Membership-set estimation using random scanning and principal component analysis

A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake

Application of flexible recipes for model building, batch process optimization and control

Unlike the traditionally fixed recipes in batch process operation, flexible recipes allow the adjustment of some of its relevant recipe items. These adjustments can either be predefined in cases of planned experimentation, or suggested by a formal process optimization or control algorithm on the basis of actual information. In both the response surface methodology and the simplex evolutionary operation (EVOP), some well-known methods for empirical model building and process optimization, flexible recipes are involved. Another application of flexible recipes arises in a feedforward quality control strategy of batch processes when variations in market or process conditions are known a priori. The experimental results of these strategies are presented for the batchwise production of benzylalcohol on a pilotplant scale. Experiments have been performed to obtain a reliable model of the yield. On the basis of this model, better process conditions have been suggested, which substantially deviate from the final simplex resulted from experiments within simplex EVOP. Finally, an adaptive feedforward control strategy has been applied for a priori known disturbances in the process inputs

A numerical study of the F-model with domain-wall boundaries

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multi-cluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyse local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Sylju{\aa}sen and Zvonarev, and recently studied by Lyberg et al. We point out '(anti)ferroelectric' oscillations close to the corresponding frozen regions as well as 'higher-order' oscillations forming an intricate pattern with saddle-point-like features.Comment: v4: 15 pages, 11 figures, 1 table; various minor improvements; supplementary material available upon reques

Linear regression techniques for state-space models with application to biomedical/biochemical example

In this paper a novel approach to estimate parameters in an LTI continuous-time statespace model is proposed. Essentially, the approach is based on a so-called pqR-decomposition of the numerator and denominator polynomials of the system’s transfer function. This approach allows the physical knowledge of the system to be preserved. As an illustrative example, a biomedical/biochemical process with two compartments in parallel and with first-order reaction is used.First, the process is approximated by a discrete-time state-space model. Next, after deriving the corresponding discrete-time transfer function, the rational transfer function is decomposed into pqR form and then reparametrized to obtain a set of linear regressive equations. Subsequently, the unknown linear regression parameters, which are a polynomial function of the original physical parameters, are uniquely estimated from real data of the biomedical/biochemical process using the ordinary least-squares method. This approach is favourable when there is a need to preserve physical interpretations in the parameters. Furthermore, by taking into account the original model structure, a smaller number of parameters than in the case of direct transfer function estimation may result and the identifiability property naturally appears

Uncertainty propagation and speculation in projective forecasts of environmental change: a lake-eutrophication example

The issue of whether models developed for current conditions can yield correct predictions when used under changed control, as is often the case in environmental management, is discussed. Two models of different complexity are compared on the basis of performance criteria, but it appears that good performance at the calibration stage does not guarantee correctly predicted behavior. A requirement for the detection of such a failure of the model is that the prediction uncertainty range is known. Two techniques to calculate uncertainty propagation are presented and compared: a stochastic first-order error propagation based on the extended Kalman filter (EKF), and a newly developed and robust Monte Carlo set-membership procedure (MCSM). The procedures are applied to a case study of water quality, generating a projective forecast of the algal dynamics in a lake (Lake Veluwe) in response to management actions that force the system into a different mode of behavior. It is found that the forecast from the more complex model falls within the prediction uncertainty range, but its informative value is low due to large uncertainty bounds. As a substitute for time-consuming revisions of the model, educated speculation about parameter shifts is offered as an alternative approach to account for expected but unmodelled changes in the system

Dynamical Eigenmodes of Star and Tadpole Polymers

The dynamics of phantom bead-spring chains with the topology of a symmetric star with $f$ arms and tadpoles ($f=3$, a special case) is studied, in the overdamped limit. In the simplified case where the hydrodynamic radius of the central monomer is $f$ times as heavy as the other beads, we determine their dynamical eigenmodes exactly, along the lines of the Rouse modes for linear bead-spring chains. These eigenmodes allow full analytical calculations of virtually any dynamical quantity. As examples we determine the radius of gyration, the mean square displacement of a tagged monomer, and, for star polymers, the autocorrelation function of the vector that spans from the center of the star to a bead on one of the arms.Comment: 21 pages in double spacing preprint format, 5 figures, minor changes in the "Discussion" section, to appear in JSTA

Climate control of a bulk storage room for foodstuffs

A storage room contains a bulk of potatoes that produce heat due to respiration. A ventilator blows cooled air around to keep the potatoes cool and prevent spoilage. The aim is to design a control law such that the product temperature is kept at a constant, desired level. This physical system is modelled by a set of nonlinear coupled partial differential equations (pde's) with nonlinear input. Due to their complex form, standard control design will not be adequate. A novel modelling procedure is proposed. The input is considered to attain only discrete values. Analysis of the transfer functions of the system in the frequency domain leads to a simplification of the model into a set of static ordinary differential equations ode's). The desired control law is now the optimal time to switch between the discrete input values on an intermediate time interval. The switching time can be written as a symbolic expression of all physical parameters of the system. Finally, a dynamic controller can be designed that regulates the air temperature on a large time interval, by means of adjustment of the switching time