Stacked Sparse Autoencoders and Classical Artificial Neural Networks for the Inverse Uncertainty Quantification of Dynamic Engineering Systems Models

Abstract

In the analysis of complex, safety-critical dynamic engineering systems, it is necessary to provide the uncertainty quantification of the outputs of the mathematical models (and the corresponding computer codes) used to simulate the system behavior. Such characterization is important for: (i) making robust decisions; (ii) optimally designing and operating such systems; and (iii) driving resource allocation for uncertainty reduction. To this aim, the uncertainty affecting the selected model inputs needs to be quantified (coherently with the information available on the system) and propagated through the code.

Two types of uncertainties are considered: (i) aleatory, due the random nature of several phenomena occurring during operation (here represented by multivariate probability distributions); (ii) epistemic, related to the incomplete knowledge about some phenomena and operating conditions (here described by intervals or sets).

Within this framework, the aim of the present paper is to propose an efficient approach for the inverse (joint) quantification of heterogeneous input uncertainties by means of code simulation results and raw output data coming from the analyzed engineering system. Emphasis is given to those challenging situations where: (i) the simulation models are computationally demanding; (ii) several input and/or output variables are functions of time; (iii) the experimental datasets employed exhibit complex, nonlinear dependence patterns.

The method is based on an efficient combination of: (i) Stacked Sparse Autoencoders (SSAEs) to reduce the problem dimensionality by projecting the time-dependent (output) variables onto a proper feature space; (ii) classical Artificial Neural Networks to lower the computational burden and replace the original simulation code by learning the relationship between the model inputs and the SSAE-based projected features; (iii) heuristic, global optimization tools (Genetic Algorithms) to perform the inverse identification (retrieval) of the uncertain input values corresponding to the available raw output data, projected onto the SSAE feature space; (iv) Sliced Normal (SN) distributions to fit the retrieved input data and quantify the overall input uncertainty: actually, it has been shown that the versatile SNs can characterize multivariate data and complex dependencies with minimal modeling effort; also, another advantage of SNs is that the corresponding uncertainty characterization can be given in terms of both probability distributions and semi-algebraic sets, which allows tightly enclosing the data.

The effectiveness and criticalities of the approach are tested on the quantification of mixed probabilistic and set-based uncertainties affecting the model of a dynamic aerospace system, proposed within the NASA Langley Uncertainty Quantification Challenge on Optimization Under Uncertainty.