gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.

Using statistical inverse methods for detecting defects in electronic components

The thermal modeling of electronic components is mandatory to optimize the cooling design versus reliability. Indeed most of failures are due to thermal phenomena [1]. Some of them are neglected or omitted by lack of data: ageing, manufacturing issues like voids in glue or solder joints, or material properties variability. Transient measurements of the junction-to-board temperature supply real thermal behavior of the component and PCB assembly to complete these missing data[2]. To complement and supplement the numerical model, inverse methods identification based on a statistical deconvolution approach, such as Bayesian one, is applied on these measurements to extract a Foster RC thermal network. The identification algorithm performances have been demonstrated on numerical as well as experimental dataset. Furthermore defects or voids can be detected using the extracted Foster RC networks.

Analysis of Inverse Methods in Empirical Structural Mechanics

The application of inverse methods in empirical structural mechanics is the subject of this study. After a broad introduction to Inverse Problems (IPs), which includes a discussion of the many domains of application in general structural mechanics, the focus is limited to the critical area of material identification, with a special focus on the use of complete surveys. In this example, a more detailed explanation of the IPs to solve is provided, as well as the primary approaches to solving it. Lastly, there are several illustrations of exploratory uses of such techniques.

Adjoint-Based Inverse Design of Axial Compressor Airfoils

Design methodologies for axial compressor airfoils have undergone significant changes over the past decades. While inverse design methods have played a significant historical role, today they are mostly replaced by direct methods. Inverse methods do impose either the desired pressure or velocity distribution and search for the corresponding blade profile, in contrast to direct methods which modify directly the blade shape to reduce losses. Inverse methods therefore require the designer to know pressure or velocity profiles which provide low losses, and are as such mostly effective only in the hands of an experienced designer. Inverse methods, however, pose some advantages: through setting velocity profiles which feature good off-design performance, the computational cost for the design of profiles can be significantly reduced compared to direct methods, which require to simulate multiple operating points. Additionally, inverse methods offer a way to adapt blades for experimental testing if the wind tunnel imposes restrictions on e.g. Mach number, allowing for similar boundary layer conditions. Finally, inverse methods can be used to deduce the blade geometry from measured or published velocity distributions. Within this article, we aim to verify the use of inverse methods by applying more recent optimisation techniques to the inverse problem. Specifically, we test the performance of an inverse method that uses a gradient based technique to solve the inverse problem. The merits of the inverse method are investigated for different use cases. It is found that conventional, direct design methods are preferred for design improvement, although more expensive. The inverse method is, however, well-suited for adapting existing profiles to altered operating conditions, and for reproducing the blade shape based on published data.