Chaos in bubbling—nonlinear analysis and modelling

In the present paper, nonlinear features and analytical results for the chaotic bubbling from a submerged orifice are described. A chain of air bubbles was produced from the single orifice of in diameter and micro-convection induced by the bubble generation was recorded using hot-probe anemometer located close to the orifice. The air flow rate was varied widely from q=100 to and the aspects of bubbling were observed by high-speed video. The nonlinear analysis is performed for the time series data of hot-probe anemometer especially in the range of q=435-. The calculated largest Lyapunov exponent shows that with increase of air volume flow rate, the time period for the process of liquid flow to lose stability becomes shorter and at high air flow rate such as , it is shorter than the time period between subsequent bubbles. To explain such chaotic behaviors of bubbling, a simple model has been proposed. The model simulates the process of interaction between the elastic bubble wall and liquid. Simulation results compared well with the analytical results of experimental data. Summarizing, it is concluded that one of the reasons for chaos appearance is the nonlinear character of interaction between an elastic bubble wall and the liquid stream.     

Nonlinear multiobjective model-predictive control scheme for wastewater treatment process

A nonlinear multiobjective model-predictive control (NMMPC) scheme, consisting of self-organizing radial basis function (SORBF) neural network prediction and multiobjective gradient optimization, is proposed for wastewater treatment process (WWTP) in this paper. The proposed NMMPC comprises a SORBF neural network identifier and a multiple objectives controller via the multi-gradient method (MGM). The SORBF neural network with concurrent structure and parameter learning is developed as a model identifier for approximating on-line the states of WWTP. Then, this NMMPC optimizes the multiple objectives under different operating functions, where all the objectives are minimized simultaneously. The solution of optimal control is based on the MGM which can shorten the solution time. Moreover, the stability and control performance of the closed-loop control system are well studied. Numerical simulations reveal that the proposed control strategy gives satisfactory tracking and disturbance rejection performance for WWTP. Experimental results show the efficacy of the proposed method.     

Nonlinear time series forecasting with Bayesian neural networks

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.     

A tutorial review of economic model predictive control methods

An overview of the recent results on economic model predictive control (EMPC) is presented and discussed addressing both closed-loop stability and performance for nonlinear systems. A chemical process example is used to provide a demonstration of a few of the various approaches. The paper concludes with a brief discussion of the current status of EMPC and future research directions to promote and stimulate further research potential in this area.     

Fast economic model predictive control based on NLP-sensitivities

This study adapts the advanced step NMPC framework to Economic NMPC. Here, sufficient conditions for nominal stability are derived for NMPC controllers that incorporate economic stage costs with appropriate regularization. To guarantee these conditions, we derive a constructive strategy to calculate the regularization term directly. Moreover, we extend the sensitivity components in the advanced step NMPC framework to consider a rigorous path-following algorithm. This approach accounts for active set changes and allows much weaker constraint qualifications. Moreover, using an ℓ₁ formulation of the NMPC problem satisfies these constraint qualifications and allows more reliable solution of the moving horizon optimization problem, even in the presence of noise. Finally, all of these concepts are demonstrated on a detailed case study with a continuously stirred tank reactor.     

Fault identification for process monitoring using kernel principal component analysis

In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T²and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.     

Fabrication and amplification of Rhodamine B‐doped step‐index polymer optical fiber

A step‐index polymer optical fiber (SI POF) containing Rhodamine B in poly(methyl methacrylate) (PMMA) has been fabricated by a preform technique. Fluorescence of different fiber lengths were observed and discussed. A high gain (23 dB) for a SI POF with 60‐cm length, 400‐μm diameter was obtained. The Rhodamine B content of the doped SI POF is 5 ppm‐wt. The signal wavelength providing the highest gain for a 60 cm SI POF is around 630 nm, and the optimum fiber length is about 60 cm at 10 kW launched pump power. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 681–685, 2004     

On constrained infinite-time nonlinear optimal control

In this work, we consider the infinite-time optimal control of input affine nonlinear systems subject to point-wise in time inequality constraints on both the process inputs and outputs. Fundamental to solving this constrained infinite-time nonlinear optimal control (CITNOC) problem is the ability to calculate the value function of it's unconstrained counterpart, the infinite-time nonlinear optimal control (ITNOC) problem. Unfortunately, the traditional ITNOC solution procedure of specifying an objective function and then solving for the optimal control policy and corresponding value function is computationally intractable in all but the simplest of examples. However, in many cases one can easily identify a stabilizing feedback for near operating point regulation. Building from this local policy, the proposed method is to construct a meaningful optimal control objective function as well as its corresponding value function. These functions are then used to analyze the closed-loop stability of the proposed policy. Upon return to the constrained case the constructed objective and value functions are again used to develop a self-consistent constrained finite-time scheme that will, for the first time, provide an exact solution to the CITNOC problem. The mechanics of the proposed method are then illustrated by an example from chemical reactor control.     

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.