An interval type-2 fuzzy logic system-based method for prediction interval construction

This paper introduces a new non-parametric method for uncertainty quantification through construction of prediction intervals (PIs). The method takes the left and right end points of the type-reduced set of an interval type-2 fuzzy logic system (IT2FLS) model as the lower and upper bounds of a PI. No assumption is made in regard to the data distribution, behaviour, and patterns when developing intervals. A training method is proposed to link the confidence level (CL) concept of PIs to the intervals generated by IT2FLS models. The new PI-based training algorithm not only ensures that PIs constructed using IT2FLS models satisfy the CL requirements, but also reduces widths of PIs and generates practically informative PIs. Proper adjustment of parameters of IT2FLSs is performed through the minimization of a PI-based objective function. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Performance of the proposed method is examined for seven synthetic and real world benchmark case studies with homogenous and heterogeneous noise. The demonstrated results indicate that the proposed method is capable of generating high quality PIs. Comparative studies also show that the performance of the proposed method is equal to or better than traditional neural network-based methods for construction of PIs in more than 90% of cases. The superiority is more evident for the case of data with a heterogeneous noise. © 2014 Elsevier B.V.

Uncertainty handling using neural network-based prediction intervals for electrical load forecasting

The complexity and level of uncertainty present in operation of power systems have significantly grown due to penetration of renewable resources. These complexities warrant the need for advanced methods for load forecasting and quantifying uncertainties associated with forecasts. The objective of this study is to develop a framework for probabilistic forecasting of electricity load demands. The proposed probabilistic framework allows the analyst to construct PIs (prediction intervals) for uncertainty quantification. A newly introduced method, called LUBE (lower upper bound estimation), is applied and extended to develop PIs using NN (neural network) models. The primary problem for construction of intervals is firstly formulated as a constrained single-objective problem. The sharpness of PIs is treated as the key objective and their calibration is considered as the constraint. PSO (particle swarm optimization) enhanced by the mutation operator is then used to optimally tune NN parameters subject to constraints set on the quality of PIs. Historical load datasets from Singapore, Ottawa (Canada) and Texas (USA) are used to examine performance of the proposed PSO-based LUBE method. According to obtained results, the proposed probabilistic forecasting method generates well-calibrated and informative PIs. Furthermore, comparative results demonstrate that the proposed PI construction method greatly outperforms three widely used benchmark methods. © 2014 Elsevier Ltd.

An optimized mean variance estimation method for uncertainty quantification of wind power forecasts

A statistical optimized technique for rapid development of reliable prediction intervals (PIs) is presented in this study. The mean-variance estimation (MVE) technique is employed here for quantification of uncertainties related with wind power predictions. In this method, two separate neural network models are used for estimation of wind power generation and its variance. A novel PI-based training algorithm is also presented to enhance the performance of the MVE method and improve the quality of PIs. For an in-depth analysis, comprehensive experiments are conducted with seasonal datasets taken from three geographically dispersed wind farms in Australia. Five confidence levels of PIs are between 50% and 90%. Obtained results show while both traditional and optimized PIs are hypothetically valid, the optimized PIs are much more informative than the traditional MVE PIs. The informativeness of these PIs paves the way for their application in trouble-free operation and smooth integration of wind farms into energy systems. © 2014 Elsevier Ltd. All rights reserved.

Quantification of spatial and thematic uncertainty in the application of underwater video for benthic habitat mapping

This study presents an analysis of the application of underwater video data collected for training and validating benthic habitat distribution models. Specifically, we quantify the two major sources of error pertaining to collection of this type of reference data. A theoretical spatial error budget is developed for a positioning system used to co-register video frames to their corresponding locations at the seafloor. Second, we compare interpretation variability among trained operators assessing the same video frames between times over three hierarchical levels of a benthic classification scheme. Propagated error in the positioning system described was found to be highly correlated with depth of operation and varies from 1.5m near the surface to 5.7m in 100m of water. In order of decreasing classification hierarchy, mean overall observer agreement was found to be 98% (range 6%), 82% (range 12%) and 75% (range 17%) for the 2, 4, and 6 class levels of the scheme, respectively. Patterns in between-observer variation are related to the level of detail imposed by each hierarchical level of the classification scheme, the feature of interest, and to the amount of observer experience. © 2014 Copyright © Taylor & Francis Group, LLC.

A Bayesian nonparametric model for hierarchical sequence of images

 Scale features are useful for a great number of applications in computer vision. However, it is difficult to tolerate diversities of features in natural scenes by parametric methods. Empirical studies show that object frequencies and segment sizes follow the power law distributions which are well generated by Pitman-Yor (PY) processes. Based on mid-level segments, we propose a hierarchical sequence of images to obtain scale information stored in a hierarchical structure through the hierarchical Pitman-Yor (HPY) model which is expected to tolerate uncertainty of natural images. We also evaluate our representation by the application of segmentation.

A parametric study of a monolithic microfluidic system for on-chip biomolecular separation

A microfabricated poly(dimethylsiloxane) (PDMS) chip containing channel filled with polymer monolith has been developed for on-chip biomolecule separation. Methacrylate monolithic polymers were prepared by photo-initiated polymerization within the channel to serve as a continuous stationary phase. The monolithic polymer was functionalized with a weak anion-exchange ligand, and key parameters affecting the binding characteristics of the system were investigated. The total binding capacity was unaffected by the flow rate of the mobile phase but varied significantly with changes in ionic strength and pH of the binding buffer. The binding capacity decreased with increasing buffer ionic strength, and this is due to the limited available binding sites for protein adsorption resulting from cationic shielding effect. Similarly, the binding capacity decreased with decreasing buffer pH towards the isoelectric point of the protein. A protein mixture, BSA and ovalbumin, was used to illustrate the capacity of the methacrylate-based microfluidic chip for rapid biomolecule separation.

Extending scheduling algorithms to minimise the impact of bounded uncertainty using interval programming

 This research proposed a new methodology to extend algorithms to accept interval-based uncertain parameters. The methodology is applied on scheduling algorithms, including heuristic and meta-heuristic algorithms and produced optimal results with higher accuracy. The research outcomes are effective for decision making process using uncertain or predicted data.

A computational framework for uncertainty integration in stochastic unit commitment with intermittent renewable energy sources

The penetration of intermittent renewable energy sources (IRESs) into power grids has increased in the last decade. Integration of wind farms and solar systems as the major IRESs have significantly boosted the level of uncertainty in operation of power systems. This paper proposes a comprehensive computational framework for quantification and integration of uncertainties in distributed power systems (DPSs) with IRESs. Different sources of uncertainties in DPSs such as electrical load, wind and solar power forecasts and generator outages are covered by the proposed framework. Load forecast uncertainty is assumed to follow a normal distribution. Wind and solar forecast are implemented by a list of prediction intervals (PIs) ranging from 5% to 95%. Their uncertainties are further represented as scenarios using a scenario generation method. Generator outage uncertainty is modeled as discrete scenarios. The integrated uncertainties are further incorporated into a stochastic security-constrained unit commitment (SCUC) problem and a heuristic genetic algorithm is utilized to solve this stochastic SCUC problem. To demonstrate the effectiveness of the proposed method, five deterministic and four stochastic case studies are implemented. Generation costs as well as different reserve strategies are discussed from the perspectives of system economics and reliability. Comparative results indicate that the planned generation costs and reserves are different from the realized ones. The stochastic models show better robustness than deterministic ones. Power systems run a higher level of risk during peak load hours.

Education in the age of uncertainty: an eagle's eye-view

 How are we to educate young people of, and for, these times in a way which takes into account the existential and moral dilemmas of our age? We argue that the current education system fails to address the full implications of historical change in relation to ethics and equity. In what follows, we offer some ways of describing and theorising contemporary life in an age of uncertainty. We offer it as a knowledge base from which teachers, principals and policy makers might draw in creating new morally and ethically sound policy discourses. We follow with some new frameworks for helping students to deal with the altered context of moral and political life.

Parametric investigation of batch adsorption of proteins onto polymeric particles

Background: Effective bimolecular adsorption of proteins onto solid matrices is characterized by in-depth understanding of the biophysical features essential to optimize the adsorption performance. Results: The adsorption of bovine serum albumin (BSA) onto anion-exchange Q-sepharose solid particulate support was investigated in batch adsorption experiments. Adsorption kinetics and isotherms were developed as a function of key industrially relevant parameters such as polymer loading, stirring speed, buffer pH, protein concentration and the state of protein dispersion (solid/aqueous) in order to optimize binding performance and adsorption capacity. Experimental results showed that the first order rate constant is higher at higher stirring speed, higher polymer loading, and under alkaline conditions, with a corresponding increase in equilibrium adsorption capacity. Increasing the stirring speed and using aqueous dispersion protein system increased the adsorption rate, but the maximum protein adsorption was unaffected. Regardless of the stirring speed, the adsorption capacity of the polymer was 2.8 mg/ml. However, doubling the polymer loading increased the adsorption capacity to 9.4 mg/ml. Conclusions: The result demonstrates that there exists a minimum amount of polymer loading required to achieve maximum protein adsorption capacity under specific process conditions.

Business strateBusiness strategies under conditions of uncertainty: The rise of mutual life insurers in colonial Australiagies under conditions of uncertainty

The early development of Australian life insurance was marked by the failure of stock companies to successfully establish a market presence. Mutual insurers emerged in the mid-nineteenth century in response to this gap in supply. The underlying rationale behind their establishment differed but the business model adopted proved remarkably successful. Mutual life insurers dominated the market for life insurance for nearly a century. This chapter investigates mutualism as a business strategy that addressed particular problems associated with doing business in a small and underdeveloped economy. Business and social networks were important facilitators of new business. In addition, most mutual life insurers had a social/philanthropic charter and they were able to utilize this to build business. An outcome of this mix was the emergence of a particular type of entrepreneurship that fostered innovative product development and cemented the role of mutual insurers as market leaders.. The Variety, Choice, Governance, and Regulation of Organizational Forms 2.

Accounting for uncertainty in volumes of seabed change measured with repeat multibeam sonar surveys

Seafloors of unconsolidated sediment are highly dynamic features; eroding or accumulating under the action of tides, waves and currents. Assessing which areas of the seafloor experienced change and measuring the corresponding volumes involved provide insights into these important active sedimentation processes. Computing the difference between Digital Elevation Models (DEMs) obtained from repeat Multibeam Echosounders (MBES) surveys has become a common technique to identify these areas, but the uncertainty in these datasets considerably affects the estimation of the volumes displaced. The two main techniques used to take into account uncertainty in volume estimations are the limitation of calculations to areas experiencing a change in depth beyond a chosen threshold, and the computation of volumetric confidence intervals. However, these techniques are still in their infancy and, as a result, are often crude, seldom used or poorly understood. In this article, we explored a number of possible methodological advances to address this issue, including: (1) using the uncertainty information provided by the MBES data processing algorithm CUBE, (2) adapting fluvial geomorphology techniques for volume calculations using spatially variable thresholds and (3) volumetric histograms. The nearshore seabed off Warrnambool harbour - located in the highly energetic southwest Victorian coast, Australia - was used as a test site. Four consecutive MBES surveys were carried out over a four-months period. The difference between consecutive DEMs revealed an area near the beach experiencing large sediment transfers - mostly erosion - and an area of reef experiencing increasing deposition from the advance of a nearby sediment sheet. The volumes of sediment displaced in these two areas were calculated using the techniques described above, both traditionally and using the suggested improvements. We compared the results and discussed the applicability of the new methodological improvements. We found that the spatially variable uncertainty derived from the CUBE algorithm provided the best results (i.e. smaller confidence intervals), but that similar results can be obtained using as a fixed uncertainty value derived from a reference area under a number of operational conditions.

Prediction Of Hydrological Models’ Uncertainty By A Committee Of Machine Learning-Models

This study presents an approach to combine uncertainties of the hydrological model outputs predicted from a number of machine learning models. The machine learning based uncertainty prediction approach is very useful for estimation of hydrological models' uncertainty in particular hydro-metrological situation in real-time application [1]. In this approach the hydrological model realizations from Monte Carlo simulations are used to build different machine learning uncertainty models to predict uncertainty (quantiles of pdf) of the a deterministic output from hydrological model . Uncertainty models are trained using antecedent precipitation and streamflows as inputs. The trained models are then employed to predict the model output uncertainty which is specific for the new input data. We used three machine learning models namely artificial neural networks, model tree, locally weighted regression to predict output uncertainties. These three models produce similar verification results, which can be improved by merging their outputs dynamically. We propose an approach to form a committee of the three models to combine their outputs. The approach is applied to estimate uncertainty of streamflows simulation from a conceptual hydrological model in the Brue catchment in UK and the Bagmati catchment in Nepal. The verification results show that merged output is better than an individual model output. [1] D. L. Shrestha, N. Kayastha, and D. P. Solomatine, and R. Price. Encapsulation of parameteric uncertainty statistics by various predictive machine learning models: MLUE method, Journal of Hydroinformatic, in press, 2013.

Uncertainty Characterization Of A Conceptual Rainfall-Runoff Model By Using Grey Numbers

A procedure for characterizing global uncertainty of a rainfall-runoff simulation model based on using grey numbers is presented. By using the grey numbers technique the uncertainty is characterized by an interval; once the parameters of the rainfall-runoff model have been properly defined as grey numbers, by using the grey mathematics and functions it is possible to obtain simulated discharges in the form of grey numbers whose envelope defines a band which represents the vagueness/uncertainty associated with the simulated variable. The grey numbers representing the model parameters are estimated in such a way that the band obtained from the envelope of simulated grey discharges includes an assigned percentage of observed discharge values and is at the same time as narrow as possible. The approach is applied to a real case study highlighting that a rigorous application of the procedure for direct simulation through the rainfall-runoff model with grey parameters involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the grey numbers representing the simulated discharges. Relying on this simplified procedure, the conceptual rainfall-runoff grey model is thus calibrated and the uncertainty bands obtained both downstream of the calibration process and downstream of the validation process are compared with those obtained by using a well-established approach, like the GLUE approach, for characterizing uncertainty. The results of the comparison show that the proposed approach may represent a valid tool for characterizing the global uncertainty associable with the output of a rainfall-runoff simulation model.

Uncertainties In Future Projections Of Extreme Rainfall: The Role Of Climate Model, Emission Scenario And Randomness

Climate change has resulted in substantial variations in annual extreme rainfall quantiles in different durations and return periods. Predicting the future changes in extreme rainfall quantiles is essential for various water resources design, assessment, and decision making purposes. Current Predictions of future rainfall extremes, however, exhibit large uncertainties. According to extreme value theory, rainfall extremes are rather random variables, with changing distributions around different return periods; therefore there are uncertainties even under current climate conditions. Regarding future condition, our large-scale knowledge is obtained using global climate models, forced with certain emission scenarios. There are widely known deficiencies with climate models, particularly with respect to precipitation projections. There is also recognition of the limitations of emission scenarios in representing the future global change. Apart from these large-scale uncertainties, the downscaling methods also add uncertainty into estimates of future extreme rainfall when they convert the larger-scale projections into local scale. The aim of this research is to address these uncertainties in future projections of extreme rainfall of different durations and return periods. We plugged 3 emission scenarios with 2 global climate models and used LARS-WG, a well-known weather generator, to stochastically downscale daily climate models’ projections for the city of Saskatoon, Canada, by 2100. The downscaled projections were further disaggregated into hourly resolution using our new stochastic and non-parametric rainfall disaggregator. The extreme rainfall quantiles can be consequently identified for different durations (1-hour, 2-hour, 4-hour, 6-hour, 12-hour, 18-hour and 24-hour) and return periods (2-year, 10-year, 25-year, 50-year, 100-year) using Generalized Extreme Value (GEV) distribution. By providing multiple realizations of future rainfall, we attempt to measure the extent of total predictive uncertainty, which is contributed by climate models, emission scenarios, and downscaling/disaggregation procedures. The results show different proportions of these contributors in different durations and return periods.