Evaluation of Dosimetric Impact of Uncertainty of Measurement in Estimating External Radiotherapy Dose

Cancer is a major societal public health and economic problem, responsible for one in every six deaths. Radiotherapy is the main technique of treatment for more than half of cancer patients. To achieve a successful outcome, the radiation dose must be delivered accurately and precisely to the tumor, within ± 5% accuracy. Smaller uncertainties are required for better treatment outcome. The objective of the study is to investigate the uncertainty of measurement of external radiotherapy beam using a standard ionization chamber under reference conditions. Clinical farmers type ionization chamber measurement was compared against the National Reference standard, by exposing it in a beam 60Co gamma source. The measurement set up was carried out according to IAEA TRS 498 protocol and uncertainty of measurement evaluated according to GUM TEDDOC-1585. Evaluation and analysis were done for the identified subjects of uncertainty contributors. The expanded uncertainty associated with 56 mGy/nC ND,W was found to be 0.9% corresponding to a confidence level of approximately 95% with a coverage factor of k = 2. The study established the impact of dosimetry uncertainty of measurement in estimating external radiotherapy dose. The investigation established that the largest contributor of uncertainty is the stability of the ionization chamber at 36%, followed by temperature at 22% and positioning of the chamber in the beam at 8%. The effect of pressure, electrometer, resolution, and reproducibility were found to be minimal to the overall uncertainty. The study indicate that there is no flawless measurement, as there are many prospective sources of variation. Measurement results have component of unreliability and should be regarded as best estimates of the true value. .

Evaluation on Uncertainty of Determining Aspartame in Beverage by HPLC

[Objective] The aim was to evaluate the uncertainty of determining aspartame in beverage by high performance liquid chromatography （ HPLC）. [Method] The content of aspartame in beverage was determined by HPLC, then the source of uncertainty in the whole determination process was analyzed, and each component of uncertainty was evaluated and combined. [ Result] Through 6 repeated determinations by the method in GB/T 22254-2008 ＂Determination of Aspartame in Food＂, the average content of aspartame in beverage was （0.806 ±0.038） g/kg, and k =2. The main sources of uncertainty to affect the process were the sample weighting process, the preparation process of standard solution introduced by sample constant volume and the uncertainty introduced by fitting standard curve. ①The uncertainty of standard work-solution. The combined uncertainty of standard work-solution was 0.013 9, among them the uncertainty introduced by standard sample purity was 0.005 8, the standard uncertainty introduced by standard material weighting was 1.49 ×10^4, the relative uncertainty introduced by glass apparatus calibration in the preparation process of aspartame standard reserving solution was 0. 007 88, and the uncertainty introduced by glass apparatus calibration in the preparation process of standard work-solution was 0. 009 9. ②The uncertainty introduced by the preparation process of sample specimen. Among them the relative standard uncertainty introduced by sample weighting process was 0. 009, and the uncertainty introduced by sample constant volume was 0.000 78. ③The uncertainty introduced by the fitting process of standard curve. Among them the relative uncertainty of curve fitting was 0.002 46, the uncertainty introduced by the determined results of aspartame was 0.017 0, the total combined standard uncertainty was 0.023 9, and the expanded standard uncertainty was 0.019. [ Conclusion] The uncertainty components of standard solution, standard curve and repeatability are the main sources of uncertainty, while those of sample weighting and sample constant volume account for little proportion.

Effect of quality uncertainty of parts on performance of reprocessing system in remanufacturing environment

Aimed at the problem of stochastic routings for reprocessing operations and highly variable processing times,an open queuing network is utilized to model a typical reprocessing system.In the model,each server is subject to breakdown and has a finite buffer capacity,while repair times,breakdown times and service time follow an exponential distribution.Based on the decomposition principle and the expansion methodology,an approximation analytical algorithm is proposed to calculate the mean reprocessing time,the throughput of each server and other parameters of the processing system.Then an approach to determining the quality of disassembled parts is suggested,on the basis of which the effect of parts quality on the performance of the reprocessing system is investigated.Numerical examples show that there is a negative correlation between quality of parts and their mean reprocessing time.Furthermore,marginal reprocessing time of the parts decrease with the drop in their quality.

Hybrid Slip Model for Near-Field Ground Motion Estimation Based on Uncertainty of Source Parameters

The hybrid slip model used to generate a finite fault model for near-field ground motion estimation and seismic hazard assessment was improved to express the uncertainty of the source form of a future earthquake.In this process, source parameters were treated as normal random variables, and the Fortran code of hybrid slip model was modified by adding a random number generator so that the code could generate many finite fault models with different dimensions and slip distributions for a given magnitude.Furth...

Theoretical analysis and verification of uncertainty of measurement on a cantilever coordinate measuring machine

A cantilever coordinate measuring machine(CCMM)is proposed according to the in-situ measurement requirement of workpieces with complex structures limited by the finite space of the5-axes computerized numerical control(CNC)processing site.Factors affecting uncertainty of measurement(UM)are classified and analyzed on the basis of uncertainty evaluation criteria,and the estimation technique of UM for measuring systems is presented.UM of the CCMM is estimated from the factors such as temperature,error motions as well as the mechanism deformations.Measurement results show that the actual measurement error is smaller than that of measurement requirement.

The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

Evaluation of Uncertainty of Earthquake Parameters for the Purpose of Seismic Zoning of Iran

An efficient procedure is used for explicit description and evaluation of uncertainty of earthquake parameters in the uniform catalog of earthquakes in Iran and neighboring regions.An inadequate number of local and regional seismographic stations,poor station distribution,and Inadequacy of velocity models have resulted in conspicuous uncertainty in different parameters of recorded events.In a comprehensive seismic hazard analysis such uncertainties should be considered.Uncertainty of magnitude and location of events are evaluated for three different time periods,namely,historical,early instrumental,and modern instrumental time periods,for which existing seismological information differ widely in quantity,quality,and type.It is concluded that an uncertainty of 0.2-0.3 units of magnitude and 10-15 km in epicenter determinations should be considered in the most favorable conditions.None of the hypocenters of earthquakes in Iran can be considered as reliable,unless supported by other information such as

Low-carbon generation expansion planning considering uncertainty of renewable energy at multi-time scales

With the development of carbon electricity,achieving a low-carbon economy has become a prevailing and inevitable trend.Improving low-carbon expansion generation planning is critical for carbon emission mitigation and a lowcarbon economy.In this paper,a two-layer low-carbon expansion generation planning approach considering the uncertainty of renewable energy at multiple time scales is proposed.First,renewable energy sequences considering the uncertainty in multiple time scales are generated based on the Copula function and the probability distribution of renewable energy.Second,a two-layer generation planning model considering carbon trading and carbon capture technology is established.Specifically,the upper layer model optimizes the investment decision considering the uncertainty at a monthly scale,and the lower layer one optimizes the scheduling considering the peak shaving at an hourly scale and the flexibility at a 15-minute scale.Finally,the results of different influence factors on low-carbon generation expansion planning are compared in a provincial power grid,which demonstrate the effectiveness of the proposed model.

Bayesian data analysis to quantify the uncertainty of intact rock strength

One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σand mused in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student’s t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.

The Uncertainty of Tropical Cyclone Intensity and Structure Based on Different Parameterization Schemes of Planetary Boundary Layer

Based on different parameterization schemes of planetary boundary layer (PBL), the uncertainty of intensity and structure of the Super-strong Typhoon Rammasun (1409) is investigated using the WRF model (v3.4) with six PBL parameterization schemes. Results indicate that PBL uncertainty leads to the uncertainty in tropical cyclone (TC)prediction, which increases with forecast time. The uncertainty in TC prediction is mainly reflected in the uncertainty in TC intensity, with significant differences in the TC intensity forecasts using various PBL schemes. The uncertainty in TC prediction is also reflected in the uncertainty in TC structures. Greater intensity is accompanied by smaller vortex width,tighter vortex structure, stronger wind in the near-surface layer and middle and lower troposphere, stronger inflow(outflow) wind at the lower (upper) levels, stronger vertical upward wind, smaller thickness of the eye wall, smaller outward extension of the eye wall, and warmer warm core at the upper levels of eye. PBL height, surface upward heat flux and water vapor flux are important factors that cause the uncertainty in TC intensity and structure. The more surface upward heat flux and water vapor flux and the lower PBL height, the faster TC development and the stronger TC intensity.

Study on the Uncertainty of the Available Time Under Ship Fire Based on Monte Carlo Sampling Method

Available safety egress time under ship fire （SFAT） is critical to ship fire safety assessment, design and emergency rescue. Although it is available to determine SFAT by using fire models such as the two-zone fire model CFAST and the field model FDS, none of these models can address the uncertainties involved in the input parameters. To solve this problem, current study presents a framework of uncertainty analysis for SFAT. Firstly, a deterministic model estimating SFAT is built. The uncertainties of the input parameters are regarded as random variables with the given probability distribution functions. Subsequently, the deterministic SFAT model is employed to couple with a Monte Carlo sampling method to investigate the uncertainties of the SFAT. The Spearman＇s rank-order correlation coefficient （SRCC） is used to examine the sensitivity of each input uncertainty parameter on SFAT. To illustrate the proposed approach in detail, a case study is performed. Based on the proposed approach, probability density function and cumulative density function of SFAT are obtained. Furthermore, sensitivity analysis with regard to SFAT is also conducted. The results give a high-negative correlation of SFAT and the fire growth coefficient whereas the effect of other parameters is so weak that they can be neglected.

Uncertainty of Climate Response to Natural and Anthropogenic Forcings Due to Different Land Use Scenarios

The A.M.Obukhov Institute of Atmospheric Physics,Russian Academy of Sciences （IAP RAS） climate model （CM） of intermediate complexity is extended by a spatially explicit terrestrial carbon cycle module.Numerical experiments with the IAP RAS CM are performed forced by the reconstructions of anthropogenic and natural forcings for the 16th to the 20th centuries and by combined SRES （Special Report on Emission Scenarios） A2-LUH （Land Use Harmonization） anthropogenic scenarios for the 21st century.Hereby,the impact of uncertainty in land-use scenarios on results of simulations with a coupled climate-carbon cycle model is tested.The simulations of the model realistically reproduced historical changes in carbon cycle characteristics.In the IAP RAS CM,climate warming reproduced in the 20th and 21st centuries enhanced terrestrial net primary production but terrestrial carbon uptake was suppressed due to an overcompensating increase in soil respiration.Around year 2100,the simulations the model forced by different land use scenarios diverged markedly,by about 70 Pg （C） in terms of biomass and soil carbon stock but they differed only by about 10 ppmv in terms of atmospheric carbon dioxide content.

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis,engineering design,and safe construction in rock mechanics and engineering.The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass,but this does not consider the uncertainty.This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data,then integrating the monitored data,prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC)simulation.The proposed approach is illustrated by a circular tunnel with an analytical solution,which was then applied to an experimental tunnel in Goupitan Hydropower Station,China.The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables.The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements.It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically.Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data.Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.

Uncertainty of Slope Length Derived from Digital Elevation Models of the Loess Plateau, China

Although many studies have investigated slope gradient uncertainty derived from Digital Elevation Models(DEMs), the research concerning slope length uncertainty is far from mature. This discrepancy affects the availability and accuracy of soil erosion as well as hydrological modeling. This study investigates the formation and distribution of existing errors and uncertainties in slope length derivation based on 5-m resolution DEMs of the Loess Plateau in the middle of China. The slope length accuracy in three different landform areas is examined to analyse algorithm effects. The experiments indicate that the accuracy of the flat test area is lower than that of the rougher areas. The value from the specific contributing area(SCA) method is greater than the cumulative slope length(CSL), and the differences between these two methods arise from the shape of the upslope area. The variation of mean slope length derived from various DEM resolutions and landforms. The slope length accuracy decreases with increasing grid size and terrain complexity at the six test sites. A regression model is built to express the relationship of mean slope length with DEM resolution less than 85 m and terrain complexity represented by gully density. The results support the understanding of the slope length accuracy, thereby aiding in the effective evaluation of the modeling effect of surface process.

Uncertainty of the Numerical Solution of a Nonlinear System’s Long-term Behavior and Global Convergence of the Numerical Pattern

The computational uncertainty principle in nonlinear ordinary differential equations makes the numerical solution of the long-term behavior of nonlinear atmospheric equations have no meaning. The main reason is that, in the error analysis theory of present-day computational mathematics, the non-linear process between truncation error and rounding error is treated as a linear operation. In this paper, based on the operator equations of large-scale atmospheric movement, the above limitation is overcome by using the notion of cell mapping. Through studying the global asymptotic characteristics of the numerical pattern of the large-scale atmospheric equations, the definitions of the global convergence and an appropriate discrete algorithm of the numerical pattern are put forward. Three determinant theorems about the global convergence of the numerical pattern are presented, which provide the theoretical basis for constructing the globally convergent numerical pattern. Further, it is pointed out that only a globally convergent numerical pattern can improve the veracity of climatic prediction.

Effect of Uncertainty of Grid DEM on TOPMODEL:Evaluation and Analysis

TOPMODEL,a semi-distributed hydrological model,has been widely used.In the process of simulation of the model,Digital Elevation Model(DEM) is used to provide the input data,such as topographic index and distance to the drainage outlet;thus DEM plays an important role in TOPMODEL.This study aims at examining the impacts of DEM uncertainty on the simulation results of TOPMODEL.In this paper,the effects were evaluated mainly from quantitative and qualitative aspects.Firstly,DEM uncertainty was simulated by using the Monte Carlo method,and for every DEM realization,the topographic index and distance to the drainage outlet were extracted.Secondly,the obtained topographic index and the distance to the drainage outlet were input to the TOPMODEL to simulate seven rain-storm-flood events,and four evaluation indices,such as Nash and Sutcliffe efficiency criterion(EFF),sum of squared residuals over all time steps(SSE),sum of squared log residuals over all time steps(SLE) and sum of absolute errors over all time steps(SAE) were recorded.Thirdly,these four evaluation indices were analyzed in statistical manner(minimum,maximum,range,standard deviation and mean value),and effect of DEM uncertainty on TOPMODEL was quantitatively analyzed.Finally,the simulated hydrographs from TOPMODEL using the original DEM and realizations of DEM were qualitatively evaluated under each flood cases.Results show that the effect of DEM uncertainty on TOPMODEL is inconsiderable and could be ignored in the model’s application.This can be explained by:1) TOPMODEL is not sensitive to the distribution of topographic index and distance to the drainage outlet;2) the distri-bution of topographic index and distance to the drainage outlet are slightly affected by DEM uncertainty.

Assessing geological uncertainty of a cement raw material deposit,southern Vietnam,based on hierarchical simulation

Resource modeling plays a crucial role in raw material quality management for cement manufacturing.Research has shown that geological uncertainty in resource modeling is inevitable and results in risk to future extraction planning and operations of the cement plant.This study aims to assess the geological uncertainty and associated risk in modeling a cement raw material deposit in southern Vietnam.For this deposit,soil,clay,laterite,and limestone are the four primary rock types,controlling the occurrence and spatial distribution of chemical grades.In this study,hierarchical simulation method was used to evaluate the uncertainty.Rock types were first simulated,and the chemical grades conditioning to the rock types were then generated.The results demonstrated the capability of the hierarchical simulation approach to incorporate the uncertainty of rock types in resource modeling and to allow evaluating the risks in providing the desired raw material for the cement plant in the form of grade-tonnage curves.

Effect of Uncertainty of the Pre-Exponential Factor on Kinetic Parameters of Hydrocarbon Generation from Organic Matter and its Geological Applications

The source rock sample of the Shahejie Formation （upper Es4） in Jiyang Sag was pyrolyzed under open system with the Rock-Eval-lI apparatus, and then kinetic model parameters were calibrated for investigating the effect of uncertainty of pre-exponential factors on kinetic parameters and geological applications, where the parallel first-order reaction rate model with an average pre- exponential factor and discrete distribution activity energies was used. The results indicate that when the pre-exponential factor changes from low to high, an extreme value for residual errors occurs. And with the increasing pre-exponential factor, the distribution shape of activation energies are nearly the same, but the values of activation energies move higher integrally, and the average activation energy increases about 12 kJ/mol for every 10-fold of the pre-exponential factors. Extrapolating the geological heating rate of 3.3 ~C/Ma, the results show that with the increases in pre-exponential factor, the geological temperature corresponding to TRo.5 （transforming ratio of hydrocarbon generation is 50%） increases gradually, and the additional temperature gradually decreases. Combined with geochemical data of source rock, the kinetic parameters with different pre-exponentia[ factors are used to calculate the transformation ratio of hydrocarbon generation, and the result indicates that kinetic parameters corresponding to the better optimized pre-exponential factor are more suitable. It is suggested that the risk assessment of hydrocarbon generation kinetic parameters should be enhanced when using the kinetic method to appraise the oil-gas resources. Meantime, the application result of different kinetic parameters should be verified with geological and geochemical data of source rock in the target area; therefore, the most suitable kinetic parameters for target can be obtained.

Using radium isotopes to evaluate the uncertainty of submarine groundwater discharge in the northeast and entirety of Daya Bay

Submarine groundwater discharge(SGD),which can be traced using naturally occurring radium isotopes,has been recognized as a significant nutrient source and land-ocean interaction passage for the coastal waters of the Daya Bay,China.However,uncertainties in assessing SGD fluxes must still be discussed in detail.In this study,we attempted to utilize the Monte Carlo method to evaluate the uncertainties of radium-derived SGD flux in the northeast and entirety of the Daya Bay.The results show that the uncertainties of the SGD estimate in the northeast bay are very sensitive to variations in excess radium inventories as well as radium inputs from bottom sediments,while the uncertainties of the SGD estimate for the entire bay are strongly affected by fluctuations in radium inputs from bottom sediments and radium end-members of SGD.This study will help to distinguish the key factors controlling the accuracy of SGD estimates in similar coastal waters.

PREDICTION AND UNCERTAINTY OF CLIMATE CHANGE IN CHINA DURING 21ST CENTURY UNDER RCPS

Based on integrated simulations of 26 global climate models provided by the Coupled Model Intercomparison Project(CMIP), this study predicts changes in temperature and precipitation across China in the 21 st century under different representative concentration pathways(RCPs), and analyzes uncertainties of the predictions using Taylor diagrams. Results show that increases of average annual temperature in China using three RCPs(RCP2.6, RCP4.5,RCP8.5) are 1.87 ℃, 2.88 ℃ and 5.51 ℃, respectively. Increases in average annual precipitation are 0.124, 0.214, and 0.323 mm/day, respectively. The increased temperature and precipitation in the 21 st century are mainly contributed by the Tibetan Plateau and Northeast China. Uncertainty analysis shows that most CMIP5 models could predict temperature well, but had a relatively large deviation in predicting precipitation in China in the 21 st century. Deviation analysis shows that more than 80% of the area of China had stronger signals than noise for temperature prediction;however, the area proportion that had meaningful signals for precipitation prediction was less than 20%. Thus, the multi-model ensemble was more reliable in predicting temperature than precipitation because of large uncertainties of precipitation.