Shankar Narasimhan S

This article is concerned with the identification of autoregressive models with exogenous inputs (ARX). Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized to estimate ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input- output orders and delay. In this paper, we propose a novel automated spectral decomposition framework that recovers orders, delay, output noise distribution, along with parameter estimates. The proposed algorithm systematically estimates all the parameters in two steps. The first step estimates the order bv examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the proposed method's efficacy and are observed to deliver consistent estimates even at low signal-to-noise ratio (SNR).

In process design, the insights obtained by applying pinch technology have played an important role in maximizing energy efficiency through energy integration [1]. Pinch technology exclusively addresses temperature variations in process streams resulting from indirect heat exchange. The analysis does not take into account temperature changes in process streams induced by changes in stream pressure. In this work, a systematic procedure for applying pinch analysis to the Liquid Air Energy Storage (LAES) process is proposed. In this process, air undergoes significant pressure changes, which results in phase changes as well as wide variations in the specific heat capacity. Since the air temperature varies from well above ambient to well below ambient conditions, multiple minimum approach temperature specifications have to be imposed. A parameterized version of the Grand Composite Curves (GCCs) is proposed for pinch analysis that takes into account for all of these special features. The parameterized GCCs are used to identify the feasible design space for a LAES process.

Identification of autoregressive models with exogenous input (ARX) is a classical problem in system identification. This article considers the errors-in-variables (EIV) ARX model identification problem, where input measurements are also corrupted with noise. The recently proposed Dynamic Iterative Principal Components Analysis (DIPCA) technique solves the EIV identification problem but is only applicable to white measurement errors. We propose a novel identification algorithm based on a modified DIPCA approach for identifying the EIV-ARX model for single-input, single-output (SISO) systems where the output measurements are corrupted with coloured noise consistent with the ARX model. Most of the existing methods assume important parameters like input-output orders, delay, or noise-variances to be known. This work's novelty lies in the joint estimation of error variances, process order, delay, and model parameters. The central idea used to obtain all these parameters in a theoretically rigorous manner is based on transforming the lagged measurements using the appropriate error covariance matrix, which is obtained using estimated error variances and model parameters. Simulation studies on two systems are presented to demonstrate the efficacy of the proposed algorithm.

The paper is concerned with identifying transfer functions of individual input channels in minimal realization form of a Multi-Input Single Output (MISO) from the input-output data corrupted by the error in all the variables. Such a framework is commonly referred to as error-in-variables (EIV). A common approach in the existing methods for identification of MISO systems is to estimate a non-minimal order transfer function under a subset of simplistic assumptions like homoskedastic error variances, known order, and delay. In this work, we deal with the challenging problem of identifying order, delay in each input of minimal realization form separately while estimating the transfer functions. We also estimate the heteroskedastic noise variances in each of the multiple inputs and output variables. An automated approach for the identification of MISO systems of minimal realization form in the EIV framework is proposed. Numerical case studies are presented to illustrate the efficacy of the proposed algorithm in identifying the transfer function along with the order, delay, and noise variances.

Development of dynamic process models from input–output data, also known as system identification, is a well-studied problem. The classical approach to system identification assumes that the input variables are measured without error. However, in practice all data collected from evolving processes (inputs and outputs) will contain errors. System identification using noisy inputs and outputs is known as Errors-in-Variables (EIV) identification. Existing methods for EIV model identification assume that the error variances are known and/or assume the system order to be known. We propose a novel approach combining subspace-based identification and a dynamic iterative principal components approach for identifying EIV MIMO models. The proposed method simultaneously estimates process order, delay, model coefficients, and error variances using a rigorous theoretical basis. A benchmark simulation example from literature is used to exhibit the effectiveness of the proposed approach.

Pure component thermodynamic models are developed for solvent extraction involving ionic reaction equilibrium for distribution of macro concentrations of zirconium and hafnium between an aqueous phase containing HNO3 and an organic solvent phase containing diluted TBP. The concentration range considered is 10−03 to 100 M. A framework based on chemical speciation calculation is used for the purpose. Experimental procedures adopted to obtain the required solvent extraction data for modeling and validating these models are detailed. Measured equilibrium concentrations of total zirconium, total HNO3, total nitrate in the aqueous phase and total zirconium in the organic phase are used to obtain the thermodynamic parameters such as equilibrium constants and activity coefficient model parameters for zirconium and hafnium extraction systems. The novel framework is useful for computing equilibrium concentrations of all the species present in the respective systems. It is also demonstrated that the pure component models developed for extraction of zirconium and hafnium are effective over a wide range of concentrations. These pure component models can be used to simulate and optimize industrial scale zirconium – hafnium separation process.

Dynamic model identification from time series data is a critical component of process control, monitoring, and diagnosis. An important adjunct of model identification is the derivation of filtered estimates of the variables and consequent one-step-ahead prediction errors (residuals) which are very useful for model assessment and iterative model identification. In this work, we present an optimal filtering and residual generation method for the errors-in-variables (EIV) scenario, wherein both the input and output variable measurements are contaminated with errors. The main idea is to combine an EIV-identification strategy with the EIV-Kalman filter (EIV-KF) that is known to provide optimal filtered estimates and residuals of both inputs and outputs for a linear dynamical process in the EIV case. In this work, we combine the EIV-KF with the dynamic iterative principal component analysis (DIPCA) approach that has been recently developed for EIV model identification. This work assumes prominence in that the optimally generated residuals are critical to the tasks of model assessment, fault detection, and diagnosis. The use of residuals in model assessment and reidentification is illustrated in this article, while pointing out that the use of DIPCA alone leads to nonunique filtered estimates and hence nonunique residuals. We remark that the proposed method can be used with any other EIV identification technique.

Process industries have variables that are measured at different rates, with some measurements, such as composition or quality variables, obtained after associated measurement delays. This work introduces a novel “sampled output augmentation” method for fusing delayed and infrequent primary measurements within a multirate Kalman filter (KF) framework. This is a state-augmentation-based method and is more parsimonious than other approaches. The stability of the sampled output augmentation is analyzed. We analytically show the equivalence of the proposed method with the traditional fixed-lag smoothing method for a linear system. Extension to nonlinear systems through extended Kalman filter (EKF) is presented. Finally, we assess the performance of the proposed method in comparison with other available estimators through linear and non-linear case studies.

Optimal operation of water distribution networks can be posed as a scheduling problem where the objective is to meet the time varying demand while meeting constraints on supply, pressure etc. In the present work, we propose a robust optimization problem to address uncertainty in the parameters of the model used for optimization. The resulting problem is a second order cone program that can be solved efficiently. The formulation ensures a high probability of meeting the demands, adding to the practical significance. Further, we provide the results of applying this technique on a laboratory scale water distribution network.