Kernel-based local order estimation of nonlinear nonparametric systems

We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples.

Polymer conditioning of alum sludge and discrepancies between estimates of the optimum dosage

The paper outlines the effects of polymer conditioning on alum sludge properties, such as floc size, density, fractal dimension (DF) and rheological properties. Experimental results demonstrate that polymer conditioning of alum sludge leads to: larger floc size with a plateau reached in higher doses; higher densities associated with higher doses; increased degree of compactness; and an initial decrease followed by an increase of supernatant viscosity with continued increase in polymer dose. The secondary focus of this paper dwells on a comparison of the estimates of optimum dose using different criteria that emanate from established dewatering tests such as CST, SRF, liquid phase viscosity and modified SRF as well as a simple settlement test in terms of CML30. Alum sludge was derived from a water works treating coloured, low-turbidity raw waters.

Multi-Party Negotiation When Agents Have Subjective Estimates of Bargaining Powers

This paper presents a method for generating Pareto-optimal solutions in multi-party negotiations. In this iterative method, decision makers (DMs) formulate proposals that yield a minimum payoff to their opponents. Each proposal belongs to the efficient frontier, DMs try to adjust to a common one. In this setting, each DM is supposed to have a given bargaining power. More precisely each DM is supposed to have a subjective estimate of the power of the different parties. We study the convergence of the method, and provide examples where there is no possible agreement resulting from it.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.