Mean Square Error Analysis Research Articles

Modeling of the Black Sea circulation using equations of heat and salt advection–diffusion having discrete nonlinear invariants

In this work the accuracy of reconstructing the Black Sea circulation by using new approximations of nonlinear terms in the transport equations, ensuring the conservation of temperature and salinity to a power greater than two, is analyzed based on the results of forecast calculations. Three numerical experiments with differences in the schemes for calculating temperature and salinity are carried out. In the first experiment – traditional schemes are used to conserve of temperature and salinity in the first and second degrees; in the second one – the temperature is conserved in the first and fifth degrees, salinity in the first and third; in the third one – the temperature in the first and third, salinity in the first and fifth degrees. Calculations are performed on the basis of the MHI model with a resolution of 1.6 km and taking into account realistic atmospheric forcing for 2016. Validation of the results is carried out based on comparison of model fields with in-situ and satellite measurements of temperature and salinity in 2016. Analysis of mean and root mean square errors showed that new schemes for the advection-diffusion equations of heat and salt, ensuring the conservation of predictive parameters to a power greater than two, improve the accuracy of reconstructing the salinity in the Black Sea upper 100m layer throughout the year compared with traditional approximation. The root mean square errors in the salinity field are reduced by 15–20%, the thickness of the upper mixed layer in winter and the depth of the upper boundary of the thermocline layer in summer in the central part of the sea are modeled approximately 10% more accurately. Based on the results of three experiments, the smallest deviations from observational data are obtained when using approximations that ensure the conservation of temperature to the third power and salinity to the fifth power.

A design method based on neural network to predict thermoacoustic Stirling engine parameters: Experimental and theoretical assessment

A neural network-based design method for thermoacoustic Stirling engines (TASE) is presented in this work. The main goal of the article is to predict the design parameters (Length of resonator (stub) (LR), Length of inertance tube (Lin), Mean pressure (Pm)) of the thermoacoustic Stirling engine in such a way that the dynamic instability is guaranteed. In this regard, the governing equations of the engine are presented first. Next, with the help of the data extracted from the simulation of the governing equations of the engine, a neural network with the structure of 9–35-3 is trained. The effectiveness of the artificial neural network (ANN) structure is explored via regression and MSE (mean square error) analyses. Next, in order to evaluate and validate the neural network, the experimental data of the constructed thermoacoustic Stirling engine (SUTech-SR-4) is considered. It is important to note that the SUTech-SR-4 is introduced for the first time in this work. Investigations have shown that the neural network could estimate the engine design parameters well and with an acceptable approximation in such a way that the dynamic instability of the engine is also established. Besides, the value of the estimated design parameters for the engine made by the neural network was close to the experimental values. Following, the developed engine is introduced and its performance is discussed. The developed engine has been able to produce a power equivalent to 0.346 W at a pressure of 1 bar (with air working fluid) and a working frequency of 15.9 Hz. It should be noted that the method presented in this article can be used for other types of thermoacoustic Stirling engines. Moreover, the selection of design parameters for the presented method will depend on the physics of the engine and the available facilities.

Enhancing Integer Time Series Model Estimations through Neural Network-Based Fuzzy Time Series Analysis

This investigation explores the effects of applying fuzzy time series (FTSs) based on neural network models for estimating a variety of spectral functions in integer time series models. The focus is particularly on the skew integer autoregressive of order one (NSINAR(1)) model. To support this estimation, a dataset consisting of NSINAR(1) realizations with a sample size of n = 1000 is created. These input values are then subjected to fuzzification via fuzzy logic. The prowess of artificial neural networks in pinpointing fuzzy relationships is harnessed to improve prediction accuracy by generating output values. The study meticulously analyzes the enhancement in smoothing of spectral function estimators for NSINAR(1) by utilizing both input and output values. The effectiveness of the output value estimates is evaluated by comparing them to input value estimates using a mean-squared error (MSE) analysis, which shows how much better the output value estimates perform.

Numerical investigation of a fractional order Wolbachia invasive model using stochastic Bayesian neural network

The major goal of this research study is to solve the fractional order Wolbachia invasive model (FWIM) by developing a computational framework based on the Bayesian regularization backpropagation neural network (BRB-NN) approach. The population of mosquitoes is categorized into two classes, Wolbachia-infected mosquitoes and Wolbachia-uninfected mosquitoes. We also incorporate incomplete cytoplasmic incompatibility and imperfect maternal transmission. We investigate the effects of the fractional order derivative (α) and reproduction rate of Wolbachia-infected mosquitoes ϕw on the dynamics of mosquitoes. The proposed Bayesian regularization backpropagation scheme is applied to three distinct cases using 80% and 20% of the created dataset for training and testing, respectively, with 15 hidden neurons. Comparisons of the results are presented to verify the validity of the proposed technique for solving the model. The Bayesian regularization approach is used to lower the mean square error (MSE) for the fractional order Wolbachia invasive model. The achieved results are based on MSE, correlation, state transitions, error histograms, and regression analysis to confirm the effectiveness of the suggested approach. Additionally, the absolute error value modifies the designed approach’s accuracy.

ANN model for magnetised Casson fluid flow under the influence of thermal radiation and temperature stratification: Comparative analysis

AbstractThe article compares the performance of multi‐layer back‐propagated neural networks using the Levenberg–Marquardt (LMS) method and Bayesian Regularization Scheme (BRS) for analysing heat transfer in magnetized Casson fluid over flat and cylindrical surfaces. Factors like mixed convection, Joule heating, thermal radiation and temperature stratification are considered. Both LMS and BRS prove effective in handling complex interactions in numerical studies. Non‐linear ODE systems are solved using a shooting technique to obtain Nusselt number datasets, which are then divided for training, testing and validation purposes. The accuracy of the artificial neural network (ANN) results is confirmed by the agreement between predicted and target Nusselt numbers. Analysis of mean square error (MSE), regression fitness and error histogram further validates ANN adeptness. Furthermore, heat transfer rate is increasing for the Casson parameter, Grashof number and radiation parameter, while, it declines for stratification parameter, Prandtl and Eckert number. The study explores the impact of various parameters on velocity and temperature profiles, revealing that ANN provides accurate Nusselt number results for both flat and cylindrical surfaces. The research contributes a novel perspective to understanding ANN behaviour in heat transfer analysis, particularly for magnetized Casson fluid flow over two stretching surfaces.

An introduction to double stain normalization technique for brain tumour histopathological images

Stain normalization is an image pre-processing method extensively used to standardize multiple variances of staining intensity in histopathology image analysis. Staining variations may occur for several reasons, such as unstandardized protocols while preparing the specimens, using dyes from different manufacturers, and varying parameters set while capturing the digital images. In this study, a double stain normalization technique based on immunohistochemical staining is developed to improve the performance of the conventional Reinhard’s algorithm. The proposed approach began with preparing a target image by applying the contrast-limited adaptive histogram equalization (CLAHE) technique to the targeted cells. Later, the colour distribution of the input image will be matched to the colour distribution of the target image through the linear transformation process. In this study, the power-law transformation was applied to address the over-enhancement and contrast degradation issues in the conventional method. Five quality metrics comprised of entropy, tenengrad criterion (TEN), mean square error (MSE), structural similarity index (SSIM) and correlation coefficient were used to measure the performance of the proposed system. The experimental results demonstrate that the proposed method outperformed all conventional techniques. The proposed method achieved the highest average values of 5.59, 3854.11 and 94.65 for entropy, TEN, and MSE analyses.

An experimental and numerical study on an innovative metastructure for 3D printed thermoplastic polyurethane with auxetic performance

AbstractMetamaterials are specifically designed materials that possess unique properties that cannot be found in naturally occurring substances. These remarkable materials have the capability to bring about a significant transformation across a wide range of industries. Auxetic structures are a recent area of research possess a distinctive characteristic known as a negative Poisson's ratio. Unlike conventional materials that contract when stretched, auxetic structures actually expand in two dimensions. In this study, a new auxetic structure was introduced, and thermoplastic polyurethane samples were 3D printed using a fused filament fabrication method. The samples are then subjected to strains ranging from 5% to 50% and Poisson's ratios are measured both experimentally and numerically using finite element method in Ansys software. By comparing the results of the experimental research and simulation, it is evident that applying strains within this range causes the Poisson's ratio of the samples to change from −0.81 to −0.14 and it showed that the newly introduced structure is auxetic. According to the analysis of root mean square error, the hexagonal mesh with a size of 0.7 mm consistently produced the most accurate results, aligning closely with the experimental sample. Given that this is an entirely novel auxetic structure within the category of arrow‐head auxetic structures, there is potential for future research to be conducted in order to further develop and enhance this model.

Wavelet structuring element-based morphological filtering method in wire rope inspection signal denoising

Aiming at the multi-source interference signals in wire rope inspection, while common morphological filtering methods with traditional structuring elements are hard to distinguish, a new wavelet structuring element-based one-dimensional (1D) generalized morphological filtering method is proposed. First, principles and related theories of the generalized morphological filter are introduced and then the new wavelet structuring elements are analyzed. Thereafter, simulation and comparison regarding common structuring element morphological filter and the new wavelet function-based models are conducted through signal-to-noise ratio (SNR) and mean square error (MSE) analysis. Meanwhile, the influence of different noises and main structuring element parameters of length L, amplitude H to the signal processing results are revealed. Finally, experiments for different wire rope defects inspection by magnetic flux leakage testing are conducted, and characterizations of the wavelet structuring element-based morphological filtering methods are presented and compared through six case studies. Besides, the superior performance of the wavelet structuring morphological gradient models are compared and validated by short-time Fourier transform, SNR, MSE analysis, and quantitative defect recognition. The comparison results show that db4 and sym4 wavelet structuring elements-based 1D morphological filter features the highest wire rope defect detection and signal recognition accuracy under the gradient operation, which demonstrates the feasibility and effectiveness of the proposed methods. Additionally, advantages and disadvantages of the new models are summarized and discussed.

Estimated Sulfur Dioxide Pollutant Concentrations In Medan City Using Ordinary Kriging and Inverse Distance Weighting Approaches

Sulfur dioxide (SO2) pollution is a serious problem that negatively affects air quality and human health. So2 is generated by various human activities, especially the combustion of fossil fuels, as well as from natural sources such as volcanic eruptions. The emission of SO2 in urban areas, including Medan, Indonesia, has raised concerns as it is associated with respiratory diseases and the formation of acid rain. This research aimed to estimate comparative SO2 concentrations in Medan City using geostatistical methods, specifically ordinary kriging and inverse distance weighted (IDW). Air quality monitoring data from the Dinas Lingkungan Hidup Kota Medan were collected during a certain period. The collected data were analyzed and then interpolated using ordinary kriging and IDW methods. Furthermore, the Ordinary Kriging method involves testing the OK assumption, calculation of the experimental semivariogram, calculation of the theoretical semivariogram, structural analysis, and calculation of Root Mean Square Error (RMSE). Meanwhile, the Inverse Distance Weighted method involves calculating the Euclidean distance, determining the weights based on the power parameter, calculating the RMSE value, and estimating the SO2 concentration. The comparison results show that the OK method is more accurate in determining SO2 concentration compared to the IDW method in Medan City. In the estimation of sulfur dioxide (SO2) concentration, the OK method used the best theoretical semivariogram model, namely the exponential model, and in the estimation process of the IDW method, the power parameter 1 was used.

A fluorescence-based multivariate method for biodiesel quantification in undiluted diesel-biodiesel blends without sample preparation

In this work, excitation-emission matrices (EEMs) were used in association with parallel factor analysis (PARAFAC) to assess biodiesel content in undiluted diesel-biodiesel blends (DBBs) without pre-sample preparation. EEMs were decomposed using the PARAFAC (EEMs-PARAFAC), and the loading values of the PARAFAC component as a function of biodiesel content in the blends were used to build an analytical model to quantify the biodiesel content in DBBs. The proposed model presenting a limit of detection (LOD) and a limit of quantification (LOQ) of 2.5% and 11% w/w, respectively, successfully predicted the biodiesel content in the validation samples. The robustness of the model was confirmed by a close analysis of the root mean square error of prediction, standard error of prediction, relative standard deviation of prediction, and Bias. Therefore, an accurate and robust analytical model based on EEMs-PARAFAC was developed to quantify the biodiesel content in undiluted DBBs without sample preparation.

Demand Forecasting and Budget Planning for Automotive Supply Chain

Over the past 20 years, there have been significant changes in the supply chain business. One of the most significant changes has been the development of supply chain management systems. It is now essential to use cutting-edge technologies to maintain competitiveness in a highly dynamic environment. Restocking inventories is one of a supplier’s main survival strategies and knowing what expenses to expect in the next month aids in better decision-making. This study aims to solve the three most common industry problems in Supply Chain – Inventory Management, Budget Fore-casting, and Cost vs Benefit of every supplier. The selection of the best forecasting model is still a major problem in much research in literature. In this context, this article aims to compare the performances of Auto-Regressive Integrated Moving Average (ARIMA), Holt-Winters (HW), and Long Short-Term Memory (LSTM) models for the prediction of a time series formed by the dataset of Supply Chain products. As performance measures, metric analysis of the Root Mean Square Error (RMSE) is used. The main concentration is on the Automotive Business Unit with the top 3 products under this segment and the country United States being in focus. All three models, ARIMA, HW, and LSTM obtained better results regarding the performance metrics.

Improving Linear Interpolation of Missing Hydrological Data by Applying Integrated Autoregressive Models

The application of linear interpolation for handling missing hydrological data is unequivocal. On one hand, such an approach offers good reconstruction in the vicinity of last observation before a no-data gap and first measurement after the gap. On the other hand, it omits irregular variability of hydrological data. Such an irregularity can be described by time series models, such as for instance the autoregressive integrated moving average (ARIMA) model. Herein, we propose a method which combines linear interpolation with autoregressive integrated model (ARI, i.e. ARIMA without a moving average part), named LinAR (available at GitHub), as a tool for inputing hydrological data. Linear interpolation is combined with the ARI model through linear scaling the ARI-based prediction issued for the no-data gap. Such an approach contributes to the current state of art in gap-filling methods since it removes artificial jumps between last stochastic prediction and first known observation after the gap, also introducing some irregular variability in the first part of the no-data gap. The LinAR method is applied and evaluated on hourly water level data collected between 2016 and 2021 (52,608 hourly steps) from 28 gauges strategically located within the Odra/Oder River basin in southwestern and western Poland. The data was sourced from Institute of Meteorology and Water Management (Poland). Evaluating the performance with over 100 million assessments in the validation experiment, the study demonstrates that the LinAR approach outperforms the purely linear method, especially for short no-data gaps (up to 12 hourly steps) and for rivers of considerable size. Based on rigorous statistical analysis of root mean square error (RMSE) – expressed (1) absolutely, (2) as percentages and (3) using RMSE error bars – the percentage improvement, understood as percentage difference between RMSE of linear and LinAR interpolations, was found to reach up to 10%.

Comparesion the electrical parameters of photovoltaic cell using numerical methods

For a research problem: as a single-diode model (electrical circuit) is difficult to discover the precise answer to employing analytical approaches, develop and compute the electrical parameters of the PV cell roughly using numerical algorithms. Therefore, the goal of this work is to create an algorithm that aids in the approximate solution of the electrical parameters of solar cells. Three methods have been proposed for these calculations, each of which has a quicker calculation time and a higher level of accuracy.
 By streamlining the calculation process, the proposed method solves the problems of complexity and precision. The I-V and P-V characteristic curves of solar cells can then be utilized to compare the efficacy of the tested methods. In addition, the analysis of root mean square error indicates that the proposed method is more applicable than alternative methods. In fact, this extraction procedure can be regarded as an efficient and precise method for estimating the single diode model parameters of solar cells.
 The results indicate that this precise and effective strategy can play an important role in the retrieval of single diode model parameters. In fact, the method proposed in this paper makes numerically implementing parameter models in technology simpler. In addition, it provides an optimization suggestion for the production of solar cells

Comparative Analysis of Eight Numerical Methods Using Weibull Distribution to Estimate Wind Power Density for Coastal Areas in Pakistan

Currently, Pakistan is facing severe energy crises and global warming effects. Hence, there is an urgent need to utilize renewable energy generation. In this context, Pakistan possesses massive wind energy potential across the coastal areas. This paper investigates and numerically analyzes coastal areas’ wind power density potential. Eight different state-of-the-art numerical methods, namely an (a) empirical method, (b) graphical method, (c) wasp algorithm, (d) energy pattern method, (e) moment method, (f) maximum likelihood method, (g) energy trend method, and (h) least-squares regression method, were analyzed to calculate Weibull parameters. We computed Weibull shape parameters (WSP) and Weibull scale parameters (WCP) for four regions: Jiwani, Gwadar, Pasni, and Ormara in Pakistan. These Weibull parameters from the above-mentioned numerical methods were analyzed and compared to find an optimal numerical method for the coastal areas of Pakistan. Further, the following statistical indicators were used to compare the efficiency of the above numerical methods: (i) analysis of variance (R2), (ii) chi-square (X2), and (iii) root mean square error (RMSE). The performance validation showed that the energy trend and graphical method provided weak performance for the observed period for four coastal regions of Pakistan. Further, we observed that Ormara is the best and Jiwani is the worst area for wind power generation using comparative analyses for actual and estimated data of wind power density from four regions of Pakistan.

A predictive neuro-computing approach for micro-polar nanofluid flow along rotating disk in the presence of magnetic field and partial slip

<abstract> <p>The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation.</p> </abstract>

Packet Loss Characterization Using Cross Layer Information and HMM for Wi-Fi Networks.

Packet loss is a major problem for wireless networks and has significant effects on the perceived quality of many internet services. Packet loss models are used to understand the behavior of packet losses caused by several reasons, e.g., interferences, coexistence, fading, collisions, and insufficient/excessive memory buffers. Among these, the Gilbert-Elliot (GE) model, based on a two-state Markov chain, is the most used model in communication networks. However, research has proven that the GE model is inadequate to represent the real behavior of packet losses in Wi-Fi networks. In this last category, variables of a single network layer are used, usually the physical one. In this article, we propose a new packet loss model for Wi-Fi that simultaneously considers the temporal behavior of losses and the variables that describe the state of the network. In addition, the model uses two important variables, the signal-to-noise ratio and the network occupation, which none of the packet loss models available for Wi-Fi networks simultaneously take into account. The proposed model uses the well-known Hidden Markov Model (HMM), which facilitates training and forecasting. At each state of HMM, the burst-length of losses is characterized using probability distributions. The model was evaluated by comparing computer simulation and real data samples for validation, and using the log-log complementary distribution of burst-length. We compared the proposed model with competing models through the analysis of mean square error (MSE) using a validation sample collected from a real network. Results demonstrated that the proposed model outperforms the currently available models for packet loss in Wi-Fi networks.

A design of predictive computational network for the analysis of fractional epidemical predictor-prey model

Studying the dynamical system that represents the transmission of an outbreak from prey to predatory is crucial and significant because the results may be used to highlight a variety of real-world issues. Infections and predator-prey interplay have been linked to provide a complicated cumulative influence as regulators of prey and predator size range in predator-prey ecology. This paper presents a novel implementation of intelligent computation to analyze the dynamics of a fractional epidemiological model with disease infection in both the population (FEM-DIBP) using supervised machine learning (SMLs) optimized with the Bayesian Regularization methodology (BRM). The FOLotkaVoltera solver based on Grunwald-Letnikov is used to build the dataset for the FEM-DIBP for observation approach of the SML model of the system. Also state variables trajectories and Lorenz curves are constructed using FOLorenz to analyze the dynamics of the epidemical model. The BRM learned SMLs models are used in the train, test, and validating procedures to find the FEM-DIBP solutions to various situations depending on changing epidemical factors. The effectiveness of SML in solving FEMDIBP is demonstrated by estimated regression measurements, error histogram visualizations, and mean-squared error analyses. The suitability of the created BRMNNs for such a simulated situation is demonstrated by the most appealing mathematical findings for A.E within the range of 10−2 to 10−6.

Image recognition by FFT, artificial intelligence and k-nearest neighbors approach

This paper presents procedures of processing and recognition of color images by means of artificial intelligence and computer aided training. Two stages of processing have been applied with regard to extraction of features. Processing involves conversion of RGB images in grayscale and binary; and conversion of RGB, grayscale and binary into index formats. Spectral analysis is also applied in here with Fourier’s algorithm for fast conversion concerning indicated graphic formats and segmentation of the real and imaginary complex parts. Activities related with training, assessment and synthesis of feed-forward neural networks and probabilistic neural networks, based on Accuracy and Mean-Squared Error analysis. Special emphasis is made on a method for computer aided training k-nearest neighbors with Euclidean, Euclidean squared, Cityblock and Chebychev metric distances in relation to Cross-validation accuracy value. Some positive indications have been achieved in recognition of assigned graphic images by means of the employed mathematical apparatus.

Up-to-Date Optimization of the 90Y-PET/CT Reconstruction Protocol for Volumetric Quantification in Trans-Arterial RadioEmbolization (TARE) Procedures in the Era of Theranostics

(1) Background: New generation of PET-CT scanners allows performing volumetric dosimetry based on 90Y-activity distribution. The aim of this study was to perform an up-to-date evaluation of the optimal 90Y-PET-CT reconstruction parameters for a Siemens Biograph mCT scanner. (2) Methods: A cylindrical uniform phantom (P1), IEC NEMA Body-phantom (P2) and IEC NEMA Torso-phantom (P3) filled with 90Y were acquired. The matrix size and number of Equivalent Iterations (E.I.) were evaluated through the Recovery Coefficient (RC) and the Coefficient of Variation (CoV). The optimal post-reconstruction Gaussian Filter (GF) was assessed through an analysis of Root Mean Square Error (RMSE) and Full Width at Half Maximum (FWHM) in DVHs. (3) Results: For P1, RC values showed constant trends varying the matrix size (slope m = 1.25 × 10−3) or E.I. (slope m = −2.16 × 10−4). For P2, CoV decreased increasing the matrix size and it grew increasing the E.I. For P3, RMSE and mean dose values showed constant trends varying the Gaussian filter (slope m = 1.51 × 10−2) while FWHM decreased increasing filter. For smaller volumes, RMSE grew increasing the filter (from 34% to 74%) and the use of larger filters resulted in a dose underestimation (from 172 to 133 Gy). (4) Conclusions: The optimal reconstruction parameters for the Siemens Biograph mCT PET/CT scanner are presented, combining old metrics with new ones involving a dosimetric approach.

High-Resolution Direction of Arrival Estimation of Underwater Multitargets Using Swarming Intelligence of Flower Pollination Heuristics

Developing the parameter estimation, particularly direction of arrival (DOA), utilizing the swarming intelligence-based flower pollination algorithm (FPA) is considered an optimistic solution. Therefore, in this paper, the features of FPA are applied for viable DOA in the case of several robust underwater scenarios. Moreover, acoustic waves impinging from the far-field multitarget are evaluated using the different number of hydrophones of uniform linear array (ULA). The measuring parameters like robustness against noise and element quantity, estimation accuracy, computation complexity, various numbers of hydrophones, variability analysis, frequency distribution and cumulative distribution function of root mean square error (RMSE), and resolution ability are applied for analyzing the performance of the proposed model with additive white Gaussian noise (AWGN). For this purpose, particle swarm optimization (PSO), minimum variance distortion-less response (MVDR), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance technique (ESPRIT) standard counterparts are employed along with Crammer–Rao bound (CRB) to improve the worth of the proposed setup further. The proposed scheme for estimating the DOA generates efficient outcomes compared to the state-of-the-art algorithms over the Monte Carlo simulations.