Robust Design Framework Research Articles

Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties

It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions. In order to seek a more robust natural laminar flow control effect, it is necessary to develop an effective optimization design method. Meanwhile, attention must be given to the impact of crossflow (CF) instability brought on by the sweep angle. This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos. Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes (RANS) and simplified eN method, which can consider both Tollmien-Schlichting (TS) wave and crossflow vortex instability. We have performed gradient enhancement processing on the general Polynomial Chaos Expansion (PCE), which is advantageous to reduce the computational cost of single uncertainty propagation. This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition. The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations. The framework is applied to the robust design of a 25° swept wing with infinite span in transonic flow. The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy, and qualitatively reveals the factors that dominate in different flow field regions. By the robust optimization design, the mean and standard deviation of the drag coefficient can be reduced by 29% and 45%, respectively, and compared with the deterministic optimization design results, there is less possibility of forming shock waves under flight condition uncertainties. Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.

Surrogate-based optimization of capture chromatography platforms for the improvement of computational efficiency

In this work, we discuss the use of surrogate functions and a new optimization framework to create an efficient and robust computational framework for process design. Our model process is the capture chromatography unit operation for monoclonal antibody purification, an important step in biopharmaceutical manufacturing. Simulating this unit operation involves solving a system of non-linear partial differential equations, which can have high computational cost. We implemented surrogate functions to reduce the computational time and make the framework more attractive for industrial applications. This strategy yielded accurate results with a 93% decrease in processing time. Additionally, we developed a new optimization framework to reduce the number of simulations needed to generate a solution to the optimization problem. We demonstrate the performance of our new framework, which uses MATLAB built-in tools, by comparing its performance against individual optimization algorithms for problems with integer, continuous, and mixed-integer variables.

Two-stage vibration-suppression framework for optimal robust placements design and reliable PID gains design via set-crossing theory and artificial neural network

• Atwo-stage controlmodelfor design of placements and PID parametersis proposed. • The optimal placementsrobust design of uncertain vibration systemsis proposed. • The optimal PID gainsdesign withtime-dependent reliabilitylimitsis proposed. • The ANNis appliedin vibratory controloptimization to improve the efficiency. Structure vibration control is a significant problem in practical engineering, and Proportional-Integral-Differential (abbreviated as “PID”) control is widely used. The design of a PID controller contains the robust design of placements of actuators and sensors (abbreviated as “ASPD”), and the reliable design of PID gains. Because of the uncertain parameters in practical engineering, the controller designed from the deterministic system has the possibility of failure when applied to a practical system. To solve this problem, this paper proposed a two-stage framework for uncertain vibration active control systems via non-probabilistic time-dependent reliability (abbreviated as “NTDR”) and artificial neutral network (abbreviated as “ANN”). This framework decouples the ASPD and PID gains design as two stages. Considering the insufficient sample data, uncertain parameters are quantified with non-probabilistic interval forms. The optimization objective of ASPD combines the deterministic eigenvalues of controllability gramian or observability gramian, the robust theory and placements constraints to carry out the optimization. In this way the optimization objective can be less affected by uncertain parameters and has practical significance. For the reliable design of PID gains, the NTDR is adapted to evaluate the safety of an uncertain system. Then ANNs from uncertain parameters and PID gains to the optimization objective considering NTDR are established. By carrying out the optimization to the last ANN, the efficiency of optimization is improved while the accuracy is guaranteed. Two numerical examples and one experimental example show the practicability and effectiveness of the proposed method.

A Robust Design for Lifecycle Cost with Reliability Analysis Integration

Maintenance, repair, and overhaul (MRO) is the most significant cost driver over a complex engineering asset lifecycle. Therefore, high-value manufacturers are required to plan MRO occurrences to optimize the overhaul cost while achieving the desired performance. This trade-off imposes a shift towards a proactive maintenance strategy. However, creating a long-term proactive maintenance plan is challenging due to uncertainties in the performance of the asset and its critical components. Hence, this paper presents a robust design framework for the lifecycle cost estimation process by integrating reliability life data analysis. The level of data availability across the lifecycle is considered. The framework is proposed based on a literature review and the Delphi method. This study highlights that the level of robustness in the lifecycle cost estimates can be achieved by continuous feedback to the design phase and to the body of knowledge over the asset lifecycle. Moreover, this study suggests that the optimization model for the trade-off between cost and reliability should fulfil safety and environmental sustainability requirements when providing a cost-effective reliability solution.

A Robust Bayesian Optimization Framework for Microwave Circuit Design under Uncertainty

In modern electronics, there are many inevitable uncertainties and variations of design parameters that have a profound effect on the performance of a device. These are, among others, induced by manufacturing tolerances, assembling inaccuracies, material diversities, machining errors, etc. This prompts wide interests in enhanced optimization algorithms that take the effect of these uncertainty sources into account and that are able to find robust designs, i.e., designs that are insensitive to the uncertainties early in the design cycle. In this work, a novel machine learning-based optimization framework that accounts for uncertainty of the design parameters is presented. This is achieved by using a modified version of the expected improvement criterion. Moreover, a data-efficient Bayesian Optimization framework is leveraged to limit the number of simulations required to find a robust design solution. Two suitable application examples validate that the robustness is significantly improved compared to standard design methods.

Analysis of Methods to Estimate Abundance of River Cooters, Pseudemys concinna: An Example from the Santa Fe River, Florida

A multitude of different statistical models are commonly used to monitor trends in wildlife populations. Most are used to estimate abundance or survival (or both), and these estimates are then examined over time to infer trends in a population. The choice of which model to use is influenced by the key research question of interest and the types of data available. The accuracy and precision of any estimate from a population model are determined by whether the data meet the model assumptions. We assessed the performance of both closed and open capture–recapture models for determining trends in abundance and survival of River Cooters, Pseudemys concinna, in the Santa Fe River, Florida from 2009–2019. We fit three closed models to estimate abundance, one open model to estimate survival, and two robust design models to estimate both abundance and survival. We then used simulation to generate three datasets that represented different sampling designs, including one that mimics our field data, to assess model performance and compare tradeoffs in sampling design. We recommend using the robust design framework when possible as this design and model estimation returned accurate and precise estimates of abundance and survival. This model estimated survival ranging from 0.69–0.95 and capture probability from 0.21–0.25. This design requires consistent sampling of at least three events per year during a closed period, repeated over at least five years, to estimate survival between years. In situations where samples could not be repeated across years, closed population models are likely the most reliable framework in terms of model precision and accuracy. Overall, sampling designs that allow for repeated sampling and align the biology of the study species and the assumptions of the statistical model are likely the most informative approaches for sampling River Cooters and similar species.

Robust simulation-optimization framework for synthesis and design of natural gas downstream Incorporating renewable hydrogen network under uncertainty

Many intrinsic uncertainties are part of natural gas downstream synthesis, design, and operation. This work extends the earlier developed deterministic model to account for new decision variables, unit operations, and uncertainty in the network. The uncertainty includes the feedstock composition and flowrate, utility requirements, by-products, and final product market price. The proposed two-stage stochastic model includes new major processing units (helium recovery units), hydrogen production via renewable technologies (biomass gasification, water electrolysis), and operating modes. The stochastic formulation simultaneously considers uncertainty in 12 different model parameters. The model's first stage aims to find the optimal network's design variables, such as processing units, technologies, and operating modes common to all scenarios. The second stage is concerned with deriving operational variables, for example, the network's overall inlet feedstock flowrates, individual units' inlet flowrates, and units' capacity. Outcomes obtained for a range of uncertain material/energy feedstock and products/by-products market prices result in higher expected operating profits than the equivalent deterministic model. The analysis's key takeaways show that the most prevailing network consists of two syngas technologies: (1) auto-thermal reforming to feed a low-temperature Fischer Tropsch synthesis unit and (2) steam methane reforming for hydrogen production. Additionally, renewable hydrogen is produced via electrolysis and biomass gasification. There is an improvement of 2.22% in the objective function value using the stochastic approach instead of the deterministic.

Squaring a Circle: To What Extent Are Traditional Circuit Analogies Impeding Synthetic Biology?

Synthetic biology has been significantly shaped by modular design principles through analogies to electrical and computer engineering. Although convenient, these parallels often break down in practice, and we are still largely unable to engineer sophisticated systems that behave as predicted. As nature has achieved robust and intricate programs without requiring strict modularity, we may want to revisit genetic circuit design approaches. Rather than pursuing modularity, we could aim for a robust and scalable design framework that embraces the uncertainty that context dependence brings to engineering in a biological chassis. Systems and control theory offer a starting point, but a substantial conceptual leap will be needed to quantitatively predict system behavior and establish flexible context-aware design processes. Only by overcoming these hurdles shall we be able to capitalize on synthetic biology in particular—and on biotechnology in general—for medicine, environmental engineering, and energy production.

A Computational Framework for Human-Centric Vehicular Crashworthiness Design and Decision-Making Under Uncertainty

Abstract Government agencies, globally, strive to minimize the likelihood and frequency of human death and severe injury on road transport systems. From an engineering design standpoint, the minimization of these road accident effects on occupants becomes a critical design goal. This necessitates the quantification and management of injury risks on the human body in response to several vehicular impact variables and their associated uncertainties for different crash scenarios. In this paper, we present a decision-based, robust design (RD) framework to quantify and manage the impact-based injury risks on occupants for different computational model-based car crash scenarios. The key functionality offered is the designer's capability to conduct robust concept exploration focused on managing the selected impact variables and associated uncertainties, such that injury risks are controlled within acceptable levels. The framework's efficacy is tested for near-side impact scenarios with impact velocity and angle of impact as the critical variables of interest. Two injury criteria, namely, head injury criterion (HIC) and lateral neck injury criteria (Lateral Nij) are selected to quantitatively measure the head and neck injury risks in each crash simulation. Using the framework, a RD problem is formulated to determine the combination of impact variables that best satisfies the injury goals defined. The framework and associated design constructs are generic and support the formulation and decision-based robust concept exploration of similar problems involving models under uncertainty. Our focus in this paper is on the framework rather than the results per se.

Pareto-optimal performance-based robust design of braced excavations in soft clay with response surface methodology

This paper presents a methodology for robust design optimization of braced excavations in soft clay with response surface methodology based on the pareto-optimal trade-off between system performance and cost. As prediction of maximum ground settlement induced by excavation is generally accompanied by an implicit numerical model, the response surface methodology is employed to build the performance function with respect to both design parameters and uncertain geotechnical parameters. Then a pareto-optimal performance-based robust design framework of braced excavations in soft clay is formulated to find the optimal design that meets the design requirements while optimizing the system performance and construction cost. With the aid of a multi-objective optimization approach, trade-off relationship between performance robustness and cost efficiency are developed to help identify the most robust design based on the targeted performance levels. A design example of braced excavation in Taipei soft clay is used to illustrate the significance of the proposed methodology.

Poroelastic near-field inverse scattering

A multiphysics data analytic platform is established for imaging poroelastic interfaces of finite permeability (e.g., hydraulic fractures) from elastic waveforms and/or acoustic pore pressure measurements. This is accomplished through recent advances in design of non-iterative sampling methods to inverse scattering. The direct problem is formulated via the Biot equations in the frequency domain where a network of discontinuities is illuminated by a set of total body forces and fluid volumetric sources, while monitoring the induced (acoustic and elastic) scattered waves in an arbitrary near-field configuration. A thin-layer approximation is deployed to capture the rough and multiphase nature of interfaces whose spatially varying hydro-mechanical properties are a priori unknown. In this setting, the well-posedness analysis of the forward problem yields the admissibility conditions for the contact parameters. In light of which, the poroelastic scattering operator and its first and second factorizations are introduced and their mathematical properties are carefully examined. It is shown that the non-selfadjoint nature of the Biot system leads to an intrinsically asymmetric factorization of the scattering operator which may be symmetrized at certain limits. These results furnish a robust framework for systematic design of regularized and convex cost functionals whose minimizers underpin the multiphysics imaging indicators. The proposed solution is synthetically implemented with application to spatiotemporal reconstruction of hydraulic fracture networks via deep-well measurements.

Framework for effective robust design of building energy systems: Bridging the gap between predicted and actual energy use

Practitioners working on building performance simulations do seldom apply uncertainty and sensitivity analysis using state-of-the-art global methods in their daily workflow. With stricter building regulations imposed year by year, a corresponding change in workflow has been identified as one important way to bridge the increasing gap between predicted and actual energy use. This study describes how statistical methods from research can be adapted to an efficient workflow in a practical setting, concretised through description of a proposed framework and methodology, and application on a case study for a hospital in Northern Norway.

Multiscale thermal and thermo-structural optimization of three-dimensional lattice structures

This paper develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored thermal and thermo-structural characteristics. A multiscale approach is implemented where the discrete evaluations of small-scale lattice unit cell characteristics are converted to response surface models so that the properties exist as continuous functions of the lattice micro-parameters. The derived framework constitutes free material optimization in the space of manufacturable lattice micro-architecture. The optimization of individual lattice member dimensions is enabled by the adjoint method and the explicit expressions of the response surface material property sensitivities. The approach is demonstrated by solving thermal and thermo-structural optimization problems, significantly extending previous work which focused on linear structural response. The thermal optimization solution shows a design with improved optimality compared to the SIMP methodology. The thermo-structural optimization solution demonstrates the method’s capability for attaining a prescribed displacement in response to temperature gradients.

Persuasion-Based Robust Sensor Design Against Attackers With Unknown Control Objectives

We introduce a robust sensor design framework to provide “persuasion-based” defense in stochastic control systems against an unknown type attacker with a control objective exclusive to its type. We design a robust “linear-plus-noise” signaling strategy in order to persuade the attacker to take actions that lead to minimum damage with respect to the system's objective. The specific model we adopt is a Gauss–Markov process driven by a controller with a (partially) “unknown” malicious/benign control objective. We seek to defend against the worst possible distribution over control objectives in a robust way under the solution concept of Stackelberg equilibrium, where the sensor is the leader. We show that a necessary and sufficient condition on the covariance matrix of the posterior belief is a certain linear matrix inequality. This enables us to formulate an equivalent tractable problem, indeed a semidefinite program, to compute the robust sensor design strategies “globally” even though the original optimization problem is nonconvex and highly nonlinear. We also extend this result to scenarios where the sensor makes noisy or partial measurements.

Robust observer design and Nash-game-driven fuzzy optimization for uncertain dynamical systems

The estimation of system state is pivotal especially when system state can't be directly measured. In this paper, an optimal robust observer is proposed for uncertain dynamical systems. The fuzzy set theory is utilized to interpret the uncertainty bound. Unlike fuzzy-logic based observer, the proposed observer is not IF-THEN fuzzy rules-based. The uniform boundedness and ultimate uniform boundedness of estimation error are guaranteed. Then, the optimal design problem of the two tunable parameters is formulated under the framework of a two-player Nash game. The fuzzy-set theoretic cost functions of the two players are associated with the observer performance. We prove that the Nash equilibria does exist, and provide procedures in solving this optimal problem. Numerical simulations are conducted on an inverted pendulum using MATLAB/Simulink. The theory is illustrated by the observer design for an inverted pendulum subject to the earthquake excitation. The novelty of this work is an integrated framework for optimal robust observer design, which creatively blends the state estimation theory, the fuzzy set theory and the Nash game theory.

High-throughput computational design for 2D van der Waals functional heterostructures: Fragility of Anderson's rule and beyond

The heart of current high-throughput computational design for two-dimensional (2D) van der Waals (vdW) functional heterostructures is Anderson's rule (AR). This non-interacting model, however, inevitably introduces error and uncertainty in design results, problems which remain neglected. We report that, even for a non-magnetic system, the current high-throughput design framework commonly omits potential candidates in specific fields, such as heterostructure solar cell research. Therefore, this framework is fragile to extend to all subfields of functional vdW heterostructures. Through the analysis of several factors, such fragility is found to arise mainly from interlayer orbital coupling. This effect is omitted by AR and causes statistical deviation in the prediction of electronic properties. In the absence of a more advanced and universal physical model for describing interlayer orbital coupling, we propose a robust high-throughput design framework to reduce the omission of potential candidates. This work deepens the understanding of high-throughput design for 2D vdW functional heterostructures and provides insight into their development.

Optimizing machine learning models for granular NdFeB magnets by very fast simulated annealing

The macroscopic properties of permanent magnets and the resultant performance required for real implementations are determined by the magnets’ microscopic features. However, earlier micromagnetic simulations and experimental studies required relatively a lot of work to gain any complete and comprehensive understanding of the relationships between magnets’ macroscopic properties and their microstructures. Here, by means of supervised learning, we predict reliable values of coercivity (μ0Hc) and maximum magnetic energy product (BHmax) of granular NdFeB magnets according to their microstructural attributes (e.g. inter-grain decoupling, average grain size, and misalignment of easy axes) based on numerical datasets obtained from micromagnetic simulations. We conducted several tests of a variety of supervised machine learning (ML) models including kernel ridge regression (KRR), support vector regression (SVR), and artificial neural network (ANN) regression. The hyper-parameters of these models were optimized by a very fast simulated annealing (VFSA) algorithm with an adaptive cooling schedule. In our datasets of randomly generated 1,000 polycrystalline NdFeB cuboids with different microstructural attributes, all of the models yielded similar results in predicting both μ0Hc and BHmax. Furthermore, some outliers, which deteriorated the normality of residuals in the prediction of BHmax, were detected and further analyzed. Based on all of our results, we can conclude that our ML approach combined with micromagnetic simulations provides a robust framework for optimal design of microstructures for high-performance NdFeB magnets.

Short‐term responses of freshwater mussels to floods in a southwestern U.S.A. river estimated using mark–recapture sampling

Abstract Floods can directly affect riverine organisms by displacing them, and population‐level responses to floods can vary depending on flood magnitude and organism mobility. Benthic organisms can resist displacement until substrates become unstable, whereas mobile organisms are generally more resilient. Freshwater mussels are benthic organisms with low mobility, and there is limited research on their population‐level responses to floods. This study provides novel insights to population‐level responses of mussels to large floods (>500 m3/s). Population dynamics (i.e. abundance, survival, and site fidelity) and sampling efficiency (i.e. detection probability) were estimated in a robust design framework for four freshwater mussel species (Cyclonaias petrina, Cyclonaias pustulosa, Amblema plicata, and Tritogonia verrucosa) from 2017 to 2019 at two sites (upper and lower sites) within riffle habitats in the Colorado River, Texas, U.S.A. Individuals of each species were affixed with shellfish tags, with C. petrina and C. pustulosa individuals also being affixed with passive integrated transponder tags. Changes in population dynamics related to the flood event at each site were directly tested. During sampling, a major flood occurred at each of the two study sites; the floods differed in magnitude but were in the 99th percentile of historical flows at their respective gages. There were site‐ and species‐specific differences in estimated abundances, survival, and site fidelity during periods with the floods. Estimated abundances of C. petrina, C. pustulosa, and T. verrucosa were reduced 40–78% by the lesser flood magnitude (1,283 m3/s) at the upper site. Estimated abundances of C. petrina, C. pustulosa, and A. plicata were reduced 93–95% by the greater flood magnitude (4,332 m3/s) at the lower site. There was a reduction in survival of C. petrina at the upper site, while initially high survival at the lower site was reduced during the interval with the flood for all species. Finally, there was a reduction in site fidelity of C. pustulosa at the lower site. Floods reduced the abundance of all species within riffle habitats at the two sites. Large floods, therefore, affect population dynamics of mussels, but the fate of the displaced mussels is unknown, and with limited inference, reach‐scale effects are unknown. This study adds to the growing body of knowledge about responses of aquatic organisms to large floods, although quantification of recolonisation and fate of displaced mussels are needed to fully understand long‐term effects of large floods on mussel communities.

Possibility-Based Robust Control for Fuzzy Mechanical Systems

This article proposes a new robust control design framework for uncertain mechanical systems, which may be fully actuated or underactuated. The uncertainty is (possibly fast) time varying, which lies in prescribed fuzzy sets (hence fuzzy mechanical systems) and may be unbounded. The control goal is formulated as servo constraints (hence constraint-following control), which may be holonomic or nonholonomic. We introduce the possibility theory into the Lyapunov stability analysis (LSA), proposing possibility-based LSA (PBLSA), which allows a maximum failure possibility (generally small) prescribed by designers. It can be viewed as a generalization of the conventional LSA, and the resultant performance is interpreted in the context of possibility. By the PBLSA, a class of robust constraint-following controls that is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not</i> IF–THEN heuristic rules based is proposed, which renders approximate constraint following for the system performance with a prescribed maximal failure possibility. Optimal design of a control parameter considering both system performance and control cost is investigated. The benefits of the proposed design framework are discussed and simulations on two applications are given for demonstrations.

Robust Design for IRS-Aided Communication Systems With User Location Uncertainty

In this letter, we propose a robust design framework for IRS-aided communication systems in the presence of user location uncertainty. By jointly designing the transmit beamforming vector at the BS and phase shifts at the IRS, we aim to minimize the transmit power subject to the worse-case quality of service (QoS) constraint, i.e., ensuring the user rate is above a threshold for all possible user location error realizations. With unit-modulus, this problem is not convex. The location uncertainty in the QoS constraint further increases the difficulty of solving this problem. By utilizing techniques of Taylor expansion, S-Procedure and semidefinite relaxation (SDP), we transform this problem into a sequence of semidefinite programming (SDP) sub-problems. Simulation results show that the proposed robust algorithm substantially outperforms the non-robust algorithm proposed in the literature, in terms of probability of reaching the required QoS target.