Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

SOME PROBLEMS AND TREATMENT IN THE REGRESSION ANALYSIS OF METEOROLOGICAL DATA

In this paper,some problems of regression analysis in the meteorological application are discussed and main reasons for statistical inference failures are analysed.We may find the failure problems with diagnos- tic method and solve them by different treatment.It has been proved that the treatment make the accuracy and stability of forecasting improved greatly.

DATA PREORDERING IN GENERALIZED PAV ALGORITHM FOR MONOTONIC REGRESSION

Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.

Towards explicit representation of an artificial neural network model: Comparison of two artificial neural network rule extraction approaches

In the quest for interpretable models,two versions of a neural network rule extraction algorithm were proposed and compared.The two algorithms are called the Piece-Wise Linear Artificial Neural Network(PWL-ANN)and enhanced Piece-Wise Linear Artificial Neural Network(enhanced PWL-ANN)algorithms.The PWL-ANN algorithm is a decomposition artificial neural network(ANN)rule extraction algorithm,and the enhanced PWL-ANN algorithm improves upon the PWL-ANN algorithm and extracts multiple linear regression equations from a trained ANN model by approximating the hidden sigmoid activation functions using N-piece linear equations.In doing so,the algorithm provides interpretable models from the originally trained opaque ANN models.A detailed application case study illustrates how the generated enhanced-PWL-ANN models can provide understandable IF-THEN rules about a problem domain.Comparison of the results generated by the two versions of the PWL-ANN algorithm showed that in comparison to the PWL-ANN models,the enhanced-PWL-ANN models support improved fidelities to the originally trained ANN models.The results also showed that more concise rule sets could be generated using the enhanced-PWL-ANN algorithm.If a more simplified set of rules is desired,the enhanced-PWL-ANN algorithm can be combined with the decision tree approach.Potential application of the algorithms to domains related to petroleum engineering can help enhance understanding of the problems.

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.