DIPE: Determination of Input Parameters Uncertainties Methodology Applied to CATHARE V2.51

In nuclear safety, the Best-Estimate (BE) codes may be used in safety demonstration and licensing, provided that uncertainties are added to the relevant output parameters before comparing them with the acceptance criteria. The uncertainty of output parameters, which comes mainly from the lack of knowledge of the input parameters, is evaluated by estimating the 95% percentile with a high degree of confidence. IRSN, technical support of the French Safety Authority, developed a method of uncertainty propagation. This method has been tested with the BE code used is CATHARE-2 V2.5 in order to evaluate the Peak Cladding Temperature (PCT) of the fuel during a Large Break Loss Of Coolant Accident (LB-LOCA) event, starting from a large number of input parameters. A sensitivity analysis is needed in order to limit the number of input parameters and to quantify the influence of each one on the response variability of the numerical model. Generally, the Global Sensitivity Analysis (GSA) is done with linear correlation coefficients. This paper presents a new approach to perform a more accurate GSA to determine and to classify the main uncertain parameters: the Sobol′ methodology. The GSA requires simulating many sets of parameters to propagate uncertainties correctly, which makes of it a time-consuming approach. Therefore, it is natural to replace the complex computer code by an approximate mathematical model, called response surface or surrogate model. We have tested Artificial Neural Network (ANN) methodology for its construction and the Sobol′ methodology for the GSA. The paper presents a numerical application of the previously described methodology on the ZION reactor, a Westinghouse 4-loop PWR, which has been retained for the BEMUSE international problem [8]. The output is the first maximum PCT of the fuel which depends on 54 input parameters. This application outlined that the methodology could be applied to high-dimensional complex problems.

End-users conduct various on-line activities. Quite often they re-visit websites and use services to perform repeated activities, such as on-line shopping. The end-users are required to enter the same information into various web services to accomplish such repeated tasks. Typing redundant information repetitively into such services negatively impacts the user experience. In this study, we propose an approach to prevent end-users from such unnecessary interruption. Our approach propagates user inputs across services by linking similar input and output parameters. Our approach also pre-fills values to the input parameters which could not be filled by the values from other input or output parameters. We propose a meta-data model for storing user inputs and an Input Parameter Context Model for identifying similar input or output parameters. We have implemented our approach and evaluated it on the real world services through an empirical study. Our overall approach can reduce on average 37% of input parameters through the execution of composed services.

Multilayer artificial neural networks (ANN) are often used for the solution of classification problems or for the time series forecasting. An appropriate number of learning and testing patterns must be available for the ANN training. Each training pattern is composed of n input parameters and m output parameters. Number m is usually given by the problem formulation, but the number n may be often selected from a greater set of input parameters. An optimal selection of input parameters is a very important task especially in a situation when the number of usable input parameters is great and the analytical relations between the input and output parameters are not known. The number of neurons in all ANN layers must be generally kept as small as possible because of the optimal generalisation ability. In this paper we present a possible way for the selection of significant input parameters (the so called markers), which are the most important ones from the point of view of influence on the output parameters. These parameters are later used for the training of ANN. A statistical approach is usually used for this reason [5]. After some experience in the ANN application we recognised that the approach based on mathematical logic, i. e. the GUHA method (General Unary Hypotheses Automaton) is also suitable for the determination of markers. Besides the minimisation of the number of elements in the input layer of ANN, also the number of neurons in hidden layers must be optimised. For this reason standard methods of pruning can be used, described e. g. in [1]. We have used this method in the following applications: - Optimisation of the intervals between the major overhaul of plane engines by the analysis of tribodiagnostic data. Only selected types of chemical pollution in oil can be taken into account. - Prediction of bleeding of patients with chronic lymphoblastic leukemia. Only a part of parameters about the patient is important from this point of view (see [2]). - Optimisation of the quality and reliability prediction of artificial resin production in chemical factory. Only a part of the production parameters (times of production phases, temperatures, percentage of components etc.) have straight influence on the product. - Optimisation of the prosody control in the text-to-speech synthesis. This application is described in the paper.

Fuzzy expert system design for operating room air-condition control systems

This study is concerned with uncertainty analysis of MELCOR simulation of a hypothetical severe accident initiated by station blackout (SBO) in a Swedish pressurized water reactor (PWR). 9 input parameters are chosen, and 12 safety-related output parameters are selected as the figures of merit (FOMs). In random sampling (RS) method, 800 MELCOR cases are run to produce empirical cumulative distribution functions (CDFs) and empirical 95th percentiles of FOMs. Given this sufficient sample size, uncertainty analyses through statistical analysis, can be performed to obtain the first two statistical moments and 95/95 estimates from the first order Wilks’ method. However, RS method including Wilks’ method turns out to be time consuming and computationally expensive since many MELCOR cases require iterative tuning of MELCOR input to restart and finish calculations. To overcome this issue encountered in RS method, in the present study three deterministic sampling (DS) methods are applied to uncertainty analyses, and a coupled approach by combining DS methods with a coverage factor 1.65 is proposed. Comparable results show that DS methods can generally capture the first two statistical moments quickly, and acceptably accurate 95th percentiles can be calculated by the coupled approach when the output parameters can be described as normal distributions. Besides, estimated 95th percentiles from the coupled approach are covered by estimates (boxplots) from the first order Wilks’ method. Hence, it can be concluded that the coupled approach has its potential to work as an alternative in engineering to RS method including Wilks’ method for numerically equivalent estimates of 95/95 tolerance limit with an acceptable accuracy and a significantly less computational cost in MELCOR severe accident simulation.

It is of vital importance to be able to determine the seismic hazard in advance of any geothermal operation in the subsurface, especially in a densely populated area such as The Netherlands. The author aims to arrive at a practical assessment of the seismic hazard in low-enthalpy geothermal doublet systems specifically designed for heat exchange in porous and permeable aquifers operated on a volume balance, at a depth range of 1800 to 3300 m having temperatures in the range of 60 °C to 100 °C. The article presents a practical workflow aiming to determine the probability distribution for mechanical re-activation along pre-existing weak faults. After presenting the tectonic structural setting the criticality criterion based on shear mobilisation is introduced. Existing stress models are reviewed and a practical manner to estimate and limit all geomechanical input parameters is presented, including fault mechanical properties. The workflow is demonstrated both for early period operation times and at final thermal breakthrough. The uncertainty is addressed through probabilistic logic tree analysis quantifying the variation of the four most uncertain input parameters: fault cohesion and friction coefficient, the thermal stress parameter and the initial minimum Earth stress. The probabilistic hazard assessment is characterised by four output parameters: the expected value, the probability that unity is exceeded and two more probabilities. In case unity is exceeded the range of fault dips prone to mechanical re-activation is shown. Exceedance of this first necessary condition requires the assessment of the other two necessary conditions: seismogeneity and moment magnitude.Article highlightsThe article presents a practical workflow to assess the seismic hazard associated with geothermal operations.To be able to perform the necessary uncertainty analysis, four main input parameters are treated probabilistic.The first necessary condition for seismicity to occur is characterised by four probabilities: the expected probability, the probability that seismicity can occur and two higher probabilities.

Identification of a Moss Growth System using an Artificial Neural Network Model

The steel plant’s workplace environmental hazard parameters in Ilorin, Nigeria was evaluated using response surface methodology (RSM). Three environmental parameters (illumination, temperature and noise level) were measured. The data obtained were compared with the Occupational Safety and Health (OSHA) standard for the workplace environment. Based on the preliminary analysis of the workplace environment, five variables (No. of lightings, no. of windows, no. of machines, no. of workers and age of machines) were considered as input parameters. RSM was used to perform the modelling and optimization to identify functional relationships between the input and output parameters. Three (3) model equations one for each of the output parameters were developed and checked for adequacy and validity. All developed model equations were found to present functional relationships between input and output parameters. Hence, all developed model equations can be used as reliable tools for estimating, predicting, and conducting analysis for workplace environmental hazard. Best optimized results were selected based on desirability (0–1). Illumination, temperature and noise level got desirability rate of 0.921, 1.000 and 0.983 respectively. The outcome of this study suggested that the environmental parameters studied within the workplace do not conform with the OSHA standard and as a result may constitute long-term health risks to the workers.

FEMA 356 backbone relations tend to provide conservative estimates of the available strengths and deformation capacities of reinforced concrete components, leading to costly seismic rehabilitation solutions for California hospitals. The conservatism is driven by the lack of test data for older, typically poorly detailed, structural components. Although FEMA 356 does provide for building specific component testing, this approach is not common due to cost concerns and/or schedule constraints. However, a test program on lightly-reinforced, poorly-detailed wall segments was undertaken at UCLA in 2004–2005 to support seismic rehabilitation projects on several southern California hospitals. Presented test results are compared with FEMA 356 backbone relations to highlight the advantages associated with building-specific test programs. In general, the test specimens revealed more strength and deformation capacity than assumed by FEMA 356, and more gradual strength deterioration. The test results, when coupled with the FEMA 356 Nonlinear Static Procedure (NSP) and Nonlinear Dynamic Procedure (NDP), enabled the development of more rational and substantially more economical rehabilitation solutions. The test results were used to help develop new backbone relations that were incorporated into ASCE-41-06 Supplement #1.

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 94357, "Treating Uncertainties in Reservoir-Performance Prediction With Neural Networks," by J.P. Lechner, SPE, OMV A.G., and G. Zangl, SPE, Schlumberger Information Solutions, prepared for the 2005 SPE Europec/EAGE Annual Conference, Madrid, Spain, 13–16 June. In development projects, reservoir parameters are known only within certain ranges, which results in various realizations of the subsurface. Because of the computational time involved, simulation models to obtain a probability distribution of possible outcomes cannot cover all possible parameter combinations. Creating a response surface based on a reduced number of simulation runs becomes necessary. Such a response surface can be used to approximate results for several variations of input parameters. An approach in which reservoir response is captured by an artificial neural network (ANN) has been investigated. The trained ANN model was used in Monte Carlo simulations to generate the probability distribution of possible outcomes. Introduction Often, simulation models are built to design field-development plans. Because of the low level of information during the early development stage, a range of uncertainty in the prediction scenarios must be considered. Such uncertainties can be handled with ANNs. Numerical models (simulation models) are detailed and powerful predictive tools that can answer many questions regarding subsurface engineering. However, especially in the early development phase, uncertainties are large, and prediction results will span a broad range. To take into account the whole range of possible outcomes of reservoir simulation, optimization routines would have to run the numerical models perhaps thousands of times. Although the most likely solution that respects subsurface uncertainties is of interest, the most profitable solution for reservoir management must be found. Because of the computational time involved, these methodologies often are not used. Building a response surface that can predict many possible outcomes of a numerical simulation by processing a large variety of input parameters could provide a solution to this problem. The response surface must cover the non-linear dependencies between input and output parameters. Experimental design and response-surface modeling has been used to delineate subsurface uncertainty. Common applications include determining the probability distribution of original oil in place from geological models, quantifying uncertainty in predevelopment or preredevelopment projects, predicting production performance from different realizations of a geological model, and optimizing the location of new wells to maximize net profit. Methodology Fig. 1 shows the proposed workflow. As a first step, a limited number of simulation runs is carried out to define the most sensitive input parameters. In these runs, parameters are altered one at a time, either to the minimum or to the maximum. After selecting the most influential input parameters, three values (minimum, best-estimate, and maximum) are defined, and an experimental design is set up. The experimental design aims at obtaining the maximum information with a minimum number of simulation runs. However, practice showed that a minimum number of training data sets are required by the ANN to be able to make sufficiently accurate predictions. With these data sets containing varying input parameters and the corresponding output, an ANN is trained and tested with several additional simulation runs. After defining the probability distribution of the input parameters, the trained ANN is used as a proxy function for a Monte Carlo simulation. Thereby, a probability distribution of the desired output parameter (e.g., cumulative production after a certain number of years) is gained. The quality of the ANN is measured by the root-mean-square error of the deviation between the predicted and the actual output.

Retrieval of integrated water vapor content (WVC) from remote sensing data is often ill-posed because of insufficient observational information. There are many factors that cause WVC changes, which yield instability in the accuracy of many traditional algorithms. To overcome this problem, we developed a novel fully-coupled paradigm for the robust retrieval of WVC from thermal infrared remote sensing data. Through the derivation of the physical radiative transfer equation, we determined two conditions that need to be satisfied for the deep learning retrieval paradigm of WVC. The first condition is that the input parameters and output parameters of the deep learning need to be able to build a complete set of solvable equations in theory. The second condition is that, if there is a strong relationship between input parameters and output parameters, it can be directly retrieved. If it is a weak relationship, we need to use prior knowledge to improve the portability and accuracy of the algorithm. The training and test data of deep learning is composed of representative solutions of physical methods and solutions of statistical methods. The representative solutions of the physical methods were obtained from the physical forward model, and the statistical solutions were obtained from multi-source data which can compensate for the defect that the physical model cannot simulate mixed pixels. MODIS L1B data was used for case analysis of paradigm retrieval, and the analysis indicated that four thermal infrared bands were usually needed as the input parameters of deep learning and the integrated water vapor content as the output parameter. When land surface temperature and emissivity were taken as prior knowledge, the root-mean-square error (RMSE) of the retrieved WVC was 0.07 g/cm2. The optimal accuracy RMSE was 0.27 g/cm2. When there was a strong correlation between input parameters and output parameters, i.e., if there were two bands that were very sensitive to WVC in the band combination, high-precision retrieval could also be achieved without prior knowledge. All the analyses show that the paradigm of deep learning coupling physics and statistics can accurately retrieve WVC, which is a significant improvement on the traditional method and solves the problem of lack of physical interpretation of deep learning.

Using slotted grinding wheel in machining is a new approach in grinding technology. The slotted grinding wheel is used to improve the introduction of cool lubricant into the cutting zone, improve chip release condition and heat release condition during machining, thereby facilitating to improve the efficiency of the grinding process. However, up to now, the studies that are performed using this type of grinding wheel is very limited. To contribute some results to this rather new research direction, in this article we present the grinding process of SUJ2 steel using CBN slotted grinding wheel. The orthogonal Taguchi matrix with nine experiments was used to design the experimental matrix with three input parameters including workpiece velocity, feed rate, and depth of cut. The output parameters that were used to evaluate the quality and effectiveness of the grinding process were surface roughness, system vibrations in X, Y, Z directions, and the material removal rate. In surface grinding process using CBN slotted grinding wheel, all three input parameters (workpiece velocity, feed rate, and depth of cut) have a significant influence on the surface roughness, vibration. In which, the feed rate has the most influence on the output parameters. The second factor that influenced on the output parameter was the depth of cut. The workpiece velocity has the smallest influence on the output parameters. Data Envelopment Analysis Based Ranking (DEAR) method was used to solve the multi-objective optimization problem in surface grinding process. By applying this method, the optimal value of input parameter that were determined to obtain the minimum values of surface roughness and system vibration components, and to obtain the maximum of material removal rate. The optimum values of input parameters were the workpiece velocity of 15 m/min, the feed rate of 4 mm/stroke, and cutting depth of 0.015 mm. DEAR method can be applied to improve the quality and the effectiveness of the grinding process by reducing the surface roughness and system vibration components and increasing the material removal rate.

The nature of a line heating process is very complex since a variety of factors affects the amount of residual deformation. A linear relationship between input and output parameters, which has been derived from simple experiments, is successively used. This relationship, however, is very limited since it does not include important parameters and the line heating process is not linear. A rigorous approach is presented here in an attempt to obtain new relationships between input parameters and final deformations during the line heating process. The residual deformations are investigated by using a thermal elastic-plastic analysis based on finite-element analysis (FEA). Experiments are carried out in order to verify the validity of the FEA results. The nondimensional input parameters are then determined by the dimensional analysis. The relationships between the input parameters and the residual deformations are developed by using multi-variate analysis (MVA) and multiple-regression methods. The final form of the relationships is nonlinear and includes relevant information.

Structured treatment of model uncertainty in complex thermal-hydraulics codes: Technical challenges, prospective and characterization

The present work is to be considered as additional research to the authors' previous studies. It is dedicated to the specification of the significance and impact of certain selected technological parameters on mechanical properties of the composite material based on scrap tires. The special method what is known as the “Greece-Latin square” was applied to estimate significance of each technological parameter (input parameter) for selected properties (output parameters) of the material. Moulding pressure (P), formation time (x), polymer binder content (Cpol.) and the size of rubber particles (R) were selected as the input parameters. Compressive modulus of elasticity (Ec), compressive stress at 10% deformation (σ10%), permanent deformation after 10% deformation in compressive mode (ε) and apparent density (AD) were chosen as the output parameters. An analysis of the obtained dispersion diagrams confirms that composition of the composite material (polymer content) has a greater impact on selected mechanical properties of the material than any other technological input parameter, but apparent density of the composite material demonstrates higher sensitivity to the formation time and moulding pressure of the material than to other input parameters. The obtained results of the experiment enable further optimization of the composite material production technology and at the same time securing the predictable mechanical properties of the material.