Conventional Linear Regression Method Research Articles

Optimization method of parameters inverse identification for hot deformation constitutive model of 2Cr13 martensitic stainless steel using genetic algorithm

Constitutive models are considered a key prerequisite to investigate the thermal deformation behavior of materials. Accurate identification of their parameters is crucial for enhancing the predictive precision of the models. A novel optimization method for accurate inverse identification of parameters using the genetic algorithm (GA) in the Modified Zerilli-Armstrong (MZA) model was proposed in this work. Under conditions of temperatures ranging from 1223 K to 1473 K at intervals of 50 K and strain rates of 0.01, 0.1, 1, and 5 s−1, uniaxial isothermal hot compression tests were performed on 2Cr13 martensitic stainless steel (MSS) employing a Gleeble-1500D thermal simulation test machine. Based on the experimental data, the conventional linear regression method was utilized to solve the MZA model of 2Cr13 MSS. Initial values for the material constants I1, S1, C5, and C6 to be optimized were assigned drawing from the calculated results. The GA-based iteratively optimized MZA (G-ZA) model was established by minimizing the mean squared error as an objective function between the experimental and predicted flow stress values. Compared to the MZA model, a significant enhancement in predictive performance was achieved with the G-ZA model, while good generalization was also demonstrated. Both models were successfully integrated into the Forge® finite element analysis software through the secondary development of user subroutines. Numerical simulation results indicated that the G-ZA model demonstrated a better agreement with the experimental data in predicting the load-displacement curve. This validated that a more accurate constitutive model for the hot deformation of 2Cr13 MSS can be effectively constructed using the GA-based parameter inverse identification strategy.

Modeling the thermal transport properties of hydrogen and its mixtures with greenhouse gas impurities: A data-driven machine learning approach

This study introduces machine learning (ML) algorithms to predict hydrogen (H2) thermodynamic properties for geological storage, focusing on its mixtures with natural gas, nitrogen (N2), and carbon dioxide (CO2). Employing 1167 data samples, this research utilizes multiple linear regression (MLR), random forest (RF), gradient boosting (GB), and decision tree (DT) models, enhanced by sensitivity analysis for feature engineering. GB model's superior accuracy and efficiency over conventional statistical linear regression methods. The finding reveals that the GB model achieves superior performance, with an R2 value of 0.9998 for thermal capacity and the lowest mean absolute error (MAE)/root mean square error (RMSE) across all H2 properties—density (1.51%, 2.06 kg/m3), viscosity (0.000078%, 0.000117 cp), thermal conductivity (0.000427%, 0.000849 W/m.K), and thermal capacity (8.79%, 26.06 J/g.K). Moreover, this ML-based approach not only demonstrates remarkable accuracy and efficiency but also suggests the potential of smart paradigms to further enhance the safety and transportability of underground hydrogen storage projects. Ultimately, this work will help the reservoir simulation at field scale to be more robust and reliable.

Temperature analysis and prediction for road-rail steel truss cable-stayed bridges based on the structural health monitoring

A growing number of road-rail steel truss bridges have been built worldwide in recent years. Due to the complex cross-sectional structure and increasing span length, these main girders are prone to developing uneven temperature fields and significant local thermal effects, which can lead to excessive temperature stresses and structural damage. An accurate assessment of the temperature distribution in road-rail steel truss girders is critical as it aids in the thermal response analysis of the bridge and the structural safety evaluation. The paper analyses the temperature distribution of the road-rail steel truss girder base on the light conditions and the structure of the main girder. A modified method for calculating the effective temperature (ET) and temperature difference (TD) is also proposed. Comparing with the conventional regional weighted averaging method, the modified method improves the accuracy of ET calculation by 20 %. A prediction method based on the long short-term memory (LSTM) network is proposed, which estimates ET and TD for road-rail steel truss girders based on the environment around the bridge. The deep learning-based method improves accuracy by 40 % compared with the conventional linear regression method for ET prediction. Meanwhile, the proposed method alleviates the current lack of prediction methods for TD of road-rail steel truss girders. A detailed analysis of the temperature of a road-rail steel truss bridge is also presented based on the structural health monitoring (SHM) system. A negative vertical temperature difference was observed in the fringe truss. The maximum transverse temperature difference (TTD) was much greater than the maximum vertical temperature difference (VTD). The above features deserve extra attention from bridge designers.

Does artificial intelligence predict orthognathic surgical outcomes better than conventional linear regression methods?

To evaluate the performance of an artificial intelligence (AI) model in predicting orthognathic surgical outcomes compared to conventional prediction methods. Preoperative and posttreatment lateral cephalograms from 705 patients who underwent combined surgical-orthodontic treatment were collected. Predictors included 254 input variables, including preoperative skeletal and soft-tissue characteristics, as well as the extent of orthognathic surgical repositioning. Outcomes were 64 Cartesian coordinate variables of 32 soft-tissue landmarks after surgery. Conventional prediction models were built applying two linear regression methods: multivariate multiple linear regression (MLR) and multivariate partial least squares algorithm (PLS). The AI-based prediction model was based on the TabNet deep neural network. The prediction accuracy was compared, and the influencing factors were analyzed. In general, MLR demonstrated the poorest predictive performance. Among 32 soft-tissue landmarks, PLS showed more accurate prediction results in 16 soft-tissue landmarks above the upper lip, whereas AI outperformed in six landmarks located in the lower border of the mandible and neck area. The remaining 10 landmarks presented no significant difference between AI and PLS prediction models. AI predictions did not always outperform conventional methods. A combination of both methods may be more effective in predicting orthognathic surgical outcomes.

On a class of linear regression methods

In this paper, a unified study is presented for the design and analysis of a broad class of linear regression methods. The proposed general framework includes the conventional linear regression methods (such as the least squares regression and the Ridge regression) and some new regression methods (e.g. the Landweber regression and Showalter regression), which have recently been introduced in the fields of optimization and inverse problems. The strong consistency, the reduced mean squared error, the asymptotic Gaussian property, and the best worst case error of this class of linear regression methods are investigated. Various numerical experiments are performed to demonstrate the consistency and efficiency of the proposed class of methods for linear regression.

Childhood neighborhoods and health: Census-based neighborhood measures versus residential lived experiences.

This study examines the impact of neighborhood disadvantage and neighborhood social connectedness during childhood on subsequent health status during early adulthood. We link longitudinal data from the Panel Study of Income Dynamics with Census data on children's surrounding neighborhoods. We estimate results with conventional linear regression and novel methods that better adjust for neighborhood selection processes. We find that neighborhood connectedness in childhood is protective against psychological distress in early adulthood, net of selection effects. However, greater connectedness exacerbates the risk of obesity within disadvantaged contexts for Black youth. Our results highlight a potential pathway for improving population health by investing in the social connectedness of neighborhoods alongside reducing structural inequalities.

Comparison of the Nucleation Kinetics Obtained from the Cumulative Distributions of the Metastable Zone Width and Induction Time Data.

A linearized integral model based on classical nucleation theory is applied in this work to determine the interfacial energy and pre-exponential factor using a linear plot from the cumulative distributions of the metastable zone width (MSZW) data for some systems reported in the literature, including isonicotinamide, butyl paraben, dicyandiamide, and salicylic acid. Based on the same criterion for the nucleation point, the interfacial energy and pre-exponential factor are determined using the conventional linear regression method from the cumulative distributions of the induction time data for the same systems. The results indicate that the interfacial energy and pre-exponential factor calculated from the MSZW data are consistent with those calculated from the induction time for the studied systems.

Robust Kalman Filter Soil Moisture Inversion Model Using GPS SNR Data—A Dual-Band Data Fusion Approach

This article aims to attempt to increase the number of satellites that can be used for monitoring soil moisture to obtain more precise results using GNSS-IR (Global Navigation Satellite System-Interferometric Reflectometry) technology to estimate soil moisture. We introduce a soil moisture inversion model by using GPS SNR (Signal-to-Noise Ratio) data and propose a novel Robust Kalman Filter soil moisture inversion model based on that. We validate our models on a data set collected at Lamasquère, France. This paper also compares the precision of the Robust Kalman Filter model with the conventional linear regression method and robust regression model in three different scenarios: (1) single-band univariate regression, by using only one observable feature such as frequency, amplitude, or phase; (2) dual-band data fusion univariate regression; and (3) dual-band data fusion multivariate regression. First, the proposed models achieve higher accuracy than the conventional method for single-band univariate regression, especially by using the phase as the input feature. Second, dual-band univariate data fusion achieves higher accuracy than single-band and the result of the Robust Kalman Filter model correlates better to the in situ measurement. Third, multivariate variable fusion improves the accuracy for both models, but the Robust Kalman Filter model achieves better improvement. Overall, the Robust Kalman Filter model shows better results in all the scenarios.

Voxel-wise partial volume correction method for accurate estimation of tissue sodium concentration in 23 Na-MRI at 7 T.

Sodium is crucial for the maintenance of cell physiology, and its regulation of the sodium‐potassium pump has implications for various neurological conditions. The distribution of sodium concentrations in tissue can be quantitatively evaluated by means of sodium MRI (23Na‐MRI). Despite its usefulness in diagnosing particular disease conditions, tissue sodium concentration (TSC) estimated from 23Na‐MRI can be strongly biased by partial volume effects (PVEs) that are induced by broad point spread functions (PSFs) as well as tissue fraction effects. In this work, we aimed to propose a robust voxel‐wise partial volume correction (PVC) method for 23Na‐MRI. The method is based on a linear regression (LR) approach to correct for tissue fraction effects, but it utilizes a 3D kernel combined with a modified least trimmed square (3D‐mLTS) method in order to minimize regression‐induced inherent smoothing effects. We acquired 23Na‐MRI data with conventional Cartesian sampling at 7 T, and spill‐over effects due to the PSF were considered prior to correcting for tissue fraction effects using 3D‐mLTS. In the simulation, we found that the TSCs of gray matter (GM) and white matter (WM) were underestimated by 20% and 11% respectively without correcting tissue fraction effects, but the differences between ground truth and PVE‐corrected data after the PVC using the 3D‐mLTS method were only approximately 0.6% and 0.4% for GM and WM, respectively. The capability of the 3D‐mLTS method was further demonstrated with in vivo 23Na‐MRI data, showing significantly lower regression errors (ie root mean squared error) as compared with conventional LR methods (p < 0.001). The results of simulation and in vivo experiments revealed that 3D‐mLTS is superior for determining under‐ or overestimated TSCs while preserving anatomical details. This suggests that the 3D‐mLTS method is well suited for the accurate determination of TSC, especially in small focal lesions associated with pathological conditions.

Improving CAT bond pricing models via machine learning

Enhanced machine learning methods provide an encouraging alternative to forecast asset prices by extending or generalizing the possible model specifications compared to conventional linear regression methods. Even if enhanced methods of machine learning in the literature often lead to better forecasting quality, this is not clear for small asset classes, because in small asset classes enhanced machine learning methods may potentially over-fit the in-sample data. Against this background, we compare the forecasting performance of linear regression models and enhanced machine learning methods in the market for catastrophe (CAT) bonds. We use linear regression with variable selection, penalization methods, random forests and neural networks to forecast CAT bond premia. Among the considered models, random forests exhibit the highest forecasting performance, followed by linear regression models and neural networks.

End-to-End Deep Learning Architecture for Continuous Blood Pressure Estimation Using Attention Mechanism.

Blood pressure (BP) is a vital sign that provides fundamental health information regarding patients. Continuous BP monitoring is important for patients with hypertension. Various studies have proposed cuff-less BP monitoring methods using pulse transit time. We propose an end-to-end deep learning architecture using only raw signals without the process of extracting features to improve the BP estimation performance using the attention mechanism. The proposed model consisted of a convolutional neural network, a bidirectional gated recurrent unit, and an attention mechanism. The model was trained by a calibration-based method, using the data of each subject. The performance of the model was compared to the model that used each combination of the three signals, and the model with the attention mechanism showed better performance than other state-of-the-art methods, including conventional linear regression method using pulse transit time (PTT). A total of 15 subjects were recruited, and electrocardiogram, ballistocardiogram, and photoplethysmogram levels were measured. The 95% confidence interval of the reference BP was [86.34, 143.74] and [51.28, 88.74] for systolic BP (SBP) and diastolic BP (DBP), respectively. The values were 0.52 and 0.49, and the mean-absolute-error values were 4.06 ± 4.04 and 3.33 ± 3.42 for SBP and DBP, respectively. In addition, the results complied with global standards. The results show the applicability of the proposed model as an analytical metric for BP estimation.

Visual Field Prediction using Recurrent Neural Network

Artificial intelligence capabilities have, recently, greatly improved. In the past few years, one of the deep learning algorithms, the recurrent neural network (RNN), has shown an outstanding ability in sequence labeling and prediction tasks for sequential data. We built a reliable visual field prediction algorithm using RNN and evaluated its performance in comparison with the conventional pointwise ordinary linear regression (OLR) method. A total of 1,408 eyes were used as a training dataset and another dataset, comprising 281 eyes, was used as a test dataset. Five consecutive visual field tests were provided to the constructed RNN as input and a 6th visual field test was compared with the output of the RNN. The performance of the RNN was compared with that of OLR by predicting the 6th visual field in the test dataset. The overall prediction performance of RNN was significantly better than OLR. The pointwise prediction error of the RNN was significantly smaller than that of the OLR in most areas known to be vulnerable to glaucomatous damage. The RNN was also more robust and reliable regarding worsening in the visual field examination. In clinical practice, the RNN model can therefore assist in decision-making for further treatment of glaucoma.

Group Low-Rank Representation-Based Discriminant Linear Regression

In this paper, a novel least square regression method, named group low-rank representation-based discriminant linear regression (GLRRDLR), is proposed for multi-class classification. Unlike the conventional linear regression methods, the proposed method aims to learn a more discriminative projection. Specially, two main techniques are adopted to improve the discriminability of the projection. The first approach is to make the transformed samples locate in their own subspace by introducing a group low-rank constraint to the model, such that the distance between samples from the same class can be decreased greatly. The second approach is to simultaneously learn a discriminative target matrix for regression. The extensive experimental results show that the proposed method performs much better than the state-of-the-art methods, which proves the effectiveness of the above two approaches in improving the discriminability of the projection.

A Machine Learning Method for Predicting Driving Range of Battery Electric Vehicles

It is of great significance to improve the driving range prediction accuracy to provide battery electric vehicle users with reliable information. A model built by the conventional multiple linear regression method is feasible to predict the driving range, but the residual errors between -3.6975 km and 3.3865 km are relatively unfaithful for real-world driving. The study is innovative in its application of machine learning method, the gradient boosting decision tree algorithm, on the driving range prediction which includes a very large number of factors that cannot be considered by conventional regression methods. The result of the machine learning method shows that the maximum prediction error is 1.58 km, the minimum prediction error is -1.41 km, and the average prediction error is about 0.7 km. The predictive accuracy of the gradient boosting decision tree is compared against that of the conventional approaches.

A hybrid approach using machine learning to predict the cutting forces under consideration of the tool wear

The cutting process is a complex nonlinear system. Predicting such a system with conventional regression models is inefficient. In this paper, a hybrid approach using deep neural networks (DNN) is proposed to predict the specific cutting forces. With the aim of obtaining the hybrid training data, orthogonal cutting tests and 2D FEM chip formation simulations have been performed under diverse cutting parameters, tool geometries and tool wear conditions. Predictive models using a DNN and a conventional linear regression method were established. In comparison with the conventional linear regression method, the hybrid model using the machining learning is more accurate.

EEG Emotion Recognition Based on Graph Regularized Sparse Linear Regression

In this paper, a novel regression model, called graph regularized sparse linear regression (GRSLR), is proposed to deal with EEG emotion recognition problem. GRSLR extends the conventional linear regression method by imposing a graph regularization and a sparse regularization on the transform matrix of linear regression, such that it is able to simultaneously cope with sparse transform matrix learning while preserve the intrinsic manifold of the data samples. To detailed discuss the EEG emotion recognition, we collect a set of 14 subjects EEG emotion data and provide the experiment results on different features. To evaluate the proposed GRSLR model, we conduct experiments on the SEED database and RCLS database. The experimental results show that the proposed algorithm GRSLR is superior to the classic baselines. The RCLS database is made publicly available and other researchers could use it to test their own emotion recognition method.

Generation of Radiometric, Phenological Normalized Image Based on Random Forest Regression for Change Detection

Efforts have been made to detect both naturally occurring and anthropogenic changes to the Earth’s surface by using satellite remote sensing imagery. There is a need to maintain the homogeneity of radiometric and phenological conditions to ensure accuracy in change detection, but images to assess long-term changes in time-series data that satisfy such conditions are difficult to obtain. For this reason, image normalization is essential. In particular, the normalizing compositive conditions require nonlinear modeling, and random forest (RF) techniques can be utilized for this normalization. This study employed Landsat-5 Thematic Mapper satellite images with temporal, radiometric and phenological differences, and obtained Radiometric Control Set Samples by selecting no-change pixels between the subject image and reference image using scattergrams. In the obtained no-change regions, RF regression was modeled, and normalized images were obtained. Next, normalization performance was evaluated by comparing the results against the following conventional linear regression methods: mean-standard deviation regression, simple regression, and no-change regression. The normalization performance of RF regression was much higher. In addition, for an additional usefulness evaluation in normalization, the normalization performance was compared with other nonlinear ensemble regressions, i.e. Adaptive Boosting regression and Stochastic Gradient Boosting regression, which confirmed that the normalization performance of RF regression was significantly higher. In other words, it was found to be highly useful for normalization when compared to other nonlinear ensemble regressions. Finally, as a result of performing change detection, normalized subject images generated by RF regression showed the highest accuracy, which indicated that the proposed method (where the image was normalized using RF regression) may be useful in change detection between multi-temporal image datasets.

High Temporal Resolution Rainfall Information Retrieval from Tipping-bucket Rain Gauge Measurements

Disdrometer can play a vital role in restoring detailed rainfall process by providing rainfall at a high temporal resolution. Rainfall rate derived from the widely used “Tipping-Bucket rain gauge” usually neglects its temporal variation especially during the low rainfall intensity periods. This study explores a heuristic artificial neural networks (ANN) approach along with the conventional Cubic Spline Algorithm (CSA) and Multivariate Linear Regression method (MLR) for high temporal resolution rainfall rate retrieval for the period of 2007 to 2009 at Chilbolton, U.K. The Supervised Levenberg-Marquardt backpropagation algorithm and the K-folds cross-validation method are integrated in a feed-forward neural network as to implicitly detect complex nonlinear relationships and to avoid model overfitting. Results indicate ANN is performing equivalently well with CSA after training, however, with poor generalisation in test due to low correlation between input and target data, as well as the curse of dimensionality in optimum model complexity selection. MLR can be an alternative approach in rainfall rate estimation but it highly depends on the data quality.

Parametric analysis of the biomechanical response of head subjected to the primary blast loading – a data mining approach

Traumatic brain injury due to primary blast loading has become a signature injury in recent military conflicts and terrorist activities. Extensive experimental and computational investigations have been conducted to study the interrelationships between intracranial pressure response and intrinsic or ‘input’ parameters such as the head geometry and loading conditions. However, these relationships are very complicated and are usually implicit and ‘hidden’ in a large amount of simulation/test data. In this study, a data mining method is proposed to explore such underlying information from the numerical simulation results. The heads of different species are described as a highly simplified two-part (skull and brain) finite element model with varying geometric parameters. The parameters considered include peak incident pressure, skull thickness, brain radius and snout length. Their interrelationship and coupling effect are discovered by developing a decision tree based on the large simulation data-set. The results show that the proposed data-driven method is superior to the conventional linear regression method and is comparable to the nonlinear regression method. Considering its capability of exploring implicit information and the relatively simple relationships between response and input variables, the data mining method is considered to be a good tool for an in-depth understanding of the mechanisms of blast-induced brain injury. As a general method, this approach can also be applied to other nonlinear complex biomechanical systems.

Forecasting and Modelling of Electricity Prices by Radial Basis Functions: Turkish Electricity Market Experiment

Elektrik piyasası son 30 yılda gelişmekte olan ülkeler de dâhil olmak üzere pek çok ülkede özelleştirilmiş ve elektrik bir kamu yararı olmaktan çıkarılmıştır. Bu nedenle kısa dönem için elektrik fiyatı tahmini rekabetçi bir ortamda iş yapan piyasa oyuncuları için oldukça önemli hale gelmiştir. Bu çalışmada önce zaman içerisinde aynı elektrik fiyatlarının tekrar tekrar gözlendiği gösterilmiş ve bu nedenle radyal tabanlı modellerin bu yapıyı açıklayabileceği tartışılmıştır. Daha sonra radyal tabanlı fonksiyon ağı ve geleneksel doğrusal regresyon analizi yöntemleri kullanılarak saatlik gün öncesi piyasa fiyatı tahmin edilmeye çalışılmıştır. Radyal tabanlı fonksiyon ağının örneklem dışı tahmin performansının az da olsa daha iyi olduğu gösterilmiştir.