Set Of Parameter Vectors Research Articles

STABLE – a stability algorithm for parametric model reduction by matrix interpolation

ABSTRACTIn this article, an algorithm guaranteeing asymptotic stability for parametric model order reduction by matrix interpolation is proposed for the general class of high-dimensional linear time-invariant systems. In the first step, the system matrices of the high-dimensional parameter-dependent system are computed for a set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method and stabilized, if necessary. Secondly, the low-order systems are transformed into a consistent set of generalized coordinates. Thirdly, a new procedure using semidefinite programming is applied to the low-order systems, converting them into strictly dissipative form. Finally, an asymptotically stable reduced order model can be calculated for any new parameter vector of interest by interpolating the system matrices of the local low-order models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications. The method is illustrated by two numerical examples.

Parameter estimation algorithms for multivariable Hammerstein CARMA systems

This paper considers parameter identification problems for multivariable Hammerstein controlled autoregressive moving average (CARMA) systems. We transform a multivariable Hammerstein CARMA system into a new identification model which contains a set of bilinear parameter vectors, i.e., two sets of parameter vectors. To solve the difficulty of estimating the two sets of parameter vectors, this paper constructs two different forms of the identification model in each of which the output is linear about one set of parameter vectors, and presents an extended stochastic gradient algorithm to interactively estimate the two sets of parameter vectors by using the hierarchical identification principle. The proposed hierarchical identification algorithm has a higher computational efficiency than the over-parametrization model based stochastic gradient algorithm. The simulation results indicate that the proposed algorithm is effective, and an example of modeling a photovoltaic array system with the multivariable Hammerstein model is given.

Robust model-based fault diagnosis for air handling units

Fault detection and diagnosis (FDD) for heating, ventilation and air conditioning (HVAC) equipment significantly impact energy consumption in both residential and commercial buildings. In most modern building management systems (BMS), HVAC historical data logs in large quantity and high resolution are recorded and available for further online or offline analysis, including automated FDD. In this paper, a model-based fault diagnosis method is developed by applying support vector machine (SVM) techniques to model parameters recursively calculated by an online estimator. The estimator presumes an autoregressive time series model with exogenous variables (ARX). A real-world air handling unit (AHU) dataset containing process variables measured at regular intervals is pre-processed by the online estimation algorithm. Each data vector in the original dataset (measured), together with a small number of appropriately selected lags, is converted to a parameter vector representing the state at the same instant. The set of parameter vectors is sub-divided into classes by SVM, enabling fault classification. Validation via experimental data demonstrates that the proposed hybrid approach produce superior performance measured by F-measure scores compared to alternative methods. Robustness to model uncertainty is also established.

Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation

Abstract. The development of methods for estimating the parameters of hydrologic models considering uncertainties has been of high interest in hydrologic research over the last years. In particular methods which understand the estimation of hydrologic model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth found growing research interest. Bárdossy and Singh (2008) presented a first Robust Parameter Estimation Method (ROPE) and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. The basic idea of this algorithm is to identify a set of model parameter vectors with high model performance called good parameters and subsequently generate a set of parameter vectors with high data depth with respect to the first set. Both steps are repeated iteratively until a stopping criterion is met. The results estimated in this case study show the high potential of the principle of data depth to be used for the estimation of hydrologic model parameters. In this paper we present some further developments that address the most important shortcomings of the original ROPE approach. We developed a stratified depth based sampling approach that improves the sampling from non-elliptic and multi-modal distributions. It provides a higher efficiency for the sampling of deep points in parameter spaces with higher dimensionality. Another modification addresses the problem of a too strong shrinking of the estimated set of robust parameter vectors that might lead to overfitting for model calibration with a small amount of calibration data. This contradicts the principle of robustness. Therefore, we suggest to split the available calibration data into two sets and use one set to control the overfitting. All modifications were implemented into a further developed ROPE approach that is called Advanced Robust Parameter Estimation (AROPE). However, in this approach the estimation of the good parameters is still based on an ineffective Monte Carlo approach. Therefore we developed another approach called ROPE with Particle Swarm Optimisation (ROPE-PSO) that substitutes the Monte Carlo approach with a more effective and efficient approach based on Particle Swarm Optimisation. Two case studies demonstrate the improvements of the developed algorithms when compared with the first ROPE approach and two other classical optimisation approaches calibrating a process oriented hydrologic model with hourly time step. The focus of both case studies is on modelling flood events in a small catchment characterised by extreme process dynamics. The calibration problem was repeated with higher dimensionality considering the uncertainty in the soil hydraulic parameters and another conceptual parameter of the soil module. We discuss the estimated results and propose further possibilities in order to apply ROPE as a well-founded parameter estimation and uncertainty analysis tool.

Track-draw: A graphical interface for controlling the parameters of a speech synthesizer

In this report we describe a graphical interface for generating voiced speech using a frequency-domain implementation of the Klatt (1980) cascade formant synthesizer. The input to the synthesizer is a set of parameter vectors, calledtracks, which specify the overall amplitude, fundamental frequency, formant frequencies, and formant bandwidths at specified time intervals. Tracks are drawn with the aid of a computer mouse that can be used either inpoint-draw mode, which selects a parameter value for a single time frame, or inline-draw mode, which uses piecewise linear interpolation to connect two user-selected endpoints. Three versions of the program are described: (1) SYNTH draws tracks on an empty time-frequency grid, (2) SPECSYNTH creates a spectrogram of a recorded signal upon which tracks can be superimposed, and (3) SWSYNTH is similar to SPECSYNTH, except that it generatessine-wave speech (Remez, Rubin, Pisoni, & Carrell, 1981) using a set of time-varying sinusoids rather than cascaded formants. The program is written for MATLAB, an interactive computing environment for matrix computation. Track-Draw provides a useful tool for investigating the perceptually salient properties of voiced speech and other sounds.

Response of the Eastern Scheldt ecosystem to a changing environment: Functional or adaptive?

A storm-surge barrier situated at the mouth of the Eastern Scheldt (Oosterschelde) estuary (S.W. Netherlands) and two secondary dams in the northern and eastern parts of the estuary were completed by 1987. The exchange between the Eastern Scheldt and the North Sea, the freshwater discharges into the estuary and the flow velocities decreased. The results of an extensive ecological research programme in the Eastern Scheldt before and during the building of the storm-surge barrier were integrated into a dynamical ecosystem model. With this simulation model, the carbon and nutrient fluxes between the most dominant functional groups of the Eastern Scheldt ecosystem could be quantified. Subsequent research (after completion of the storm-surge barrier) allowed a quantification of the impact of the engineering works on the ecosystem of the Eastern Scheldt, and therefore the ecosystem model was calibrated for the pre- and post-barrier periods. Both calibrations resulted in a set of parameter vectors. Each set reflects the uncertainty in the calibration result for the variables and the period for which the model was calibrated. Results of the calibrations are compared with respect to the carbon flows of the ecosystem. By definition, adaptive responses take place within the functional groups of the model, while functional responses occur between the functional groups of the model. The simulation model is used to test whether the ecosystem response to the changing environment is functional or adaptive. It is shown that while the modelled ecosystem is superficially unchanged, adaptive responses still take place within the functional groups of phytoplankton and (probably) zooplankton.

Parametric eigenstructure assignment by output-feedback control: the case of multiple eigenvalues

This paper deals with closed-loop eigenstructure assignment by output-feedback control in linear multivariable systems for the general case of multiple eigenvalues. The approach is algebraic in nature and operates directly on the closed-loop characteristic equation using fundamental properties of determinants and their derivatives. A compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non-uniqueness of the solution of the eigenvalue-assignment problem. Some of these parameter vectors assume restricted forms while others are free. A computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least-square-error sense. An illustrative numerical example is included.