Dynamic Predictive Modeling Under Measured and Unmeasured Continuous-Time Stochastic Input Behavior

Many input variables of chemical processes have a continuous-time stochastic (CTS) behavior. The nature of these variables is a persistent, time-correlated variation that manifests as process variation as the variables deviate in time from their nominal levels. This work introduces methodologies in process identification for improving the modeling of process outputs by exploiting CTS input modeling under cases where the input is measured and unmeasured. In the measured input case, the output variable is measured offline, infrequently, and at a varying sampling rate. A method is proposed for estimating CTS parameters from the measured input by exploiting statistical properties of its CTS model. The proposed approach is evaluated based on both output accuracy and predictive ability several steps ahead of the current input measurement. Two parameter estimation techniques are proposed when the input is unmeasured. The first is a derivative-free approach that uses sample moments and analytical expressions for population moments to estimate the CTS model parameters. The second exploits the CTS input model and uses the analytical solution of the dynamic model to estimate these parameters. The predictive ability of the latter approach is evaluated in the same way as the measured input case. All of the data in this work were artificially generated under the probabilistic CTS model.Reprinted (adapted) with permission from Industrial and Engineering Chemistry Research 51 (2012): 5469, doi: 10.1021/ie201998b. Copyright 2012 American Chemical Society.</p

Continuous-time block-oriented nonlinear modeling with complex input noise structure

The continuous-time closed-form algorithms to sinusoidal input changes are proposed and presented for single-input, single-output (SISO) Hammerstein and Wiener systems with the first-order, second-order, and second-order plus lead dynamics. By simulation on theoretical Hammerstein and Wiener systems, the predicted responses agree exactly with the true process values. They depend on only the most recent input change. The algorithms to SISO Hammerstein and Wiener systems can be conveniently extended to the multiple-input, multiple-output (MIMO) systems as shown by the two-input, two-output examples and demonstrated by the simulated seven-input, five-output continuous stirred tank reactor (CSTR). The predictions and the simulated theoretical responses agree exactly and the predicted multiple CSTR outputs are close to the true process outputs. The proposed algorithms can predict the responses closer to the true values when comparing with the piece-wise step input approximation of the sinusoidal input changes on a simulated MIMO CSTR. In addition, as the noisy process input could be decomposed as summation of sinusoidal signals imposed on a step input change; the proposed algorithms can be employed to predict outputs for the noisy process inputs once the decomposition is done and the predicted noisy process outputs are shown to be close to the true ones, and are much better than the predictions based on the perfect filtering of the input signals.;The estimating equations based on the moment method are proposed for the Wiener dynamic process with stochastically correlated process input disturbances or noises and they work well for the parameter estimation. No one has ever proposed such method before. This approach has led to stable and robust estimators that have reasonable estimation errors and there is no need to measure the input disturbances or noises, or to calculate the time derivative of the observed output variable. Only the original process output observations over time are needed. The original model can be shifted to an approximate model under some conditions. This approximation is acceptable based on some analysis and derivation. The estimating equation methodology was shown to work well for the approximate model, while other existing methods do not work at all

Analysis and design of nonlinear systems in the frequency domain

Nonlinear system analyses have been widely applied in engineering practice, where the frequency domain approaches have been developed to satisfy the requirement of the analysis and design of nonlinear systems. However, there exist many problems with current techniques including the challenges with the nonlinear system representation using physically meaningful models, and difficulties with the evaluation of the frequency properties of nonlinear systems. In the present work, some new approaches, that have potential to be used to systematically address these problems, are developed based on the NDE (Nonlinear Differential Equation) model and the NARX (Nonlinear Auto Regressive with eXegenous input) model of nonlinear systems. In this thesis, the background of the frequency domain analysis and design of nonlinear systems is introduced in Chapter 1, and the existing approaches are reviewed in Chapter 2. In general, the frequency analysis of nonlinear systems is conducted based on the Volterra series representation of nonlinear systems, and as basic issues, the evaluation of the Volterra series representation and its convergence are discussed in Chapters 3 and 4, respectively. An extension of the existing frequency analysis and design techniques is discussed in Chapter 5 to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems. An experimental study is conducted in Chapter 6 to show how a nonlinear component can benefit the engineering system, such to emphasis the significance of developing the analysis and design approaches of nonlinear systems. The main contributions are summarized as below. (1) The GALEs is proposed that can accurately evaluate the system Volterra series representation. By using the GALEs, the solution to the NDE model or the NARX model of nonlinear systems can be obtained by simply dealing with a series of linear differential or difference equations, which can facilitate a wide range of nonlinear system analyses and associated practical applications. (2) A new criterion is derived to determine the convergence of the Volterra series representation of nonlinear systems described by a NARX model. The analysis is performed based on a new function known as Generalized Output Bound Characteristic Function (GOBCF), which is defined in terms of the input, output and parameters of the NARX model of nonlinear systems. Compared to the existing results, the new criterion provides a much more rigorous and effective approach to the analysis of the convergence conditions and properties of the Volterra series representation of nonlinear systems. (3) The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems. (4) Nonlinear damping can achieve desired isolation performance of a system over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Both simulation and laboratory experiments are studied, demonstrating the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems