Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production

This paper addresses the problem of the optimal design of batch plants with imprecise demands and proposes an alternative treatment of the imprecision by using fuzzy concepts. For this purpose, we extended a multiobjective genetic algorithm (MOGA) developed in previousworks, taking into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The former is computed by comparing the fuzzy computed production time to a given fuzzy production time horizon and the latter is based on the additional fuzzy demand that the plant is able to produce. The methodology provides a set of scenarios that are helpful to the decision’s maker and constitutes a very promising framework for taken imprecision into account in new product development stage

An Incremental Construction of Deep Neuro Fuzzy System for Continual Learning of Non-stationary Data Streams

Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically extracted from data streams or removed if they play limited role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely gClass, drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of dimensionality of input space due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using seven datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four popular continual learning algorithms and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy. Moreover, it is also shown that the concept drift detection method is an effective tool to control the depth of network structure while the hidden layer merging scenario is capable of simplifying the network complexity of a deep network with negligible compromise of generalization performance.Comment: This paper has been published in IEEE Transactions on Fuzzy System

Conditional prediction intervals of wind power generation

International audienceA generic method for the providing of prediction intervals of wind power generation is described. Prediction intervals complement the more common wind power point forecasts, by giving a range of potential outcomes for a given probability, their so-called nominal coverage rate. Ideally they inform of the situation-specific uncertainty of point forecasts. In order to avoid a restrictive assumption on the shape of forecast error distributions, focus is given to an empirical and nonparametric approach named adapted resampling. This approach employs a fuzzy inference model that permits to integrate expertise on the characteristics of prediction errors for providing conditional interval forecasts. By simultaneously generating prediction intervals with various nominal coverage rates, one obtains full predictive distributions of wind generation. Adapted resampling is applied here to the case of an onshore Danish wind farm, for which three point forecasting methods are considered as input. The probabilistic forecasts generated are evaluated based on their reliability and sharpness, while compared to forecasts based on quantile regression and the climatology benchmark. The operational application of adapted resampling to the case of a large number of wind farms in Europe and Australia among others is finally discussed

Fuzzy correlation and regression analysis.

The first half of the dissertation focuses on the motivation and concept of fuzzy correlation. Fuzzy data will be formulated in a mathematical way, and then we will build models of two types of fuzzy correlations, their computation methods are also presented in this dissertation. For the first type of fuzzy correlation problem we proposed an approximate bound as well as a number of computationally efficient algorithms. Monte Carlo sampling method is used to compute the second type of fuzzy correlation problem. The results provided by the second type of fuzzy correlation are more informative than the result of the classical correlation.Some application examples are given at the end. Fuzzy regression models could be applied in short term stock price prediction. Intel Corp. 2003 stock price data are used in this demo. The Dosage-film response is estimated with a fuzzy regression model, this procedure is presented in detail in the last section. It is found that fuzzy regression gives more consistent results than the conventional regression model since it successfully models the inherent vagueness which exists in the application by formulated form.In the second part of the dissertation, eight fuzzy regression models are discussed. In order to enhance the central tendency and remove outliers which have important impact on the regression result, different techniques are used to improve the original model. The fuzzy regression method presented in this dissertation also applies to crisp data regression cases. Numerical examples are given for all the fuzzy correlation and fuzzy regression models we explored in this dissertation for illustration and verification purpose.Correlation and regression analysis are widely used in all kinds of data mining applications. However many real world data have the characteristic of vagueness; the classical data analysis techniques have limitation in managing this vagueness systematically. Fuzzy sets theory can be applied to model this kind of data. New concepts and methods of correlation and regression analysis for data with uncertainty are presented in this dissertation. Recently, fuzzy correlation and regression have been applied to many applications. Successful examples include quality control, marketing, image processing, robot control, medical diagnosis, etc. The purpose of this dissertation is to revisit the ongoing research work that people have already done on this issue and to develop some new models related to fuzzy data correlation and regression. In this dissertation, we define and conceptualize the correlation and regression concepts within the fuzzy context. Then the presently available methods are explored in light of their limitations. Then new concepts and new models are presented. Throughout this dissertation, a number of test data sets are used to verify how our ideas are implemented. Suggestions for further research will be provided

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output