Hidden Layer Biases Research Articles

State of Health Estimation of Lithium-Ion Batteries Using Fusion Health Indicator by PSO-ELM Model

The accurate estimation of the State of Health (SOH) of lithium-ion batteries is essential for ensuring their safe and reliable operation, as direct measurement is not feasible. This paper presents a novel SOH estimation method that integrates Particle Swarm Optimization (PSO) with an Extreme Learning Machine (ELM) to improve prediction accuracy. Health Indicators (HIs) are first extracted from the battery’s charging curve, and correlation analysis is conducted on seven indirect HIs using Pearson and Spearman coefficients. To reduce dimensionality and eliminate redundancy, Principal Component Analysis (PCA) is applied, with the principal component contributing over 94% used as a fusion HI to represent battery capacity degradation. PSO is then employed to optimize the weights (ε) between the input and hidden layers, as well as the hidden layer bias (u) in the ELM, treating these parameters as particles in the PSO framework. This optimization enhances the ELM’s performance, addressing instability issues in the standard algorithm. The proposed PSO-ELM model demonstrates superior accuracy in SOH prediction compared with ELM and other methods. Experimental results show that the mean absolute error (MAE) is 0.0034, the mean absolute percentage error (MAPE) is 0.467%, and the root mean square error (RMSE) is 0.0043, providing a valuable reference for battery safety and reliability assessments.

Research on Pattern Classification Based on Double Pseudo-Inverse Extreme Learning Machine

This research aims to address the limitations inherent in the traditional Extreme Learning Machine (ELM) algorithm, particularly the stochastic determination of input-layer weights and hidden-layer biases, which frequently leads to an excessive number of hidden-layer neurons and inconsistent performance. To augment the neural network’s efficacy in pattern classification, Principal Component Analysis (PCA) is employed to reduce the dimensionality of the input matrix and alleviate multicollinearity issues during the computation of the input weight matrix. This paper introduces an enhanced ELM methodology, designated the PCA-DP-ELM algorithm, which integrates PCA with Double Pseudo-Inverse Weight Determination (DP). The PCA-DP-ELM algorithm proposed in this study consistently achieves superior average classification accuracy across various datasets, irrespective of whether assessed through longitudinal or cross-sectional experiments. The results from both experimental paradigms indicate that the optimized algorithm not only enhances accuracy but also improves stability. These findings substantiate that the proposed methodology exerts a positive influence on pattern classification.

Hybrid firefly algorithm–neural network for battery remaining useful life estimation

Abstract Accurately estimating the remaining useful life (RUL) of batteries is crucial for optimizing maintenance, preventing failures, and enhancing reliability, thereby saving costs and resources. This study introduces a hybrid approach for estimating the RUL of a battery based on the firefly algorithm–neural network (FA–NN) model, in which the FA is employed as an optimizer to fine-tune the network weights and hidden layer biases in the NN. The performance of the FA–NN is comprehensively compared against two hybrid models, namely the harmony search algorithm (HSA)–NN and cultural algorithm (CA)–NN, as well as a single model, namely the autoregressive integrated moving average (ARIMA). The comparative analysis is based mean absolute error (MAE) and root mean squared error (RMSE). Findings reveal that the FA–NN outperforms the HSA–NN, CA–NN, and ARIMA in both employed metrics, demonstrating superior predictive capabilities for estimating the RUL of a battery. Specifically, the FA–NN achieved a MAE of 2.5371 and a RMSE of 2.9488 compared with the HSA–NN with a MAE of 22.0583 and RMSE of 34.5154, the CA–NN with a MAE of 9.1189 and RMSE of 22.4646, and the ARIMA with a MAE of 494.6275 and RMSE of 584.3098. Additionally, the FA–NN exhibits significantly smaller maximum errors at 34.3737 compared with the HSA–NN at 490.3125, the CA–NN at 827.0163, and the ARIMA at 1.16e + 03, further emphasizing its robust performance in minimizing prediction inaccuracies. This study offers important insights into battery health management, showing that the proposed method is a promising solution for precise RUL predictions.

Combined two-level guided wave structural health monitoring strategy using multifeature integration and machine learning: application to early-age grouted sleeves

Structural health monitoring of grouted sleeves is one of the assembly industry’s huge challenges. In this study, a combined two-level damage detection was introduced. It comprises defect classification (healthy, rebar eccentricity, and grout leakage) and severity evaluation for early-age grouted sleeves using guided waves. Multiple features (MF) from time-, frequency-, and time-frequency domains were extracted and defined according to the diverse defects and ages of grouted sleeves to represent complex damage characteristics. Moreover, the egret swarm algorithm optimization–extreme learning machine (ESAO-ELM) models were proposed to avoid the influence of subjective experience and judgment from experts. ESAO optimized the initial random parameters (input weights and hidden layer bias) of ELM. Then, two MF-ESAO-ELM models were trained for two-level damage detection on the experimental dataset. The performance of the proposed models was comprehensively evaluated using accuracy, recall, precision, and confusion matrix. MF-ESAO-ELM performs better than ELM and PSO-ELM in accuracy. In this strategy, the defect classification model works in the outer layer to distinguish the state and types of defects of grouted sleeves (healthy, eccentric, or leakage). In comparison, the inner layer starts predicting the severity only if the defect type is leakage. MF-ESAO-ELM offers advantages in terms of accuracy, strategy, and calculation time.

Underwater Image Color Constancy Calculation with Optimized Deep Extreme Learning Machine Based on Improved Arithmetic Optimization Algorithm

To overcome the challenges posed by the underwater environment and restore the true colors of marine objects’ surfaces, a novel underwater image illumination estimation model, termed the iterative chaotic improved arithmetic optimization algorithm for deep extreme learning machines (IAOA-DELM), is proposed. In this study, the gray edge framework is utilized to extract color features from underwater images, which are employed as input vectors. To address the issue of unstable prediction results caused by the random selection of parameters in DELM, the arithmetic optimization algorithm (AOA) is integrated, and the search segment mapping method is optimized by using hidden layer biases and input layer weights. Furthermore, an iterative chaotic mapping initialization strategy is incorporated to provide AOA with a better initial search proxy. The IAOA-DELM model computes illumination information based on the input color vectors. Experimental evaluations conducted on actual underwater images demonstrate that the proposed IAOA-DELM illumination correction model achieves an accuracy of 96.07%. When compared to the ORELM, ELM, RVFL, and BP models, the IAOA-DELM model exhibits improvements of 6.96%, 7.54%, 8.00%, and 8.89%, respectively, making it the most effective among the compared illumination correction models.

A Digital Twin-Based Visual Servoing with Extreme Learning Machine and Differential Evolution

The technology of visual servoing, with the digital twin as its driving force, holds great promise and advantages for enhancing the flexibility and efficiency of smart manufacturing assembly and dispensing applications. The effective deployment of visual servoing is contingent upon the robust and accurate estimation of the vision-motion correlation. Network-based methodologies are frequently employed in visual servoing to approximate the mapping between 2D image feature errors and 3D velocities, offering promising avenues for improving the accuracy and reliability of visual servoing systems. These developments have the potential to fully leverage the capabilities of digital twin technology in the realm of smart manufacturing. However, obtaining sufficient training data for these methods is challenging, and thus improving model generalization to reduce data requirements is imperative. To address this issue, we offer a learning-based approach for estimating Jacobian matrices of visual servoing that organically combines an extreme learning machine (ELM) and a differential evolutionary algorithm (DE). In the first stage, the pseudoinverse of the image Jacobian matrix is approximated using the ELM, which solves the problems associated with traditional visual servoing and is resistant to outside influences such as image noise and mistakes in camera calibration. In the second stage, differential evolution is utilized to select input weights and hidden layer bias and to determine ELM’s output weights. Experimental results conducted on a digital twin operating platform for 4-DOF robot with an eye-in-hand configuration demonstrate better performance than classical visual servoing and traditional ELM-based visual servoing in various cases.

Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine.

In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm. Considering the ELM algorithm, sine-cosine basis functions, and several classes of integral equations, the improved model is designed. The novel neural network model consists of an input layer, a hidden layer, and an output layer, in which the hidden layer is eliminated by utilizing the sine-cosine basis function. Meanwhile, by using the characteristics of the ELM algorithm that the hidden layer biases and the input weights of the input and hidden layers are fully automatically implemented without iterative tuning, we can greatly reduce the model complexity and improve the calculation speed. Furthermore, the problem of finding network parameters is converted into solving a set of linear equations. One advantage of this method is that not only we can obtain good numerical solutions for the first- and second-kind Volterra integral equations but also we can obtain acceptable solutions for the first- and second-kind Fredholm integral equations and Volterra-Fredholm integral equations. Another advantage is that the improved algorithm provides the approximate solution of several kinds of linear integral equations in closed form (i.e., continuous and differentiable). Thus, we can obtain the solution at any point. Several numerical experiments are performed to solve various types of integral equations for illustrating the reliability and efficiency of the proposed method. Experimental results verify that the proposed method can achieve a very high accuracy and strong generalization ability.

A low-resolution real-time face recognition using extreme learning machine and its variants

ABSTRACT Extreme Learning Machine (ELM) is an excellent candidate for its exemplary performance as a generalized Single Layer Feed-forward Network (SLFN). In this regard, ELM has attracted widespread attention for tackling multiclass classification and regression problems with relative ease. Due to the random allocation of weights to the input and hidden layer biases, the running time spans of ELM are observed to be in seconds and agree with real-time events whilst giving a competitive performance. In this work, the suitability of ELM and its Online Sequential variant for recognition of unknown face samples is investigated under uncontrolled environments, including varying pose, variance, and illumination. The presented face recognition approach is evaluated sing four datasets from YALE, CMU, BIOID, and LFW. To track the face features of a sample face in its spatial domain with varying windows corresponding to different datasets, the Viola-Jones object detection framework is used. The face features are then extracted and evaluated using a Histogram of Oriented Gradients, which forms the dataset to be fed to ELM and OS-ELM classifiers. The running time for training the proposed face recognition approach is found to span within milliseconds to seconds with the computed time complexity of , justifying the suitability of ELM and OS-ELM classifiers for real-time face recognition applications with a high recognition rate outcome.

A novel correlation Gaussian process regression-based extreme learning machine.

An obvious defect of extreme learning machine (ELM) is that its prediction performance is sensitive to the random initialization of input-layer weights and hidden-layer biases. To make ELM insensitive to random initialization, GPRELM adopts the simple an effective strategy of integrating Gaussian process regression into ELM. However, there is a serious overfitting problem in kernel-based GPRELM (kGPRELM). In this paper, we investigate the theoretical reasons for the overfitting of kGPRELM and further propose a correlation-based GPRELM (cGPRELM), which uses a correlation coefficient to measure the similarity between two different hidden-layer output vectors. cGPRELM reduces the likelihood that the covariance matrix becomes an identity matrix when the number of hidden-layer nodes is increased, effectively controlling overfitting. Furthermore, cGPRELM works well for improper initialization intervals where ELM and kGPRELM fail to provide good predictions. The experimental results on real classification and regression data sets demonstrate the feasibility and superiority of cGPRELM, as it not only achieves better generalization performance but also has a lower computational complexity.

Extreme learning machine model for state-of-charge estimation of lithium-ion battery using salp swarm algorithm

Accurate capacity estimation of lithium-ion batteries can effectively avoid over charge/discharge and improve life span. This paper proposes a state-of-charge (SOC) estimation model based on an improved extreme learning machine (ELM). ELM is a single hidden layer network with fast learning speed and good generalization performance, suitable for SOC estimation. For the ELM performance is highly dependent on network weights and hidden layer biases, a salp swarm algorithm (SSA) is applied to search for these parameters. Chaotic mapping is introduced in SSA to make the initialized individuals uniformly distributed. And a sine cosine algorithm (SCA) is embedded in swarm position formulation to promote communication. The model robustness and computational cost are verified by energy storage devices. The mean absolute error is 0.538, and the mean absolute percentage error is 0.887%. The results verified that the proposed model has better performance than other popular models, and shows good traceability and generality.

Color constancy with an optimized regularized random vector functional link based on an improved equilibrium optimizer.

In order to improve the accuracy of illumination estimation, this paper proposes a color constancy algorithm based on an improved equilibrium optimizer (IEO) to optimize the network structure parameters and common parameters of the regularized random vector functional link (RRVFL) at the same time. First, the initial search agent (population) of the equilibrium optimizer algorithm is generated through opposition-based learning, and the particles (individuals in the population) of the search agent are updated using the IEO algorithm. Compared with the completely randomly generated search agent, the method of initializing the search agent through the IEO algorithm has a better convergence effect. Then, each segment of the search agent is mapped to the corresponding parameters of the RRVFL, and the effective input weight and hidden layer bias are selected according to the node activation to generate the network structure, which can realize the simultaneous optimization of hyperparameters and common parameters. Finally, by calculating the output weight, the light source color prediction of the image under unknown illumination is performed, and the image is corrected. Comparison experiments show that the IEO-RRVFL color constancy algorithm proposed in this paper has higher accuracy and better stability than other comparison algorithms.

Illumination estimation via random vector functional link based on improved arithmetic optimization algorithm

AbstractIn order to solve the problem that the existing illumination estimation methods have low accuracy in image restoration, a random vector functional link illumination estimation algorithm based on whale optimization arithmetic algorithm is proposed in this article. First, in order to improve the optimization accuracy of arithmetic optimization algorithm, the whale optimization algorithm is applied to optimize the initial population of the arithmetic optimization algorithm. Then, we utilize the improved arithmetic optimization algorithm to improve the input weight and hidden layer offset of random vector functional link, and exclude the uncertainty caused by the random generation of random vector functional link's input weight and hidden layer bias. Finally, the proposed whale arithmetic optimization algorithm‐random vector functional link model is applied to SFU lab dataset and Gehler‐Shi dataset for illumination estimation. Compared with the other earlier illumination estimation algorithms, the proposed illumination estimation model in this article has better effect and higher stability. In addition, due to the diagonal mapping method for color correction and image restoration, the proposed illumination estimation algorithm can also get better results in image restoration.

Fault diagnosis and prognosis of steer-by-wire system based on finite state machine and extreme learning machine

In this paper, an integrated condition monitoring method combining model-based fault diagnosis and data-driven prognosis is proposed for steer-by-wire (SBW) system. First, the SBW system is modeled by bond graph (BG) technique and a two-degree-of-freedom (2-DOF) state-space model of the vehicle is built. Based on the 2-DOF model, the estimated self-aligning torque is used for the control of feedback motor. The fault detection is carried out by evaluating the analytical redundancy relations derived from the BG model. Since the fault isolation performance is essential to subsequent fault estimation process, a new fault isolation method based on finite state machine is developed to improve the isolation ability by combining the dependent and independent analytical redundancy relations, where the number of potential faults could be decreased. In order to refine the possible fault set to determine the true fault, a cuckoo search (CS)–particle filter is developed for fault estimation. Based on the estimated true fault, prognosis can be implemented which is important to achieve failure prevention and prolong system lifespan. To this end, an optimized extreme learning machine (OELM) is proposed where the input weights and hidden layer biases are optimized by CS. Based on data representing fault values obtained from the fault identification, the OELM model is trained for remaining useful life prediction of failing component. Finally, the proposed methodologies are validated by simulations.

Hybrid condition monitoring of nonlinear mechatronic system using biogeography-based optimization particle filter and optimized extreme learning machine

This paper proposes a hybrid condition monitoring approach, which integrates bond graph model-based diagnostic technique and data-driven remaining useful life (RUL) prediction, for a nonlinear mechatronic system. In this approach, various degrading faults can be considered and the physical degradation model is not required for RUL prediction. Firstly, an integrated fault signature matrix is proposed by the causal path of bicausal-bond graph model to improve fault isolation performance. After that, a biogeography-based optimization (BBO)-particle filter is developed for fault identification. For prognosis, an optimized extreme learning machine (OELM) is proposed where the hidden layer biases and input weights are optimized by BBO. The fault identification results provide data set to train the OELM for prognosis. Finally, the effectiveness of the approach is verified by simulation and experiment results.

An iterative updating heuristic search strategy for groundwater contamination source identification based on an ACPSO–ELM surrogate system

The simulation-random statistics (SRS) method is one of the effective approaches to solving groundwater contamination source identification (GCSI) challenges. In this paper, we applied a heuristic search iterative process (HSIP) based on SRS to provide interval estimation and probability distribution for an unknown variable to enhance our understanding of the unknown variable. Posterior distribution has been a subject of interest in HSIP; therefore, it is imperative to update prior distributions using final iterations obtained from posterior distributions, which has been seldom considered in previous research. This paper first proposed such updates and subsequently designed an updating HSIP (UHSIP). This paper first proposed a feedback correction step and incorporated it into UHSIP to achieve feedback improvements and simultaneous updates of an unknown variable and prior distribution. In UHSIP, a surrogate system such as extreme learning machine (ELM) is usually established for a numerical simulation model to reduce computational cost. The particle swarm optimization (PSO) algorithm has been demonstrated to optimize input weights and hidden layer biases in ELM. However, the PSO algorithm is prone to premature convergence and its calculation accuracy does not satisfy precision requirements when optimizing complex functions. To enhance accuracy, this paper first proposed a new adaptive chaotic PSO (ACPSO) algorithm to establish ACPSO–ELM surrogate system. The two newly proposed approaches were tested in two case studies based on groundwater inorganic and organic contaminations. Results reveal that UHSIP can effectively enhance identification accuracy, and ACPSO–ELM surrogate system has a higher approximation accuracy to the simulation model than PSO–ELM. Overall, the two main innovations in this paper (UHSIP and ACPSO–ELM surrogate system) present promising and effective solutions to GCSI challenge.

Fabric wrinkle evaluation model with regularized extreme learning machine based on improved Harris Hawks optimization

Aiming at the problem of low manual efficiency and inaccuracy in the traditional evaluation of fabric wrinkle-resistance performance relying on the eye of experts and subjective judgment, this paper proposes a fabric wrinkle grade evaluation model based on optimized regularized extreme learning machine. First, this paper extracts four image characteristics of fabric wrinkle image, including wrinkle density, gray level co-occurrence matrix, wavelet parameter standard deviation and data fusion feature, combined with the grade evaluation standard, and then obtains a complete wrinkle grade data set. Then, differential evolution is used to initialize the initial population of the Harris Hawks optimization, and the improved Harris Hawks optimization is used to optimize the input weights and hidden layer bias of the regularized extreme learning machine. Finally, this optimized regularized extreme learning machine is used to evaluate the fabric wrinkle grade. Experimental results show that the classification accuracy of the model proposed in this paper can reach 96.39%, and the proposed algorithm has no abnormal points in the analysis of the stability of the box plot.

Detecting Water Depth from Remotely Sensed Imagery Based on ELM and GA-ELM

The shallow seawater depth inversion based on remote sensing technology is important for water depth detection, which is of considerable significance to marine engineering, shipping, and marine military security. In this study, we took the Taiping Island and its adjacent waters in the South China Sea as a test bed and developed a water depth inversion model on the basis of extreme learning machine (ELM) and extreme learning machine optimized by genetic algorithm (GA-ELM). In GA-ELM, the input weights and the hidden layer biases were optimized by genetic algorithm. The two models allowed the evaluation of nonlinear relationships between the reflectance of high-resolution imagery from WorldView-2 and actual water depth obtained from the S-57 sea chart. The eight bands of the high-resolution image and the actual water depth were used as the input layer and the output layer, and the sigmoid function was introduced as activation function. Finally, the model accuracy was evaluated by using mean relative error (MRE), root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and the regression analysis between the retrieved water depth and the actual data. The simulation results showed that the two models had better stability than the second-order polynomial regression, BP neural network, and RBF neural network. Furthermore, GA-ELM had a more compact network structure and better generalization ability than ELM. Thus, we concluded that GA-ELM had higher precision and could achieve a better inversion result in the experimental area.

Advantages of direct input-to-output connections in neural networks: The Elman network for stock index forecasting

The Elman neural network (ElmanNN) is well-known for its capability of processing dynamic information, which has led to successful applications in stock forecasting. In this paper, we introduce direct input-to-output connections (DIOCs) into the ElmanNN and show that the proposed Elman neural network with DIOCs (Elman-DIOCs) significantly out-performs the original ElmanNN without such DIOCs. Four different global stock indices, i.e., the Shanghai Stock Exchange (SSE) Composite Index, the Korea Stock Price Index (KOSPI), the Nikkei 225 Index (Nikkei225), and the Standard & Poor’s 500 Index (SPX), are used to demonstrate the affecacy of the Elman-DIOCs in time-series prediction. We systematically evaluate 8 models, depending whether or not there are hidden layer biases, whether or not there are output layer biases, and whether or not there are DIOCs. The experimental results show that DIOCs lead to much better prediction accuracy, while requiring fewer than a half of the hidden neurons. Take the SPX index, for example - the root mean squared error (RMSE) and the mean absolute error (MAE) of the Elman-DIOCs are improved by 44.2% and 41.1%, respectively, compared to the ElmanNN, and 65.6% and 60.8%, respectively, compared to the multi-layer perceptron (MLP). We argue that (1) DIOCs can always help to improve accuracy, while reducing network complexity and computational burden, as long as the problem at hand (either regression or classification) has linear components, and (2) most real-world applications contain linear components. Therefore DIOCs will be almost always beneficial in any types of neural networks for classification or regression. We also point out that in rare cases where the problem at hand is entirely nonlinear, DIOCs should not be used.

Imbalanced Data Fault Diagnosis Based on an Evolutionary Online Sequential Extreme Learning Machine

To quickly and effectively identify an axle box bearing fault of high-speed electric multiple units (EMUs), an evolutionary online sequential extreme learning machine (OS-ELM) fault diagnosis method for imbalanced data was proposed. In this scheme, the resampling scale is first determined according to the resampling empirical formulation, the K-means synthetic minority oversampling technique (SMOTE) method is then used for oversampling the minority class samples, a method based on Euclidean distance is applied for undersampling the majority class samples, and the complex data features are extracted from the reconstructed dataset. Second, the reconstructed dataset is input into the diagnosis model. Finally, the artificial bee colony (ABC) algorithm is used to globally optimize the combination of input weights, hidden layer bias, and the number of hidden layer nodes for an OS-ELM, and the diagnosis model is allowed to evolve. The proposed method was tested on the axle box bearing monitoring data of high-speed EMUs, on which the position of the axle box bearings was symmetrical. Numerical testing proved that the method has the characteristics of faster detection and higher classification performance regarding the minority class data compared to other standard and classical algorithms.

Fabric wrinkle level classification via online sequential extreme learning machine based on improved sine cosine algorithm

Because it is difficulty to classify level of fabric wrinkle, this paper proposes a fabric winkle level classification model via online sequential extreme learning machine based on improved sine cosine algorithm (SCA). The SCA has excellent global optimization ability, can explore different search spaces, and effectively avoid falling into local optimum. Because the initial population of SCA will have an impact on its optimization speed and quality, the SCA is initialized by differential evolution (DE) to avoid local optimization, and then the output weight and hidden layer bias are optimized; that is, the improved SCA is used to select the optimal parameters of the online sequential extreme learning machine (OSELM) to improve the generalization performance of the algorithm. To verify the performance of the proposed model DE-SCA-OSELM, it will be compared with other algorithms using a fabric wrinkles dataset collected under standard conditions. The experimental results indicate that the proposed model can effectively find the optimal parameter value of OSELM. The average classification accuracy increased by 6.95%, 3.62%, 6.67%, and 3.34%, respectively, compared with the partial algorithms OSELM, SCAELM, RVFL and PSOSVM, which meets expectations.