Space Systems Resilience Engineering and Global System Reliability Optimisation Under Imprecision and Epistemic Uncertainty

The paper introduces the concept of design for resilience in the context of space systems engineering and proposes a method to account for imprecision and epistemic uncertainty. Resilience can be seen as the ability of a system to adjust its functioning prior to, during, or following changes and disturbances, so that it can sustain required operations under both expected and unexpected conditions. Mathematically speaking this translates into the attribute of a dynamical system (or time dependent system) to be simultaneously robust and reliable. However, the quantification of robustness and reliability in the early stage of the design of a space systems is generally affected by uncertainty that is epistemic in nature. As the design evolves from Phase A down to phase E, the level of epistemic uncertainty is expected to decrease but still a level of variability can exist in the expected operational conditions and system requirements. The paper proposes a representation of a complex space system using the so called Evidence Network Models (ENM): a non-directed (unlike Bayesian network models) network of interconnected nodes where each node represents a subsystem with associated epistemic uncertainty on system performance and failure probability. Once the reliability and uncertainty on the performance of the spacecraft are quantified, a design optimisation process is applied to improve resilience and performance. The method is finally applied to an example of preliminary design of a small satellite in Low Earth Orbit (LEO). The spacecraft is divided in 5 subsystems, AOCS, TTC, OBDH, Power and Payload. The payload is a simple camera acquiring images at scheduled times. The assumption is that each component has multiple functionalities and both the performance of the component and the reliability associated to each functionality are affected by a level of imprecision. The overall performance indicator is the sum of the performance indicators of all the components

Human sit-to-stand transfer modeling towards intuitive and biologically-inspired robot assistance

© 2016, Springer Science+Business Media New York. Sit-to-stand (STS) transfers are a common human task which involves complex sensorimotor processes to control the highly nonlinear musculoskeletal system. In this paper, typical unassisted and assisted human STS transfers are formulated as optimal feedback control problem that finds a compromise between task end-point accuracy, human balance, energy consumption, smoothness of motion and control and takes further human biomechanical control constraints into account. Differential dynamic programming is employed, which allows taking the full, nonlinear human dynamics into consideration. The biomechanical dynamics of the human is modeled by a six link rigid body including leg, trunk and arm segments. Accuracy of the proposed modelling approach is evaluated for different human healthy and patient/elderly subjects by comparing simulations and experimentally collected data. Acceptable model accuracy is achieved with a generic set of constant weights that prioritize the different criteria. Finally, the proposed STS model is used to determine optimal assistive strategies suitable for either a person with specific body segment weakness or a more general weakness. These strategies are implemented on a robotic mobility assistant and are intensively evaluated by 33 elderlies, mostly not able to perform unassisted STS transfers. The validation results show a promising STS transfer success rate and overall user satisfaction

Multi-fidelity surrogate-assisted design optimisation under uncertainty for computationally expensive aerospace applications

Virtual design analysis has become an indispensable component in most engineering disciplines. Despite the immense developments and availability of computational resources, the relative computational cost of high-fidelity simulations is getting more and more expensive. This opened the chapter of multi-fidelity learning techniques in the field of automated design optimisation. This work presents a novel multi-fidelity surrogate-assisted design optimisation approach for computationally expensive aerospace applications under uncertainty. The proposed optimisation framework overcomes the challenges of probabilistic design optimisation of computationally expensive problems and is capable of finding designs with optimal statistical performance for both single- and multi-objective problems, as well as constrained problems. Our approach performs the design optimisation with a limited computational budget thanks to the integrated multi-fidelity surrogates for design exploration and uncertainty quantification. The design optimisation is realised following the principles of Bayesian optimisation. The acquisition function balances exploration and exploitation of the design space and allocates the available budget efficiently considering the cost and accuracy of the fidelity levels. To validate the proposed optimisation framework, available multi-fidelity test functions were tailored for benchmarking problems under uncertainty. The benchmarks showed that it is profitable to use multi-fidelity surrogates when the computational budget is too limited to allow for the construction of an accurate surrogate with high-fidelity simulations but is large enough to generate a great number of low-fidelity data. The applicability of the proposed optimisation framework for aerospace applications is presented through optimisation studies of a propeller blade airfoil and a 3D propeller blade

SURROGATE-BASED OPTIMISATION UNDER UNCERTAINTY AND APPLICATIONS

In an expanding world with limited resources and increasing uncertainty, optimisation and uncertainty quantification (O&UQ) is becoming more a necessity rather than an option. Optimisation can turn a problem into a solution but neglecting the impact of uncertainty can lead to unreliable, or unsustainable, design solutions. The common approach based on safety margins to account for uncertainty in design and manufacturing is not adequate to fully capture the growing complexity of engineering systems and provide reliable and optimal solutions. In addition, this approach may eventually lead to oversized, resource-demanding systems. UTOPIAE is a European research and training network looking at cutting edge methods bridging O&UQ applied to aerospace systems. UTOPIAE mission is to develop new approaches to treat uncertainty in complex engineering systems and novel optimisation techniques to efficiently deal with large scale problems, many objectives and uncertainties. Aerospace engineering is taken as a paradigmatic area of research and development concerned with complex systems in which optimality and reliability are of paramount importance. However, these approaches are equally applicable to an ample variety of cases, where complexity and uncertainty play a major role, like e.g. transportation systems, water distribution and environmental remediation. UTOPIAE (funded by the European Commission through the H2020 Marie Sk\u142odowska-Curie Actions) runs from 2017 to 2021. The network consists of 15 partners across 6 European countries (including UK) and 1 partner in the USA, collecting mathematicians, engineers and computer scientists from academia, industry, public and private sectors. UTOPIAE is training the future generation of engineers and mathematicians who will be able to tackle the complexity of aerospace systems and provide greener, more affordable and safer transportation solutions. This session aims at presenting and discussing UTOPIAE and its challenges.

Surrogate models and surrogate-based design optimisation

Surrogate modelling refers to statistical and numerical techniques to model the relationship between multiple input variables and an output variable. A surrogate model can be considered as a multidimensional surface fitting of the output variable based on the observed data in multidimensional input space. Generally speaking, a surrogate model (a.k.a. response surface model or metamodel) is used to replace expensive numerical or physical experiments with a computationally cheap and sufficiently accurate model. In engineering, decisions are made on information obtained from various kinds of analyses. One way to get information and increase the knowledge of a problem is to conduct experiments; however, in many cases the cost and complexity of the experiments is so high that only a limited number, if any, of observations is feasible. For example, in aerospace engineering, experiments can be very expensive (e.g. extra-territorial missions) or can take a long time (e.g. high-fidelity simulations). Surrogate models help increase the knowledge gained from the observations and predict performance values which cannot be directly observed. Design optimisation aims at finding the best design solution among various alternatives. This typically requires the evaluation of many design candidates. In many engineering applications design evaluations are computationally expensive and there is a constraint on the optimisation budget which makes the optimisation impracticable. In such cases, surrogate models can be used to predict design performance with a small number of evaluations. However, surrogates are an approximation of the experiment of interest. Thus, a good strategy for surrogate-based design optimisation must take into account the inherent approximation errors. Outline: -Introduction into surrogate models and motivation -Performance measures Surrogates: -Least squares problem -RBF -Gaussian Process Regression (Kriging) -Multi-fidelity Gaussian Process Regression (co-Kriging) Surrogate-based optimisation: -General overview -Bayesian Optimisation (Efficient Global Optimization

DeepGPLAEN: Deep Gaussian Process Learning for Aerospace Engineering

DeepGPLAEN aims to investigate the applicability of Deep Gaussian Process (DGP) as a surrogate model for stochastic design optimisation in aerospace engineering. In addition, DGP performance is going to be compared with traditional Gaussian Process (GP) performance when leading with non-stationary optimisation problems. The expected output of the project will be a optimisation open source toolbox for surrogate based aerodynamic design problems under uncertainty

Response Surface Methodology

Response Surface Methods (RSMs) are statistical and numerical models that approximate the relationship between multiple input variables and an output variable. This chapter introduces the methodology and its importance for engineer- ing design optimisation. The basic steps to build RSMs and validate the model accuracy are explained. An overview of three classical methods (Least Squares, Radial Basis Functions, and Kriging) is provided. A simple wing structure design optimisation problem is used to illustrate the different phases of the response surface methodology and its application to design optimisation. This example also includes the case of noisy data