Avoiding Overfitting in Inverse Modeling of Chloride Migration in Concrete

Inverse analysis for reactive transport of chlorides through concrete in the presence of electric field is presented. The model is solved using MATLAB’s built-in solvers “pdepe.m” and “ode15s.m”. The results from the model are compared with experimental measurements from accelerated migration test and a function representing the lack of fit is formed. This function is optimised with respect to varying amount of key parameters defining the model. Levenberg-Marquardt trust-region optimisation approach is employed. The paper presents a method by which the degree of inter-dependency between parameters and sensitivity (significance) of each parameter towards model predictions can be studied on models with or without clearly defined governing equations. Eigen value analysis of the Hessian matrix was employed to investigate and avoid over-parametrisation in inverse analysis. We investigated simultaneous fitting of parameters for diffusivity, chloride binding as defined by Freundlich isotherm (thermodynamic) and binding rate (kinetic parameter). Fitting of more than 2 parameters, simultaneously, demonstrates a high degree of parameter inter-dependency. This finding is significant as mathematical models for representing chloride transport rely on several parameters for each mode of transport (i.e., diffusivity, binding, etc.), which combined may lead to unreliable simultaneous estimation of parameters.

Balancing the (carbon) budget: Using linear inverse models to estimate carbon flows and mass-balance 13C:15N labelling experiments in low oxygen sediments.

Over 1 million km² of seafloor experience permanent low-oxygen conditions within oxygen minimum zones (OMZs). OMZs are predicted to grow as a consequence of climate change, potentially affecting oceanic biogeochemical cycles. The Arabian Sea OMZ impinges upon the western Indian continental margin at bathyal depths (150 - 1500 m) producing a strong depth dependent oxygen gradient at the sea floor. The influence of the OMZ upon the short term processing of organic matter by sediment ecosystems was investigated using in situ stable isotope pulse chase experiments. These deployed doses of ¹³C:¹⁵N labeled organic matter onto the sediment surface at four stations from across the OMZ (water depth 540 - 1100 m; [O₂] = 0.35 - 15 μM). In order to prevent experimentally anoxia, the mesocosms were not sealed. ¹³C and ¹⁵N labels were traced into sediment, bacteria, fauna and ¹³C into sediment porewater DIC and DOC. However, the DIC and DOC flux to the water column could not be measured, limiting our capacity to obtain mass-balance for C in each experimental mesocosm. Linear Inverse Modeling (LIM) provides a method to obtain a mass-balanced model of carbon flow that integrates stable-isotope tracer data with community biomass and biogeochemical flux data from a range of sources. Here we present an adaptation of the LIM methodology used to investigate how ecosystem structure influenced carbon flow across the Indian margin OMZ. We demonstrate how oxygen conditions affect food-web complexity, affecting the linkages between the bacteria, foraminifera and metazoan fauna, and their contributions to benthic respiration. The food-web models demonstrate how changes in ecosystem complexity are associated with oxygen availability across the OMZ and allow us to obtain a complete carbon budget for the stationa where stable-isotope labelling experiments were conducted.

Cross-validation of geo-electrical and hydrogeological models to evaluate seawater intrusion in coastal aquifers

The validation of variable-density flow models simulating seawater intrusion in coastal aquifers requires information about concentration distribution in groundwater. Electrical resistivity tomography (ERT) provides relevant data for this purpose. However, inverse modeling is not accurate because of the non-uniqueness of solutions. Such difficulties in evaluating seawater intrusion can be overcome by coupling geophysical data and groundwater modeling. First, the resistivity distribution obtained by inverse geo-electrical modeling is established. Second, a 3-D variable-density flow hydrogeological model is developed. Third, using Archie's Law, the electrical resistivity model deduced from salt concentration is compared to the formerly interpreted electrical model. Finally, aside from that usual comparison-validation, the theoretical geophysical response of concentrations simulated with the groundwater model can be compared to field-measured resistivity data. This constitutes a cross-validation of both the inverse geo-electrical model and the groundwater model.
[Comte, J.-C., and O. Banton (2007), Cross-validation of geo-electrical and hydrogeological models to evaluate seawater intrusion in coastal aquifers, Geophys. Res. Lett., 34, L10402, doi:10.1029/2007GL029981.]

Inverse Gaussian Modeling of Turbulence-Induced Fading in Free-Space Optical Systems

We propose the inverse Gaussian distribution, as a less complex alternative to the classical log-normal model, to describe turbulence-induced fading in free-space optical (FSO) systems operating in weak turbulence conditions and/or in the presence of aperture averaging effects. By conducting goodness of fit tests, we define the range of values of the scintillation index for various multiple-input multiple-output (MIMO) FSO configurations, where the two distributions approximate each other with a certain significance level. Furthermore, the bit error rate performance of two typical MIMO FSO systems is investigated over the new turbulence model; an intensity-modulation/direct detection MIMO FSO system with Q-ary pulse position modulation that employs repetition coding at the transmitter and equal gain combining at the receiver, and a heterodyne MIMO FSO system with differential phase-shift keying and maximal ratio combining at the receiver. Finally, numerical results are presented that validate the theoretical analysis and provide useful insights into the implications of the model parameters on the overall system performance. © 2011 IEEE.

Kinematic modeling of Exechon parallel kinematic machine

The studies on PKMs have attracted a great attention to robotics community. By deploying a parallel kinematic structure, a parallel kinematic machine (PKM) is expected to possess the advantages of heavier working load, higher speed, and higher precision. Hundreds of new PKMs have been proposed. However, due to the considerable gaps between the desired and actual performances, the majorities of the developed PKMs were the prototypes in research laboratories and only a few of them have been practically applied for various applications; among the successful PKMs, the Exechon machine tool is recently developed. The Exechon adopts unique over-constrained structure, and it has been improved based on the success of the Tricept parallel kinematic machine. Note that the quantifiable theoretical studies have yet been conducted to validate its superior performances, and its kinematic model is not publically available. In this paper, the kinematic characteristics of this new machine tool is investigated, the concise models of forward and inverse kinematics have been developed. These models can be used to evaluate the performances of an existing Exechon machine tool and to optimize new structures of an Exechon machine to accomplish some specific tasks.

Improvement of the Performance of Hysteresis Compensation in SMA Actuators by Using Inverse Preisach Model in Closed – Loop Control System

The aim of this paper is to increase the performance of hysteresis compensation for Shape Memory Alloy (SMA) actuators by using inverse Preisach model in closed — loop control system. This is used to reduce hysteresis effects and improve accuracy for the displacement of SMA actuators. Firstly, hysteresis is identified by numerical Preisach model implementation. The geometrical interpretation from first order transition curves is used for hysteresis modeling. Secondly, the inverse Preisach model is formulated and incorporated in closed-loop PID control system in order to obtain desired current-to-displacement relationship with hysteresis reducing. The experimental results for hysteresis compensation by using this method are also shown in this paper.

The κ− μ / Inverse Gamma Fading Model

Statistical distributions have been extensively used in modeling fading effects in conventional and modern wireless communications. In the present work, we propose a novel κ − µ composite shadowed fading model, which is based on the valid assumption that the mean signal power follows the inverse gamma distribution instead of the lognormal or commonly used gamma distributions. This distribution has a simple relationship with the gamma distribution, but most importantly, its semi heavy-tailed characteristics constitute it suitable for applications relating to modeling of shadowed fading. Furthermore, the derived probability density function of the κ − µ / inverse gamma composite distribution admits a rather simple algebraic representation that renders it convenient to handle both analytically and numerically. The validity and utility of this fading model are demonstrated by means of modeling the fading effects encountered in body centric communications channels, which have been known to be susceptible to the shadowing effect. To this end, extensive comparisons are provided between theoretical and respective real-time measurement results. It is shown that these comparisons exhibit accurate fitting of the new model for various measurement set ups that correspond to realistic communication scenarios.