision of standalone ELM model was compared with two-phase optimized state-of-the-arts models, e.g., ELM–PSO, ELM–MOA, ELM–PSOGWO, and ELM–SAMOA, respectively. Hydro-meteorological data acquired from Gorai and Padma Hardinge Bridge stations at Padma River Basin, northwestern Bangladesh, were utilized as inputs in this study to employ models in the form of seven different input combinations. The model’s performances are appraised using Nash–Sutcliffe efficiency, root-mean-square-error (RMSE), mean absolute error, mean absolute percentage error and determination coefficient. The tested results of both stations reported that the ELM–SAMOA and ELM–PSOGWO models offered the best accuracy in the prediction of monthly streamflows compared to ELM–PSO, ELM–MOA, and ELM models. Based on the local data, the ELM–SAMOA reduced the RMSE of ELM, ELM–PSO, ELM–MOA, and ELM–PSOGWO by 31%, 27%, 19%, and 14% for the Gorai station and by 29%, 27%, 19%, and 14% for Padma Hardinge bridge station, in the testing stage, respectively. In contrast, based on external data, ELM–PSOGWO improves in RMSE of ELM, ELM–PSO, ELM–MOA, and ELM–SAMOA by 20%, 5.1%, 6.2%, and 4.6% in the testing stage, respectively. The results confirmed the superiority of two-phase optimized ELM–SAMOA and ELM–PSOGWO models over a single ELM model. The overall results suggest that ELM–SAMOA and ELM–PSOGWO models can be successfully applied in modeling monthly streamflow prediction with either local or external hydro-meteorological datasets.

An enhanced monthly runoff time series prediction using extreme learning machine optimized by salp swarm algorithm based on time varying filtering based empirical mode decomposition

Reliable runoff prediction plays a significant role in reservoir scheduling, water resources management, and efficient utilization of water resources. To effectively enhance the prediction accuracy of monthly runoff series, a hybrid prediction model (TVF-EMD-SSA-ELM) combining time varying filtering (TVF) based empirical mode decomposition (EMD), salp swarm algorithm (SSA) and extreme learning machine (ELM) is proposed. Firstly, the monthly runoff series is decomposed into several sub-series using TVF-EMD. Secondly, SSA is used to optimize the input weights and hidden layer biases of the selected ELM model. Finally, the prediction results are generated by summing and reconstructing each sub-series based on the SSA optimized ELM model. This hybrid model is applied to the monthly runoff prediction of Manwan hydropower, Hongjiadu hydropower, and Yingluoxia hydrological station, and compared with back propagation (BP), ELM, SSA-ELM, PSO-ELM, GSA-ELM, TVF-EMD-ELM, EMD-SSA-ELM, extreme-point symmetric mode decomposition (ESMD)-SSA-ELM, wavelet decomposition (WD)-SSA-ELM and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-SSA-ELM models. The prediction performance of various models is reflected by four evaluation indicators (R, NSEC, NRMSE, MAPE). Results reveal that the prediction effect of the ELM model is better than that of BP, the optimization accuracy of SSA is better than those of particle swarm optimization (PSO) and gravitational search algorithm (GSA), and the prediction accuracy of the hybrid TVF-EMD and SSA is better than that of only TVF-EMD or SSA. TVF-EMD-SSA-ELM model has the highest prediction accuracy. When compared with the single ELM model, it’s NRMSE and MAPE at Manwan hydropower decrease by 84.4% and 72.38%, those of Hongjiadu hydropower decrease by 85.21% and 78.38%, and those of Yingluoxi hydrological station decrease by 68.42% and 39.51%, respectively. R and NSEC of the three sites are close to 1. Therefore, the proposed model provides a new method for the prediction of monthly runoff, and the results can provide a reference for the prediction of monthly runoff in the study area.

Aerodynamic Parameter Identification of Projectile Based on Improved Extreme Learning Machine and Ensemble Learning Theory

The firing accuracy of the projectile has a positive relation with aerodynamic parameters. Due to the complex dynamic characteristics of projectiles, there is an overfitting risk when a single extreme learning machine (ELM) is used to identify the aerodynamic parameters of the projectile, and the identification results oscillate transonic region. To obtain the aerodynamic parameters of the projectile accurately, an aerodynamic parameter identification model based on ensemble learning theory and ELM optimized by improved particle swarm optimization is proposed. The improved particle swarm optimization algorithm (IPSO) with an adaptive update strategy is used to optimize the weight and threshold of ELM. Combined with the ensemble learning theory, the improved ELM neural network is regarded as a weak learner to generate a strong learner. The structural parameters of the strong learner were continuously optimized through training, and an aerodynamic parameter identification model of projectile based on ensemble learning theory is obtained. The simulation results show that the introduction of the IPSO and ensemble learning theory enables the model to exhibit excellent generalization ability. The proposed identification model can accurately describe the variation of aerodynamic parameters with the Mach number.

Displacement prediction of open-pit mine slope based on SSA-ELM

Mine geological disaster is a complex non-linear system. The traditional prediction model has the disadvantages of low prediction accuracy and poor reliability. In order to solve this problem, the open-pit mine slope displacement is taken as the research object. Based on a new algorithm extreme learning machine (ELM), the new intelligent algorithm sparrow search algorithm (SSA) are introduced to determine the weights and thresholds of the input layer and hidden layer of ELM. The open-pit mine slope displacement prediction model of improved ELM is constructed and applied to an engineering example. The results show that the root mean square error of SSA-ELM model is only a quarter of that of BP model, which is 50% higher than that of GM (1,1) and ELM models. The correlation coefficient of the prediction results of the SSA-ELM model is 0.983, and the accuracy is better than that of the traditional model. The single ELM model and the PSO-ELM model show that the SSA algorithm has better improvement effect. The SSA model has good comprehensive performance and high prediction accuracy. It is feasible to apply it to the prediction of slope displacement in open-pit mines.

A Novel Hybrid Model for Short-Term Traffic Flow Prediction Based on Extreme Learning Machine and Improved Kernel Density Estimation

Short-term traffic flow prediction is the basis of and ensures intelligent traffic control. However, the conventional models cannot make accurate predictions due to the strong nonlinearity and randomness in short-term traffic flow data. To this end, the authors of this paper developed a novel hybrid model based on extreme learning machine (ELM), adaptive kernel density estimation (AKDE), and conditional kernel density estimation (CKDE). Specifically, the ELM model was employed for nonlinear prediction. Then, AKDE was established to estimate the bandwidth of CKDE (i.e., AKDE-CKDE), which predicted the training residuals obtained by ELM. Finally, the predicted results of the two models were superimposed to derive the final prediction of the hybrid model. Two case studies based on measured data were conducted to evaluate the performance of the proposed method. The experimental results indicate that the proposed method can realize a significant improvement in terms of forecasting accuracy in comparison with the other concerned models. For instance, it performed better than the single ELM model, with an improvement in the evaluation criterion of a mean relative percentage error of 7.46%.

Parallel Extreme Learning Machines Based on Frequency Multiplexing

In a recent work, we reported on an Extreme Learning Machine (ELM) implemented in a photonic system based on frequency multiplexing, where each wavelength of the light encodes a different neuron state. In the present work, we experimentally demonstrate the parallelization potentialities of this approach. We show that multiple frequency combs centered on different frequencies can copropagate in the same system, resulting in either multiple independent ELMs executed in parallel on the same substrate or a single ELM with an increased number of neurons. We experimentally tested the performances of both these operation modes on several classification tasks, employing up to three different light sources, each of which generates an independent frequency comb. We also numerically evaluated the performances of the system in configurations containing up to 15 different light sources.

Deterministic Analysis and Uncertainty Analysis of Ensemble Forecasting Model Based on Variational Mode Decomposition for Estimation of Monthly Groundwater Level

Precise multi-time scales prediction of groundwater level is essential for water resources planning and management. However, credible and reliable predicting results are hard to achieve even to extensively applied artificial intelligence (AI) models considering the uncontrollable error, indefinite inputs and unneglectable uncertainty during the modelling process. The AI model ensembled with the data pretreatment technique, the input selection method, or uncertainty analysis has been successfully used to tackle this issue, whereas studies about the comprehensive deterministic and uncertainty analysis of hybrid models in groundwater level forecast are rarely reported. In this study, a novel hybrid predictive model combining the variational mode decomposition (VMD) data pretreatment technique, Boruta input selection method, bootstrap based uncertainty analysis, and the extreme learning machine (ELM) model named VBELM was developed for 1-, 2- and 3-month ahead groundwater level prediction in a typical arid oasis area of northwestern China. The historical observed monthly groundwater level, precipitation and temperature data were used as inputs to train and test the model. Specifically, the VMD was used to decompose all the input-outputs into a set of intrinsic mode functions (IMFs), the Boruta method was applied to determine input variables, and the ELM was employed to forecast the value of each IMF. In order to ascertain the efficiency of the proposed VBELM model, the performance of the coupled model (VELM) hybridizing VMD with ELM algorithm and the single ELM model were estimated in comparison. The results indicate that the VBELM performed best, while the single ELM model performed the worst among the three models. Furthermore, the VBELM model presented lower uncertainty than the VELM model with more observed groundwater level values falling inside the confidence interval. In summary, the VBELM model demonstrated an excellent performance for both certainty and uncertainty analyses, and can serve as an effective tool for multi-scale groundwater level forecasting.

Proposing several hybrid PSO-extreme learning machine techniques to predict TBM performance

A proper planning schedule for tunnel boring machine (TBM) construction is considered as a necessary and difficult task in tunneling projects. Therefore, prediction of TBM performance with high degree of accuracy is needed to prepare a suitable planning schedule. This study aims to predict the advance rate of TBMs using optimized extreme learning machine (ELM) model with six particles swam optimization (PSO) techniques. Hence, six deterministically adaptive models, including time-varying acceleration (TAC)–PSO–ELM, improved PSO–ELM, Modified PSO–ELM, TAC–MeanPSO–ELM, improved MeanPSO–ELM, and Modified MeanPSO–ELM were developed. A number of performance criteria along with ranking system were used to identify the best model. The results showed that modified MeanPSO–ELM achieved the highest cumulative ranking (56), while the modified PSO–ELM achieved the lowest cumulative ranking (51). For training phase, improved PSO–ELM and TAC–PSO–ELM achieved the highest ranking (30) for each. The TAC–MeanPSO–ELM obtained the lowest ranking in the testing phase (29). Concerning the coefficient of determination (R2), modified PSO–ELM, improved PSO–ELM, TAC–PSO–ELM, and modified MeanPSO–ELM showed a similar behavior and achieved 0.97 for training and 0.96 for testing phases. Two models, including improved MeanPSO–ELM and TAC–MeanPSO–ELM achieved the same R2 of 0.96 for both training and testing phases. The findings of this study suggest that the hybridization of ELM and PSO may result in more accurate results than single ELM model to predict the TBM advance rate.

Streamflow Forecasting via Two Types of Predictive Structure-Based Gated Recurrent Unit Models

Data-intelligent methods designed for forecasting the streamflow of the Fenhe River are crucial for enhancing water resource management. Herein, the gated recurrent unit (GRU) is coupled with the optimization algorithm improved grey wolf optimizer (IGWO) to design a hybrid model (IGWO-GRU) to carry out streamflow forecasting. Two types of predictive structure-based models (sequential IGWO-GRU and monthly IGWO-GRU) are compared with other models, such as the single least-squares support vector machine (LSSVM) and single extreme learning machine (ELM) models. These models incorporate the historical streamflow series as inputs of the model to forecast the future streamflow with data from January 1956 to December 2016 at the Shangjingyou station and from January 1958 to December 2016 at the Fenhe reservoir station. The IGWO-GRU model exhibited a strong ability for mapping in streamflow series when the parameters were carefully tuned. The monthly predictive structure can effectively extract the instinctive hydrological information that is more easily learned by the predictive model than the traditional sequential predictive structure. The monthly IGWO-GRU model was found to be a better forecasting tool, with an average qualification rate of 91.66% in two stations. It also showed good performance in absolute error and peak flow forecasting.

An Ensemble Learning-Based Data-Driven Method for Online State-of-Health Estimation of Lithium-Ion Batteries

The state-of-health (SOH) estimation of lithium-ion batteries (LIBs) is of great importance to the safety of systems. In this article, a novel ensemble learning method is proposed to accurately estimate the SOH of LIBs. A feature defined as the duration of the same charging voltage range (DSCVR) is extracted as the key health indicator for the LIB. The Pearson correlation analysis is performed to select four optimal indicators that are used as inputs of the prediction model. A random learning algorithm named extreme learning machine (ELM) is applied to extract the mapping knowledge relationship between the health indicators and the SOH due to its fast learning speed and efficient tuning mechanism. Moreover, an ensemble learning structure is proposed to reduce the prediction error of the single ELM models. A reliable decision-making rule is then designed to evaluate the credibility of the output of each single ELM model and remove the unreliable outputs, thereby significantly improving the accuracy and reliability of the estimation results. The testing results on two public data sets show that the proposed method can accurately estimate the SOH in 1 ms and is robust to the operating temperature and load profile. The average root-mean-square error (RMSE) is as low as 0.78%. The proposed method does not require any additional hardware or downtime of the system, which makes the method suitable for online practical applications.

Bayesian robust multi-extreme learning machine

Outliers usually exist in the collected data due to human or instrumentation errors. Their existence makes the regression error obey a non-Gaussian distribution. So, people assume that the regression error obeys finite mixture distributions, such as mixture of Gaussians and mixture of Student’s t-distributions. This paper proposed two Bayesian robust regression models based on multiple extreme learning machines. First, the finite mixture error distributions are extended to their infinite counterparts according to the theory of stick-breaking construction, which can avoid selecting the optimal number of components in mixture models. Second, a multi-extreme learning machine, which combines many single extreme learning machines with different numbers of hidden nodes, is constructed, which can avoid the effects of different numbers of hidden nodes on the final regression performance. Besides, sparse Bayesian learning has also been derived to perform the sparse model weight and output weight inference automatically. The experimental results on artificial datasets and eight benchmark datasets show that the proposed two models outperform the other compared models under different rates of outliers. Also, they generate better multi-step ahead wind speed and traffic speed forecasts in real applications.

An ELM-Embedded Deep Learning Based Intelligent Recognition System for Computer Numeric Control Machine Tools

In modern manufacturing industry featured with automation and flexibility, the intelligent tool management for Computer Numeric Control (CNC) machine plays an essential role in manufacturing automation. The automatic tool recognition in terms of geometric shapes, materials and usage functions could facilitate the seamless integration with downstream process planning and scheduling processes. In this paper, a intelligent tool recognition system is proposed with a novel hybrid framework of multi-channel deep learning network with non-iterative and fast feedforward neural network to meet high efficiency and accuracy requirement in intelligent manufacturing. The combination of the fine-tuning Convolutional Neural Networks (CNNs) with the random parameter assignment mechanism of Extreme Learning Machines (ELMs) reach a balance in accurate feature extraction and fast recognition. In the proposed hybrid framework, features extracted from efficient CNNs are aggregated into robust ELM auto-encoders (ELM-AEs) to generate the compact but rich feature information, which are then feed to the subsequent single layer ELM network for tool recognition. The performance of proposed framework is verified on several standardized 3D shape retrieval and classification dataset, as well as on a self-constructed multi-view 3D data represented tool library database. Numerical experiments reveal a promising application perspective of proposed intelligent recognition system on manufacturing automation.

Robust and Lightweight Ensemble Extreme Learning Machine Engine Based on Eigenspace Domain for Compressed Learning

Compressive sensing (CS) is applied to electrocardiography (ECG) telemonitoring system to address the energy constraint of signal acquisition in sensors. In addition, on-sensor-analysis transmitting only abnormal data further reduces the energy consumption. To combine both advantages, “On-CS-sensor-analysis” can be achieved by compressed learning (CL), which analyzes signals directly in compressed domain. Extreme learning machine (ELM) provides an effective solution to achieve the goal of low-complexity CL. However, single ELM model has limited accuracy and is sensitive to the quality of data. Furthermore, hardware non-idealities in CS sensors result in learning performance degradation. In this work, we propose the ensemble of sub-eigenspace-ELM (SE-ELM), including two novel approaches: 1) We develop the eigenspace transformation for compressed noisy data, and further utilize a subspace-based dictionary to remove the interferences, and 2) Hardware-friendly design for ensemble of ELM provides high accuracy while maintaining low complexity. The simulation results on ECG-based atrial fibrillation show the SE-ELM can achieve the highest accuracy with 61.9% savings of the required multiplications compared with conventional methods. Finally, we implement this engine in TSMC 90 nm technology. The postlayout results show the proposed CL engine can provide competitive area- and energy-efficiency compared to existing machine learning engines.

A New Data-driven Roll Force and Roll Torque Model Based on FEM and Hybrid PSO-ELM for Hot Strip Rolling

In this paper, a new Extreme Learning Machine (ELM) regression model of roll force and roll torque based on data-driven is proposed. The three-dimensional elastic-plastic finite element model (FEM) is established to solve the roll force and roll torque under different parameters (including rolling reduction rate, roll radius, rolling speed, average width of strip, entry temperature of strip). The regression model of ELM optimized by Particle Swarm Optimization (PSO) is established through using the datasets obtained by FEM. The PSO-ELM model prediction values of roll force and roll torque are compared with the single ELM and PSO-SVM model, and the error results of the prediction values are analyzed. The error results fully verify the feasibility and accuracy of the PSO-ELM model proposed. It is found that the new data-drive model of roll force and roll torque is simple in structure and it can make up for the deficiency of traditional mathematical mechanism model in dealing with nonlinear problems. The research result reveals that PSO-ELM method is suitable for parameters prediction and model optimization in strip rolling process.

Modular Wavelet–Extreme Learning Machine: a New Approach for Forecasting Daily Rainfall

A rainfall forecasting method based on coupling wavelet analysis and a novel artificial neural network technique called extreme learning machine (ELM) is proposed. In this way, the unique characteristics of each technique are combined to capture different patterns in the data. At first, wavelet analysis is used to decompose rainfall time series into wavelet coefficients, and then the wavelet coefficients are used as inputs into the ELM model to forecast rainfall. The accuracy of the model is further improved using a modular learning approach. In the modular learning, an innovative approach to determine the optimum number of clusters entitled threshold cluster number is introduced. The relative performances of the proposed models are compared with the single ELM model for three cases consisting of one daily rainfall series from Iran (Kharjeguil station), one daily rainfall series from India (Ajmer station) and one daily rainfall series from the United States (Barton Pond station). The correlation coefficient (r), root mean square errors (RMSE) and Nash–Sutcliffe efficiency coefficient (NS) statistics are used as the comparing criteria. The comparison results indicate that the proposed modular wavelet–ELM method could significantly increase the forecast accuracy and perform much better than both the wavelet–ELM and single ELM. Moreover, three case study results indicate the importance of determining the optimum number of clusters based on the new concept of threshold cluster number in order to achieve optimum forecast results.

Multi extreme learning machine approach for fault location in multi-terminal high-voltage direct current systems

A method based on extreme learning machine (ELM) is suggested to locate faults in multi-terminal high-voltage direct current systems. S-transform and wavelet transform are used for extraction of the features used for the learning. The accuracy of the technique for various types of input signals and different lengths of the analyzed window is investigated. Two different approaches are considered for employing the ELM in this application. In the first approach, an ELM is used for total length of the line. In the second one, a multi-ELM technique is applied to different sections of the transmission line. In this approach, one ELM is considered for each of the divided sections. It is proved that the performance of the method is improved by the multi-ELM approach in comparison with the single ELM one. The performance of the ELM approach is compared with the artificial neural network and support vector regression techniques.

A Review of the Research on the Prediction Model of Extreme Learning Machine

With the wide application of prediction, the research of prediction algorithm and theory has made a great progress. In recent years, extreme learning machines have been used in the field of prediction, such as stock price prediction. The prediction algorithms of ELM are reviewed in this paper, which includes the single extreme learning machine prediction algorithm and the combined prediction algorithm. At the same time, the existing problems and research directions are pointed out.

Seemingly unrelated extreme learning machine

A seemingly unrelated regression (SUR) system simultaneously studies the groups of samples that are related with each other through the covariance of decision attributes. Each group of samples is studied by a regression equation, and the error terms of the regression equations are correlated in SUR system. Extreme Learning Machine (ELM) is a training method for single-hidden layer feedforward neural network, it is widely used in many machine learning domains due to the good generalization capability and fast training speed. Since a single ELM ignores the correlated information among different groups of samples, it fails to solve the SUR problem effectively. This ineffectiveness becomes more obvious with the correlation among equations going up. In order to overcome this problem, an extended ELM model is proposed in this paper, described as Seemingly Unrelated ELM (SUELM). SUELM simultaneously learns multiple ELMs by sufficiently using the correlated information among different groups of samples, thus it can solve the SUR problem effectively. In comparison with a single ELM, SUELM significantly improves the performance. Simulation results show that SUELM performs better than the single ELM with respect to mean square error and generalization ability, especially when significant correlations exist among different groups of samples. This paper provides an effective way for solving the SUR problem by adopting ELM as the learning model.

An Incremental Learning Ensemble Strategy for Industrial Process Soft Sensors

With the continuous improvement of automation in industrial production, industrial process data tends to arrive continuously in many cases. The ability to handle large amounts of data incrementally and efficiently is indispensable for modern machine learning (ML) algorithms. According to the characteristics of industrial production process, we address an ILES (incremental learning ensemble strategy) that incorporates incremental learning to extract information efficiently from constantly incoming data. The ILES aggregates multiple sublearning machines by different weights for better accuracy. When new data set arrives, a new submachine will be trained and aggregated into ensemble soft sensor model according to its weight. The other submachines′ weights will be updated at the same time. Then a new updated soft sensor ensemble model can be obtained. The weight updating rules are designed by considering the prediction accuracy of submachines with new arrived data. So the update can fit the data change and obtain new information efficiently. The sizing percentage soft sensor model is established to learn the information from the production data in the sizing of industrial processes and to test the performance of ILES, where the ELM (Extreme Learning Machine) is selected as the sublearning machine. The comparison is done among new method, single ELM, AdaBoost.R ELM, and OS‐ELM, and the test of the extensions is done with three test functions. The results of the experiments demonstrate that the soft sensor model based on the ILES has the best accuracy and ability of online updating.