Non-equal-interval direct optimizing Verhulst model that x(n) be taken as initial value and its application

To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.

IFCEM based recognition method for target with interval-overlapped hybrid attributes

When the attributes of unknown targets are not just numerical attributes,but hybrid attributes containing linguistic attributes,the existing recognition methods are not effective.In addition,it is more difficult to identify the unknown targets densely distributed in the feature space,especially when there is interval overlap between attribute measurements of different target classes.To address these problems,a novel method based on intuitionistic fuzzy comprehensive evaluation model(IFCEM)is proposed.For numerical attributes,targets in the database are divided into individual classes and overlapping classes,and for linguistic attributes,continuous interval-valued linguistic term set(CIVLTS)is used to describe target characteristic.A cloud modelbased method and an area-based method are proposed to obtain intuitionistic fuzzy decision information of query target on numerical attributes and linguistic attributes respectively.An improved inverse weighted kernel fuzzy c-means(IWK-FCM)algorithm is proposed for solution of attribute weight vector.The possibility matrix is applied to determine the identity and category of query target.Finally,a case study composed of parameter sensitivity analysis,recognition accuracy analysis.and comparison with other methods,is taken to verify the superiority of the proposed method.

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

Uncertain Multidisciplinary Design Optimization on Next Generation Subsea Production System by Using Surrogate Model and Interval Method

The innovative Next Generation Subsea Production System(NextGen SPS)concept is a newly proposed petroleum development solution in ultra-deep water areas.The definition of NextGen SPS involves several disciplines,which makes the design process difficult.In this paper,the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization(MDO)problem.The deterministic optimization model is formulated,and three concerning disciplines—cost calculation,hydrodynamic analysis and global performance analysis are presented.Surrogate model technique is applied in the latter two disciplines.Collaborative optimization(CO)architecture is utilized to organize the concerning disciplines.A deterministic CO framework with two disciplinelevel optimizations is proposed firstly.Then the uncertainties of design parameters and surrogate models are incorporated by using interval method,and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively.The optimization results illustrate that,although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result,the latter is more reliable than the former.

Stable Routh-Padé-type approximation in model reduction of interval systems

An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical

Sensitivity analysis of soil parameters based on interval

Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented. With practial examples, rationality and feasibility are validated. Comparison is made with some published results.

The Non-Equidistant Grey GRM (1, 1) Model and Its Application

Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.

基于FSRce模型的机电产品绿色概念设计方案生成方法

针对部分机电产品在概念设计阶段未综合考虑客户和环境的需求,进而影响产品详细设计的问题,提出了一种基于功能—结构—客户和环境需求(function‒structure‒requirements of customer and environment,FSRce)模型的机电产品绿色概念设计方案生成方法。首先,从案例库中选择合适的功能和结构对现有产品设计树中的节点进行扩展和关联;同时通过数据挖掘、专家打分等方法获得产品的客户和环境需求重要度,以构建基于FSRce模型的产品概念设计空间。然后,先利用加权区间粗糙数法对客户和环境需求重要度进行分析,得到需求相对重要度,再运用模糊质量功能展开(fuzzy quality function deployment,FQFD)将需求相对重要度转化为产品的工程特性权重。最后,利用物元理论构建基于工程特性的产品物元域和各结构物元集,并结合工程特性权重得到各结构的满意度分值,通过比较满意度优选得到满足客户和环境需求的产品概念设计方案。以某小型工业吹风机为例,基于上述方法对其概念设计方案进行优化。相比于原始方案,优化后的吹风机在能源消耗上降低了15.38%,在碳排放上降低了15.32%,且客户满意度提高了44.66%,由此验证了所提出方法的可行性与有效性。所提出的方法为机电产品概念设计方案的生成提供了一种新思路,能更好地辅助设计人员实现对机电产品的绿色设计。

基于频域分析的机载液压驱动装置疲劳寿命预测方法研究

目的 采用时域雨流法和4种频域振动疲劳分析方法对机载液压驱动装置的危险部位进行寿命预测及频域方法适用性研究。方法 首先通过有限元随机振动分析得到该结构耳片危险区域的应力PSD,计算的谱宽系数都集中在0.3~0.35,是窄带和宽带分界区域。然后运用4种典型的载荷谱估计模型,即三区间法、基于Dirlik雨流幅值经验模型、用于窄带过程的Rayleigh分布模型、Weibull分布模型,得到危险位置的疲劳寿命安全系数。接着将应力PSD映射为应力-时间序列,并基于雨流计数法得到疲劳寿命安全系数。最后以时域疲劳预测结果基准,对4种频域方法的适用性进行讨论。结果 预测结果显示,Dirlik方法预测的9个安全系数最为可靠,Rayleigh法结果一般,三区间法和Weibull法最差。结论 在窄带和宽带分界区域的谱宽系数,建议采用Dirlik方法,不建议采用三区间法和Weibull法。

湘西竹编经纬间隔法色彩创新设计参数模型研究

传统湘西竹编中,垂直经纬挑压斜纹是最基础、最常见的纹样,其色彩结构规律有序。针对斜纹竹编经纬3种间隔形式的挑压逻辑,建立二阶进制图像、颜色信息的提取和色彩间隔结构单元,以及斜纹竹编编织图案的数字表达模型、斜纹竹编应力矩阵和色彩间隔矩阵的数学模型。色彩经纬带间隔矩阵模型是由Grasshopper软件实现的参数化计算机模型样品,通过计算机仿真模型证明:色彩经纬间隔法可以有效进行竹编的色彩创新设计,达到竹产品的快速开发、获取产品有色竹条备材数据的目的。

基于GLUE和标准Bayesian方法对TOPMODEL模型的参数不确定性分析

目前,水文模型不确定性的量化问题在水文研究中受到很大关注,在一些文章中提到了许多不确定性量化的方法,其中,GLUE方法和标准Bayesian方法是两种最常用的方法。主要讨论这两种方法在研究TOPMODEL模型时计算有效性和不同之处.通过用GLUE和标准Bayesian方法估计TOPMODEL模型参数的不确定性和模拟的不确定性,对这两种方法的结果进行评价,并讨论产生不同的原因,研究的主要结果为:(1)由Bayesian方法得到的参数后验分布比GLUE方法得到的离散型小。(2)给定GLUE中阈值(=0.8)的情况下,由Bayesian方法得到模拟流量的不确定性置信区间与GLUE方法得到的很接近。

区间过程激励下刚柔耦合系统动态不确定性分析的序列模拟方法

针对动态不确定性激励作用下的刚柔耦合系统动力学问题,提出了一种基于区间过程模型的动力学不确定性序列模拟方法,旨在通过区间过程序列抽样及刚柔耦合动力学序列模拟计算结构振动与机构运动等系统动态响应的上下边界。介绍了中心刚体柔性梁刚柔耦合系统动力学方程的构建与数值求解方法。针对动态不确定性激励作用下的刚柔耦合系统动力学分析,引入区间过程模型及其区间K-L展开对动态不确定性进行了度量和高效表征,提出了一种求解系统机构运动与结构振动等动力学响应上下边界的序列模拟方法。该方法利用序列模拟策略识别当前模拟序列中对动态响应上边界或下边界具有贡献的区间过程参数样本集,作为下一模拟序列中的局部加密抽样中心,可有效避免直接蒙特卡罗模拟在计算动力学响应上下边界时因过多无效抽样模拟而导致的低效收敛问题。最后,通过三个算例对所提方法的有效性进行了验证。研究结果表明,对于刚柔耦合系统大范围运动及振动响应上下边界的求解,序列模拟方法相比于直接蒙特卡罗模拟方法具有更好的计算效率和计算精度。

综合能源系统建模与能流计算方法研究综述

围绕综合能源系统的能流计算问题,从网络模型及求解、不确定性能流分析方法2个层面综述了各类能流计算方法。首先,在综合能源系统网络特性建模方面,讨论了偏微分方程模型、动态特性模型和稳态特性模型及其求解方法。其次,归纳了应对系统外部输入不确定性的概率和区间2类传统能流分析方法,以及概率-区间混合不确定性能流分析方法。最后,从工程应用角度分析当前综合能源系统能流计算的难点与热点,进而对其发展方向进行展望。

Oxygen uptake response to switching stairs exercise by non-parametric modeling

Oxygen uptake plays a crucial role in the evaluation of endurance performance during exercise and is extensively utilized for metabolic assessment. This study records the oxygen uptake during the exercise phase (i.e., ascending or descending) of the stair exercise, utilizing an experimental dataset that includes ten participants and covers various exercise periods. Based on the designed experiment protocol, a non-parametric modeling method with kernel-based regularization is generally applied to estimate the oxygen uptake changes during the switching stairs exercise, which closely resembles daily life activities. The modeling results indicate the effectiveness of the non-parametric modeling approach when compared to fixed-order models in terms of accuracy, stability, and compatibility. The influence of exercise duration on estimated fitness reveals that the model of the phase-oxygen uptake system is not time-invariant related to respiratory metabolism regulation and muscle fatigue. Consequently, it allows us to study the humans’ conversion mechanism at different metabolic rates and facilitates the standardization and development of exercise prescriptions.

基于多维联系云的巷道围岩稳定性评价模型

为提高地下金属矿山巷道围岩稳定性评估的准确性,根据工程实际,选取5个典型影响因素,构建了围岩稳定性评价指标体系,运用区间层次分析法(Improved Analytic Hierarchy Process, IAHP)和改进CRITIC法(Criteria Importance Though Intercrieria Correlation, CRITIC)分别计算指标主、客观权重,基于博弈论思想,确定指标最优综合权重,结合多维联系云模型理论,建立了地下金属矿山巷道围岩稳定性综合评价模型。以国内14条巷道工程为样本数据进行模型检验,并与模糊综合、物元可拓判别结果及实际情况进行对比。最后,将模型应用到某金矿巷道围岩稳定性评估中。结果表明,基于博弈论-多维联系云的地下金属矿山巷道围岩稳定性评估结果与现场调查结论完全一致,验证了本模型在巷道围岩稳定性评价方面具有可行性和有效性,可以为地下金属矿山巷道围岩稳定性评估提供一种准确的、可量化分析的新思路。

基于子区间修正摄动法的汽车高频噪声优化设计

为抑制声学包零件参数较强的不确定性引起的车内高频噪声大范围波动,提出了一种基于子区间修正摄动法的汽车高频噪声不确定性分析与优化方法,首先建立汽车高频噪声分析的统计能量基本方程,将不确定性参数划分为若干子区间,采用修正区间摄动法计算每个子区间的摄动半径,得到高频噪声性能的中心值和摄动半径,并利用区间不确定性优化方法对车辆的高频噪声性能和零件质量进行了优化设计。应用该方法对某车型的内前围、地毯进行分析和优化设计,结果表明,优化后,声学包零件质量减轻了3%,噪声波动区间下降幅度超过35%,系统的稳健性显著提升。

混合相依删失数据下非参数比例风险模型的半参数分析

目的构建一种处理混合相依删失数据的非参数比例风险(PH)模型,探讨心脏移植手术风险与风险因子直接的关系并预测心脏移植手术风险。方法基于混合相依区间删失数据的复杂性,考虑失效时间过程与观测时间过程的相依关系,假设风险因子与心脏移植手术风险存在非线性函数关系,建立具有非参数结构的比例风险模型,并给出两步Sieve估计极大似然算法。根据观测过程模型建立估计方程,获得脆弱变量的估计;再分别利用I-样条和B-样条去近似基准风险函数和非参数结构函数,获得Sieve空间中的工作似然函数,对于模型参数求偏导获得得分方程;最后通过求解方程获得参数的极大似然估计,绘制风险因子影响心脏移植手术风险的函数曲线。结果模拟研究揭示了各种设置下所提方法获得的估计量是相合的且渐近有效的,同时获得很好的参数拟合曲线。心脏移植手术数据分析结果显示,心脏供体的年龄对患者手术风险影响呈现正向线性关系,患者(受体)发病年龄影响先增大后平稳,最后有缓慢增大,供体与受体的年龄差对患者手术风险影响呈现正向线性关系。结论本研究建立了一个可分析复杂相依删数据的非参数PH模型,该模型应用于分析预测心脏移植手术风险,通过模型可探索出心脏移植手术风险与风险因子之间的函数关系。

Ranking environmental projects model based on multicriteria decision-making and the weight sensitivity analysis

With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental quality and economic benefits is an important problem for the decision makers. The purpose of this paper is to develop a decision-making model to rank a finite number of alternatives with several and sometimes conflicting criteria. A model for ranking the projects of municipal sewage treatment plants is proposed by using exports＇ information and the data of the real projects. And, the ranking result is given based on the PROMETHEE method. Furthermore, by means of the concept of the weight stability intervals （WSI）, the sensitivity of the ranking results to the size of criteria values and the change of weights value of criteria are discussed. The result shows that some criteria, such as “proportion of benefit to project cost”, will influence the ranking result of alternatives very strong while others not. The influence are not only from the value of criterion but also from the changing the weight of criterion. So, some criteria such as “proportion of benefit to project cost” are key critera for ranking the projects. Decision makers must be cautious to them.

A Bootstrapping Approach for Software Reliability Measurement Based on a Discretized NHPP Model

Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test runs, the number of executed test cases. This paper discusses discrete software reliability measurement based on a discretized nonhomogeneous Poisson process (NHPP) model. Especially, we use a bootstrapping method in our discrete software reliability measurement for discussing the statistical inference on parameters and software reliability assessment measures of our model. Finally we show numerical examples of interval estimations based on our bootstrapping method for the several software reliability assessment measures by using actual data.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.