Monte Carlo Method for the Uncertainty Evaluation of Spatial Straightness Error Based on New Generation Geometrical Product Specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

Data Driven Uncertainty Evaluation for Complex Engineered System Design

Complex engineered systems are often difficult to analyze and design due to the tangled interdependencies among their subsystems and components. Conventional design methods often need exact modeling or accurate structure decomposition, which limits their practical application. The rapid expansion of data makes utilizing data to guide and improve system design indispensable in practical engineering. In this paper, a data driven uncertainty evaluation approach is proposed to support the design of complex engineered systems. The core of the approach is a data-mining based uncertainty evaluation method that predicts the uncertainty level of a specific system design by means of analyzing association relations along different system attributes and synthesizing the information entropy of the covered attribute areas, and a quantitative measure of system uncertainty can be obtained accordingly. Monte Carlo simulation is introduced to get the uncertainty extrema, and the possible data distributions under different situations is discussed in detail The uncertainty values can be normalized using the simulation results and the values can be used to evaluate different system designs. A prototype system is established, and two case studies have been carded out. The case of an inverted pendulum system validates the effectiveness of the proposed method, and the case of an oil sump design shows the practicability when two or more design plans need to be compared. This research can be used to evaluate the uncertainty of complex engineered systems completely relying on data, and is ideally suited for plan selection and performance analysis in system design.

Uncertainty entropy-based exploratory evaluation method and its applications on missile effectiveness evaluation

Some attributes are uncertain for evaluation work because of incomplete or limited information and knowledge.It leads to uncertainty in evaluation results.To that end,an evaluation method,uncertainty entropy-based exploratory evaluation(UEEE),is proposed to guide the evaluation activities,which can iteratively and gradually reduce uncertainty in evaluation results.Uncertainty entropy(UE)is proposed to measure the extent of uncertainty.First,the belief degree distributions are assumed to characterize the uncertainty in attributes.Then the belief degree distribution of the evaluation result can be calculated by using uncertainty theory.The obtained result is then checked based on UE to see if it could meet the requirements of decision-making.If its uncertainty level is high,more information needs to be introduced to reduce uncertainty.An algorithm based on the UE is proposed to find which attribute can mostly affect the uncertainty in results.Thus,efforts can be invested in key attribute(s),and the evaluation results can be updated accordingly.This update should be repeated until the evaluation result meets the requirements.Finally,as a case study,the effectiveness of ballistic missiles with uncertain attributes is evaluated by UEEE.The evaluation results show that the target is believed to be destroyed.

Fire risk evaluation research on fully mechanized coalface based on the uncertainty measure theory

A relatively perfect coalmine fire risk-evaluating and order-arranging model that includes sixteen influential factors was established according to the statistical information of the fully mechanized coalface ground on the uncertainty measure theory. Then the single-index measure function of sixteen influential factors and the calculation method of computing the index weight ground on entropy theory were respectively established. The value assignment of sixteen influential factors was carried out by the qualitative analysis and observational data, respectively, in succession. The sequence of fire danger class of four experimental coalfaces could be obtained by the computational aids of Matlab according to the confidence level criterion. Some conclusions that the fire danger class of the No.l, No.2 and No.3 coalface belongs to high criticality can be obtained. But the fire danger class of the No.4 coalface belongs to higher criticality. The fire danger class of the No.4 coalface is more than that of the No.2 coalface. The fire danger class of the No.2 coalface is more than that of the No.1 coalface. Finally, the fire danger class of the No.1 coalface is more than that of the No.3 coalface.

Uncertainty Evaluation of Preparation of Organophosphorus Pesticide Mixed Standard Solution

The uncertainty of standard solution plays an important role in detection of pesticide residues. It may affect the accuracy of detection results. In this study, the 14 organophosphorus pesticides mixed standard solution was used as the material to analyze all the influencing factors for the preparation of mixed standard solution with uncertainty as the only judging index. The preparation uncertainty of mixed standard solution was calculated with the top-down calculation method. In the end, the expanded uncertainty was presented. The results showed that the preparation of mixed standard solution from stock solution with precise pipettes had a relatively low uncertainty.

Maximum Entropy Distribution Function and Uncertainty Evaluation Criteria

Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.

Measurement Uncertainty Evaluation of Conicity Error Inspected on CMM

The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification（GPS）, the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm（IlEA） is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement（GUM） method to evaluate measurement uncertainty. Adaptive Monte Carlo method（AMCM） is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine（CMM）. The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error（MZCE） rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.

Quantitative Evaluation Research on Uncertainty Factors in Production Scheduling of Manufacturing Enterprises

Shop scheduling problem is core part and research hot in modern manufacture system,it has important meaning for decreasing operating costs,shortening production period and so on.Based on shop scheduling problems,this paper mainly dis- cuss and classify uncertainty factors of the shop scheduling,Meanwhile set up corresponding reliability evaluation model according to some uncertainty factors,and so it can better direct shop scheduling.

Adaptive Method for State Estimation of Sound Environment System with Uncertainty and its Application to Psychological Evaluation

The actual sound environment system exhibits various types of linear and non-linear characteristics, and it often contains uncertainty. Furthermore, the observations in the sound environment are often in the level-quantized form. In this paper, two types of methods for estimating the specific signal for sound envi-ronment systems with uncertainty and the quantized observation are proposed by introducing newly a system model of the conditional probability type and moment statistics of fuzzy events. The effectiveness of the proposed theoretical methods is confirmed by applying them to the actual problem of psychological evalua-tion for the sound environment.

Uncertainty Evaluation for the Determination of Dibutyl Phthalate(DBP) Concentration in Liqueur by GC-MS

The dibutyl phthalate （DBP） concentration in liqueur was measured by gas chromatography-mass spectrometry （GC-MS）, and the uncertainty during the mea-surement was evaluated in this study. The results showed that the combined stan-dard uncertainty was determined as 0.028 and the expanded uncertainty was 0.056 at confidence probability p=95%, coverage factor k=2, by fol owing the methods de-scribed in GB/T 21911-2008 ＂Determination of Phthalate Esters in Foods＂. The av-erage DBP concentration in the liqueur of eight repeated measurements was（0.985＆#177; 0.056） mg/kg finaly.

Uncertainty Evaluation of Determination of Microcystin MC-LR in Environmental Samples by Solid Phase Extraction-Ultra Performance Liquid Chromatography-Tandem Mass Spectrometry

To assess uncertainty of determination of MC-LR in environmental samples by solid phase extraction- ultra performance liquid chromatography- tandem mass spectrometry,the sources of the uncertainty were evaluated firstly,and the expanded uncertainty was calculated finally.The results show that when MC-LR concentration in the water samples was 0.50 μg/L,the expanded uncertainty was 0.00628 μg/L(k=2).

Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field:an investigation into propagating uncertainties for independent model parameters

Based on the Monte Carlo approach and conventional error analysis theory,taking the heaviest doubly magic nucleus 208Pb as an example,we first evaluate the propagated uncertainties of universal potential parameters for three typical types of single-particle energy in the phenomenological Woods–Saxon mean field.Accepting the Woods–Saxon modeling with uncorrelated model parameters,we found that the standard deviations of singleparticle energy obtained through the Monte Carlo simulation and the error propagation rules are in good agreement.It seems that the energy uncertainty of the single-particle levels regularly evoluate with certain quantum numbers to a large extent for the given parameter uncertainties.Further,the correlation properties of the single-particle levels within the domain of input parameter uncertainties are statistically analyzed,for example,with the aid of Pearson’s correlation coefficients.It was found that a positive,negative,or unrelated relationship may appear between two selected single-particle levels,which will be extremely helpful for evaluating the theoretical uncertainty related to the single-particle levels(e.g.,K isomer)in nuclear structural calculations.

The Evaluation of Measurement Uncertainty and Its Application in the Vacuum Pressure Measurement

In order to accurately measure the pressure and the pressure difference between two points in the vacuum chamber, a large number of experimental data were used to research the performance of the three capacitance diaphragm gauge and analysis the main influences of the uncertainly degree of pressure in the process. In this paper, three kind of uncertainty, such as the single uncertainty, the synthesis uncertainty and the expanded uncertainty of the three capacitance diaphragm gauges are introduced in detail in pressure measurement. The results show that the performance difference of capacitance diaphragm gauge can be very influential to the accuracy of the pressure difference measurement and the uncertainty of different pressure can be very influential to pressure measurement. That for accurately measuring pressure and pressure difference has certain reference significance.

Study on evaluation standard of uncertainty of design wave height calculation model

The accurate calculation of marine environmental design parameters depends on the probability distribution model,and the calculation results of different distribution models are often different.It is very important to determine which distribution model is more stable and reasonable when extrapolating the recurrence level of the studied sea area.In this paper,we constructed an evaluation method of the overall uncertainty of the calculation results and a measurement of the uncertainty of the design parameters derivation model,by incorporating the influence of sample information on the model information entropy,such as sample size,degree of dispersion,and sampling error.Results show that the sample data size and the degree of dispersion are directly proportional to the information entropy.Within the same group of data,the maximum entropy distribution model has the lowest overall uncertainty,while the Gumbel distribution model has the largest overall uncertainty.In other words,the maximum entropy distribution model has good applicability in the accurate calculation of marine environmental design parameters.

Certification and uncertainty evaluation of flavonoids certified reference materials

Flavonoids are the most widely used in the field of the food, medicine, and cosmetic due to their pharmacological functions and biological activities, such as anti-tumor, anti-inflammatory and antioxidation. This work described the assignment of purity values to 3 flavonoids certified reference materials (CRMs) including baicalein, 5,7-dihydoxy flavones and naringenine which?were developed in this study according to the ISO Guides 34 and 35. The qualitative analysis was performed by liquid chromatography-mass spectrometry (LC-MS) and infrared spectroscopy (IR). The CRMs’ purity values were assigned based on the weighted average of quantitative nuclear magnetic resonance method and mass balance approach with high resolution liquid chromatography-VWD. All the three CRMs with following value mass fractions: baicalein at a certified purity P ± U (k = 2) of 98.8% ± 0.8%;5,7-dihydoxy flavones of 99.1% ± 0.7% and naringenine of 99.5% ± 1.0% respectively. The homogeneity of the CRMs was determined by an in-house validated liquid chromatographic method. Potential degradation during storage was also investigated and a shelf-life based on this value was established.

Proposing a novel comprehensive evaluation model for the coal burst liability in underground coal mines considering uncertainty factors

Coal burst is a severe hazard that can result in fatalities and damage of facilities in underground coal mines.To address this issue,a robust unascertained combination model is proposed to study the coal burst hazard based on an updated database.Four assessment indexes are used in the model,which are the dynamic failure duration(DT),elastic energy index(WET),impact energy index(KE)and uniaxial compressive strength(RC).Four membership functions,including linear(L),parabolic(P),S and Weibull(W)functions,are proposed to measure the uncertainty level of individual index.The corresponding weights are determined through information entropy(EN),analysis hierarchy process(AHP)and synthetic weights(CW).Simultaneously,the classification criteria,including unascertained cluster(UC)and credible identification principle(CIP),are analyzed.The combination algorithm,consisting of P function,CW and CIP(P-CW-CIP),is selected as the optimal classification model in function of theory analysis and to train the samples.Ultimately,the established ensemble model is further validated through test samples with 100%accuracy.The results reveal that the hybrid model has a great potential in the coal burst hazard evaluation in underground coal mines.

Uncertainty Evaluation for Comparison Result of National Radiometric Standardsand World Radiometric Reference

Theuse of data of National Radiometric Standardtook place in the WMO International Pyrheliometer Comparisons IPCXI to evaluate the expended uncertainty of the comparison resultbetweenN ational Radiometric Standards( NRS) and the World Radiometric Reference( WRR) in Davos/World Radiometric Center. The result of expended uncertaintyis 0.17%,which meets the requirements of the World Meteorological Organization( WMO) and has reached the world advanced level.In this paper,the method can be used as a reference and basis for evaluating the uncertainty of thecomparison results of the Provincial solar radiation standard.

Uncertainty Evaluation of Anticipated Transient without Scram Plant Response in the Monju Reactor Considering Reactivity Coefficients within the Design Range

This paper describes the methods and results of an uncertainty evaluation of a significant plant response analysis of reactor trip failure events,specifically anticipated transients without scram in the Japanese prototype fast breeder reactor Monju.Unprotected loss of heat sink(ULOHS)has a relatively large contribution to the core damage frequency due to reactor trip failure.The uncertainty in the allowable time to core damage in this event has so far been estimated by considering the range of reactivity coefficients.There are some cases where it is considered that core damage will be avoided.Specifically,if the primary heat transport system(PHTS)pump inlet sodium temperature stays below 650℃for 1 h,the avoidance of core damage due to a ULOHS event is assumed.This is the temperature at which the probability of cavitation in the static pressure bearing begins to increase.In this study,a success scenario was investigated in two aspects:identification of influential input parameters and estimation of the probability of success.In the parameter identification,input parameters that satisfy the pump inlet temperature being below 650°C are clarified by treating the reactivity coefficients and reactor kinetics parameters as variables that can be taken to be within the design range.In the probability estimation,the results are fitted to a lognormal distribution function,from which the output variable was found to fall between 640 and 679℃with a probability of 90%,the probability of the temperature being 650℃or lower was 0.23,and the average and mode value was 659℃.

Helical angle measurement of worm by a coordinate measuring machine and its uncertainty evaluation

The purpose of the study concerns the measurement of worm's helical angle by a coordinate measurement machine in the ambient industrial environment. The novel measurement method and sampling strategy were described firstly. This method used the coordinate measurement machine to measure both of the worm gear's left and right surfaces. The worm surface was reconstructed based on the measured data of all the sampling points. Then a middle cylinder was established to truncate the fitted worm surfaces, and the truncated spiral lines were straightened to calculate the helical angle. The measurement uncertainty of worm's helical angle was evaluated by taking the difference of calculated helical angles along the truncated spiral lines on both the left and right side surfaces of the worm. Twenty-four measurement experiments show that the maximum measurement error of the proposed method is 0.105, and the measurement error ratios are all less than 3.5%. The result means that the measurement method can realize the precision measurement of worm's helical angle and can be employed in the generally industrial application.

Uncertainty Evaluation of Simultaneous Determination of Lead, Cadmium and Arsenic in Cosmetics by Inductively Coupled Plasma Mass Spectrometry

This study aimed to evaluate the uncertainty of simultaneous determination of lead(Pb),cadmium(Cd)and arsenic(As)in cosmetics by microwave digestion-inductively coupled plasma mass spectrometry(ICP-MS)with ^72Ge,^115In and ^209Bi as internal standards.According to the method of Safety and Technical Standards for Cosmetics(2015),a mathematical model was established to evaluate the sources and components of uncertainty for the determination of lead,cadmium and arsenic in cosmetics.The results showed that the uncertainties in the determination of lead,cadmium,and arsenic elements in cosmetics were(10.1±0.6)mg/kg,k=2,(4.84±0.28)mg/kg,k=2,(2.04±0.18)mg/kg,k=2,respectively.The main factors that affect the uncertainty of determination results were standard substance,calibration curve,recovery and measurement repeatability.