Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Uncertainty Updating in the Description of Coupled Heat and Moisture Transport in Heterogeneous Materials

To assess the durability of structures, heat and moisture transport need to be analyzed. To provide a reliable estimation of heat and moisture distribution in a certain structure, one needs to include all available information about the loading conditions and material parameters. Moreover, the information should be accompanied by a corresponding evaluation of its credibility. Here, the Bayesian inference is applied to combine different sources of information, so as to provide a more accurate estimation of heat and moisture fields [1]. The procedure is demonstrated on the probabilistic description of heterogeneous material where the uncertainties consist of a particular value of individual material characteristic and spatial fluctuations. As for the heat and moisture transfer, it is modelled in coupled setting [2]

MIT's interferometer CST testbed

The MIT Space Engineering Research Center (SERC) has developed a controlled structures technology (CST) testbed based on one design for a space-based optical interferometer. The role of the testbed is to provide a versatile platform for experimental investigation and discovery of CST approaches. In particular, it will serve as the focus for experimental verification of CSI methodologies and control strategies at SERC. The testbed program has an emphasis on experimental CST--incorporating a broad suite of actuators and sensors, active struts, system identification, passive damping, active mirror mounts, and precision component characterization. The SERC testbed represents a one-tenth scaled version of an optical interferometer concept based on an inherently rigid tetrahedral configuration with collecting apertures on one face. The testbed consists of six 3.5 meter long truss legs joined at four vertices and is suspended with attachment points at three vertices. Each aluminum leg has a 0.2 m by 0.2 m by 0.25 m triangular cross-section. The structure has a first flexible mode at 31 Hz and has over 50 global modes below 200 Hz. The stiff tetrahedral design differs from similar testbeds (such as the JPL Phase B) in that the structural topology is closed. The tetrahedral design minimizes structural deflections at the vertices (site of optical components for maximum baseline) resulting in reduced stroke requirements for isolation and pointing of optics. Typical total light path length stability goals are on the order of lambda/20, with a wavelength of light, lambda, of roughly 500 nanometers. It is expected that active structural control will be necessary to achieve this goal in the presence of disturbances

Determining Cosserat constants of 2D cellular solids from beam models

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence

A finite element based formulation for sensitivity studies of piezoelectric systems

Sensitivity Analysis is a branch of numerical analysis which aims to quantify the affects that variability in the parameters of a numerical model have on the model output. A finite element based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology

Modelling and simulation framework for reactive transport of organic contaminants in bed-sediments using a pure java object - oriented paradigm

Numerical modelling and simulation of organic contaminant reactive transport in the environment is being increasingly relied upon for a wide range of tasks associated with risk-based decision-making, such as prediction of contaminant profiles, optimisation of remediation methods, and monitoring of changes resulting from an implemented remediation scheme. The lack of integration of multiple mechanistic models to a single modelling framework, however, has prevented the field of reactive transport modelling in bed-sediments from developing a cohesive understanding of contaminant fate and behaviour in the aquatic sediment environment. This paper will investigate the problems involved in the model integration process, discuss modelling and software development approaches, and present preliminary results from use of CORETRANS, a predictive modelling framework that simulates 1-dimensional organic contaminant reaction and transport in bed-sediments