Error Index Research Articles

A Comparative Study on the Estimation of Wind Speed and Wind Power Density Using Statistical Distribution Approaches and Artificial Neural Network-Based Hybrid Techniques in Çanakkale, Türkiye

In recent years, wind energy has become remarkably popular among renewable energy sources due to its low installation costs and easy maintenance. Having high energy potential is of great importance in the selection of regions where wind energy investments will be made. In this study, the wind power potential in Çanakkale Province, located in the northwest of Türkiye, is examined, and the wind speed is estimated using hourly and daily data over a one-year period. The data, including 12 different meteorological parameters, were taken from the Turkish State Meteorological Service. The two-parameter Weibull and Rayleigh distributions, which are the most widely preferred models in wind energy studies, are employed to estimate the wind power potential using hourly wind speed data. The graphical method is implemented to calculate the shape (k) and scale (c) parameters of the Weibull distribution function. Daily average wind speed estimation is performed with artificial neural network–genetic algorithm (ANN-GA) and ANN–particle swarm optimization (ANN-PSO) hybrid approaches. The proposed hybrid ANN-GA and ANN-PSO algorithms provide correlation coefficient values of 0.94839 and 0.94042, respectively, indicating that the predicted and measured wind speed values are notably close. Statistical error indices reveal that the ANN-GA model outperforms the ANN-PSO model.

An Asynchronous Linear Filter Architecture for Hybrid Event-Frame Cameras.

Event cameras are ideally suited to capture High Dynamic Range (HDR) visual information without blur but provide poor imaging capability for static or slowly varying scenes. Conversely, conventional image sensors measure absolute intensity of slowly changing scenes effectively but do poorly on HDR or quickly changing scenes. In this paper, we present an asynchronous linear filter architecture, fusing event and frame camera data, for HDR video reconstruction and spatial convolution that exploits the advantages of both sensor modalities. The key idea is the introduction of a state that directly encodes the integrated or convolved image information and that is updated asynchronously as each event or each frame arrives from the camera. The state can be read-off as-often-as and whenever required to feed into subsequent vision modules for real-time robotic systems. Our experimental results are evaluated on both publicly available datasets with challenging lighting conditions and fast motions, along with a new dataset with HDR reference that we provide. The proposed AKF pipeline outperforms other state-of-the-art methods in both absolute intensity error (69.4% reduction) and image similarity indexes (average 35.5% improvement). We also demonstrate the integration of image convolution with linear spatial kernels Gaussian, Sobel, and Laplacian as an application of our architecture.

Design and Development of Intelligent Learning System for University Innovation and Entrepreneurship Based on Knowledge Visualisation

To build a comprehensive learning resource system covering learning process, learning users, learning resources and other aspects, an intelligent learning system for innovation and entrepreneurship in universities was constructed and designed combined with knowledge visualisation theory. The system includes student information record module, system recommendation calculation module, learning material module, and knowledge visualisation module. The research focuses on the system recommendation calculation module, including the User-based Collaborative Filtering Algorithm (UCF) and the Joint Recommendation (JR) algorithm of the application content recommendation algorithm. The best neighbour number of JR is 20, and the best transmission path length is 2. The recommendation effect is optimal under this setting. The convergence iterations of the training and test set of the joint recommendation algorithm are 80 times and 100 times, respectively. For the training set and test set, the accuracy, precision, sensitivity, recall, running time, error, and other performance evaluation indicators of the joint recommendation algorithm are better than the corresponding values of other recommendation algorithms. The system has a good design effect and experience effect in the application of the online learning platform.

Intelligent algorithms-aided modeling and optimization of the deturbidization of abattoir wastewater by electrocoagulation using aluminium electrodes

The removal of turbidity from abattoir wastewater (AWW) by electrocoagulation (EC) was modeled and optimized using Artificial Intelligence (AI) algorithms. Artificial neural networks (ANN), adaptive neuro-fuzzy inference systems (ANFIS), particle swarm optimization (PSO), and genetic algorithms (GA) were the AI tools employed. Five input variables were considered: pH, current intensity, electrolysis time, settling time, and temperature. The ANN model was evaluated using the Levenberg-Marquardt (trainlm) algorithm, while the ANFIS modeling was accomplished using the Sugeno-type FIS. The ANN and ANFIS models demonstrated linear adequacy with the experimental data, with an R2 value of 0.9993 in both cases. The corresponding statistical error indices were RMSE (ANN = 5.65685E-05; ANFIS = 2.82843E-05), SSE (ANN = 1.60E-07; ANFIS = 3.4E-08), and MSE (ANN = 3.2E-09; ANFIS = 8E-10). The error indices revealed that the ANFIS model had the least performance error and is considered the most reliable of the two. The process optimization performed with GA and PSO considered turbidity removal efficiency, energy requirement, and electrode material loss. An optimal turbidity removal efficiency of 99.39 % was predicted at pH (3.1), current intensity (2 A), electrolysis time (20 min), settling time (50 min), and operating temperature (50 °C). This represents a potential for the delivery of cleaner water without the use of chemicals. The estimated power consumption and the theoretical mass of the aluminium electrode dissolved at the optimum condition were 293.33 kW h/m3 and 0.2237 g, respectively. The work successfully affirmed the effectiveness of the EC process in the removal of finely divided suspended particles from AWW and demonstrated the suitability of the AI algorithms in the modeling and optimization of the process.

CFD Modeling and Experimental Validation of the Flow Processes of an External Gear Pump

This article presents computational fluid dynamics (CFD) modeling of the flow processes at a certain specimen of an external gear pump. The purpose of the developed two-dimensional (2D) CFD model is to carry out a numerical study to obtain the main characteristics of the pump flow rate, especially the flow rate as a function of the pressure and the flow rate as a function of the time. A numerical study was carried out at forty-two different operating modes that were expressed as a variation of two parameters: rotational frequency (950–1450 min−1) and pressure (5–150 bar). The validation of the numerical results was carried out through an experimental study. For this purpose, a laboratory experimental setup equipped with a modern data acquisition (DAQ) system was designed and implemented. It allows the gear pump to be tested at the same operating modes as the numerical study. A validation analysis was performed by comparing the numerical and experimental results using the average relative error index (FIT). A detailed description of the 2D CFD model development (CAD model, mesh, general settings, boundary conditions, etc.) is provided. Based on the 2D CFD model, an original methodology was proposed to take into account the influence of the discharge channels on the displacement volume of the pump by adjusting the face width of the gears. Despite the limitations of the simple 2D CFD model, which are discussed in this article, a very good match between numerical and experimental results is analyzed by calculating the FIT level, which is in the range of 93–97%.

Static Series Compensator for the compensation of voltage-quality disturbances based on particle swarm optimization techniques

Static Series Compensator (SSC) is a power electronic based device that provides three-phase controllable voltage source to restore the load voltage to pre-sag conditions within few milliseconds. This paper proposes a new control technique based on an adaptive tunning PI controller that uses a selective controller to describe the effectiveness of SSC for mitigating voltage sags in power distribution systems at critical loads. The integral of time multiply squared error (ITSE) index is minimized to reach the optimal tuning of PI controllers based on particle swarm optimization (PSO) technique to determine whether the best fitting solution is achieved. The controller is designed in a synchronously-rotating reference frame. Independent (homopolar component, d-axis component and qaxis component) controllers are used to tackle balanced and unbalanced voltage supplies. Simulation is done using Simulink “SimPowerSystem” Toolbox to illustrate the principle and performance of an SSC operation in load voltage compensation

Extended state observer design for uncertainty estimation in electronic throttle valve system

AbstractThe Electronic Throttle Valve (ETV) is the core part of automotive engines which are recently used in control-by-wire cars. The estimation of its states and uncertainty is instructive for control applications. This study presents the design of Extended State Observer (ESO) for estimating the states and uncertainties of Electronic Throttle Valve (ETV). Two versions of ESOs have been proposed for estimation: Linear ESO (LESO) and Nonlinear ESO (NESO). The model of ETV is firstly developed and extended in state variable form such that the extended state stands for the uncertainty in system parameters. The design of both structures of ESOs are developed and a comparison study has been conducted to show the effectiveness of the proposed observers. Numerical simulation has been conducted to assess the performance of observers in estimating the states and uncertainties of ETV. The simulated results showed that both full order and reduced order models of ETV have the same transient characteristics. Moreover, the effectiveness of two versions of observers has been examined based on Root Mean Square of Error (RMSE) indicator. The results showed that the NESO has less estimation errors for both states and uncertainties than LESO.

A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions

The goal of increasing efficiency and durability of fuel cells can be achieved through optimal control of their operating conditions. In order to implement such controllers, accurate and computationally efficient fuel cell models must be developed. This work presents a hybrid (physics-based and data-driven), control-oriented model for approximating the output voltage of proton exchange membrane fuel cells (PEMFCs) while operating under dynamical conditions. First, a physics-based model, built from simplified electrochemical, membrane dynamics and mass conservation equations, is developed and validated through experimental data. Second, a data-driven, neural network (echo state network) is trained, fitted and tested with the same dataset. Then, the hybrid model is formed as a parallel structure, where the simplified physics-based model and the trained data-driven model are merged through an algorithm based on Gaussian radial basis functions. The merging algorithm compares the output of both single models and assigns weights for computing the prediction of the hybrid result. The proposed hybrid model structure is successfully trained, validated and tested with an experimental dataset originating from fuel cells within an automotive PEMFC stack. The hybrid model is assessed through the mean square error index, with the result of a low tracking error.

Biogas Production Prediction Based on Feature Selection and Ensemble Learning

The allocation of biogas between power generation and heat supply in traditional kitchen waste power generation system is unreasonable; for this reason, a biogas prediction method based on feature selection and heterogeneous model integration learning is proposed for biogas production predictions. Firstly, the working principle of the biogas generation system based on kitchen waste is analyzed, the relationship between system features and biogas production is mined, and the important features are extracted. Secondly, the prediction performance of different individual learner models is comprehensively analyzed, and the training set is divided to reduce the risk of overfitting by combining K-fold cross-validation. Finally, different primary learners and meta learners are selected according to the prediction error and diversity index, and different learners are fused to construct the stacking ensemble learning model with a two-layer structure. The experimental results show that the research method has a higher prediction accuracy in predicting biogas production, which provides supporting data for the economic planning of kitchen waste power generation systems.

Short-term wind power forecasting based on dual attention mechanism and gated recurrent unit neural network

Accurate wind power forecasting is essential for both optimal grid scheduling and the massive absorption of wind power into the grid. However, the continuous changes in the contribution of various meteorological features to the forecasting of wind power output under different time or weather conditions, and the overlapping of wind power sequence cycles, make forecasting challenging. To address these problems, a short-term wind power forecasting model is established that integrates a gated recurrent unit (GRU) network with a dual attention mechanism (DAM). To compute the contributions of different features in real time, historical wind power data and meteorological information are first extracted using a feature attention mechanism (FAM). The feature sequences collected by the FAM are then used by the GRU network for preliminary forecasting. Subsequently, one-dimensional convolution employing several distinct convolution kernels is used to filter the GRU outputs. In addition, a multi-head time attention mechanism (MHTAM) is proposed and a Gaussian bias is introduced to assign different weights to different time steps of each modality. The final forecast results are produced by combining the outputs of the MHTAM. The results of the simulation experiment show that for 5-h, 10-h, and 20-h short-term wind power forecasting, the established DAM-GRU model performs better than comparative models on the basis of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), R-squared (R2), Square sum error (SSE), Mean absolute percentile error (MAPE), and Relative root mean square error (RRMSE) index.

An adaptive fuzzy maximum power point tracking for PV systems by a mutant gray wolf optimization algorithm

Abstract An innovative and adaptive maximum power point tracking (MPPT) based on a fuzzy controller is proposed in this article. The proposed controller is optimized by the mutant gray wolf optimization (MGWO) algorithm, and the objective function uses an integral squared time squared error (ISTSE) index. To indicate the efficiency of the proposed MPPT algorithm (MGWO-AF-MPPT), the simulations for several irradiation conditions are modeled in MATLAB. In addition, two fair comparisons are performed between the simulation results of the proposed MPPT method with an adaptive fuzzy controller that optimized with particle swarm optimization (PSO-AF-MPPT), as well as a Perturbation and Observation method (P&O-MPPT). The comparison results illustrate that the amount of generated electrical power from the PV system for all adaptive MPPT systems is almost close to each other, indicating the high accuracy of both fuzzy-based controllers. However, the PV power generation of the proposed MGWO-AF-MPPT is higher, and also its ripple is lower than PSO-AF-MPPT. Note that, the calculated total harmonic distortion (THD) for the P&O-MPPT, PSO-AF-MPPT, and the proposed MGWO-AF-MPPT methods are calculated at 3.4%, 2.3%, and 2.1%, respectively. A lower THD indicates better power quality generated by the PV system employing the MGWO-AF-MPPT method.

Analysis of Prospective Teacher Students Errors in Making Math Test Instruments Based on Bloom's Taxonomy Revised

This study aims to describe the errors of prospective teacher students in making math test instruments based on cognitive levels from the Bloom’s Taxonomy Revised (BTR). BTR consists of LOTS (C1-C3) and HOTS (C4-C6) levels. This research included descriptive qualitative research. The subjects of this study were 19 prospective teacher students, namely the mathematics education department in the Mathematics Learning Evaluation course. Based on the results of the study, it was obtained that prospective teacher students made mistakes at both levels but more at the HOTS level. At the LOTS level, it is on the error level C3; at the HOTS level, it is spread at all levels, namely C4-C6. An indication of error that often arises is that prospective teacher students cannot compile questions according to their level of cognition. The questions made are often still below the level they should be. The level of the questions made is still below the level that it should be.

Dynamic load prediction of charging piles for energy storage electric vehicles based on Space-time constraints in the internet of things environment

Abstract This paper puts forward the dynamic load prediction of charging piles of energy storage electric vehicles based on time and space constraints in the Internet of Things environment, which can improve the load prediction effect of charging piles of electric vehicles and solve the problems of difficult power grid control and low power quality caused by the randomness of charging loads in time and space. After constructing a traffic road network model based on the Internet of Things, a travel chain model with different complexity and an electric vehicle charging model, the travel chain is randomly extracted. With the shortest travel time as a constraint, combined with the traffic road network model based on the Internet of Things, the travel route and travel time are determined. According to the State of Charge (SOC) and the travel destination, the location and charging time of the energy storage electric vehicle charging pile are determined. After obtaining the time-space distribution information of the energy storage electric vehicle charging pile at different times and in different regions, it is used as the input of the deep multi-step time-space dynamic neural network, and the network output is the dynamic electric vehicle charging pile. The experimental results show that this method can realize the dynamic load prediction of electric vehicle charging piles. When the number of stacking units is 11, the indexes of Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) are the lowest and the index of R 2 is the largest. The load of charging piles in residential areas and work areas exists in the morning and evening peak hours, while the load fluctuation of charging piles in other areas presents a decentralized change law; The higher the complexity of regional traffic network, the greater the load of electric vehicle charging piles in the morning rush hour.

A novel machine learning ensemble forecasting model based on mixed frequency technology and multi-objective optimization for carbon trading price

Carbon trading prices are crucial for carbon emissions and transparent carbon market pricing. Previous studies mainly focused on data mining in the prediction direction to quantify carbon trading prices. Although the prospect of high-frequency data forecasting mechanisms is considerable, more mixed-frequency ensemble forecasting is needed for carbon trading prices. Therefore, this article designs a new type of ensemble prediction model to increase the scope of model research. The module is divided into three parts: data denoising, mixed frequency and machine learning, multi-objective optimization, and ensemble forecasting. Precisely, the data preprocessing technology enhanced by adopting a self-attention mechanism can better remove noise and extract effective features. Furthermore, mixed frequency technology is introduced into the machine learning model to achieve more comprehensive and efficient prediction, and a new evaluation criterion is proposed to measure the optimal submodel. Finally, the ensemble model based on deep learning strategy can effectively integrate the advantages of high-frequency and low-frequency data in complex datasets. At the same time, a new multi-objective optimization algorithm is proposed to optimize the parameters of the ensemble model, significantly improving the predictive ability of the integrated module. The results of four experiments and the Mean Absolute Percent Error index of the proposed model improved by 28.3526% compared to machine learning models, indicating that the ensemble model established can effectively address the time distribution characteristics and uncertainty issues predicted by carbon trading price models, which helps to mitigate climate change and develop a low-carbon economy.

A priori and a posteriori error estimates of a space–time Petrov–Galerkin spectral method for time-fractional diffusion equation

Time-fractional diffusion equation is an important transport dynamical model for simulating fractal time random walk. This article is devoted to investigating the a priori and a posteriori error estimates for this model equation. A Petrov–Galerkin spectral method is revisited in this paper to address our problem, which the generalized Jacobi functions and Fourier-like basis functions are utilized as basis for constructing efficient and accurate space–time spectral approximations. Rigorous proofs are given for the stability of our spectral scheme. And then the convergence of the proposed method is proved by establishing an a priori error estimate. Specifically, an efficient and reliable a posteriori error estimator is introduced, and we derive that the residual-based error indicator provides an upper bound and a lower bound for the numerical error. Finally, several numerical experiments are provided to examine our theoretical claims.

Automatic variationally stable analysis for finite element computations: Transient convection-diffusion problems

We present an application of stable finite element (FE) approximations of convection-diffusion initial boundary value problems (IBVPs) using a weighted least squares FE method, the automatic variationally stable finite element (AVS-FE) method [1]. The transient convection-diffusion problem leads to issues in classical FE methods as the differential operator can be considered a singular perturbation in both space and time. The stability property of the AVS-FE method, allows us significant flexibility in the construction of FE approximations in both space and time. Thus, in this paper, we take two distinct approaches to the FE discretization of the convection-diffusion problem: i) considering a space-time approach in which the temporal discretization is established using finite elements, and ii) a method of lines approach in which we employ the AVS-FE method in space whereas the temporal domain is discretized using the generalized-α method. We also consider another space-time technique in which the temporal direction is partitioned, thereby leading to finite space-time “slices” in an attempt to reduce the computational cost of the space-time discretizations.We present numerical verifications for these approaches, including numerical asymptotic convergence studies highlighting optimal convergence properties. Furthermore, in the spirit of the discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan [2–6], the AVS-FE method also leads to readily available a posteriori error estimates through a Riesz representer of the residual of the AVS-FE approximations. Hence, the norm of the resulting local restrictions of these estimates serves as error indicators in both space and time for which we present multiple numerical verifications in mesh adaptive strategies.

Quantifying the impact of sensor precision on power output of a wind turbine: A sensitivity analysis via Monte Carlo simulation study

Wind turbines (WTs) are complex systems with multiple interacting components, posing challenges in identifying factors affecting power output (PO). Sensors play an important role; however, sensor precision can result in measured values differing from actual values. Analyzing the impact of sensor precision on PO is essential. In this study, we employ sensitivity analysis (SA) via Monte Carlo (MC) simulation, offering a novel approach to quantify the influence of sensor precision on the PO of a 4.8 MW WT. We focus on evaluations under 5–20 m/s wind profiles, representing partial and full load regions that portray normal operation. Based on mean squared error (MSE) and parameter sensitivity (PS) index analyses, findings show the generator speed sensor’s precision significantly impacts PO. Therefore, designers should prioritize high-impact sensors like the generator speed, while sensorless strategies may be considered as alternatives to low-impact sensors like the blade pitch angle sensor, where appropriate.

Modeling the compressive strength of binary and ternary blended high-performance concrete mixtures using ensemble machine learning models

In the present study, the compressive strength of binary and ternary blended high-performance concrete mixtures was modeled using different machine learning tools, such as artificial neural network (ANN), gradient tree boosting (GTB), and multivariate adaptive regression splines (MARS). The compressive strength of binary and ternary blended concrete at 28 days of curing period was modeled using seven quantitative input parameters such as cement, blast furnace slag, fly ash, superplasticizer, water, coarse aggregate, and fine aggregate based on three different training and testing (Tr–Te) scenarios. The performance of the models developed was analyzed based on several statistical evaluation metrics, of error and efficiency. During the testing phase, the compressive strength estimates obtained via modeling using ANN, GTB, and MARS had Kling–Gupta efficiency (KGE) values of 0.8389, 0.8602, and 0.8423, respectively, for the first Tr–Te scenario; similarly, the KGE values were 0.8025/0.8830, 0.8541/0.8901, and 0.8434/0.8582, respectively, for the second/third Tr–Te scenarios. The estimation accuracy of the GTB model was relatively superior to that of the ANN and MARS models, taking into consideration both the error and efficiency indices. All three models perform relatively well for the first I/O combination compared to the other two combinations.

Accurate and semantic 3D reconstruction of maize leaves

The rapid advances in equipment and technology for crop three-dimensional (3D) data acquisition have enabled the high-throughput and high-quality acquisition of crop 3D data. However, the challenge now lies in comprehending unstructured crop 3D data and extracting phenotypes and knowledge. Extracting semantic feature points from plant leaves and achieving high-precision 3D reconstruction is a prevalent and formidable issue in this field. In this study, we present an accurate method for semantic 3D reconstruction of maize leaves. The algorithm utilizes 3D point cloud data of maize leaves as the initial input. Subsequently, the semantic 3D reconstruction of maize leaves is achieved by means of point cloud preprocessing, initial triangular meshing, hole filling, remeshing, mesh parameterization, two-dimensional (2D) edge detection, 2D semantic point interpolation, 3D semantic point selection, mesh generation, and optimization of feature-point position. A total of 56 leaves from five different maize cultivars were reconstructed utilizing this method. The results indicate that the average distance error index dCDMP between the reconstructed mesh vertices and the input point cloud is less than 0.3 cm2 for all five cultivars, and the mean of the maximum distance error index dHDMP for each cultivar is within the range of 0.5–0.8 cm, indicating it is high-accuracy. The visualization of leaves shows good consistency between the reconstructed mesh and corresponding point cloud. Additionally, the reconstructed 3D mesh of the leaves exhibits enhanced triangular facet consistency. Each vertex can be precisely identified as a leaf vein point, leaf edge point, leaf tip point, or leaf surface point, and includes semantic data such as the position on the leaf blade, which can be directly employed for phenotype estimations. High-precision reconstruction of 3D models of crop organs that include semantic information and cultivar resolution yields significant benefits. This technology can improve the resolution and accuracy of crop morphological and structural research, and it is also crucial for crop phenomics, functional-structural plant modelling, and fusion research between plant phenotyping and crop models.

In the Quest for Scale-optimal Mappings

Optimal mapping is one of the longest-standing problems in computational mathematics. It is natural to measure the relative curve length error under map to assess its quality. The maximum of such error is called the quasi-isometry constant, and its minimization is a nontrivial max-norm optimization problem. We present a physics-based quasi-isometric stiffening (QIS) algorithm for the max-norm minimization of hyperelastic distortion. QIS perfectly equidistributes distortion over the entire domain for the ground-truth test (unit hemisphere flattening) and, when it is not possible, tends to create zones where all cells have the same distortion. Such zones correspond to fragments of elastic material that became rigid under stiffening, reaching the deformation limit. As such, maps built by QIS are related to the de Boor equidistribution principle, which asks for an integral of a certain error indicator function to be the same over each mesh cell. Under certain assumptions on the minimization toolbox, we prove that our method can build, in a finite number of steps, a deformation whose maximum distortion is arbitrarily close to the (unknown) minimum. We performed extensive testing: on more than 10,000 domains QIS was reliably better than the competing methods. In summary, we reliably build 2D and 3D mesh deformations with the smallest known distortion estimates for very stiff problems.