Identifying static and dynamic prediction models for NOx emissions with evolving fuzzy systems

Antipollution legislation in automotive internal combustion engines requires active control and prediction of pollutant formation and emissions. Predictive emission models are of great use in the system calibration phase, and also can be integrated for the engine control and on-board diagnosis tasks. In this paper, fuzzy modelling of the NOx emissions of a diesel engine is investigated, which overcomes some drawbacks of pure engine mapping or analytical physical-oriented models. For building up the fuzzy NOx prediction models, the FLEXFIS approach (short for FLEXible Fuzzy Inference Systems) is applied, which automatically extracts an appropriate number of rules and fuzzy sets by an evolving version of vector quantization (eVQ) and estimates the consequent parameters of Takagi-Sugeno fuzzy systems with the local learning approach in order to optimize the least squares functional. The predictive power of the fuzzy NOx prediction models is compared with that one achieved by physical-oriented models based on high-dimensional engine data recorded during steady-state and dynamic engine states.This work was supported by the Upper Austrian Technology and Research Promotion. This publication reflects only the author's view. Furthermore, we acknowledge PSA for providing the engine and partially supporting our investigation. Special thanks are given to PO Calendini, P Gaillard and C. Bares at the Diesel Engine Control Department.Lughofer, E.; Macian Martinez, V.; Guardiola García, C.; Klement, EP. (2011). Identifying static and dynamic prediction models for NOx emissions with evolving fuzzy systems. Applied Soft Computing. 11(2):2487-2500. doi:10.1016/j.asoc.2010.10.004S2487250011

What is not clear in fuzzy control systems?

The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved

POST-LARAMIDE HISTORY OF NORTH-CENTRAL WYOMING

North-central Wyoming and surrounding areas have been the subject of geological investigations for more than a century. However, the presently accepted history of the region has not been revised in relation to changes in the science of geology. This study evaluated the assumptions on which this history was based and developed a new set of assumptions in keeping with recent advances. Assumptions previously used include: (1) physiographic and orogenic mountains originate at the same time and from the same processes; (2) all significant deformation occurred during the Laramide Orogeny; (3) all streams transverse to structure were superposed from the highest level of basin fill; and (4) the Subsummit Peneplain is a pediment and represents the maximum level of basin fill. I assumed that (1) physiographic mountains are not necessarily as old as the orogenic structures they contain; (2) significant deformation has occurred in post-Laramide time as an effect of the Yellowstone Hotspot; (3) any explanation of transverse streams must be documented by analysis of regional geological data; and (4) much of the Subsummit Peneplain is a composite of non-cyclic surfaces and therefore has no relation to the level of basin fill. The Subsummit Peneplain on the east flank of the Bighorn Mountains is a planation surface created in a subtropical climate in late Eocene time. It marks the level of Eocene basin fill. Slow regional uplift and net erosion occurred during Oligocene through early Pliocene time. Relatively minor deposition of air-fall ash punctuated this erosion but was rapidly removed by streams. Late Pliocene-early Pleistocene uplift associated with migration of the Yellowstone Hotspot and climatic change created the details of the present landscape. Thus, much of the landscape is a relic of Eocene time preserved by the ineffectiveness of more recent tectonic and climatic processes of landform evolution

On practical problems with the explanation of the difference between possibility and probability

In his famous paper "Fuzzy Sets as a Basis for a Theory of Possibility" (Zadeh, 1978) Professor Lofti Zadeh introduced the notion of possibility distribution [pi]x and tlie concept of possibility measure. He denned in the paper the possibility distribution function to be numerically equal to the membership function ([pi]x = [my]F). In this paper Professor Zadeh draws the special attention of the reader to the fact that: "... there is a fundamental difference between probability and possibility". To explain this difference he had given a special example illustrating the difference, which then was cited by many authors of books on Fuzzy Set Theory and gained great importance for understanding the notion of possibility. In the paper the author presents his doubts as to this important example, explains why it is incorrect and gives a correct version of the example based on the notion of possibility distribution of Dubois and Prade

A New Definition of the Fuzzy Set

The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic