Error Criterion Research Articles

Modal-Regression-Based Broad Learning System for Robust Regression and Classification.

A novel neural network, namely, broad learning system (BLS), has shown impressive performance on various regression and classification tasks. Nevertheless, most BLS models may suffer serious performance degradation for contaminated data, since they are derived under the least-squares criterion which is sensitive to noise and outliers. To enhance the model robustness, in this article we proposed a modal-regression-based BLS (MRBLS) to tackle the regression and classification tasks of data corrupted by noise and outliers. Specifically, modal regression is adopted to train the output weights instead of the minimum mean square error (MMSE) criterion. Moreover, the l2,1 -norm-induced constraint is used to encourage row sparsity of the connection weight matrix and achieve feature selection. To effectively and efficiently train the network, the half-quadratic theory is used to optimize MRBLS. The validity and robustness of the proposed method are verified on various regression and classification datasets. The experimental results demonstrate that the proposed MRBLS achieves better performance than the existing state-of-the-art BLS methods in terms of both accuracy and robustness.

Process Capability Index for Simple Linear Profile in the Presence of Within- and Between-Profile Autocorrelation

In many situations, the quality of a process or product can be characterized by a functional relationship or profile. It is well-known that the independence assumptions of the error terms within or between profiles are not always valid and could be violated due to within or between profile autocorrelation. Since most of the process capability indices (PCIs) have been developed for simple linear profiles (SLPs) without considering autocorrelation, this paper provides some novel methods to analyze the capability of SLP under each of the two different autocorrelation effects separately, as well as the case where both autocorrelation effects are present. We assume that the first-order autoregressive AR(1) model explains the within- and between-profile autocorrelation in error terms. To evaluate the process capability, a new functional index called is introduced for SLP with independent errors, and then it is modified to include the three possible cases of within, between, and simultaneous autocorrelation. The simulation results demonstrate that the proposed schemes outperform existing schemes regarding bias and mean square error (MSE) criteria. Moreover, bootstrap confidence intervals for the proposed index are obtained. Finally, an illustrative example in the chemical industry is used to demonstrate the applicability of the proposed method.

Machine learning-based forward and inverse designs for prediction and optimization of fracture toughness of aluminum alloy

Utilization of machine learning framework to design aluminum alloy with high fracture toughness is increasing. Nonetheless, before such model can be applied, the generalizability of the model becomes imperative thus it can give a better performance not only in the present, but also against the future data. In this work, shallow and deep machine learning techniques represented by support vector regression (SVR), k-nearest neighbors (KNN), extreme gradient boosting (XGBoost) and artificial neural network (ANN) was deployed to predict the fracture toughness of various aluminum alloys in the scheme of MLDS framework. Our study reveals that the highest prediction accuracy can be obtained for XGBoost technique with R2 score, RMSE, and MAPE values were found to be 90.6 %, 2.57, and 7.0 %, respectively with robust k-fold validation value of 90.1 ± 1.5. The superior performance of Xgboost due to its capability handling non-linear regression problems with a small amount of data.The forward properties to compositions (P2C) and reverse compositions to properties (C2P) models exhibited good accuracies in predicting the fracture toughness as illustrated by the error values lower than the machine learning design system (MLDS) error criteria of 5 %. The XGBoost model feasibility to predict fracture toughness for various aluminum alloys of Alcoa 7055-T7751, AA 7055-T7751, 2024-T852, 5083-O 8090-T8151 was demonstrated as well as used to search aluminum alloy compositions with high fracture toughness. The Pearson correlation coefficient (PCC) and feature Importance results were able to reveal the effects of the alloying elements to the fracture toughness of the alloy. These results reveal the potential application of our models as a pre-screening tool in selecting material for alloying compounds.

Squirrel cage induction generator based micro grid voltage assessment with STATCOM using different metaheuristic approaches

Squirrel Cage Induction Generators are the most common machine to operate wind-based power plants. Microgrids are small-scale electrical systems that provide power to a local area, and optimization methods for microgrids aim to ensure that these systems operate in a way that is both efficient and cost-effective. In such applications, STATCOM is used as reactive power provider and It is necessary to use advanced controllers like the Genetic Algorithm (GA), Firefly Algorithm (FA), and Adaptive Neuro Fuzzy Inference System (ANFIS) as the usual approaches for setting gain factors of STATCOM controller which does not perform well in the case of sudden voltage level changes due to disturbances. The firefly algorithm is primarily required to estimate the gain factors of the STATCOM controller which is used in hybrid micro grid with SG and SCIG for controlling the output voltage in the occurrence of large probabilistic ambiguity. The effectiveness of firefly controlled STATCOM controller for voltage-reactive power control in hybrid microgrid is further examined and validated by comparing the results with other GA, ANN and ANFIS tuning techniques. The need for reactive power is accomplished by STATCOM to minimize the time required to control voltage transient response. The main contribution of this paper includes: an assessment of STATCOM performance with step variations in the input wind energy and reactive power load requirement under conditions of severe probabilistic uncertainty, system analyses conducted under dynamic conditions rather than using a composite load model. Additionally, a comparison of reactive power and voltage control by STATCOM is presented, and employing FA techniques to improve, a comparative of STATCOM reactive power and voltage control. Results comparing all tuning techniques shows that utilizing the Integral of Square of Errors (ISE) criterion, sophisticated tuning techniques can maintain excellent performances under a variety of disruptions.

The Multicollinearity Effect on the Performance of Machine Learning Algorithms: Case Examples in Healthcare Modelling

Background: The data extracted from various fields inherently consists of extremely correlated measurements in parallel with the exponential increase in the size of the data that need to be interpreted owing to the technological advances. This problem, called the multicollinearity, influences the performance of both statistical and machine learning algorithms. Statistical models proposed as a potential remedy to this problem have not been sufficiently evaluated in the literature. Therefore, a comprehensive comparison of statistical and machine learning models is required for addressing the multicollinearity problem. Methods: Statistical models (including Ridge, Liu, Lasso and Elastic Net regression) and the eight most important machine learning algorithms (including Cart, Knn, Mlp, MARS, Cubist, Svm, Bagging and XGBoost) are comprehensively compared by using two different healthcare datasets (including Body Fat and Cancer) having multicollinearity problem. The performance of the models is assessed through cross validation methods via root mean square error, mean absolute error and r-squared criteria. Results: The results of the study revealed that statistical models outperformed machine learning models in terms of root mean square error, mean absolute error and r-squared criteria in both training and testing performance. Particularly the Liu regression often achieved better relative performance (up to 7.60% to 46.08% for Body Fat data set and up to 1.55% to 21.53% for Cancer data set on training performance and up to 1.56% to 38.08% for Body Fat data set and up to 3.50% to 23.29% for Cancer data set on testing performance) among regression methods as well as compared to machine algorithms. Conclusions: Liu regression is mostly disregarded in the machine learning literature, but since it outperforms the most powerful and widely used machine learning algorithms, it appears to be a promising tool in almost all fields, especially for regression-based studies including data with multicollinearity problem.

Robust fixed‐point Kalman smoother for bilinear state‐space systems with non‐Gaussian noise and parametric uncertainties

SummaryKalman smoother is an effective algorithm to estimate the state of the dynamic systems with Gaussian noise. However, when the system is affected by non‐Gaussian noise, the traditional Kalman smoother may suffer severe performance degradation, since it is derived from the minimum mean square error criterion. By introducing the maximum correntropy criterion, which accounts for all higher order moments and has the ability to resist non‐Gaussian noise, this article studies the state estimation problem of the bilinear state‐space system with non‐Gaussian noises and parametric uncertainties. The bilinear system with parametric uncertainties is transformed into a linear time‐varying system, and a robust fixed‐point Kalman filter algorithm is derived based on the Cauchy kernel‐based correntropy criterion. To improve the state estimation accuracy, a Cauchy kernel‐based fixed‐point Kalman smoother (CK‐FPKS) algorithm is presented by introducing the backward smoothing. Simulation results show the effectiveness of the proposed algorithm.

Short-term load forecasting: cascade intuitionistic fuzzy time series—univariate and bivariate models

AbstractShort-term load forecasting (STLF) is essential for developing reliable and sustainable economic and operational strategies for power systems. This study presents a forecasting model combining cascade forward neural network (CFNN) and intuitionistic fuzzy time series (IFTS) models for STLF. The proposed cascading intuitionistic fuzzy time series forecasting model (C-IFTS-FM) offers the advantage of CFNN using the links of both linear and nonlinear to model fuzzy relations between inputs and outputs. Moreover, it offers a more reliable and realistic approach to uncertainty, taking notice of also the degree of hesitation. C-IFTS-FM works in univariate structure when it uses only hourly load data, and in bivariate structure when it uses hourly load data and hourly temperature time series together. The conversion of time series into IFTS is realized with intuitionistic fuzzy c-means (IFCM). Thus, the membership and non-membership values for each data point are produced. In modelling process, membership and non-membership values, in addition to actual lagged observations, are used as input of the CFNNs. The effectiveness of C-IFTS-FM on test sets for both structures was discussed comparatively via different error criteria, in addition, the convergence time was examined, and also the fit of forecasts and observations was presented with different illustrations. Among different combinations of hyperparameters, in the best case, approximately 86% better accuracy is achieved than the best of the others, while even in the case of the worst of hyperparameters combination, the accuracy was improved by over 20% for the PSJM data sets. For HEXING, CHENGNAN, and EUNITE data sets, these progress rates reached approximately 90% in the best case.

Almost unbiased ridge estimator in Bell regression model: theory and application to plastic polywood data

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion.

Trajectory control and optimization of PID controller parameters for dual-arms with a single-link underwater robot manipulator

ABSTRACT This paper focuses on the modeling, simulation, and control of the trajectories of a dual-arm single-link underwater robot manipulator (DS-URM), having dual arms (left and right) with a single link each. The dynamic coupling between the base and the dual arms makes trajectory control of the end effector difficult. This study attempts to simulate and control dual arms with a single-link underwater robotic manipulator using a hybrid controller. To reduce the error for a sinusoidal wave and a cycloid trajectory, a hybrid controller is the combination of the Proportional-Integral-Derivative (PID) controller and overwhelm controller. The underwater dynamic’s buoyancy, gravity, and hydrostatic forces acting on the underwater robot are modeled in an integrated SIMULINK model, including the DS-URM. The DS-URM has been investigated, revealing some significant trajectories of the left and right tips. Effective tuning methods include Ziegler-Nicholas (Z-N), genetic algorithms, Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO). The Integral of Time multiplied by Absolute Error (ITAE) criteria has been used to improve trajectory tracking via particle swarm optimization. Results show significant improvements in trajectory tracking, with ITAE error reduction by 96.44% and 98.6% for left and right arms, respectively, achieving stability in 0.000645s.

New Modification of Ranked Set Sampling for Estimating Population Mean: Neutrosophic Median Ranked Set Sampling with an Application to Demographic Data

The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability.

Replication of Radial Pulses Using Magneto-Rheological Fluids.

The radial pulse is a critical health marker with expanding applications in wearable technology. To improve these applications, developing a pulse generator that consistently produces realistic pulses is crucial for validation and training. The goal of this study was to design and test a cost-effective pulse simulator that can accurately replicate a wide range of age-dependent radial pulses with simplicity and precision. To this end, this study incorporated a magneto-rheological (MR) fluid device into a cam-based pulse simulator. The MR device, as a key component, enables pulse shaping without the need for additional cams, substantially reducing the cost and complexity of control compared with existing pulse simulators. To evaluate the performance of the MR pulse simulator, the root-mean-square (RMS) error criterion (less than 5%) was used to compare the experimentally obtained pulse waveform with the in vivo pulse waveform for specific age groups. After demonstrating that the MR simulator could produce three representative in vivo pulses, a parametric study was conducted to show the feasibility of the slope-based pulse-shaping method for the MR pulse simulator to continuously generate a range of age-related pulses.

The prediction on non-Gaussian characteristics of wind pressure for the long-span roof in the mountainous area using proper orthogonal decomposition–deep learning framework

To make an accurate prediction of the non-Gaussian characteristics of wind pressure for the long-span roof, this study combines the proper orthogonal decomposition (POD) technique, convolutional neural network (CNN), and long short-term memory (LSTM) network to propose a novel POD-CNN-LSTM framework. Then, the proposed framework was well validated based on the wind tunnel testing of a long-span roof structure, and some error criteria, such as mean square root error and correlation coefficient, were adopted to evaluate the prediction accuracy of the non-Gaussian characteristics. Furthermore, two other methods, POD-CNN and POD-LSTM, were also used to conduct a comparative study. The obtained results illustrate that compared to POD-CNN and POD-LSTM, the proposed framework can achieve better performance on the pulsating wind pressure coefficient. For predictions of non-Gaussian characteristics, the output results of the proposed POD-CNN-LSTM show fewer errors, which means the predictions are close to the measured results, including skewness, kurtosis, and wind pressure probability density distributions. To summarize, the proposed POD-CNN-LSTM framework shows superiority over others, which means the proposed framework has good potential for the practical application of non-Gaussian prediction of the engineering structure.

Extragradient method with feasible inexact projection to variational inequality problem

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint set, as in previous versions extragradient method, the proposed methods compute feasible inexact projections on the constraint set using a relative error criterion. The first version of the proposed method provided is a counterpart to the classic form of the extragradient method with constant steps. In order to establish its convergence we need to assume that the operator is pseudo-monotone and Lipschitz continuous, as in the standard approach. For the second version, instead of a fixed step size, the method presented finds a suitable step size in each iteration by performing a line search. Like the classical extragradient method, the proposed method does just two projections into the feasible set in each iteration. A full convergence analysis is provided, with no Lipschitz continuity assumption of the operator defining the variational inequality problem.

Lateral to medial fluoroscopic view improves the accuracy of identifying the MPFL femoral footprint using Schottle's technique.

This study investigated the effect of different fluoroscopy settings on the accuracy of locating Schottle's point during medial patellofemoral ligament (MPFL) reconstruction. The centre of the MPFL femoral footprint was identified and marked on 44 dry femurs. Two standard true lateral knee fluoroscopic images were obtained: (1) medial to lateral (ML) and (2) lateral to medial (LM). The deviation between the anatomically determined MPFL femoral footprint and the fluoroscopically identified point was measured on both fluoroscopic images. An 'acceptable tunnel location' was defined as within a 5- or 7-mm margin of error from the anatomic MPFL footprint. Distal femoral morphometric dimensions were also measured using digital calipers. Statistical analysis determined discrepancies between techniques and their relation to femoral morphometry. The LM view yielded a significantly smaller distance between the anatomical MPFL footprint and Schottle's point compared to the ML view (3.2 ± 1.5 vs. 4.5 ± 2.1 mm, p < 0.001). The LM view achieved acceptable tunnel locations, meeting the 5-mm error criterion in 90.9% of cases, while the ML view achieved 65.9% (p < 0.001). Both views yielded acceptable tunnel locations at similar rates using the 7-mm error criterion (n.s.). The anatomic MPFL footprint was displaced towards the anterior and proximal location in the ML view in reference to the Schottle point. No correlation was observed between any of the morphometric measurements and the deviations. This study demonstrated that using the LM fluoroscopic view improves the accuracy of femoral tunnel placement when identifying the MPFL footprint via the Schottle technique. Adopting the LM view in surgical practice will help surgeons locate the anatomical femoral footprint accurately, replicating the native MPFL and enhancing clinical outcomes. Level 4, cadaveric study.

Stopping criteria for neutron spectrum unfolding algorithms

Neutron spectrum unfolding is a crucial process in radiation protection and dosimetry. Unfolding codes using iterative algorithms require a criterion to stop the iterations. One approach often relies on the Root Mean Square Error (RMSE) criterion to assess the convergence of iterative algorithms. The aim of this work is to present a new criteria: Average Ratio Scaled (AVGS) and Relative Change in AVGS (dAVGS) to address specific challenges associated with RMSE. Extensive validation tests were conducted, covering a range of scenarios with results showing high level of agreement between the unfolded spectra and the reference.

Highway vehicle detection based on distributed acoustic sensing

Distributed acoustic sensing systems can obtain the road vibration information caused by vehicle driving vibration on highways. By characterizing the vehicle driving vibration data, a distributed acoustic sensing system based highway vehicle driving vibration detection scheme is proposed. Firstly, the out-of-bag error criterion of random forest is used to select multiple features of the vibration signals to obtain the most suitable feature quantity to characterize the road vibration signals, then the root mean square value of the signal matched filtering is calculated and compared, and the threshold is used to distinguish between the vehicle vibration signals and the noise. Finally, the improved trajectory start algorithm is used to accurately detect the vehicles travelling on the highway to obtain the real-time information of the vehicles. The experiment verified that the method can effectively detect highway vehicles.

Performance Evaluation of Fractional Proportional–Integral–Derivative Controllers Tuned by Heuristic Algorithms for Nonlinear Interconnected Tanks

This article presents an in-depth analysis of three advanced strategies to tune fractional PID (FOPID) controllers for a nonlinear system of interconnected tanks, simulated using MATLAB. The study focuses on evaluating the performance characteristics of system responses controlled by FOPID controllers tuned through three heuristic algorithms: Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Flower Pollination Algorithm (FPA). Each algorithm aims to minimize its respective cost function using various performance metrics. The nonlinear model was linearized around an equilibrium point using Taylor Series expansion and Laplace transforms to facilitate control. The FPA algorithm performed better with the lowest Integral Square Error (ISE) criterion value (297.83) and faster convergence in constant values and fractional orders. This comprehensive evaluation underscores the importance of selecting the appropriate tuning strategy and performance index, demonstrating that the FPA provides the most efficient and robust tuning for FOPID controllers in nonlinear systems. The results highlight the efficacy of meta-heuristic algorithms in optimizing complex control systems, providing valuable insights for future research and practical applications, thereby contributing to the advancement of control systems engineering.

Broad learning system based on maximum multi-kernel correntropy criterion

The broad learning system (BLS) is an effective machine learning model that exhibits excellent feature extraction ability and fast training speed. However, the traditional BLS is derived from the minimum mean square error (MMSE) criterion, which is highly sensitive to non-Gaussian noise. In order to enhance the robustness of BLS, this paper reconstructs the objective function of BLS based on the maximum multi-kernel correntropy criterion (MMKCC), and obtains a new robust variant of BLS (MKC-BLS). For the multitude of parameters involved in MMKCC, an effective parameter optimization method is presented. The fixed-point iteration method is employed to further optimize the model, and a reliable convergence proof is provided. In comparison to the existing robust variants of BLS, MKC-BLS exhibits superior performance in the non-Gaussian noise environment, particularly in the multi-modal noise environment. Experiments on multiple public datasets and real application validate the efficacy of the proposed method.

Development of a MIMO fuzzy inference system—PI controller for a closed‐circuit grinding ball mill circuit

AbstractThis article aims to study the implementation of classical proportional‐integrative (PI) controllers and their coupling with the fuzzy inference systems (FISs) in the act of closed‐circuit grinding (CCG) ball mill system. The system was formed for a multiple‐input multiple‐output (MIMO) system, with two inputs, the feed rate (WF) and speed classifier rotor (VR), and two outputs, a sieve fraction 45 μm (P45) and the amount of material by a weight inside the drum (hold up [HU]). The model was simulated based on experimental processes and control strategies. The fuzzy‐PI controllers were developed on the software, and the data from this process were used to build the database and the necessary knowledge to construct the FIS controllers (with fuzzy rules base 3 × 3 and 5 × 5). Their implementation decreases the error criteria integral of time multiplied by the absolute error (ITAE) and integral of the absolute magnitude of the error (IAE) by 35% and 65%, respectively. Although, applying fuzzy‐PI systems with a smaller rule‐based outcome gives the benefits of implementing the fuzzy logic (FL) but with a smaller oscillatory performance and a minor negative effect on HU control.

Evaluation of Total Risk-Weighted Assets in Islamic Banking through Fintech Innovations

The assessment of total risk-weighted assets (LTRWAs) in the banking sector is of the utmost importance. It serves as a critical component for regulatory compliance, risk management, and capital adequacy. By accurately assessing LTRWAs, banks can effectively meet regulatory requirements, efficiently allocate capital resources, and proactively manage risks. Moreover, the accurate assessment of LTRWAs supports performance evaluation and fosters investor confidence in the financial stability of banks. This study presents statistical analyses and machine learning methods to identify factors influencing LTRWAs. Data from Bahrain, Jordan, Qatar, the United Arab Emirates, and Yemen, spanning from 2010 to 2021, was utilized. Various statistical tests and models, including ordinary least squares, fixed effect, random effect, correlation, variance inflation factor, tolerance tests, and fintech models, were conducted. The results indicated significant impacts of the unemployment rate, inflation rate, natural logarithm of the loan-to-asset ratio, and natural logarithm of total assets on LTRWAs in regression models. The dataset was divided into a training group (90% of the data) and a testing group (10% of the data) to evaluate the predictive capabilities of various fintech models, including an adaptive network-based fuzzy inference system (ANFIS), a hybrid neural fuzzy inference system (HyFIS), a fuzzy system with the heuristic gradient descent (FS.HGD), and fuzzy inference rules with the descent method (FIR.DM) models. The selection of the optimal model is contingent upon assessing its performance according to specific error criteria. The HyFIS model outperformed others with lower errors in predicting LTRWAs. Independent t-tests confirmed statistically significant differences between original and predicted LTRWA for all models, with HyFIS showing closer predictions. This study provides valuable insights into LTRWA prediction using advanced statistical and machine learning techniques, based on a dataset from multiple countries and years.