Surrogate Modeling Techniques Research Articles

On the interpretability of the SVM model for predicting infant mortality in Bangladesh

BackgroundAlthough machine learning (ML) models are well-liked for their outperformance in prediction, greatly avoided due to the lack of intuition and explanation of their predictions. Interpretable ML is, therefore, an emerging research field that combines the performance and interpretability of ML models to create comprehensive solutions for complex decision-making analysis. Conversely, infant mortality is a global public health concern affecting health, social well-being, socio-economic development, and healthcare services. The study employs advanced interpretable ML techniques to anticipate and understand the factors affecting infant mortality in Bangladesh, overcoming the shortcomings of the conventional logistic regression (LR) model.MethodsBy utilizing the global surrogate model and local individual conditional expectation (ICE) interpretability technique, the interpretable support vector machine (SVM) has been used in this study to reveal significant characteristics of infant mortality using data from the Bangladesh Demographic and Health Survey (BDHS) 2017–18. To investigate intricate decision-making analysis of infant mortality, we adapted SVM and LR techniques with the hyperparameter tuning parameters. These models’ performances were initially assessed using the receiver operating characteristics (ROC) curve, run-time, and confusion matrix parameters with 100 permutations. Afterward, the SVM model’s model-agnostic explanation and the LR model’s interpretation were compared to enhance advanced comprehension for further insights.ResultsThe results of the 100 permutations demonstrated that the LR model (Average: accuracy = 0.9105, precision = NaN, sensitivity = 0, specificity = 1, F1-score = 0, area under the ROC curve (AUC) = 0.6780, run-time = 0.0832) outperformed the SVM model (Average: accuracy = 0.8470, precision = 0.1062, sensitivity = 0.0949, specificity = 0.9209, F1-score = 0.1000, AUC = 0.5632, run-time = 0.0254) in predicting infant mortality, but the LR model had a slower run-time and it was unable to predict any positive cases. The interpretation of LR analysis revealed that infant mortality rates decrease when mothers give birth after over two years, with higher educational attainment, overweight or obese mothers, working mothers, and families with polluted cooking fuel having lower rates. The local ICE interpretability technique, which depicts individual influences on the average likelihood of dying within the first birthday, explores the interpretable SVM model that mothers with normal BMIs, giving birth within two years, using less polluted cooking fuel, working mothers, and having male infant were more likely to experience infant death. The interpretable SVM model based on the global surrogate model also reveals that working mothers who used polluted cooking fuel at home and working women who used less polluted cooking fuel but had a longer period between pregnancies than two years would have higher infant death rates. Even among non-working mothers who used polluted cooking fuel and gave birth within two years of the preceding one, infant death rates were higher.ConclusionsThe interpretable SVM model reveals global interpretations help clinicians understand the entire conditional distribution, while local interpretations focus on specific instances, providing different insights into model behavior. Interpretable ML models aid policymakers, stakeholders, and families in understanding and preventing infant deaths by improving policy-making strategies and establishing effective family counseling services.

Navigating Technological Risks: An Uncertainty Analysis of Powertrain Technology in Hybrid-Electric Commuter Aircraft

Abstract This study addresses the uncertainties in hybrid-electric powertrain technology for a 19-passenger commuter aircraft, focusing on two future Entry-Into-Service timeframes: 2030 and 2040. The methodology is split into a preliminary optimization of aircraft design based on nominal technology scenarios followed by Monte Carlo simulations to investigate the impact of diverse technology projections and distribution types. Advanced surrogate modeling techniques, leveraging deep neural networks (DNN) trained on a dataset from an aircraft design framework, are employed. Key outcomes from this work reveal a marked increase in computational efficiency, with a speed-up factor of approximately 500 times when utilizing surrogate models. The results indicate that the 2040 entry-into-service (EIS) scenario could achieve larger reductions in fuel and total energy consumption—20.4% and 15.8% respectively—relative to the 2030 scenario, but with higher uncertainty. Across all scenarios examined, the hybrid-electric model showcased superior performance compared to its conventional counterpart. The battery-specific energy density is proved to be a critical parameter of the aircraft’s performance across both timeframes. The findings emphasize the importance of continuous innovation in battery and motor technologies to target toward greater system-level efficiency and reduced environmental impact.

Heat transfer performance optimization of turbine blade internal cooling channel with pin-fins and recessed-extruded endwalls

This paper involves implementing and optimizing a novel recessed-extruded endwall design for a rectangular cooling channel equipped with pin-fins. The study encompasses an in-depth exploration of the flow dynamics, pondering the generation and sustenance of vortices within the channel, using Reynolds-averaged Navier-Stokes analysis. The study delves into the evaluation of heat transfer characteristics, considering crucial parameters such as Nusselt number, friction factor, and overall heat transfer performance. These attributes are contrasted with the corresponding values observed in cases featuring flat endwalls, concerning Reynolds numbers spanning from 7400 to 36,000. A parametric study of the channel with recessed-extruded endwalls is conducted, aiming to comprehend the influence of geometric factors on channel heat transfer. A single-objective optimization process focusing on enhancing heat transfer effectiveness, quantified through the heat transfer efficiency index (HTEI), is conducted with three design variables. The results indicate that the new endwall configuration significantly enlarges the high heat transfer areas near the pin-fins compared to the flat endwall across all Reynolds numbers. This novel endwall design substantially elevates the heat transfer levels adjacent to the pin-fins, showcasing an impressive 62.4% increase in HTEI at Re = 21,500 compared to the flat endwall, with a protrusion height of 2.5% of the channel height. Furthermore, by increasing the height, the recessed-extruded endwall configuration can achieve a remarkable 91.1% increase in HTEI compared to the flat endwall. This achievement is reached with a protrusion height equivalent to 5% of the channel height at Re = 7400. Through design optimization using the radial basis neural network (RBNN) surrogate model and particle swarm optimization (PSO) technique, the HTEI of the recessed-extruded endwall design shows enhancements of 91.7% and 18.0% compared with the flat endwall and reference designs, respectively, at a Reynolds number of 21,500. The present work demonstrates the potential for enhancing the heat transfer of pin-fins channels by improving endwall design.

A Surrogate Model's Decision Tree Method Evaluation for Uncertainty Quantification on a Finite Element Structure via a Fuzzy-Random Approach

A novel additive manufacturing method (AM)) constructs a three-dimensional model from a computer-aided design by adding material layer by layer. This technique produces a lightweight end product with complex geometries and has gained recognition among industrial players. Nonetheless, the mechanical properties and geometry components are the uncertainties that prevail in its structures. An alternative approach using the Finite Element Method (FEM) to analyse these uncertainties demands extensive computational effort and time consumption. Therefore, a machine learning (ML) tool using the surrogate modelling technique offers an alternative way to provide and predict simulation outcomes. This study applies two surrogate modeling approaches, the decision tree (DT) and the Gaussian process regression (GPR) methods. Output data from a FEM simulation with uncertainty elements are obtained for the training purposes of the surrogate models. Both ML methods can predict simulation results with high precision. Both approaches obtained an excellent coefficient of determination value, R2 of 0.998, and Root Mean Square Error, RMSE of 0.012, successfully reducing time consumption and computational effort. The DT method shows better robustness when compared to the GPR method. A value change in the input parameter significantly impacts the surrogate model's prediction performance. An adequate quantity of data input for the training phase of both surrogate models exhibits the FEM results with the presence of uncertainty and robustness.

Characterising harmful data sources when constructing multi-fidelity surrogate models

Surrogate modelling techniques have seen growing attention in recent years when applied to both modelling and optimisation of industrial design problems. These techniques are highly relevant when assessing the performance of a particular design carries a high cost, as the overall cost can be mitigated via the construction of a model to be queried in lieu of the available high-cost source. The construction of these models can sometimes employ other sources of information which are both cheaper and less accurate. The existence of these sources however poses the question of which sources should be used when constructing a model. Recent studies have attempted to characterise harmful data sources to guide practitioners in choosing when to ignore a certain source. These studies have done so in a synthetic setting, characterising sources using a large amount of data that is not available in practice. Some of these studies have also been shown to potentially suffer from bias in the benchmarks used in the analysis. In this study, we approach the characterisation of harmful low-fidelity sources as an algorithm selection problem. We employ recently developed benchmark filtering techniques to conduct a bias-free assessment, providing objectively varied benchmark suites of different sizes for future research. Analysing one of these benchmark suites with the technique known as Instance Space Analysis, we provide an intuitive visualisation of when a low-fidelity source should be used. By performing this analysis using only the limited data available to train a surrogate model, we are able to provide guidelines that can be directly used in an applied industrial setting.

Improving the Interpretability of Data-Driven Models for Additive Manufacturing Processes Using Clusterwise Regression

Wire Arc Additive Manufacturing (WAAM) represents a disruptive technology in the field of metal additive manufacturing. Understanding the relationship between input factors and layer geometry is crucial for studying the process comprehensively and developing various industrial applications such as slicing software and feedforward controllers. Statistical tools such as clustering and multivariate polynomial regression provide methods for exploring the influence of input factors on the final product. These tools facilitate application development by helping to establish interpretable models that engineers can use to grasp the underlying physical phenomena without resorting to complex physical models. In this study, an experimental campaign was conducted to print steel components using WAAM technology. Advanced statistical methods were employed for mathematical modeling of the process. The results obtained using linear regression, polynomial regression, and a neural network optimized using the Tree-structured Parzen Estimator (TPE) were compared. To enhance performance while maintaining the interpretability of regression models, clusterwise regression was introduced as an alternative modeling technique along with multivariate polynomial regression. The results showed that the proposed approach achieved results comparable to neural network modeling, with a Mean Absolute Error (MAE) of 0.25 mm for layer height and 0.68 mm for layer width compared to 0.23 mm and 0.69 mm with the neural network. Notably, this approach preserves the interpretability of the models; a further discussion on this topic is presented as well.

Bayesian-informed fatigue life prediction in shallow shell structures with the dual boundary element method

This study introduces an innovative approach for statistically inferring the Equivalent Initial Flaw Size Distribution (EIFSD) in shallow shell structures with the aim of predicting fatigue life. The proposed approach integrates Bayesian inference and surrogate modelling techniques, and utilizes a long crack growth model. The EIFSD is crucial for estimating fatigue life and ensuring structural durability. To showcase the proposed methodology, a numerical example featuring a fuselage window structure under multi-axial loading, employing the Dual Boundary Element Method (DBEM) for crack growth modelling, is presented. Efficiency gains in the inference of the EIFSD are achieved through the development of surrogate models, notably a Co-Kriging model that significantly reduces computational time and outperforms a Kriging model in error reduction. The study explores two assumptions for inspection data sourcing, leading to enhanced methodological effectiveness across varying uncertainty levels. It considers the separate effects of Paris Law constants and loading conditions under increased uncertainty, presenting cases that demonstrate the Co-Kriging model’s high accuracy and computational efficiency. The proposed methodology’s robustness is further validated by assessing the impact of prior distribution quality on Bayesian inference, showing the method’s adaptability to high uncertainty while maintaining a good level of accuracy. This study also demonstrates an approach for fatigue life estimation of structures using the inferred EIFSD. By evaluating the structure up to a critical crack length, the methodology allows for the accurate estimation of fatigue life, which, in turn, facilitates the determination of optimal inspection intervals. Notably, under conditions of high uncertainty, the method showcased a maximum difference of 1.51% in the estimated fatigue life when compared to the true EIFSD, underscoring the technique’s high accuracy and reliability.

Data-driven surrogate modeling and optimization of supercritical jet into supersonic crossflow

For the design and optimization of advanced aero-engines, the prohibitively computational resources required for numerical simulations pose a significant challenge, due to the extensive exploration of design parameters across a vast design space. Surrogate modeling techniques offer a viable alternative for efficiently emulating numerical results within a notably compressed timeframe. This study introduces parametric Reduced-Order Models (ROMs) based on Convolutional AutoEncoders (CAE), Fully Connected AutoEncoders (FCAE), and Proper Orthogonal Decomposition (POD) to fast emulate spatial distributions of physical variables for a supercritical jet into a supersonic crossflow under different operating conditions. To further accelerate the decision-making process, an optimization model is developed to enhance fuel-oxidizer mixing efficiency while minimizing total pressure loss. Results indicate that CAE-based ROMs exhibit superior prediction accuracy while FCAE-based ROMs show inferior predictive accuracy but minimal uncertainty. The latter may be ascribed to the markedly greater number of hyperparameters. POD-based ROMs underperform in regions of strong nonlinear flow dynamics, coupled with higher overall prediction uncertainties. Both AE- and POD-based ROMs achieve online predictions approximately 9 orders of magnitude faster than conventional simulations. The established optimization model enables the attainment of Pareto-optimal frontiers for spatial mixing deficiencies and total pressure recovery coefficient.

Examining the non-linear relationship between urban form and air temperature at street level: A case of Hong Kong

The relationship between urban form and localized air temperature has been studied extensively using linear regression. However, the findings remain inconsistent, and few studies have explored alternative data modeling techniques. With the rise of machine learning, there is an opportunity to explore new methods in urban climatology research. This study aims to test the hypothesis that machine learning models, rather than linear regression, can better explain and predict urban air temperature fluctuations in space and time. Measurements of air temperature were conducted at street level in Hong Kong. Urban form characteristics surrounding the measurement locations were extracted from geo-spatial databases and street view imagery. The datasets were then used to test the performance of linear regression, Artificial Neural Network (ANN), and Random Forest (RF) in predicting the spatial-temporal temperature fluctuations. The results indicate that the relationships between urban form and air temperature are predominantly non-linear. Both ANN and RF outperformed linear regression in prediction, with an MAE of 0.43 °C and 0.33 °C respectively. This study highlights the potentials of machine learning models in advancing knowledge of the impact of urban form on localized air temperature.

Uncertainty Quantification in SAR Induced by Ultra-High-Field MRI RF Coil via High-Dimensional Model Representation.

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues' dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems.

Shape- and frequency-dependent self-excited forces emulation for the aero-structural design of bluff deck bridges

The shape design and optimization of bluff decks prone to aeroelastic phenomena require emulating the fluid-structure interaction parameters as a function of the body shape and the oscillation frequency. This is particularly relevant for long- and medium-span bridges equipped with single-box decks that are far from being considered streamlined and for other girder typologies such as traditional truss decks and modern twin- and multi-box decks. The success of aero-structural design frameworks, which are inherently iterative, relies on the efficient and accurate numerical evaluation of the wind-induced responses. This study proposes emulating the fluid-structure interaction parameters of bluff decks using surrogate modeling techniques to integrate them into aero-structural optimization frameworks. The surrogate is trained with data extracted from forced-vibration CFD simulations of a typical single-box girder to emulate the values of the flutter derivatives as a function of the deck shape and reduced velocity. The focus is on deck configurations ranging from streamlined to bluff cross-sections and on low reduced velocities to capture eventual aerodynamic nonlinearities. The girder cross-section geometry is tailored based on its buffeting performance. This design tool is fundamental to finding the optimum balance between the structural and aeroelastic requirements that drive the design of bluff deck bridges.

Impact of urban form and street infrastructure on pedestrian-motorist collisions

This study examines the impact of urban form and street infrastructure on pedestrian safety in Atlanta, Georgia, and Boston, Massachusetts. With a significant rise in pedestrian fatalities over the past decade, understanding how cities’ built environments influence safety is critical. We conducted geospatial analyses and statistical tests, revealing unique patterns in each city. Atlanta’s sprawling, motorist-oriented layout is associated with increased pedestrian accidents, particularly at crosswalks, due to limited land use diversity, arterial roads, and streets with high speed limits and multiple lanes. In contrast, Boston’s compact, pedestrian-oriented design leads to improved safety, featuring safer pedestrian crossings, greater land use diversity, reduced arterial roads and lower speed limits on single-lane streets. This study also highlights the importance of diverse urban forms and pedestrian infrastructure in shaping pedestrian safety. While population density and land use diversity impact accident rates, the presence of crosswalks and street configurations play crucial roles. Our findings underscore the urgency for urban planners to prioritize pedestrian safety through targeted interventions, such as enhancing crosswalks, reducing speed limits and promoting mixed land use. Future research should explore additional variables, alternative modelling techniques and non-linear approaches to gain a more comprehensive understanding of these complex relationships.

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

Data‐informed uncertainty quantification for laser‐based powder bed fusion additive manufacturing

AbstractWe present an efficient approach to quantify the uncertainties associated with the numerical simulations of the laser‐based powder bed fusion of metals processes. Our study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018‐01 benchmark proposed by the National Institute of Standards and Technology (NIST). The proposed approach consists of a forward uncertainty quantification analysis of the residual strains of the cantilever beam given the uncertainty in some of the parameters of the numerical simulation, namely the powder convection coefficient and the activation temperature. The uncertainty on such parameters is modelled by a data‐informed probability density function obtained by a Bayesian inversion procedure, based on the displacement experimental data provided by NIST. To overcome the computational challenges of both the Bayesian inversion and the forward uncertainty quantification analysis we employ a multi‐fidelity surrogate modelling technique, specifically the multi‐index stochastic collocation method. The proposed approach allows us to achieve a 33% reduction in the uncertainties on the prediction of residual strains compared with what we would get basing the forward UQ analysis on a‐priori ranges for the uncertain parameters, and in particular the mode of the probability density function of such quantities (i.e., its “most likely value”, roughly speaking) results to be in good agreement with the experimental data provided by NIST, even though only displacement data were used for the Bayesian inversion procedure.

Enhancing predictive capabilities in fusion burning plasmas through surrogate-based optimization in core transport solvers

This work presents the PORTALS framework (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), which leverages surrogate modeling and optimization techniques to enable the prediction of core plasma profiles and performance with nonlinear gyrokinetic simulations at significantly reduced cost, with no loss of accuracy. The efficiency of PORTALS is benchmarked against standard methods, and its full potential is demonstrated on a unique, simultaneous 5-channel (electron temperature, ion temperature, electron density, impurity density and angular rotation) prediction of steady-state profiles in a DIII-D ITER Similar Shape plasma with GPU-accelerated, nonlinear CGYRO (Candy et al 2016 J. Comput. Phys. 324 73–93). This paper also provides general guidelines for accurate performance predictions in burning plasmas and the impact of transport modeling in fusion pilot plants studies.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics.

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Surrogate modeling with non-stationary-noise based Gaussian process regression and K-Fold ANN for systems featuring uneven sensitivity distribution

In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26 % and 22 % less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25 % greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions.

Energy absorption of a novel auxetic structure reinforced by embedding tubes

To enhance structural crashworthiness while achieving lightweight design, this paper proposes a novel configuration that embeds a thin-walled square tube into auxetic structure which can take full advantage of the interaction between the auxetic structure and embedding tubes. The finite element model of auxetic structures reinforced by embedding tubes is established and validated by the compression experiments. The crashworthiness performance of auxetic structure (AUX), auxetic structure reinforced by embedding tubes (AET), and auxetic structure-filled tubes (AFT) are compared to find that the AET have the highest energy absorption and specific energy absorption (SEA). Through parametric analysis, designing the angles between short and long beams (θ1, θ2) as 70° and 40° can contribute to the crashworthiness performance, respectively. A suitable range for long beam thickness lies between 1.4 mm and 1.6 mm, while a short beam thickness of around 1.2 mm is more effective. The specific configuration can enhance the SEA and reduces peak crushing force (PCF). Increasing the thickness of the embedded tube can improve the crashworthiness by sacrificing the weight. It is a good balance between the crashworthiness performance and weight by designing the tube thickness as 1.2 mm. An analytical model is also established to predict the energy absorption of auxetic structure reinforced by embedding tubes under axial impact loadings. The surrogate modeling technique and the NSGA-II algorithm are also employed to optimize the AET configuration. The results show that the SEA of the optimized structure can increase from 14.5 kJ/kg to 18.6 kJ/kg, while the PCF can be reduced from 164.6 kN to 124.3 kN. Therefore, the auxetic structure reinforced by embedding tubes can play a critical role in the engineering field to absorb energy.

White men can't jump, but do they still get picked first? Race and player selection in the NBA draft, 1980-2021.

Despite excelling at recruiting Black players, studies have repeatedly produced evidence of racial discrimination in the National Basketball Association (NBA). Through this study, we re-examine the topic of racial discrimination within the NBA through an analysis of the Association's annual entry draft. Using a novel dataset, we statistically model the relationship between player race and draft pick number using pooled data from 1980 to 2021. Overall, we find only limited evidence of racial discrimination. These findings are generally robust to sub-sample analyses, alternative specifications of our race variable, and alternate statistical modeling techniques. However, analyses performed on sub-samples of draft picks that participated in the NBA combine-and for whom we have measurements of player athleticism-produce some evidence of racial discrimination. Through such models we estimate that Black players are picked roughly three picks later in the draft. We consider the implications of these findings for contemporary theorizing about racial discrimination in the NBA and more mainstream labor markets.

Insights from a Comprehensive Capacity Expansion Planning Modeling on the Operation and Value of Hydropower Plants under High Renewable Penetrations

This paper presents a quantitative assessment of the value of hydroelectric power plants (HPPs) in power systems with a significant penetration of variable renewable energy sources (VRESs). Through a capacity expansion planning (CEP) model that incorporates a detailed representation of HPP operating principles, the study investigates the construction and application of HPP rule curves essential for seasonal operation. A comparative analysis is also conducted between the proposed rule curve formulation and alternative modeling techniques from the literature. The CEP model optimizes installed capacities per technology to achieve predefined VRES penetration targets, considering hourly granularity and separate rule curves for each HPP. A case study involving twelve reservoir hydropower stations and two open-loop pumped hydro stations is examined, accounting for standalone plants and cascaded hydro systems across six river basins. The study evaluates the additional generation and storage required to replace the hydropower fleet under high VRES penetration levels, assessing the resulting increases in total system cost emanating from introducing such new investments. Furthermore, the study approximates the storage capabilities of HPPs and investigates the impact of simplified HPP modeling on system operation and investment decisions. Overall, the findings underscore the importance of reevaluating hydro rule curves for future high VRES penetration conditions and highlight the significance of HPPs in the energy transition towards carbon neutrality.