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NASA NTRS1994

Integration of the Response Surface Methodology with the Compromise Decision Support Problem in Developing a General Robust Design Procedure

In this paper we introduce a comprehensive and rigorous robust design procedure to overcome some limitations of the current approaches. A comprehensive approach is general enough to model the two major types of robust design applications, namely, robust design associated with the minimization of the deviation of performance caused by the deviation of noise factors (uncontrollable parameters), and robust design due to the minimization of the deviation of performance caused by the deviation of control factors (design variables). We achieve mathematical rigor by using, as a foundation, principles from the design of experiments and optimization. Specifically, we integrate the Response Surface Method (RSM) with the compromise Decision Support Problem (DSP). Our approach is especially useful for design problems where there are no closed-form solutions and system performance is computationally expensive to evaluate. The design of a solar powered irrigation system is used as an example. Our focus in this paper is on illustrating our approach rather than on the results per se.

Chen, Wei↗

NASA NTRS1997

The Problem of Size in Robust Design

To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size - combinatorial explosion in experimentation and model building with number of variables -and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.

Koch, Patrick N.↗

NASA NTRS2000

Robust Fixed-Structure Controller Synthesis

The ability to develop an integrated control system design methodology for robust high performance controllers satisfying multiple design criteria and real world hardware constraints constitutes a challenging task. The increasingly stringent performance specifications required for controlling such systems necessitates a trade-off between controller complexity and robustness. The principle challenge of the minimal complexity robust control design is to arrive at a tractable control design formulation in spite of the extreme complexity of such systems. Hence, design of minimal complexitY robust controllers for systems in the face of modeling errors has been a major preoccupation of system and control theorists and practitioners for the past several decades.

Corrado, Joseph R.↗

NASA NTRS2001

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

NASA NTRS2002

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

NASA NTRS2007

Best Practices for Reliable and Robust Spacecraft Structures

A study was undertaken to capture the best practices for the development of reliable and robust spacecraft structures for NASA s next generation cargo and crewed launch vehicles. In this study, the NASA heritage programs such as Mercury, Gemini, Apollo, and the Space Shuttle program were examined. A series of lessons learned during the NASA and DoD heritage programs are captured. The processes that "make the right structural system" are examined along with the processes to "make the structural system right". The impact of technology advancements in materials and analysis and testing methods on reliability and robustness of spacecraft structures is studied. The best practices and lessons learned are extracted from these studies. Since the first human space flight, the best practices for reliable and robust spacecraft structures appear to be well established, understood, and articulated by each generation of designers and engineers. However, these best practices apparently have not always been followed. When the best practices are ignored or short cuts are taken, risks accumulate, and reliability suffers. Thus program managers need to be vigilant of circumstances and situations that tend to violate best practices. Adherence to the best practices may help develop spacecraft systems with high reliability and robustness against certain anomalies and unforeseen events.

Raju, Ivatury S.↗

NASA NTRS2010

Robust Fault Detection and Isolation for Stochastic Systems

This paper outlines the formulation of a robust fault detection and isolation scheme that can precisely detect and isolate simultaneous actuator and sensor faults for uncertain linear stochastic systems. The given robust fault detection scheme based on the discontinuous robust observer approach would be able to distinguish between model uncertainties and actuator failures and therefore eliminate the problem of false alarms. Since the proposed approach involves precise reconstruction of sensor faults, it can also be used for sensor fault identification and the reconstruction of true outputs from faulty sensor outputs. Simulation results presented here validate the effectiveness of the robust fault detection and isolation system.

George, Jemin↗

NASA NTRS2008

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

autonomuys vehicles↗

NASA NTRS2012

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Kenny, Sean P.↗

NASA NTRS2012

On the Robustness Properties of M-MRAC

The paper presents performance and robustness analysis of the modified reference model MRAC (model reference adaptive control) or M-MRAC in short, which differs from the conventional MRAC systems by feeding back the tracking error to the reference model. The tracking error feedback gain in concert with the adaptation rate provides an additional capability to regulate not only the transient performance of the tracking error, but also the transient performance of the control signal. This differs from the conventional MRAC systems, in which we have only the adaptation rate as a tool to regulate just the transient performance of the tracking error. It is shown that the selection of the feedback gain and the adaptation rate resolves the tradeoff between the robustness and performance in the sense that the increase in the feedback gain improves the behavior of the adaptive control signal, hence improves the systems robustness to time delays (or unmodeled dynamics), while increasing the adaptation rate improves the tracking performance or systems robustness to parametric uncertainties and external disturbances.

Stepanyan, Vahram↗

NASA NTRS1996

Identification, Uncertainty Characterization and Robust Control Synthesis Applied to Large Flexible Structures Control

This paper demonstrates an approach to frequency domain identification for the explicit purpose of designing robust H(infinity) controllers. The approach transforms raw experimental data into a plant set estimate directly usable by modern robust control design software(e.g., Matlab Robust Control Toolboxes [11][2]). A key issue in control design from raw data is the question of whether the controller will work when applied to the true system. The main feature fo this approach is that the resulting controller in guaranteed to work as designed(when applied to the true system) to a prescribed statistical confidence. While the overall methodology addresses key theoretical issues, it has at the same time been specifically designed to support practical implementations. A simulation example is included to demonstrate the overall approach.

software↗

DOE OSTI2014

Robust Spring Drying in the Southwestern U.S. and Seasonal Migration of Wet/Dry Patterns in a Warmer Climate

This study compares climate simulations over the United States produced by a regional climate model with the driving global climate simulations as well as a large multi-model ensemble of global climate simulations to investigate robust changes in water availability (precipitation (P) – evapotranspiration (E)). A robust spring dry signal across multiple models is identified in the Southwest that results from a decrease in P and an increase in E in the future. In the boreal winter and summer, the prominent changes in P – E are associated with a north – south dipole pattern, while in spring, the prominent changes in P – E appear as an east – west dipole pattern. The progression of the north – south and east – west dipole patterns through the seasons manifests clearly as a seasonal “clockwise” migration of wet/dry patterns, which is shown to be a robust feature of water availability changes in the US consistent across regional and global climate simulations.

CMIP5↗

DOE OSTI2019

Robust optimization for intensity-modulated proton therapy with soft spot sensitivity regularization

In this work, we developed a novel computationally efficient robust optimization method for IMPT. The robustness is calculated as the spot sensitivity to both range and shift perturbations. The dose fidelity term is then regularized by the sensitivity term for the flexibility and trade-off between the dosimetry and the robustness. In the stress test, SenR is more resilient to unexpected uncertainties. These advantages in combination with its fast computation time make it a viable candidate for clinical IMPT planning.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2021

Explaining and predicting human behavior and social dynamics in simulated virtual worlds: reproducibility, generalizability, and robustness of causal discovery methods

Ground Truth program was designed to evaluate social science modeling approaches using simulation test beds with ground truth intentionally and systematically embedded to understand and model complex Human Domain systems and their dynamics Lazer et al. (Science 369:1060–1062, 2020). Our multidisciplinary team of data scientists, statisticians, experts in Artificial Intelligence (AI) and visual analytics had a unique role on the program to investigate accuracy, reproducibility, generalizability, and robustness of the state-of-the-art (SOTA) causal structure learning approaches applied to fully observed and sampled simulated data across virtual worlds. In addition, we analyzed the feasibility of using machine learning models to predict future social behavior with and without causal knowledge explicitly embedded. In this paper, we first present our causal modeling approach to discover the causal structure of four virtual worlds produced by the simulation teams—Urban Life, Financial Governance, Disaster and Geopolitical Conflict. Our approach adapts the state-of-the-art causal discovery (including ensemble models), machine learning, data analytics, and visualization techniques to allow a human-machine team to reverse-engineer the true causal relations from sampled and fully observed data. We next present our reproducibility analysis of two research methods team’s performance using a range of causal discovery models applied to both sampled and fully observed data, and analyze their effectiveness and limitations. We further investigate the generalizability and robustness to sampling of the SOTA causal discovery approaches on additional simulated datasets with known ground truth. Our results reveal the limitations of existing causal modeling approaches when applied to large-scale, noisy, high-dimensional data with unobserved variables and unknown relationships between them. We show that the SOTA causal models explored in our experiments are not designed to take advantage from vasts amounts of data and have difficulty recovering ground truth when latent confounders are present; they do not generalize well across simulation scenarios and are not robust to sampling; they are vulnerable to data and modeling assumptions, and therefore, the results are hard to reproduce. Finally, when we outline lessons learned and provide recommendations to improve models for causal discovery and prediction of human social behavior from observational data, we highlight the importance of learning data to knowledge representations or transformations to improve causal discovery and describe the benefit of causal feature selection for predictive and prescriptive modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Robust state estimation of feeding–blending systems in continuous pharmaceutical manufacturing

State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. In this paper, to improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding–blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Finally and moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Robust cooperative control strategy for a platoon of connected and autonomous vehicles against sensor errors and control errors simultaneously in a real-world driving environment

In a real-world driving environment, a platoon of connected and autonomous vehicles (CAVs) is subject to many internal and external disturbances, resulting in uncertain vehicle dynamics. In general, the disturbances can be categorized into two types: disturbances due to vehicle sensor errors (e.g., GPS error) and disturbances due to vehicle control errors (e.g., actuator delay). In the literature, many control strategies have been proposed to improve the robustness of the CAV platoon against uncertain vehicle dynamics induced by these disturbances. However, most of these strategies only consider one type of disturbance and cannot tackle both types of disturbances simultaneously. Furthermore, they are designed to maximize the benefits of each vehicle in the platoon independently, which can deteriorate the performance of the platoon. Here, to address these problems, this study proposes a robust cooperative control (RCC) strategy to maneuver the vehicles in the platoon cooperatively to counteract the impacts of both types of disturbances. The RCC strategy is developed based on a minimax problem, where the maximization subproblem seeks to find the worst inputs for the uncertainty terms in the vehicle dynamics equation to minimize the platoon performance, while the minimization subproblem seeks to find the optimal control decisions for all subsequent vehicles to maximize the platoon performance in the worst case. To solve the minimax problem, this study proposes a globally convergent solution algorithm. It can solve the minimax problem very efficiently to enable real time deployment of the RCC strategy. Numerical application indicates that compared to the existing methods, the RCC strategy can dramatically improve the robustness of the CAV platoon against the uncertain vehicle dynamics induced by both vehicle state detection errors and vehicle control errors. Therefore, it can maneuver the CAV platoon safely and efficiently in a real-world driving environment.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Identifying Robust Decarbonization Pathways for the Western U.S. Electric Power System Under Deep Climate Uncertainty

Climate change threatens the resource adequacy of future power systems. Existing research and practice lack frameworks for identifying decarbonization pathways that are robust to climate-related uncertainty. We create such an analytical framework, then use it to assess the robustness of alternative pathways to achieving 60% emissions reductions from 2022 levels by 2040 for the Western U.S. power system. Our framework integrates power system planning and resource adequacy models with 100 climate realizations from a large climate ensemble. Climate realizations drive electricity demand; thermal plant availability; and wind, solar, and hydropower generation. Among five initial decarbonization pathways, all exhibit modest to significant resource adequacy failures under climate realizations in 2040, but certain pathways experience significantly less resource adequacy failures at little additional cost relative to other pathways. By identifying and planning for an extreme climate realization that drives the largest resource adequacy failures across our pathways, we produce a new decarbonization pathway that has no resource adequacy failures under any climate realizations. This new pathway is roughly 5% more expensive than other pathways due to greater capacity investment, and shifts investment from wind to solar and natural gas generators. Our analysis suggests modest increases in investment costs can add significant robustness against climate change in decarbonizing power systems. Our framework can help power system planners adapt to climate change by stress testing future plans to potential climate realizations, and offers a unique bridge between energy system and climate modeling.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗