Investigation of robust optimization and evidence theory with stochastic expansions for aerospace applications under mixed uncertainty

One of the primary objectives of this research is to develop a method to model and propagate mixed (aleatory and epistemic) uncertainty in aerospace simulations using DSTE. In order to avoid excessive computational cost associated with large scale applications and the evaluation of Dempster Shafer structures, stochastic expansions are implemented for efficient UQ. The mixed UQ with DSTE approach was demonstrated on an analytical example and high fidelity computational fluid dynamics (CFD) study of transonic flow over a RAE 2822 airfoil. Another objective is to devise a DSTE based performance assessment framework through the use of quantification of margins and uncertainties. Efficient uncertainty propagation in system design performance metrics and performance boundaries is achieved through the use of stochastic expansions. The technique is demonstrated on: (1) a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems and (2) a multi-disciplinary analysis of a supersonic civil transport. Finally, the stochastic expansions are applied to aerodynamic shape optimization under uncertainty. A robust optimization algorithm is presented for computationally efficient airfoil design under mixed uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions to create surrogate models utilized in the optimization process. To reduce the computational cost, output space mapping technique is implemented to replace the high-fidelity CFD model by a suitably corrected low-fidelity one. The proposed algorithm is demonstrated on the robust optimization of NACA 4-digit airfoils under mixed uncertainties in transonic flow. --Abstract, page iii

Enablers for uncertainty quantification and management in early stage computational design. An aircraft perspective

Presented in this thesis are novel methods for uncertainty quantification and management (UQ&M) in computational engineering design. The research has been motivated by the industrial need for improved UQ&M techniques, particularly in response to the rapid development of the model-based approach and its application to the (early) design of complex products such as aircraft. Existing work has already addressed a number of theoretical and computational challenges, especially regarding uncertainty propagation. In this research, the contributions to knowledge are within the wider UQ&M area. The first contribution is related to requirements for an improved margin management policy, extracted from the FP7 European project, TOICA (Thermal Overall Integrated Conception of Aircraft). Margins are traditional means to mitigate the effect of uncertainty. They are relatively better understood and less intrusive in current design practice, compared with statistical approaches. The challenge tackled in this research has been to integrate uncertainty analysis with deterministic margin allocations, and to provide a method for exploration and trade-off studies. The proposed method incorporates sensitivity analysis, uncertainty propagation, and the set-based design paradigm. The resulting framework enables the designer to conduct systematic and interactive trade-offs between margins, performances and risks. Design case studies have been used to demonstrate the proposed method, which was partially evaluated in the TOICA project. The second contribution addresses the industrial need to properly ‘allocate’ uncertainty during the design process. The problem is to estimate how much uncertainty could be tolerated from different sources, given the acceptable level of uncertainty associated with the system outputs. Accordingly, a method for inverse uncertainty propagation has been developed. It is enabled by a fast forward propagation technique and a workflow reversal capability. This part of the research also forms a contribution to the TOICA project, where the proposed method was applied on several test-cases. Its usefulness was evaluated and confirmed through the project review process. The third contribution relates to the reduction of UQ&M computational cost, which has always been a burden in practice. To address this problem, an efficient sensitivity analysis method is proposed. It is based on the reformulation and approximation of Sobol’s indices with a quadrature technique. The objective is to reduce the number of model evaluations. The usefulness of the proposed method has been demonstrated by means of analytical and practical test-cases. Despite some limitations for several specific highly non-linear cases, the tests confirmed significant improvement in computational efficiency for high dimensional problems, compared with traditional methods. In conclusion, this research has led to novel UQ&M tools and techniques, for improved decision making in computational engineering design. The usefulness of these methods with regard to efficiency and interactivity has been demonstrated through relevant test-cases and qualitative evaluation by (industrial) experts. Finally, it is argued that future work in this field should involve research and development of a comprehensive framework, which is able to accommodate uncertainty, not only with regard to computation, but also from the perspective of (expert) knowledge and assumptions

Uncertainty Quantification of the Responses of Transient Electromagnetic Disturbance Coupling to Transmission Lines Based on Stochastic Models

L'abstract è presente nell'allegato / the abstract is in the attachmen

Methodology for the Seismic Assessment of Earthen and Timber Historic Churches. Application to Peruvian Heritage

Historic buildings, and churches in particular, are one of the most complex existing structures not only because of the structural system complexity but also due to the limited documentation on their construction that is normally available. Amongst historic buildings, earthen and timber churches built across Latin-America are one of the least studied and most vulnerable structures, as past earthquakes have shown. For instance, the 2007 Pisco earthquake caused the collapse of many historic earthen and timber colonial churches in Peru. The thesis proposes a new framework for the seismic assessment of historic buildings that measures the uncertainty of the structural analysis and its influence on the structural diagnosis due to incomplete knowledge. The methodology is validated through application to two historic earthen and timber churches built in Peru in the 17th and 18th centuries, of different complexity and cultural value, which are representative of important Latin-American colonial building types. The most important variables that govern the seismic response of these churches are identified by means of numerical simulations. Through the application of the framework, the thesis provides a modeling and structural evaluation solution for planked timber vaults and a hypothesis on the cause of failure of these vaults during the 2007 Pisco earthquake. The influence of lack or shortage of knowledge on the structural diagnosis of the churches is discussed. Alterations to current guidelines for the assessment of historic buildings are proposed from the conclusions drawn from the study