Overcoming the complexity of diagnostic problems due to sensor network architecture

In fault detection and diagnostics, limitations coming from the sensor network architecture are one of the main challenges in evaluating a system’s health status. Usually the design of the sensor network architecture is not solely based on diagnostic purposes, other factors like controls, financial constraints, and practical limitations are also involved. As a result, it quite common to have one sensor (or one set of sensors) monitoring the behaviour of two or more components. This can significantly extend the complexity of diagnostic problems. In this paper a systematic approach is presented to deal with such complexities. It is shown how the problem can be formulated as a Bayesian network based diagnostic mechanism with latent variables. The developed approach is also applied to the problem of fault diagnosis in HVAC systems, an application area with considerable modeling and measurement constraints.

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Natural convection adjacent to an inclined flat plate and in an attic space under various thermal forcing conditions

The effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment has been investigated numerically. The reduced equations are integrated by employing the implicit finite difference scheme or Ke1ler-box method and obtained the effect of heat due to viscous dissipation on the local skin-friction and loca1 Nusselt number at various stratification levels, for fluids having Prandtl number equals 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters and compared with the Finite Difference solutions. Effect of the heat transfer due to viscous dissipation and the temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region. A numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium is also considered for this study. Solutions are obtained using the implicit Finite Difference method and compared with the local non-similarity method. The velocity and temperature distributions for different values of stratification parameter are shown graphically. The results show many interesting aspects of complex interaction of the two buoyant mechanisms.

Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.