Identification of nonlinearities in dynamic process systems (original) (raw)

Data-based quantification of process nonlinearity

2015

The field of quantification of nonlinearity has drawn much attention from researchers in recent times. However, the scope of research on quantification of nonlinearity, especially for process plants, remains a vast area to explore. Nonlinearity in process plants may arise from two factors, namely, instruments and process characteristics. Instruments can induce nonlinearity due to their nonlinear dynamics or faults such as stiction, hysteresis and saturation. Process may themselves be nonlinear in nature or may show

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

Journal of Process Control, 2001

This paper considers certain practical aspects of the identi®cation of nonlinear empirical models for chemical process dynamics. The primary focus is the identi®cation of second-order Volterra models using input sequences that oer the following three advantages: (1) they are``plant friendly;'' (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the ®rst of these advantages, this paper de®nes a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra±Laguerre model. To illustrate the practical utility of the input sequences considered here, secondorder Volterra and Volterra±Laguerre models are developed that approximate the dynamics of a ®rst-principles model of methyl methacrylate polymerization. #

The identification of nonlinear models for process control using tailored

Journal of Process …, 2001

Estimation, Model Diagnosis, and Process Control Under the Normal Model

Copula-Based Markov Models for Time Series, 2020

This chapter introduces statistical methods for copula-based Markov models under the normal margin. First, the data structures and the idea of statistical process control are reviewed. The copula-based Markov models and essential assumptions are introduced as well. Next, we derive the likelihood functions under the first-order and the second-order Markov models and define the maximum likelihood estimators (MLEs). We then give the asymptotic properties of the MLEs. We propose goodness-of-fit methods to test the model assumptions based on a given dataset. In addition, a copula model selection method is discussed. We introduce an R package Copula.Markov to implement the statistical methods of this chapter. Finally, we analyze three real datasets for illustration. Keywords Asymptotic theory • Autoregressive model • Copula • Goodness-of-fit test • Maximum likelihood estimation • Markov chain • Normal distribution • Statistical process control 3.1 Serial Dependence, Statistical Process Control, and Copulas Researchers may collect data on a measurement of interest at different time points. The resultant dataset yields a time series dataset, where each measurement is recorded together with the time index. If two adjacent time points are close to each other, the measurements may be dependent. In particular, observed data collected in daily manufacturing processes are often dependent in the sense that the present sampling condition depends on the past ones. Thus, modeling dependence in time series data plays a crucial role in statistical process control (SPC) (Mastrangelo and Montgomery 1995; Montgomery 2009) and other objectives. Let {Y t : t = 1, …, n} be data collected on n different time points. In some cases, an unusually high (or low) value of Y t−1 may influence the next value of Y t (Bisgaard and Kulahci 2007). While the major goal of SPC is to monitor the marginal process parameters (mean and SD of Y t), the dependence parameter

Nonlinearity Assessment of Chemical Processes

Scientia Iranica, 2015

One of the most important issues in controller design and analysis of a nonlinear system is the degree of nonlinearity in the system. Helbig et al. proposed a method in which the system along with a linear reference model (which is the sum of a couple of rst order transfer functions) are stimulated with a set of input patterns. The outputs of these systems are then compared and the nonlinearity measure of the system is obtained as normalized di erence between the outputs of these two systems. In this paper, the linear reference model is replaced with two simpler linear models. The proposed method has been used for the assessment of the nonlinearity measure of various nonlinear systems that are used as standard benchmarks by the nonlinear process control research community. The results show that, despite the use of this simpler model with less parameters the calculated nonlinearity measure is almost similar to the one obtained by Helbig's method. Furthermore, the nonlinearity mea...

Approaches for Detection of Unstable Processes: A Comparative Study

Journal of Modern Applied Statistical Methods, 2015

A process is stable only when parameters of the distribution of a process or product characteristic remain same over time. Only a stable process has the ability to perform in a predictable manner over time. Statistical analysis of process data usually assume that data are obtained from stable process. In the absence of control charts, the hypothesis of process stability is usually assessed by visual examination of the pattern in the run chart. In this paper appropriate statistical approaches have been adopted to detect instability in the process and compared their performance with the run chart of considerably shorter length for assessing its patterns and ensuring the process stability.

Identification of nonlinearities in dynamic process systems (original) (raw)

Related papers