Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

Uncertainty quantification of mechanism motion based on coupled mechanism—motor dynamic model for ammunition delivery system

In this paper,a dynamic modeling method of motor driven electromechanical system is presented,and the uncertainty quantification of mechanism motion is investigated based on this method.The main contribution is to propose a novel mechanism-motor coupling dynamic modeling method,in which the relationship between mechanism motion and motor rotation is established according to the geometric coordination of the system.The advantages of this include establishing intuitive coupling between the mechanism and motor,facilitating the discussion for the influence of both mechanical and electrical parameters on the mechanism,and enabling dynamic simulation with controller to take the randomness of the electric load into account.Dynamic simulation considering feedback control of ammunition delivery system is carried out,and the feasibility of the model is verified experimentally.Based on probability density evolution theory,we comprehensively discuss the effects of system parameters on mechanism motion from the perspective of uncertainty quantization.Our work can not only provide guidance for engineering design of ammunition delivery mechanism,but also provide theoretical support for modeling and uncertainty quantification research of mechatronics system.

Multi-Compartment SCFA Quantification in Human

Short-chain fatty acids (SCFA) play an important role in human biochemistry. They originate primarily from the digestive system through carbohydrates microbial fermentation. Most SCFA produced in the colon are absorbed by the intestinal wall and enter the bloodstream to be distributed throughout the body for multiple purposes. At the intestinal level, SCFA play a role in controlling fat storage and fatty acid metabolism. The effects of these beneficial compounds therefore concern overall health. They facilitate energy expenditure and are valuable allies in the fight against obesity and diabetes. SCFA are also involved in the regulation of the levels of several neurotransmitters such as GABA (γ-aminobutyric acid), glutamate, serotonin, dopamine, and norepinephrine. Their role is also highlighted in many inflammatory and neurodegenerative diseases such as Alzheimer’s disease (AD) or Parkinson’s disease (PD). To have a realistic picture of the distribution of SCFA in different biological compartments of the human body, we propose to study SCFA simultaneously in five human biological samples: feces, saliva, serum, cerebrospinal fluid (CSF), and urine, as well as in Dried Blood Spot (DBS). To evaluate their concentration and repeatability, we used 10 aliquots from pooled samples, analyzed by 3-nitrophenylhydrazine (3-NPH) derivation and liquid chromatography coupled with high sensitivity mass spectrometry (LC-QqQ-MS). We also evaluated the SCFA assay on Dried Blood Spot (DBS). In this work, we adapted the pre-analytical parts for each sample to be able to use a common calibration curve, thus facilitating multi-assay quantification studies and so being less time-consuming. Moreover, we proposed new daughter ions from the same neutral loss (43 Da) to quantify SCFAs, thus improving the sensitivity. In conclusion, our methodology, based on a unique calibration curve for all samples for each SCFA, is well-suited to quantified them in a clinical context.

Investigation on mechanical properties regulation of rock-like specimens based on 3D printing and similarity quantification

3D printing is widely adopted to quickly produce rock mass models with complex structures in batches,improving the consistency and repeatability of physical modeling.It is necessary to regulate the mechanical properties of 3D-printed specimens to make them proportionally similar to natural rocks.This study investigates mechanical properties of 3D-printed rock analogues prepared by furan resin-bonded silica sand particles.The mechanical property regulation of 3D-printed specimens is realized through quantifying its similarity to sandstone,so that analogous deformation characteristics and failure mode are acquired.Considering similarity conversion,uniaxial compressive strength,cohesion and stress–strain relationship curve of 3D-printed specimen are similar to those of sandstone.In the study ranges,the strength of 3D-printed specimen is positively correlated with the additive content,negatively correlated with the sand particle size,and first increases then decreases with the increase of curing temperature.The regulation scheme with optimal similarity quantification index,that is the sand type of 70/140,additive content of 2.5‰and curing temperature of 81.6℃,is determined for preparing 3D-printed sandstone analogues and models.The effectiveness of mechanical property regulation is proved through uniaxial compression contrast tests.This study provides a reference for preparing rock-like specimens and engineering models using 3D printing technology.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

Quantification of the concrete freeze–thaw environment across the Qinghai–Tibet Plateau based on machine learning algorithms

The reasonable quantification of the concrete freezing environment on the Qinghai–Tibet Plateau(QTP) is the primary issue in frost resistant concrete design, which is one of the challenges that the QTP engineering managers should take into account. In this paper, we propose a more realistic method to calculate the number of concrete freeze–thaw cycles(NFTCs) on the QTP. The calculated results show that the NFTCs increase as the altitude of the meteorological station increases with the average NFTCs being 208.7. Four machine learning methods, i.e., the random forest(RF) model, generalized boosting method(GBM), generalized linear model(GLM), and generalized additive model(GAM), are used to fit the NFTCs. The root mean square error(RMSE) values of the RF, GBM, GLM, and GAM are 32.3, 4.3, 247.9, and 161.3, respectively. The R^(2) values of the RF, GBM, GLM, and GAM are 0.93, 0.99, 0.48, and 0.66, respectively. The GBM method performs the best compared to the other three methods, which was shown by the results of RMSE and R^(2) values. The quantitative results from the GBM method indicate that the lowest, medium, and highest NFTC values are distributed in the northern, central, and southern parts of the QTP, respectively. The annual NFTCs in the QTP region are mainly concentrated at 160 and above, and the average NFTCs is 200 across the QTP. Our results can provide scientific guidance and a theoretical basis for the freezing resistance design of concrete in various projects on the QTP.

Revolutionizing disease diagnosis and management:Open-access magnetic resonance imaging datasets a challenge for artificial intelligence driven liver iron quantification

Artificial intelligence(AI),particularly machine learning(ML)and deep learning(DL)techniques,such as convolutional neural networks(CNNs),have emerged as transformative technologies with vast potential in healthcare.Body iron load is usually assessed using slightly invasive blood tests(serum ferritin,serum iron,and serum transferrin).Serum ferritin is widely used to assess body iron and drive medical management;however,it is an acute phase reactant protein offering wrong interpretation in the setting of inflammation and distressed patients.Magnetic resonance imaging is a non-invasive technique that can be used to assess liver iron.The ML and DL algorithms can be used to enhance the detection of minor changes.However,a lack of open-access datasets may delay the advancement of medical research in this field.In this letter,we highlight the importance of standardized datasets for advancing AI and CNNs in medical imaging.Despite the current limitations,embracing AI and CNNs holds promise in revolutionizing disease diagnosis and treatment.

运用Real-time quantification PCR方法建立副溶血性弧菌在即食虾中的生长预测模型

运用Real-time quantification PCR(real-time qPCR)方法建立副溶血性弧菌在即食虾中生长预测模型。首先构建质粒标准品,梯度稀释后建立标准曲线,然后用Real-time qPCR方法检测虾中副溶血性弧菌的数量,最后建立37℃下即食虾中副溶血性弧菌生长预测模型,并与传统涂布计数方法进行比较。结果表明,Real-time qPCR方法和传统计数方法均可建立Gmopertz模型、Logistic模型和Richards模型,模型拟合的相关系数R2均在0.9以上。基于Real-timeqPCR方法省时省力、特异性好等优点,用Real-time qPCR方法建立微生物预测模型是未来预测微生物学领域的一种发展趋势。

Quantification of In Vivo Epidermal Keratinocyte Architecture Associated with the Signs of Skin Aging and the Skin Benefit Evaluation by Application of Galactomyces Ferment Filtrate (Pitera)-Containing Skin Care Product

Background: Aged skin exhibits visual alterations such as wrinkles, rough texture, pore dilation, and dull skin tone, as well as physiological aging, namely, decreased hydration and increased transepidermal water loss (TEWL). Recent advances in coherence tomography have also revealed that skin aging affects in vivo epidermal keratinocyte architecture. However, the interconnectivity between spatial architectural aging and visual/physiological aging parameters remains largely unknown. Purpose: To elucidate whether the tomographic keratinocyte architectural aging is correlated with visual and physiological skin aging parameters and to quantitatively evaluate the improvements of the architectural, visual, and physiological aging parameters by the daily treatment of the skin care formula containing Galactomyces Ferment Filtrate (GFF, 8X PiteraTM). Method: We measured the in vivo keratinocyte cellular architecture with two-photon stereoscopic tomography obtaining by-layer epidermal section images in 78 Asian females of various ages. Visual aging parameters were analyzed using a portable image capture system. Hydration and TEWL were also assessed. The anti-aging effects of GFF-containing skin moisturizer (SK-II LXP CreamTM) were also examined in two studies after twice-daily application for 2 (N = 35) and 4 (N = 32) weeks. Results: As for the keratinocyte cellular architecture, skin aging was significantly associated with decreased cell density and increased cell uniformity. These architectural aging parameters were significantly correlated with visual and physiological aging parameters, namely, rough texture, wrinkles, pore dilation, dull skin tone, dehydration, and increased TEWL. The strong interconnectivity allowed us to develop formulae to estimate the keratinocyte architecture from visual aging parameters. Moreover, twice-daily application of SK-II significantly improved the keratinocyte architecture associated with multiple skin aging visual and physiological parameters. Conclusion: Skin aging is a process involving mutual interconnections among epidermal keratinocyte cellular architecture, visual, and physiological parameters. The GFF-containing moisturizer SK-II effectively improves spatial architecture of keratinocytes in epidermis and these evaluated skin aging parameters in a new trajectory over the course of treatment. .

Application of quantification theory in risk assessment of mine flooding

Hundreds of mine flooding accidents have occurred in China since the 1950s. These flooding accidents result in submerged working faces, even entire coal mines, leading to tremendous economic losses. It is reported that among 601 state-owned mines in China, 285 mines are exposed to water-inrush risks. The water pressure is becoming larger and larger with the increase of mining depth, leading to an increase of water-inrush hazards. Only when the risk of mine flooding is predicted in a reasonable manner, can we take timely and effective measures to prevent mine flooding from taking place. In our investigation quantification（H） theory is used to study the risk prediction problem about mine flooding. By investigating the main factors which affect mine flooding, eight risk assessment items have been identified. The extent of risk is classified into 4 grades. Given the data from different periods in the Feicheng mining area, a prediction model for the risk of mine flooding is established. The test analysis indicates a model correlation coefficient of 0.97 and the incidence of discrimination is as high as 97.37%, which implies that the effect of the model is quite satisfactory. With the help of computers, this method can be widely applied.

Real-Time PCR Technique and Its Application in Quantification of Plant Nucleic Acid Molecules

Real-time PCR is a closed DNA amplification system that skillfully integrates biochemical, photoelectric and computer techniques. Fluorescence data acquired once per cycle provides rapid absolute quantification of initial template copy numbers as PCR products are generated. This technique significantly simplifies and accelerates the process of producing reproducible quantification of nucleic acid molecules. It not only is a sensitive, accurate and rapid quantitative method, but it also provides an easier way to calculate the absolute starting copy number of nucleic acid molecules to be tested. Together with molecular bio-techniques, like microarray, real-time PCR will play a very important role in many aspects of molecular life science such as functional gene analysis and disease molecular diagnostics. This review introduces the detailed principles and application of the real-time PCR technique, describes a recently developed system for exact quantification of AUX/IAA genes In Arabidopsis, and discusses the problems with the real-time PCR process.

规划设计学中的调查分析法14—数量化Ⅰ类(Quantification Theory Type Ⅰ)

回归及重回归分析和预测,被广泛地应用于各个行业中。但是,有些相当于回归分析中的说明变数,不是数量数据,而是非数量数据,例如:影响入园人数的因素有星期(平日、休日)、天气状况(晴天、阴天、雨雪天等)、季节(春、夏、秋、冬)等。这些因素因为不是“量”的数据,所以不能用回归或重回归等方法进行分析和预测,但这种情况在规划设计的调查中经常出现,所以数量化Ⅰ类,可以帮助人们进行与回归分析和预测相同的分析,这是十分有效的一种分析方法。

融合NSGA-II和CSA的多目标车间调度

针对在灵活车间系统中调度作业和自动引导车(automated guide vehicle,AGV)的同时调度问题,考虑在有限多个AGV和加工机台的情况下,以最小化最大完工时间、单个AGV搬运消耗时间及所有AGV搬运总消耗时间为目标函数,设计融合NSGA-II(non-dominated sorting genetic algorithms)和克隆选择(clonal selection algorithm,CSA)的改进算法INGCSA来解决此类问题。采用工件、加工机台和AGV三部分编码;引入非支配排序和目标函数值大小排序后总得分进行种群分层,从而有效地保留优秀个体;针对克隆后的种群,对不同等级的种群采取不同的变异概率,并对染色体进行内部交换与均匀交叉混合交换的基因重组,有效地提高了种群的多样性与防止陷入局部最优。通过三组对比实验,验证了该算法在探索最优解时,具有运行时间短、稳定性高和收敛性好等优点。

基于区间毕达哥拉斯犹豫模糊熵和交叉熵的ELECTRE II决策方法

针对属性权重完全未知或部分已知,属性值为区间毕达哥拉斯犹豫模糊数的多属性决策问题,提出了基于区间毕达哥拉斯犹豫模糊熵和交叉熵的ELECTRE II法。首先给出区间毕达哥拉斯犹豫模糊数的区间形式的得分函数和精度函数,定义新的距离测度。然后基于区间毕达哥拉斯犹豫模糊数的模糊因子、直觉因子和幅度因子,给出熵和交叉熵公式,并证明其性质,提出了基于熵和交叉熵确定属性权重的方法。最后提出了区间毕达哥拉斯犹豫模糊环境下的改进的ELECTRE II法,利用综合优势值对方案进行排序,并通过算例和比较分析验证了该方法的可行性和有效性。

基于改进NSGA-II的轨道交通接驳公交线路优化

为解决接驳公交线路规划不合理和时间安排不完善的问题,提出了基于改进NSGA-II算法的环形接驳公交线路优化方法。首先,结合双层规划理论,以乘客出行时间成本最小化、公交企业运营收益和接驳公交服务率最大化为目标函数,以接驳公交线路站点数、线路长度和发车频率作为约束条件构建上层模型,采用Logit模型构建了下层接驳客流分配模型;其次,运用Floyd算法对NSGA-II算法的初始化种群进行了优化,针对所提出的模型设计了模型求解流程;最后,以哈尔滨市轨道交通1号线医大一院轨道交通站为案例,运用笔者提出的多目标双层规划模型和算法进行求解,并与原NSGA-II算法和基于Logistic混沌映射的NSGA-II算法进行对比。研究结果表明:基于Floyd算法改进的NSGA-II算法在多目标双层规划模型求解时,收敛速度更快效果更好,求解结果可以在Pareto前沿得到多个相互非支配的最优解;不同解集对应目标函数值不同,但可以达到接驳公交网络整体效益最优,采用折衷最优解集表述求解结果。

渤海湾沿海低地第II海相层MIS5a阶段海侵与全球海平面变化的时间对比研究

【研究目的 】渤海湾地区第II海相层的形成时代仍存争议,制约着该地区海平面变化研究进展。本研究对该层进行光释光定年,以期标定准确的地层年代及对应的海侵期次。【研究方法 】以渤海湾西岸CZ80、CZ85、CZ66钻孔为研究对象,在岩心沉积结构、构造及有孔虫丰度,沉积微相研究基础上,识别出了第II海相层,并建立了第II海相层对比剖面。通过光释光测年方法对该地层的形成时代进行了准确测定,进一步讨论第II海相层的发育时间与全球海平面变化关系。【研究结果 】CZ80、CZ85及CZ66孔在全新统(含第I海相层)以下均钻遇到了第II海相层,海相层底板埋深在35~33m,对应黄海高程-31.13~-28.39m,顶板埋深32~20m,高程-25.58~-15.39 m。光释光测年结果表明第II海相层所对应的海侵事件发育时间约为94~71 ka。【结论 】光释光测年结果表明,该区第II海相层始于94 ka或更早,海水影响在距今约71 ka结束。对比全球海面曲线,第II海相层时空特征与MIS5a阶段相符,记录了MIS5a阶段海侵事件。

Precore/basal core promoter mutants quantification throughout phases of hepatitis B virus infection by Simpleprobe

AIM:To investigate precore/basal core promoter(PC/BCP) mutants throughout hepatitis B virus(HBV) infection and to determine their relationship to hepatitis B early antigen(HBeA g) titers.METHODS:We enrolled 191 patients in various stages of HBV infection at the Huashan Hospital and the Taizhou Municipal Hospital from 2010 to 2012.None of the patients received antiviral therapy.HBV DNA from serum,was quantified by real-time PCR.The HBV genotype was determined by direct sequencing of the S gene.We used the Simpleprobe ultrasensitivequantitative method to detect PC/BCP mutants in each patient.We compared the strain number,percentage,and the changes in PC/BCP mutants in different phases,and analyzed the relationship between PC/BCP mutants and HBe Ag by multiple linear regression and logistic regression.RESULTS:Patients with HBV infection(n = 191) were assigned to groups by phase:Immune tolerance(IT) = 55,Immune clearance(IC) = 67,Low-replicative(LR) = 49,and HBeA g-negative hepatitis(ENH) = 20.Of the patients(male,112; female,79) enrolled,122 were HBe Ag-positive and 69 were HBe Ag-negative.The median age was 33 years(range:18-78 years).PC and BCP mutation detection rates were 84.82%(162/191) and 96.86%(185/191),respectively.In five HBe Ag-negative cases,we detected double mutation G1896A/G1899 A.The logarithm value of PC mutant quantities(log10 PC) significantly differed in IT,IC,and LR phases,as well as in the ENH phase(F = 49.350,P < 0.001).The logarithm value of BCP mutant quantities(log10 BCP) also differed during the four phases(F = 25.530,P < 0.001).Log10 PC and log10 BCP values were high in the IT and IC phases,decreased in the LR phase,and increased in the ENH phase,although the absolute value at this point remained lower than that in the IT and IC phases.PC mutant quantity per total viral load(PC%) and BCP mutant quantity per total viral load(BCP%) differed between phases(F = 20.040,P < 0.001; F = 10.830,P < 0.001),with PC% and BCP% gradually increasing in successive phases.HBeA g titers negatively correlated with PC%(Spearman's rho =-0.354,P < 0.001) and BCP%(Spearman's rho =-0.395,P < 0.001).The negative correlation between PC% and HBeA g status was significant(B =-5.281,P = 0.001),but there was no such correlation between BCP% and HBeA g status(B =-0.523,P = 0.552).CONCLUSION:PC/BCP mutants become predominant in a dynamic and continuous process.Log10 PC,log10 BCP,PC% and BCP% might be combined to evaluate disease progression.PC% determines HBeA g status.

Quantificational indexes for design and evaluation of copper staves for blast furnaces

The quantificational and normative design is the precondition of improving the design of copper staves for blast furnaces. Based on a 3-dimensional temperature field calculation model, from the view point of heat transfer and long campaigns note with the core of forming accretion, the forming-accretion-ability （FAA） and the rib hot surface maximum temperature difference （ATmax） as quantificational indexes to direct and evaluate the design of copper staves for blast furnaces were presented. The application of the two indexes in design essentially embodies the new long campaigns in the stage of design. With the application of the two indexes, good results can be obtained. Firstly, it was suggested that the rib height of a copper stave can be reduced to 15 mm, which is a new method and theory for the reduction of copper staves. Secondly, the influence of insert on FAA and ATmax, is decided by the volume of insert. According to this, the principle of design for the hot surface geometry of copper staves was put forward that the ratio of the rib hot surface to the copper stave hot surface （abbreviated as the ratio of rib to stave） must be maintained in the range of 45% to 55%; for the present copper stave with a 35-40 mm thick rib, the ratio of rib to stave in the range of 50% to 55% can optimize the design of copper staves; for the copper stave with a smaller rib thickness, for example 15 ram, the ratio of rib to stave in the range of 45% to 50% can optimize the design of copper staves. It can be summarized that the thicker the rib thickness, the larger is the ratio of rib to stave. 2008 University of Science and Technology Beijing. All rights reserved.

Value of elastography point quantification in improving the diagnostic accuracy of early diabetic kidney disease

BACKGROUND Diabetic kidney disease(DKD)is a common complication of diabetes.The patient’s prognosis is poor once DKD progresses to advanced stage.Accurate diagnosis and timely treatment of early DKD are important for improving patient’s prognosis and reducing mortality.AIM To explore the value of elastography point quantification(ElastPQ)in improving the accuracy of early DKD diagnosis.METHODS A total of 69 patients with type 2 diabetes were recruited from Naval Military Medical University Affiliated Gongli Hospital.Patients were divided into early DKD group and medium DKD group according to pathological results and urinary albumin excretion rate(UAER).Another 40 patients with simple diabetes were included as the diabetes group.The baseline data,laboratory diagnostic indicators,and ultrasound indicators for each patient were recorded.The differences of the indicators in the three groups were compared.Multivariate logistic regression was used to analyze the influencing factors of the development from simple diabetes into early DKD and from early DKD into medium DKD.Receiver operating characteristic analyses of potential indicators in identifying early DKD and medium DKD,and early DKD and simple diabetes were established.RESULTS Multivariate logistic regression analysis showed that UAER(P<0.001),renocortical Young's Modulus(YM)(P<0.001),and renal parenchymal thickness(P=0.013)were the independent influencing factors of the development from early DKD into medium DKD.Diabetes duration(P=0.041),UAER(P=0.034),and renocortical YM(P=0.017)were the independent influencing factors of the development from simple diabetes into early DKD.Receiver operating characteristic analysis indicated that UAER,renocortical YM,and renal parenchymal thickness were accurate in identifying early DKD and medium DKD[all area under curve(AUC)>0.9].The accuracy of UAER(AUC=0.744),diabetes duration(AUC=0.757),and renocortical YM(AUC=0.782)for the diagnosis of early DKD and simple diabetes were limited.However,the combined diagnosis of UAER,diabetes duration,and renocortical YM was accurate in identifying early DKD and simple diabetes(AUC=0.906),which was significantly higher than any of the three indicators(all P<0.05).CONCLUSION ElastPQ is of great value in the diagnosis of early DKD.When combined with the diabetes duration and UAER,it is expected to diagnose accurately early DKD.

Computational intelligence approach for uncertainty quantification using evidence theory

As an alternative or complementary approach to the classical probability theory,the ability of the evidence theory in uncertainty quantification（UQ） analyses is subject of intense research in recent years.Two state-of-the-art numerical methods,the vertex method and the sampling method,are commonly used to calculate the resulting uncertainty based on the evidence theory.The vertex method is very effective for the monotonous system,but not for the non-monotonous one due to its high computational errors.The sampling method is applicable for both systems.But it always requires a high computational cost in UQ analyses,which makes it inefficient in most complex engineering systems.In this work,a computational intelligence approach is developed to reduce the computational cost and improve the practical utility of the evidence theory in UQ analyses.The method is demonstrated on two challenging problems proposed by Sandia National Laboratory.Simulation results show that the computational efficiency of the proposed method outperforms both the vertex method and the sampling method without decreasing the degree of accuracy.Especially,when the numbers of uncertain parameters and focal elements are large,and the system model is non-monotonic,the computational cost is five times less than that of the sampling method.