Mean Square Error Research Articles

Sky Images based Photovoltaic Power Forecasting: A Novel Approach with Optimized VMD and Vision Mamba

As the global demand for sustainable energy sources continues to grow, accurate prediction of photovoltaic power generation is crucial for optimizing the utilization of solar resources and enhancing the efficiency of photovoltaic systems. To improve the accuracy of photovoltaic power forecasting, this paper proposes a novel hybrid predictive model that integrates Optimized Variational Mode Decomposition (VMD), Vision Mamba (Vim) for extracting features from sky images, and advanced mechanisms like Patch Embedding and Variate-wise Cross-Attention. Initially, the proposed model employs SAO-optimized VMD to decompose the photovoltaic power series into high, medium, and low-frequency components. Subsequently, these components are patched to serve as input for the subsequent layers. In the third step, exogenous variables, including meteorological and image data, are introduced and processed through Variate Embedding combined with cross-attention mechanisms to capture the intricate interactions between these variables. Finally, by integrating the outputs from all processing steps through normalization and feed-forward layers, the final predictive results are produced. Experimental evaluations across different seasons demonstrate significant enhancements in forecasting accuracy, with the model achieving Root Mean Square Error (RMSE) values of 0.3587 in spring, 0.4376 in summer, 0.3544 in autumn, and 0.3493 in winter. Similarly, Mean Absolute Error (MAE) and Mean Squared Error (MSE) across these seasons underscore the model's effectiveness. This model offers new technical means for photovoltaic power forecasting and provides valuable decision support for the optimization and management of photovoltaic power systems.

Machine Learning and Taguchi Techniques for Predicting Wear Mechanisms of Ni-Cu Alloy Composites

Nickel-Copper alloys hybrid composite was formed in an induction furnace set up on a sand substrate. With different percentages of Al2O3 (3, 6, 9 and 12 wt.%) and TiO2 (constant 9wt.%) reinforcements, the goal is to examine the wear behavior and friction coefficient of Ni-TiO2-Al2O3. The factors considered for the wear analysis were sliding distance (1500, 1000, and 500 m), applied load (25, 50, and 75 N), and sliding velocity (1.46, 2.93, and 4.39 m/sec). The pin-on-disc equipment is utilized to perform different wear tests are carried out using in accordance with the Taguchi L27 orthogonal array. The machine learning used to correlate between actual and anticipated values for both metrics is strong, with a reasonable error margin. The Mean Squared Error (MSE) for the wear rate was 0.1025 (10.25%) in the Linear Regression model and 0.2390 (23.89%) in the Random Forest model. Regression analysis determined the impact of several parameters on wear rate, whilst machine learning approaches expanded the evaluation of wear rate and coefficient of friction beyond experimental data. The findings demonstrate the effectiveness of combining Taguchi methods with machine learning to accurately anticipate wear mechanisms in Ni-Cu alloy composites.

Pulp grade monitoring using binocular image through multi-scale feature cross-attention fusion network and saliency map constraint

Pulp grade is an important indicator for performance monitoring in froth flotation process. Previous studies have shown that the pulp grade can be predicted more accurately by using the stereo vision information of froth images. However, due to the low intra-class variation among froth images under the identical working conditions and the similarity in shape and texture among bubbles, it is challenging for current binocular image-based methods for grade prediction. Therefore, to accurately predict the key performance indicators in flotation process, a prediction model based on binocular image fusion is proposed in this paper. First, a calculation method of froth image saliency map is proposed, and the saliency map is used as a priori knowledge to guide the prediction model to learn the characteristics of the region of interest in the image. This measure aims to solve the problem of difficulty in grade prediction caused by low intra-class differences in froth images. Then, a multi-scale feature cross-attention fusion network is introduced, wherein the multi-scale features of the left and right views serve as attention mechanism gating signals to extract common feature from binocular image. After that, a pulp grade prediction model is developed based on Video Transformer Network. The results on actual industrial flotation datasets show that, compared with other pulp grade prediction methods, our proposed approach reduces the mean absolute error and root mean square error by 22.84% and 23.55%, respectively.

Beamforming-integrated neural networks for ultrasound imaging

Sparse matrix beamforming (SMB) is a computationally efficient reformulation of delay-and-sum (DAS) beamforming as a single sparse matrix multiplication. This reformulation can potentially dovetail with machine learning platforms like TensorFlow and PyTorch that already support sparse matrix operations. In this work, using SMB principles, we present the development of beamforming-integrated neural networks (BINNs) that can rationally infer ultrasound images directly from pre-beamforming channel-domain radiofrequency (RF) datasets. To demonstrate feasibility, a toy BINN was first designed with two 2D-convolution layers that were respectively placed both before and after an SMB layer. This toy BINN correctly updated kernel weights in all convolution layers, demonstrating efficiency in both training (PyTorch – 133 ms, TensorFlow – 22 ms) and inference (PyTorch – 4 ms, TensorFlow – 5 ms). As an application demonstration, another BINN with two RF-domain convolution layers, an SMB layer, and three image-domain convolution layers was designed to infer high-quality B-mode images in vivo from single-shot plane-wave channel RF data. When trained using 31-angle compounded plane wave images (3000 frames from 22 human volunteers), this BINN showed mean-square logarithmic error improvements of 21.3 % and 431 % in the inferred B-mode image quality respectively comparing to an image-to-image convolutional neural network (CNN) and an RF-to-image CNN with the same number of layers and learnable parameters (3,777). Overall, by including an SMB layer to adopt prior knowledge of DAS beamforming, BINN shows potential as a new type of informed machine learning framework for ultrasound imaging.

Short term load forecasting analysis using machine learning method: An SVM based study

Short-Term Load Forecasting (STLF) is crucial for effective energy management, enabling utilities to optimize electricity generation, distribution, and pricing strategies. This study explores the application of three machine learning models—Linear Regression (LR), Artificial Neural Networks (ANN), and Support Vector Machines (SVM)—to predict short-term electrical load demand. Each model was trained using historical load data enriched with temporal features to capture daily, seasonal, and other variations in electricity consumption. The SVM model demonstrated strong predictive capability, achieving a Mean Absolute Error (MAE) of 1887.41 MW, Mean Squared Error (MSE) of 6942.36 GW, Root Mean Squared Error (RMSE) of 2634.83 MW, and an R2 score of 91.95%. In comparison, the ANN model showed slightly higher errors, while the LR model had the highest error rates, indicating its limitations in capturing non-linear relationships. The results suggest that SVM and ANN models are more effective than LR for STLF due to their ability to handle non-linear dependencies and high-dimensional data. This study highlights the potential of machine learning techniques in enhancing the accuracy and reliability of load forecasting, ultimately supporting better decision-making in energy management.

An artificial neural network approach to characterizing the behavior of bioconvective nanofluid model using backpropagation of Levenberg–Marquardt algorithm

The study of the behavior of bioconvective nanofluid model (BC-NFM) was explored using bioconvection properties in the computational analysis of magnetized nanofluid flow that was convectively heated, which is critical for applications in energy systems and biomedical devices. We implemented a backpropagated Levenberg–Marquardt neural network approach (BLMNNA) to enhance the analysis and prediction accuracy of such fluid flows. Using the Adams numerical technique, we generated a comprehensive dataset for eight distinct scenarios by variation of thermophoresis parameter, Rayleigh number, Deborah parameter, Hartman number, Prandtl number, bioconvection Lewis number, and Schmidt number to train and test our model. The results demonstrate significant improvements in prediction accuracy and computational efficiency compared to traditional numerical solvers. The steps of training, testing, and validating the developed BLMNNA are used to get the desired numerical solutions of BC-NFM for various instances. The worth and accuracy of the stochastic numerical solutions of BC-NFM are established and authenticated by the outputs of the designed methodology BLMNNA through Adaptation graphs of Mean Square Error, regression studies, plots of error histogram and index of state transition. Excellent measurements of performance in terms of MEAN SQUARE ERROR are achieved at level 9.76E[Formula: see text], 1.41E[Formula: see text], 1.79E[Formula: see text], 1.22E[Formula: see text], 8.49E[Formula: see text], 7.19E[Formula: see text], 9.72E[Formula: see text], and 9.35E[Formula: see text] against 69, 73, 96, 76, 237, 86, 120, and 33 epochs. The significant connection between the proposed and reference findings demonstrates the validity of the BLMNNA based on error analysis, which ranges from E[Formula: see text] to E[Formula: see text] for all situations. The results show that the proposed neural network approach achieves a high level of accuracy, closely matching the outcomes obtained from the numerical solver. The method provides an efficient and precise solution for the analysis of complex fluid flow problems, representing a significant advancement over traditional numerical techniques.

Comparing MLR and ANN models for school building electrical energy prediction in Osijek-Baranja County in Croatia

This paper presents a study conducted in Osijek-Baranja County, Croatia, to predict electrical energy consumption in school buildings. Data from the Energy Management Information System (EMIS) database for primary and secondary schools were analyzed using Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN). The ANN model achieved a high R² of 0957 in the training set, with lower Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) than the MLR model, which had an R² of 0950. On the validation set, the ANN model maintained an R² of 0954 and showed slightly better performance with a lower Coefficient of Variation of RMSE (CVRMSE) of 19,79 %, compared to the MLR model’s CVRMSE of 20,50 %. These results indicate that the ANN model generally provides more accurate and reliable predictions for energy consumption in school buildings. However, both models provided a robust positive correlation between the predicted and actual values.

A robust audio steganography technique based on image encryption using different chaotic maps

The development of innovative methods for concealing critical data in multimedia files has exploded in information security in recent years. Cryptography and steganography cannot be used alone to protect data; rather, they can be combined and used in a single system. Audio steganography is among the most important information security techniques. It involves the concealment of information within audio signals to achieve covert communication. This paper introduces a comprehensive technique that integrates chaos Henon, Baker, and Arnold maps for image encryption with audio steganography to create a robust and secure audio steganography technique. First, the target image is encrypted using chaotic maps. Then, it is embeded within the high frequencies of the cover audio signal based on the Inverse Short Time Fourier Transform (ISTFT) to be transmitted to the destination through the channel. By integrating both encryption and concealment techniques, the cover audio signal quality can be preserved. Moreover, the hidden image security and robustness are improved, making the technique resistant to many types of attacks. The simulation results confirm that the suggested technique is robust in the presence of attacks. It achieves a distinct perceptual quality with an appreciated peak signal-to-noise ratio (PSNR) of 91.2 dB and a Mean Square Error (MSE) of 7.5 × 10–10. The randomness of the resulting encrypted image has successfully passed the National Institute of Standards and Technology (NIST) statistical test suite.

Deep Learning for Water Quality Prediction—A Case Study of the Huangyang Reservoir

Water quality prediction is a fundamental prerequisite for effective water resource management and pollution prevention. Accurate predictions of water quality information can provide essential technical support and strategic planning for the protection of water resources. This study aims to enhance the accuracy of water quality prediction, considering the temporal characteristics, variability, and complex nature of water quality data. We utilized the LTSF-Linear model to predict water quality at the Huangyang Reservoir. Comparative analysis with three other models (ARIMA, LSTM, and Informer) revealed that the Linear model outperforms them, achieving reductions of 8.55% and 10.51% in mean square error (MSE) and mean absolute error (MAE), respectively. This research introduces a novel method and framework for predicting hydrological parameters relevant to water quality in the Huangyang Reservoir. These findings offer a valuable new approach and reference for enhancing the intelligent and sustainable management of the reservoir.

Adaptive location and scale estimation with kernel-weighted averages

A wide variety of location and scale estimators have been developed for light-tailed distributions. Despite indisputable importance in business, finance, cybersecurity, etc., statistical estimation and inference in the presence of heavy tails have received less attention in the literature. We adopt the Kernel-Weighted Average (KWA) approach to location and scale estimation and present a set of extensive comparisons with five prominent competitors. Unlike nonparametric kernel density estimation, the optimally tuned bandwidth for KWA estimators does not necessarily converge to zero as sample size grows. We also perform a large-scale Monte Carlo simulation to search for the optimal bandwidth that minimizes the mean squared error (MSE) of KWA location and scale estimators with simulated samples from Student’s t-distribution with degrees of freedom (df) 1 , 2 , … , 30 . We further develop an adaptive technique to estimate the df that best match the observed samples using Cramér-von Mises test of goodness-of-fit. Unlike many existing methodologies, our approach is data-driven and exhibits excellent statistical performance. To illustrate this, we apply it to three real-world financial datasets containing daily closing prices of AMC Entertainment (AMC), GameStop (GME) and Meta Platforms (META) stocks to calibrate a geometric random walk model with Student’s t log-increments.

Prediction of Potato Volume by Neural Network Regression Model

Potatoes are essential for meeting the world's dietary requirements due to their high concentration of carbohydrates, vitamins, and minerals. Potato production is plentiful worldwide, but postharvest processing losses have reduced potato quality. Potatoes can be graded manually, which is time-consuming and labor-intensive. In this study, a neural network regression model was developed to predict the volume of potatoes using 2D images, which can be used as a parameter for grading potatoes automatically. The image processing method was used to extract features like the major axis, minor axis, and roundness of 400 potato samples, and each potato's volume was thoroughly measured using the water displacement method, and a dataset was generated. These attributes were used to create the neural network regression model and predict the volume. The results revealed that the mean squared error (MSE) was 83.93, the root mean squared error (RMSE) was 9.16, and R2 was approximately 0.882. The potatoes were categorized into three groups: small, medium, and large, based on their size. The utilized model demonstrated an overall accuracy rate of 91.4%. Specifically, it achieved 90% and 85% accuracy for small-sized and medium-sized potatoes, respectively, whereas the model displayed a decrease in accuracy from 60% to 70% for large-sized potatoes. To summarize, the suggested neural network regression model provided an efficient approach to volume prediction using 2D images to improve the grading process of agricultural products.

Time series forecasting using transformer neural network

Time series forecasting is a vital component of data science, giving essential insights that help decision-makers to predict future trends across a number of sectors. This paper focuses on projecting complicated stock market price dynamics, weather data variations, and hourly traffic occupancy rates. The Informer-Based Time Series Forecasting (IBTSF) model, which employs a transformer-based architecture to capture long-term relationships and give probabilistic predictions, is proposed.This model is assessed against Long Short-Term Memory (LSTM), Temporal Convolutional Network (TCN) and Gated Recurrent Unit (GRU) model to benchmark its performance. Simulation findings demonstrate that the IBTSF model considerably outperforms other models across all datasets. For traffic data, the IBTSF model achieves a Mean Squared Error (MSE) of 10.1 and a Mean Absolute Scaled Error (MASE) of 1.69, compared to other model's larger mistakes. In stock data forecasting, the IBTSF model reports an MSE of 8.04 and a MASE of 1.53, again outperforming other models. Similarly, using meteorological data, the IBTSF model obtains an MSE of 86.12 and a MASE of 0.7, whereas other models fall short. These results underline the IBTSF model's resilience and accuracy in capturing subtle patterns and relationships within time series data, giving precise insights that benefit decision-making processes.

Development and validation of claims-based algorithms for estimating gestational age of spontaneous abortion and termination.

To study the risk of spontaneous abortion (SAB) or termination using healthcare utilization databases, algorithms to estimate the gestational age (GA) are needed. Using Medicaid data, we developed a hierarchical algorithm to classify pregnancy outcomes. We identified the subset of potential SAB and termination cases, and abstracted the GA from linked electronic medical records (gold standard). We developed three approaches: (1) assign median GA for SAB and termination cases in the US; (2) draw a random GA from the population distributions; (3) estimate GA based on regression models. Algorithm performance was assessed based on the proportion of pregnancies with estimated GA within 1-4 weeks of the gold standard, the mean squared error (MSE) and the R-squared. Approach 1 and Approach 3 had similar performance, though approach 3 using random forest models with variables selected via the Boruta algorithm had better MSE and R-squared. For SAB, 58.0% of pregnancies were correctly classified within 2 weeks of the gold standard (MSE: 8.7, R-squared: 0.09). For termination, the proportions were 66.3% (MSE: 11.7; R-squared: 0.35). SABs and terminations can be studied in healthcare utilization data with careful implementation of validated algorithms though higher level of GA misclassification is expected compared to live births.

Research on a 3D Point Cloud Map Learning Algorithm Based on Point Normal Constraints

Laser point clouds are commonly affected by Gaussian and Laplace noise, resulting in decreased accuracy in subsequent surface reconstruction and visualization processes. However, existing point cloud denoising algorithms often overlook the local consistency and density of the point cloud normal vector. A feature map learning algorithm which integrates point normal constraints, Dirichlet energy, and coupled orthogonality bias terms is proposed. Specifically, the Dirichlet energy is employed to penalize the difference between neighboring normal vectors and combined with a coupled orthogonality bias term to enhance the orthogonality between the normal vectors and the subsurface, thereby enhancing the accuracy and robustness of the learned denoising of the feature maps. Additionally, to mitigate the effect of mixing noise, a point cloud density function is introduced to rapidly capture local feature correlations. In experimental findings on the anchor public dataset, the proposed method reduces the average mean square error (MSE) by 0.005 and 0.054 compared to the MRPCA and NLD algorithms, respectively. Moreover, it improves the average signal-to-noise ratio (SNR) by 0.13 DB and 2.14 DB compared to MRPCA and AWLOP, respectively. The proposed algorithm enhances computational efficiency by 27% compared to the RSLDM method. It not only removes mixed noise but also preserves the local geometric features of the point cloud, further improving computational efficiency.

Vessel Trajectory Prediction Based on Automatic Identification System Data: Multi-Gated Attention Encoder Decoder Network

Utilizing time-series data from ship trajectories to forecast their subsequent movement is crucial for enhancing the safety within maritime traffic environments. The application of deep learning techniques, leveraging Automatic Identification System (AIS) data, has emerged as a pivotal area in maritime traffic studies. Within this domain, the precise forecasting of ship trajectories stands as a central challenge. In this study, we propose the multi-gated attention encoder decoder (MGAED) network, a model based on an encoder–decoder structure specialized for predicting ship trajectories in canals. The model employs a long short-term memory network (LSTM) as an encoder, combined with multiple Gated Recurrent Units (GRUs) and an attention mechanism for the decoder. Long-term dependencies in time-series data are captured through GRUs, while the attention mechanism is used to strengthen the model’s ability to capture key information, and a soft threshold residual structure is introduced to handle sparse features, thus enhancing the model’s generalization ability and robustness. The efficacy of our model is substantiated by an extensive evaluation against current deep learning benchmarks. Through comprehensive comparison experiments with existing deep learning methods, our model shows significant improvements in prediction accuracy, with an at least 9.63% reduction in the mean error (MAE) and an at least 20.0% reduction in the mean square error (MSE), providing a new solution to improve the accuracy and efficiency of ship trajectory prediction.

Application of multimodal learning in daylight provision and view quality assessment of residential building layouts

Optimizing the layout of residential buildings based on daylight performance and view quality is crucial to visual comfort and well-being of building occupants. Machine Learning (ML) methods offer valuable support for performance-based decision-making process at the early-stage building design. In this study, a novel workflow is introduced to integrate ML models into the architectural design process. With the designer’s input floor layout designs, the presented multimodal ML model predicts daylight provision and view quality, which are then translated into practical visual representations by a post-processing step. This approach allows input designs to be evaluated by the ML model, leading to enhanced design decisions while preserving the designer’s autonomy. Results for the best-performing model, implementing ResNet50 and a fully connected network, led to a Mean Square Error (MSE) of 0.0440 and 0.0478, and an R2 score of 0.7411 and 0.7815 for the daylight and view metrics, respectively. The results of the daylight and view predictive models are further interpreted according to different apartment categories and at various resolutions. These results indicate that the method could be viable for predicting daylight provision and view quality in early design tools, providing designers with faster feedback that supports informed decision-making during design iterations. Ultimately, the challenges of the study and further improvements are discussed.

Joint Model Parameter Identification and EKF Algorithm for the SOC Estimation of LFP Battery

Abstract Accurately estimating the state of charge (SOC) of batteries is crucial for achieving the safety and efficient driving of electric vehicles. To address the negative impact of voltage platform flatness and accumulated errors in current sampling, the SOC estimation method jointing model parameter identification and extended Kalman filter (EKF) algorithm is proposed and verified through simulation in this paper. Firstly, the parameter identification method is obtained based on the second-order dual polarization model, and effective identification of the parameters under different SOC is achieved using experimental conditions of hybrid pulse power characteristic and constant current discharge. On this basis, a function model with SOC as the independent variable and model parameters as the dependent variable is established by jointing model parameter identification and EKF algorithm, and the iterative estimation of SOC is achieved through the 1stopt and cftool methods. Finally, the SOC estimation accuracy of the proposed method is validated under three operating conditions that adopt the latest standards and are closer to the actual driving environment. The simulation results show that the SOC estimation method jointing model parameter identification and EKF algorithm has higher accuracy and smaller fluctuations than the traditional AH integration method, and the mean squared error (MSE) of estimation for the four test conditions are less than 0.29%, 0.72% and 0.25%, respectively.

Advanced controller design based on interval type-2 fuzzy neural network for elementary super-lift Luo converter

The elementary super-lift Luo converter is a third-order DC/DC step-up converter developed using the super-lift method that increases input voltage with low current and voltage ripples and a high voltage gain. On account of the nonlinearity and uncertainty incorporated with voltage, load changes, and switching operation of elementary super-lift Luo (ESLL) converter, it is a challenging task to design an efficient controller. To overcome these problems, this study proposes a new control approach based on interval type-2 fuzzy neural network (IT2FNN) to regulate a DC output current and voltage of ESLL converter. The parameters of IT2FNN were trained offline using a gradient descent algorithm. Mean square error (MSE), one of the most used statistical performance indicators, was used to evaluate the convergence accuracy performance of gradient descent algorithm. The DC output voltage regulation performance of IT2FNN was evaluated via a comparative simulation with interval type-2 fuzzy controller (IT2FC) and proportional + integral (PI) controller in MATLAB/Simulink environment in terms of settling time, average computational time, and recovery time under three different operational conditions: various reference voltages, input voltage, and load. Moreover, the DC output current regulation performance of IT2FNN was evaluated via a comparative simulation with IT2FC and PI controller in MATLAB/Simulink environment in terms of settling time and steady-state error under various reference current changes. The detailed simulation results obtained from comparative simulation validated the effectiveness of IT2FNN.

An Enhanced Symmetric Sand Cat Swarm Optimization with Multiple Strategies for Adaptive Infinite Impulse Response System Identification

An infinite impulse response (IIR) system might comprise a multimodal error surface and accurately discovering the appropriate filter parameters for system modeling remains complicated. The swarm intelligence algorithms facilitate the IIR filter’s parameters by exploring parameter domains and exploiting acceptable filter sets. This paper presents an enhanced symmetric sand cat swarm optimization with multiple strategies (MSSCSO) to achieve adaptive IIR system identification. The principal objective is to recognize the most appropriate regulating coefficients and to minimize the mean square error (MSE) between an unidentified system’s input and the IIR filter’s output. The MSSCSO with symmetric cooperative swarms integrates the ranking-based mutation operator, elite opposition-based learning strategy, and simplex method to capture supplementary advantages, disrupt regional extreme solutions, and identify the finest potential solutions. The MSSCSO not only receives extensive exploration and exploitation to refrain from precocious convergence and foster computational efficiency; it also endures robustness and reliability to facilitate demographic variability and elevate estimation precision. The experimental results manifest that the practicality and feasibility of the MSSCSO are superior to those of other methods in terms of convergence speed, calculation precision, detection efficiency, regulating coefficients, and MSE fitness value.

S2HConv-Caps-BiGRU: Deep Learning-Based Heterogeneous Face Recognition Model with Divergent Stages

Real-time images of faces captured in different spectrum bands are considered heterogeneous images. Heterogeneous Face Recognition (HFR) matches faces across domains and is crucial to public safety. This paper proposes an HFR approach based on Deep Neural Networks (DNN). Feature maps are extracted from two images, such as gallery and sketch images, using Squirrel Search Heterogeneous Convolutional-Capsule- Bidirectional Gated Recurrent Unit (S2HConv-Caps-BiGRU). As a method of efficiently recognizing faces, coupled representation similarity metric (CRSM) will use the measure for the similarity of two feature maps. The experimental results will be evaluated to state-of-the-art (SOTA) statistical measures in terms of accuracy, recall, Jaccard score, dice score, mean square error (MSE), image similarity, performance and root mean square error (RMSE). Compared to other SOTA, the model produces the best results. The accuracy value of a CUFS dataset is 98.7%.