Stephan Pannier

Robust Design with Uncertain Data and Response Surface Approximation

The aim of the presented approach is to combine two views on robustness within a comprehensive design approach. These two main views are on the one hand the resistance to extraordinary (unforeseen) events, and on the other hand the consideration of uncertainty in structural parameters in order to monitor and reduce the variation of structural responses. To capture this, an enhanced robustness measure is defined and applied as design objective within the design approach which is based on the solution of an optimization problem. In addition to sophisticated numerical procedures to map physical phenomena and processes, the adequate description of available data covering the content of provided information is of prime importance. Thus, the generalized uncertainty model fuzzy randomness is applied. Furthermore, the robustness measure as well as the optimization approach are enhanced to fuzzy random based solutions.

Numerical structural monitoring with the uncertainty model fuzzy randomness

In this paper, an approach is introduced in which uncertain structural analysis, assessment of damage state and performance by indicators as well as prognosis of future structural behaviour and lifetime are combined. This approach is referred to as numerical structural monitoring and may be supported by results of in-situ monitoring. The numerical structural monitoring is based on the numerical simulation of the load and modification process. The parameters of this structural process are normally uncertain parameters which are mathematically described by means of imprecise probabilities. Here, the generalised uncertainty model fuzzy randomness is applied. A fuzzy stochastic structural analysis in the time domain is adopted to take into account fuzzy randomness of the load and modification process in the numerical simulation.

An inverse solution of the lifetime-oriented design problem

This paper presents a new solution of the lifetime-oriented design problem. This solution is based on a point-to-point allocation between the space of the design parameters and the space of structural responses. Each point in the space of the design parameters defines a feasible or non-feasible design, and all feasible designs guarantee compliance with a predetermined lifetime. From the set of feasible designs, one or more designs may be selected with the aid of technical or economic criteria. The presented solution permits the consideration of non-statistical data uncertainty, thereby leading to an uncertain lifetime. Because of the unavoidable information deficit, for example incomplete data in practical problems, the application of non-statistical data uncertainty is more realistic than the application of stochastic data models. The selection of feasible design variants is based on methods of explorative data analysis.

Reliability of Structures under Consideration of Uncertain Time-Dependent Material Behaviour

In this paper a concept for time-dependent reliability assessment of civil engineering structures is presented. This concept bases on the uncertainty model fuzzy randomness. The time-dependent behaviour of materials with fading memory is modelled with the aid of rheological elements using uncertain fractional time derivatives of strain. The presented method is applied to the reliability assessment of a pavement construction.

Optimal applicator placement in hepatic radiofrequency ablation on the basis of rare data

In this paper, a numerical procedure to determine an optimal applicator placement for hepatic radiofrequency ablation incorporating uncertain material parameters is presented. The main focus is set on the treatment of subjective and rare data-based information. For this purpose, we employ the theory of fuzzy sets and model uncertain parameters as fuzzy quantities. While fuzzy modelling has been established in structural engineering in the recent past, it is novel in biomedical engineering. Incorporating fuzzy quantities within an optimisation task is basically innovative. In our context, fuzzy modelling allows us to determine an optimal applicator placement that maximises the therapy success under the given uncertainty conditions. The applicability of our method is demonstrated by means of an example case.

Numerical design approaches of textile reinforced concrete strengthening under consideration of imprecise probability

The paper focuses on numerical approaches valuable in the design of strengthening layers made of textile reinforced concrete (TRC) applied on surfaces of RC structures. The presented methods aim at the design of structures that are components of significant buildings, e.g. power stations, historic valuable buildings and life lines. The generally existing uncertainty of material and geometry parameters of the RC structures and the TRC layers is modelled by imprecise probability. Reliability, lifetime and robustness are assessed by means of generalised uncertainty measures and considered as design objectives or constraints. Three computational methods are developed for the computation of preferential designs under consideration of imprecise probability. The methods are applied for the design of a porch roof strengthening comparing the robustness of different variants and for the reliability-based design of a T-beam strengthening.

Sectional global sensitivity measures

Abstract In this paper the approach of sectional sensitivity measures is introduced. Opposite to well-known global sensitivity measures not only a singleton value is provided to appraise the functional input–output interrelation but rather a more detailed description of these interrelation is enabled. Therefore, the domain of definition (input space) and/or the codomain (result space) are subdivided in a finite number of subdomains/subranges. The evaluation of global sensitivity measures in these subdomains/subranges allows for a proper appraisal of the functional interrelation in local regions. The theoretic background of sectional sensitivity measures is elaborated in detail and exemplified by means of analytical functions. The advantages of sectional sensitivity measures are discussed by means of a medical intervention planning of a radio frequency ablation.

Simulation-driven sequential metamodels for fuzzy reliability-based optimisation tasks

Fuzzy reliability-based optimisation tasks feature high-dimensional and highly non-linear response surfaces. Due to the computational expense, metamodels have to be applied, which are capable to approximate these response surfaces appropriately. In this paper, two complementary approaches of simulation-driven sequential metamodels are introduced for a fuzzy reliability-based optimisation. First, a function decomposition for a fuzzy reliability-based optimisation is worked out. It enables to build metamodels for the space of design variables and the space of uncertain variables separately. Second, local metamodels are applied to approximate the response surface adaptively. Thereby, the pointwise local approximations are controlled by the fuzzy reliability-based optimisation algorithm. In consequence, the function evaluation, e.g., finite element analysis, is only performed in regions of interest.