Basic model for membrane electrode assembly design for direct methanol fuel cells

This research proposes a model that predicts the effect of the anode diffusion layer and membrane properties on the electrochemical performance and methanol crossover of a direct methanol fuel cell (DMFC) membrane electrode assembly (MEA). It is an easily extensible, lumped DMFC model. Parameters used in this design model are experimentally obtainable, and some of the parameters are indicative of material characteristics. The quantification of these material parameters builds up a material database. Model parameters for various membranes and diffusion layers are determined by using various techniques such as polarization, mass balance, electrochemical impedance spectroscopy (EIS), and interpretation of the response of the cell to step changes in current. Since the investigation techniques cover different response times of the DMFC, processes in the cell such as transport, reaction and charge processes can be investigated separately. Properties of single layers of the MEA are systematically varied, and subsequent analysis enables identification of the influence of the layer's properties on the electrochemical performance and methanol crossover. Finally, a case study indicates that the use of a membrane with lower methanol diffusivity and a thicker anode micro-porous layer (MPL) yields MEAs with lower methanol crossover but similar power density.     

Maximum a posteriori estimation of activation energies that control silicon self-diffusion

Self-diffusion in crystalline silicon is controlled by a network of elementary steps whose activation energies are important to know in a variety of applications in microelectronic fabrication. The present work employs maximum a posteriori (MAP) estimation to improve existing values for these activation energies, based on self-diffusion data collected at different values of the loss rates for interstitial atoms to the surface. Parameter sensitivity analysis shows that for high surface loss fluxes, the energy for exchange between an interstitial and the lattice plays the leading role in determining the shape of diffusion profiles. At low surface loss fluxes, the dissociation energy of large-atom clusters plays a more important role. Subsequent MAP analysis provides significantly improved values for these parameters.     

An LFT approach to parameter estimation

In this paper we consider a unified framework for parameter estimation problems. Under this framework, the unknown parameters appear in a linear fractional transformation (LFT). A key advantage of the LFT problem formulation is that it allows us to efficiently compute gradients, Hessians, and Gauss–Newton directions for general parameter estimation problems without resorting to inefficient finite-difference approximations. The generality of this approach also allows us to consider issues such as identifiability, persistence of excitation, and convergence for a large class of model structures under a single unified framework.     

A Mathematica interface for FormCalc-generated code

This note describes a Mathematica interface for Fortran code generated by FormCalc. The interfacing code is set up automatically so that only minuscule changes in the driver files are required. The interface makes a function to compute the cross-section or decay rate available in Mathematica. This function depends on the model parameters chosen for interfacing in the Fortran code.     

Computation of the exact Cramer–Rao lower bound for the parameters of a nonsymmetric half-plane 2-D ARMA model

The Cramer–Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.     

Towards the robotic characterization of the constitutive response of composite materials

A historical and technical overview of a paradigm for automating research procedures on the area of constitutive identification of composite materials is presented. Computationally controlled robotic, multiple degree-of-freedom mechatronic systems are used to accelerate the rate of performing data-collecting experiments along loading paths defined in multidimensional loading spaces. The collected data are utilized for the inexpensive data-driven determination of bulk material non-linear constitutive behavior models as a consequence of generalized loading through parameter identification/estimation methodologies based on the inverse approach. The concept of the dissipated energy density is utilized as the representative encapsulation of the non-linear part of the constitutive response that is responsible for the irreversible character of the overall behavior. Demonstrations of this paradigm are given for the cases of polymer matrix composite materials systems. Finally, this computational and mechatronic infrastructure is used to create conceptual, analytical and computational models for describing and predicting material and structural performance.     

Parameter estimation from observations of first-passage times of the Ornstein–Uhlenbeck process and the Feller process

Renewal point processes show up in many different fields of science and engineering. In some cases the renewal points become the only observable parts of an anticipated hidden random variation of some physical quantity. The hypothesis might be that a hidden random process originating from zero or some other low value only becomes visible at the time of first crossing of some given value level, and that the process is restarted from scratch immediately after the level crossing. It might then be of interest to reveal the defining properties of this hidden process from a sample of observed first-passage times. In this paper the hidden process is first anticipated as a non-stationary Ornstein–Uhlenbeck (OU) process with unknown parameters that have to be estimated only by use of the information contained in a sample of first-passage times. The estimation method is a direct application of the Fortet integral equation of the OU process. A non-stationary Feller process is considered subsequently. As the OU process, the Feller process has a known transition probability distribution that allows the formulation of the integral equation. The described integral equation estimation method also provides a subjective graphical test of the applicability of the OU process or the Feller process when applied to a reasonably large sample of observed first-passage data.

These non-stationary processes have several applications in biomedical research, for example as idealized models of the neuron membrane potential. When the potential reaches a certain threshold the neuron fires, whereupon the potential drops to a fixed initial value, from where it continuously builds up again until the next firing. Also in civil engineering there are hidden random phenomena such as internal cracking or corrosion that after some random time break through to the material surface and become observable. However, the OU process has as a model of physical phenomena the defect of not being bounded to the negative side. This defect is not present for the Feller process, which therefore may provide a useful modeling alternative to the OU process.     

Generalized renewal process for repairable systems based on finite Weibull mixture

Repairable systems can be brought to one of possible states following a repair. These states are: ‘as good as new’, ‘as bad as old’ and ‘better than old but worse than new’. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last one, which is more realistic in practice. In this paper, a probabilistic model that is applicable to all of the three after-repair states, called generalized renewal process (GRP), is applied. Simplistically, GRP addresses the repair assumption by introducing the concept of virtual age into the stochastic point processes to enable them to represent the full spectrum of repair assumptions. The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions. The scope of the paper is to prove that a finite Weibull mixture, with positive component weights only, can be used as underlying distribution of the time to first failure (TTFF) of the GRP model, on condition that the unknown parameters can be estimated. To support the main idea, three examples are presented. In order to estimate the unknown parameters of the GRP model with m-fold Weibull mixture, the EM algorithm is applied. The GRP model with m mixture components distributions is compared to the standard GRP model based on two-parameter Weibull distribution by calculating the expected number of failures. It can be concluded that the suggested GRP model with Weibull mixture with an arbitrary but finite number of components is suitable for predicting failures based on the past performance of the system.     

Identification of concrete fracture parameters through size effect experiments

This paper deals with the identification of concrete fracture parameters through indirect methods based on size effect experiments. These methods utilize the size effect curve (structural strength versus structural size), associated with a certain specimen geometry, to identify the tensile strength and the initial fracture energy. These two parameters, in turn, are typically used to characterize the peak and the initial post-peak slope of the cohesive crack law. In the literature, two different approaches can be found for the calculation of the size effect curve: (a) an approach based on the polynomial interpolation of numerically calculated structural strengths of geometrically similar specimens of different sizes, and (b) the classical approach based on equivalent elastic fracture mechanics, which gives rise to the well-known Bažant’s size effect law (SEL). In this paper, the two approaches are first reviewed, the relationship between them is investigated, and a new procedure to identify the tensile strength using the SEL is proposed. Then several sets of experimental results, recently performed at the Politecnico di Milano, are analyzed with both approaches in order to assess their range of applicability and accuracy in the identification of the two fracture parameters specified above.