FUZZY REASONING USING POSITIONAL INFORMATION

Abstract

The paper argues in favour of reasoning methods that process positional information, i.e. information about the position of the input with respect to the class prototype, and thus achieve a better specification of the corresponding output class. It is shown that such an approach leads to reducing or cancelling unwanted nonlinearities (of input-output characteristic) imposed by reasoning methods, nonlinearities that alter the dependence expressed in the knowledge base. Two methods which use positional information are presented: (a) the mapping of o-cut borders (MACB) (Stoica, 1993, Proc. Fifth IFSA World Congress, pp. 1266-1269), inspired from a particular interpretation of the representation theorem and (b) the Left/Right Centre of Gravity (L/R COG) (Ghanayem, 1995, Proc. IEA/AIE, pp. 41 -45). The methods are tested in implementing a power system stabiliser (PSS) Simulation results show better performance of methods that use positional information, as compared with classic Mamdani (Mamdani, 1975, International Journal of Man-Machine Studies, 7, 1-13) reasoning. Reflections on a “best” reasoning method conclude the paper.     

Min-max optimal instrumental variable estimation method for multivariate linear time-series systems

A min-max optimal instrumental variable (IV) estimation method for multivariate linear time-series systems is presented. A Monte Carlo study is performed to assess the merits of the min-max optimal IV method using two different parametrizations of the multivariate time series system. The analysis indicates that the proposed estimation method yields accurate estimation results at modest computational cost.     

Generalized Yule-Walker equations and testing the orders of multivariate time series

Consistency condi ?ions are given for the estimates of AR-parameters of multivariate ARMA models, obtained by using generalized Yule-Walker equations. The related problem of selecting the model orders by testing the rank of the output covariance matrix is also discussed.     

Model-structure selection by cross-validation

Two criteria for choosing between different model-structures are proposed. Their derivation is within a natural cross-validatory assessment context and is fairly assumption-free. In particular, the two criteria can be used for discriminating between non-nested model structures and, more importantly, the ‘true’ system is not required to belong to the considered set of models. Should the true system belong to the model set, the two proposed criteria will asymptotically reduce to some well-known structure selection criteria. This is believed to be a desirable feature of our proposals. On the other hand, it provides a nice cross-validation interpretation of some well-known model structure selection rules. Also, the cross-validation interpretation helps one to choose which criteria to use in a given application

The paper also has a second purpose, somewhat decoupled from that mentioned above. It contains an extensive survey of the literature that is useful in its own right.     

In-situ loading neutron-diffraction studies of a cobalt-based superalloy

ULTIMET alloy is a cobalt-based superalloy that undergoes a deformation-induced phase transformation from a face-centered-cubic （fcc） phase to a hexagonal-close-packed （hcp） phase. The transformation was studied during monotonic loading, stress-controlled high-cycle fatigue （HCF） and strain-controlled low-cycle fatigue （LCF）. The HCF was performed at a maximum stress of σmax =840 MPa and a minimum stress of σmin =84 MPa, while the tensile experiment was terminated after reaching 15max =890 MPa. The LCF was performed at a maximum strain of σmax=1.25 % and a minimum strain of σmin=-1.25 %. The monotonic-loading experiment results reveal that the hcp phase forms after reaching the yield stress. During HCF, the hexagonal phase forms immediately upon the first fatigue cycle, with no further change in structure upon subsequent deformation. In contrast to HCF, the hcp phase forms gradually during LCF. In fact, fatigue cycle 12 is reached before the hcp phase is resolved by neutron diffraction. Diffraction patterns from subsequent fatigue cycles reveal that the hcp phase continues to accumulate as LCF progresses These observations can be related to the input of mechanical energy during different loading modes.     

FUZZY MODELS FOR ENERGY DEMAND MANAGEMENT

Abstract

Energy planning is a management and control tool meant to deal medium- and long-term with the interaction process between the economic development and efficient resource allocation of a given country. The paper gives a complementary approach to an econometric model which by means of fuzzy sets theory enables the social planner to estimate the energy vector at a given moment within the content of a given industrial structure. The fuzzy approach is used to quantify the preferences and/or the given information states that are neither deterministic in use nor certain and so they have to be dynamically approached. This approach is used to compute and evaluate end use energy demand on a time scale. The management-oriented results illuminate further dimensions of the complex problem of energy use management by means of models and the interaction with the social planner, its way of thinking and preferences.     

Optimal instrumental variable multistep algorithms for estimation of the AR parameters of an ARMA process

Multistep implementations are derived for the optimal instrumental variable (OIV) estimators introduced by Stoica et al. in 1985. The proposed algorithms provide asymptotically efficient estimates of the AR parameters of an ARMA process. The computational complexity of these algorithms is modest compared with the maximum likelihood estimator. The performance of the OIV algorithms is illustrated by some numerical examples.     

Approximate maximum-likelihood approach to ARMA spectral estimation

A three-step approximate maximum-likelihood method for ARMA spectral estimation is derived, based on an idea due to Walker. The asymptotic properties of the proposed estimator are investigated and an explicit expression for its asymptotic covariance matrix is presented. The estimator provides the asymptotic accuracy of a maximum-likelihood technique, at a modest computational cost.