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Results for “Smoothed boundary method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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53 records · Page 3

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗

Magneto-Structural Combined Dimensional and Topology Optimization of Interior Permanent Magnet Synchronous Machine Rotors

A magneto-structural combined dimensional and topology optimization approach for interior permanent magnet synchronous machine (IPMSM) rotor design is proposed using the Solid Isotropic Material Penalization (SIMP) density-based topology optimization method. This method optimizes the location and dimensions of the permanent magnets (PMs) embedded in the rotor, while simultaneously optimizing the lamination flux barriers using topology optimization.To allow for the location and dimensions of the PMs to change while retaining the same number of mesh elements and connectivity, the mesh must be deformed. Mesh deformation is accomplished using a Laplace smoothing technique. To increase the range of PM displacement and size changes, the non-PM areas of the rotor design domain are divided into sub-regions along whose boundaries the mesh nodes are redistributed also using a Laplace smoothing algorithm. Three examples of IPMSM rotor optimizations are presented to demonstrate the proposed approach.

33 ADVANCED PROPULSION SYSTEMS↗

Methods to Evaluate Subcolumn Profiles Based on Two-Point Diagnostics

In atmospheric models, stochastic generation of subgrid-scale profiles or “subcolumns” has been used for a variety of purposes. Such subcolumns can be generated from subgrid probability density functions (PDFs) at different vertical levels, when such PDFs are available. To do so, the generator needs to decide how strongly points should be correlated in the vertical, that is, how much the values should be overlapped. This is sometimes called “PDF overlap.” To assess vertical correlation in a simplified, observable setting, here the vertical correlation of vertical velocity in subcloud layers is examined. Doppler lidar is used to evaluate the vertical profiles of vertical velocity produced by a large-eddy simulation (LES) model and the Subgrid Importance Latin Hypercube Sampler (SILHS) subcolumn generator. In order to diagnose unrealistic features in subcolumn profiles, various statistical diagnostics are examined here, including the bivariate PDF of vertical velocity at two separated points (i.e., altitudes), the two-point velocity correlation, the integral correlation length, the PDF of two-point velocity differences, and the skewness and kurtosis of two-point velocity differences. The profiles produced by LES match lidar well, except that they are too smooth at small scales. The profiles produced by SILHS exhibit sharp jumps from updraft to downdraft that are not observed in the lidar data. To reduce the generation of these unrealistically sharp jumps, the SILHS sampling method is revised. The diagnostics confirm that the revised sampling method reduces the overprediction of sharp jumps.

54 ENVIRONMENTAL SCIENCES↗

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

Computational Analysis of Water Film Thickness During Rain Events for Assessing Hydroplaning Risk Part 2: Rough Road Surfaces

Hydroplaning occurs when a water film forms on a road during a rain event and vehicles are traveling at a speed that does not provide sufficient time for the tires to push the water film out of the tire path. Under these conditions, the tire loses contact with the road and the driver may lose control over the vehicle. The present study is a part of a multiyear research effort aimed at gaining a better understanding of the factors that contribute to hydroplaning risk in order to minimize the occurrence of hydroplaning accidents. Three-dimensional computational fluid dynamics (CFD) analysis was used to investigate the water film thickness on multilane roads, one of the key parameters in evaluating hydroplaning risk. In the first part of the study, water films forming on wide roadways, i.e. multilane highways with 2, 4, and 6 lanes per side, were analyzed, with varying cross slope, longitudinal slope, and rainfall rate. Roadways with and without curbs and drainage were included in the analysis. The analysis in the first part was limited to nearly smooth asphalt or concrete surfaces because the maximum roughness height that can be specified in a CFD model using wall functions to determine shear stress at the road surface boundary is one half the thickness of computational cell layer adjacent to the boundary and the need to resolve the vertical velocity distribution in a thin water film requires cell layers that are a fraction of a millimeter thick. In this part of the study, the analysis was extended to consider the influence of pavement roughness over a range extending up 3.6 mm on the development of water film thickness. Various methods of modeling roughness were investigated and are presented: the roughness height model, a meshed-out geometry of the macrotexture of the pavement, and a porous region model. The computational results were analyzed and compared with experimental measurements performed by Gallaway et al.

42 ENGINEERING↗

Application of Recursive Estimation to Heat Tracing for Groundwater/Surface‐Water Exchange

Abstract We present and demonstrate a recursive‐estimation framework to infer groundwater/surface‐water exchange based on temperature time series collected at different vertical depths below the sediment/water interface. We formulate the heat‐transport problem as a state‐space model (SSM), in which the spatial derivatives in the convection/conduction equation are approximated using finite differences. The SSM is calibrated to estimate time‐varying specific discharge using the Extended Kalman Filter (EKF) and Extended Rauch‐Tung‐Striebel Smoother (ERTSS). Whereas the EKF is suited to real‐time (“online”) applications and uses only the past and current measurements for estimation (filtering), the ERTSS is intended for near‐real time or batch‐processing (“offline”) applications and uses a window of data for batch estimation (smoothing). The two algorithms are demonstrated with synthetic and field‐experimental data and are shown to be efficient and rapid for the estimation of time‐varying flux over seasonal periods; further, the recursive approaches are effective in the presence of rapidly changing flux and (or) nonperiodic thermal boundary conditions, both of which are problematic for existing approaches to heat tracing of time‐varying groundwater/surface‐water exchange.

54 ENVIRONMENTAL SCIENCES↗

A Boundary Topology Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing

Minimizing the mass in electric machines while maintaining superior performance has become a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization for light-weighting electric machines using traditional approaches typically explore a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods like cell-based density approaches suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary TO where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the IEA-15MW radial flux direct-drive wind turbine generator. The free-from boundary TO resulted in smooth and concise shapes that can be easily additively manufactured with upto 20-ton reduction in electrical steel mass.

additive manufacturing↗

A New Shape Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing: Preprint

Minimizing the mass in electric machines while maintaining superior performance is a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization (TO) for lightweighting electric machines using traditional approaches typically explores a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods, such as cell-based density approaches, suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary TO where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning-based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque, and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the International Energy Agency (IEA) 15-MW radial flux direct-drive wind turbine generator. The free-form boundary TO resulted in smooth and concise shapes that can be easily additively manufactured with up to a 20-ton reduction in electrical steel mass.

additive manufacturing↗

A New Shape Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing

Minimizing the mass in electric machines while maintaining superior performance is a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization (TO) for lightweighting electric machines using traditional approaches typically explores a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods, such as cell-based density approaches, suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary optimization where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning-based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque, and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the International Energy Agency (IEA) 15-MW radial flux direct-drive wind turbine generator. The new approach to shape optimization resulted in smooth and concise shapes that can be easily additively manufactured with up to a 20-ton reduction in electrical steel mass.

additive manufacturing↗

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

Non-smooth Bayesian optimization in tuning scientific applications

Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

97 MATHEMATICS AND COMPUTING↗

Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design

Abstract Porous biomaterials design for bone repair is still largely limited to regular structures (e.g. rod-based lattices), due to their easy parameterization and high controllability. The capability of designing stochastic structure can redefine the boundary of our explorable structure–property space for synthesizing next-generation biomaterials. We hereby propose a convolutional neural network (CNN) approach for efficient generation and design of spinodal structure—an intriguing structure with stochastic yet interconnected, smooth, and constant pore channel conducive to bio-transport. Our CNN-based approach simultaneously possesses the tremendous flexibility of physics-based model in generating various spinodal structures (e.g. periodic, anisotropic, gradient, and arbitrarily large ones) and comparable computational efficiency to mathematical approximation model. We thus successfully design spinodal bone structures with target anisotropic elasticity via high-throughput screening, and directly generate large spinodal orthopedic implants with desired gradient porosity. This work significantly advances stochastic biomaterials development by offering an optimal solution to spinodal structure generation and design.

59 BASIC BIOLOGICAL SCIENCES↗

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

Engineering↗

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reinforcement Learning-Based Oscillation Dampening: Scaling Up Single-Agent Reinforcement Learning Algorithms to a 100-Autonomous-Vehicle Highway Field Operational Test

In this article, we explore the technical details of the reinforcement learning (RL) algorithms that were deployed in the largest field test of automated vehicles designed to smooth traffic flow in history as of 2023, uncovering the challenges and breakthroughs that come with developing RL controllers for automated vehicles. We delve into the fundamental concepts behind RL algorithms and their application in the context of self-driving cars, discussing the developmental process from simulation to deployment in detail, from designing simulators to reward function shaping. We present the results in both simulation and deployment, discussing the flow-smoothing benefits of the RL controller. From understanding the basics of Markov decision processes to exploring advanced techniques such as deep RL, our article offers a comprehensive overview and deep dive of the theoretical foundations and practical implementations driving this rapidly evolving field. We also showcase real-world case studies and alternative research projects that highlight the impact of RL controllers in revolutionizing autonomous driving. From tackling complex urban environments to dealing with unpredictable traffic scenarios, these intelligent controllers are pushing the boundaries of what automated vehicles can achieve. Furthermore, we examine the safety considerations and hardware-focused technical details surrounding deployment of RL controllers into automated vehicles. As these algorithms learn and evolve through interactions with the environment, ensuring their behavior aligns with safety standards becomes crucial. Here, we explore the methodologies and frameworks being developed to address these challenges, emphasizing the importance of building reliable control systems for automated vehicles.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗