复杂系统仿真模型的分层确认

介绍一种解决复杂系统仿真可信性问题的模型确认方法.该方法首先将复杂系统划分成相对简单的子系统、基准系统、单元,得到一分层模型树;接下来对模型树中的模型进行排序并安排确认试验;然后利用信息差方法对拥有试验数据的子层模型进行单层确认;最后通过灵敏度分析将子层模型的确认结果传播到父层模型,最后得到全系统模型的确认结果.文中提出的方法适用于试验数据少、可分层的复杂系统.     

基于反例确认的CPS不确定性模型校准

信息物理系统被广泛应用于众多关键领域,例如工业控制与智能制造.作为部署在这些关键领域中的系统,其系统质量尤为重要.然而,由于信息物理系统自身的复杂性以及系统中存在的不确定性（例如系统通过传感器感知环境时的偏差）,信息物理系统的质量保障面临巨大挑战.验证是保障系统质量的有效途径之一,基于系统模型与规约它可以证明系统是否满足要求的性质.现有一些信息物理系统的验证工作也取得了显著进展,例如模型检验技术就被已用工作用于验证系统在不确定性影响下的行为是否满足性质规约,并在性质违反的情况给出具体的反例.这些验证工作的一个重要输入就是不确定性模型,它描述了系统中不确定性的具体情况.而实际中要对系统中不确定性精确建模却并非易事,因此验证中使用的不确定性模型很可能与实际不完全相符,这将导致验证结果不准确并与现实偏离.针对这一问题,本文提出了一种基于反例确认的不确定性模型校准方法,来进一步精化验证结果以提高其准确度.首先通过确认反例在系统的执行中能否被触发来判断验证使用的不确定性模型是否精确.对于不精确的模型再利用遗传算法进行校准,并根据反例确认的结果来构造遗传算法的适应度函数以指导搜索,最后结合假设检验来帮助决定是否接受校准后的结果.在代表案例上的实验结果表明了我们提出的不确定性模型校准方法的有效性.     

考虑认知不确定性的模型确认贝叶斯因子法*

针对认知不确定性条件下计算机建模仿真所面临的模型确认问题,提出一种结合了二阶概率法与区间数排序的改进贝叶斯模型确认方法。该方法首先采用二阶概率法对模型的不确定性进行量化,量化结果被做为先验模型输出,再基于实验数据对模型输出的先验概率密度进行贝叶斯更新,最后通过区间数排序的方式对比模型输出的后验和先验概率密度。由此所得的贝叶斯因子能够在模型存在认知不确定性的情况下为模型确认提供可信的结果。算例分析结果显示了本文方法的合理性。     

概率盒框架下多响应模型确认度量方法

在随机和认知混合不确定性表征的概率盒框架下,提出一种多响应模型确认度量方法.概率盒框架下的模型确认度量主要采用面积方法量化仿真与实验结果的一致程度,但传统面积度量方法并不适用于多个相关响应量的多输出确认度量问题.不确定性条件下多响应量模型确认度量问题,实质上是量化计算模型的多个响应量的联合概率分布与实验观测数据所服从的联合概率分布之间的差异程度.对此,引入马氏距离的概念对多响应量模型确认度量问题进行降维,以马氏距离作为转换的统计量,将多响应量的多指标确认度量问题转化为马氏距离的综合指标度量问题.数值仿真算例验证了所提出方法的正确性和稳定性,并将该方法应用于“2014年圣地亚验证与确认挑战问题”的研究.研究表明,基于概率盒和马氏距离的确认度量方法可以有效解决多相关响应量多输出模型确认度量问题.     

未确知数分析的仿真模型确认方法

文中首先指出了仿真模型确认中出现的不确定性问题，针对模型的不确定性引出了未确知有理数的相关概念及其信息处理方法．在此基础上，给出了未确知数仿真模型确认方法，并通过实例说明该方法的应用，从而说明了该方法的应用前景．     

考虑不确定性的供应链计划模型

对供应链计划建立了考虑不确定性的战略层模型和运作层模型。以一啤酒厂进行了实例研究,对所建模型和确定性的供应链计划模型进行了比较,并对柔性参数进行了灵敏度分析。结果表明,该模型能帮助设计具有柔性的供应链系统,通过灵敏度分析,可以更好地理解供应链的特性。     

基于概率分布距离的多响应模型确认度量

针对模型确认中的确认度量问题,构造实验观测数据经验概率分布的置信包络。通过计算其与模型响应概率分布之间距离的上/下确界,给出基于概率分布距离确认度量的置信区间。通过构造与实验观测数据有关的协方差矩阵,给出基于概率分布距离的多响应模型确认度量及其置信区间的求解方式。该度量利用了模型输出与实验观测的完整概率分布信息,并且考虑了各模型响应间的相关性。算例仿真结果表明其确认错误率低于现有的其他两种确认度量。     

对一种基于证据理论的不确定性处理模型的重要扩充

本文分析了文[1]中的不确定性处理模型中存在的问题,提出了有序命题概念,并针对有序命题的情况,给出了一种新的组合不确定性值的综合函数。     

考虑模型响应不确定性的稳健参数设计

针对模型响应不确定性的稳健参数设计问题,在高斯过程回归(Gaussian process regression,GPR)建模的框架下,结合贝叶斯超参数最大后验(Maximum a posteriori estimation,MAP)估计和多目标线性加权方法构建一个新的优化模型.首先,利用MAP方法获得最优超参数组合,构建高斯回归模型;然后,考虑响应不确定性与响应之间的交互效应,采用线性加权准则,构建多响应稳健优化模型;最后,利用聚类分析方法获得最优参数解.该方法考虑了输出响应不确定性对优化结果的影响,权衡了最优因子水平与多元质量特性之间的关系.结合实际案例和软件仿真对所提出方法进行实证研究,结果表明,该方法能够较好地兼顾输出响应的最优性和稳健性,从而实现稳健参数设计.     

噪声环境下基于不确定性度量的随机HT直线检测

含噪图像中直线的自动检测是机器视觉和图像处理中的热点问题之一。基于Hough变换的直线检测算法中采用硬投票方案,在噪声环境下检测精度下降且占用内存大。为了提高检测算法的抗噪性和降低算法的计算复杂性,提出了一种新的将边缘点不确定性度量和随机Hough变换相结合的直线检测算法。该算法在所建立的点属于某直线上不确定性度量概率模型基础上,根据随机选择的两点间直线参数,按照Bayesian法则用基于不确定度量的参数空间软投票提高了检测算法的抗噪能力。实验结果表明,算法在较高的噪声（方差大于0.03）时,检测误差小于1‰,检测时间是单纯不确定度量直线检测方法的1/2,比传统Hough变换算法快10-15倍。     

Stabilization of a nonlinear multivariable discrete-time time-invariant plant with uncertainty on a linear pseudoinverse model

This paper addresses the problem of the robust stabilization of a nonlinear multivariable time-invariant plant on a semi-infinite discrete time interval under arbitrary nonmeasurable bounded additive disturbances. A guaranteed value of the quality criterion is given by the functional representing the weighted sum of the limiting norms of the control vectors and output variables. To generate control actions, a controller containing a linear generalized inverse model and discrete-time integrators is introduced into the feedback loop. Sufficient conditions for the robust stability of the control system, as well as the conditions for the ultimate boundedness of all its signals (dissipativity conditions), are formulated. A corresponding simulation example is presented.     

On time-invariant realizations of discrete random processes

A class of discrete second-order random processes, described by linear time-invariant state-space models, is investigated. Equivalent realizations with reduced number of noise inputs are presented. In contrast to the innovations approach these realizations have time-invariant parameters.     

On the robust stability of linear time-invariant plants with unstructured uncertainty

We consider general families of linear time-invariant plants described by a nominal plant model with unstructured uncertainty. We show, under a rather weak assumption, that when a family of systems is not robustly stabilizable by any linear time-invariant feedback controller, then no nonlinear time-varying controller can robustly stabilize the given family.     

On the design of optimal time-invariant compensators for linear stochastic time-invariant systems

Design equations are developed for an optimal limited state feedback controller problem. These equations are developed for the stochastic case, in which both plant noise and measurement noise may be present, and for the case of a dynamic compensator. Four possible approaches to the solution of the nonlinear design equations are described. A fourth-order example illustrates some of the difficulties associated with the solution of these equations and suggests additional areas for study.     

Model-based robust control design and experimental validation of collaborative industrial robot system with uncertainty

Based on the traditional PID control and robust control algorithm, a novel practical robust control method is designed for the 6-DOF collaborative industrial robot with uncertainty. The proposed algorithm consists of a robust term and a model-based PD control term, which we call MPDP controller. It is demonstrated by Lyapunov theoretical analysis that the algorithm is able to guarantee uniform boundedness and uniform ultimate boundedness of the system. Simulations and experiments show the good performance of MPDP control in a robot with smaller steady-state tracking errors and better robustness compared to PID controllers.     

Experiment design for maximum-power model validation

The paper considers the problem of input signal selection to maximize power of an Asymptotic Locally Most Powerful (ALMP) test. It is shown that the input signal which maximizes the test power simultaneously yields maximum accuracy of identification if disturbances are Gaussian. For linear multivariable discrete-time systems described by transfer functions both the input signal optimality criterion and its gradient are derived. This allows input signal optimization by means of a gradient hill-climbing method. The theory is illustrated by the optimal experiment design for a zero-order system with additive coloured disturbances.     

Simulation validation with sparse random data

A simulation validation technique based on Theil's inequality coefficient (TIC) is developed for handling correlated random time-series having only sparse data sets. Specifically, a new TIC estimate containing unbiased system and model component variance estimates is derived. Comparisons with this new estimate for serially correlated data indicate that Theil's original inequality coefficient is quite robust with respect to the assumption of utilizing only independent data points. Initially, Theil's inequality coefficient is related to familiar error variance concepts. Thereafter, the new TIC estimate for sparse correlated data sets is derived, and the corresponding continuous formulas for component variance estimates are identified. A grouping procedure is then used to determine confidence intervals in these sparse data cases. Several examples are provided througout to illustrate the special utility of Theil's inequality coefficient for simulation validation.     

The design of economic policy under model uncertainty

This paper examines how considerations of model uncertainty can affect policy design. Without such considerations one may expect that choice of policy control rules for a macroeconomic model would depend on some welfare criterion based on the model as given. However if there is uncertainty in the structure of the model or in the values of particular model parameters then it is argued that choice of policy should take this into account.We introduce and define some measures ofrobustness which describe how well a particular control rule performs when the model is uncertain. These can only be evaluated using Monte-Carlo simulations; in that sense they are ex post. Then we define a number of indicators which may be of use in predicting robustness, and which do not require simulations to calculate. In that sense they are ex ante.Lastly we evaluate the ex ante indicators on a small macromodel by comparing their predictions with the actual robustness outturn for the range of possible control rules. We find that use of the indicators in choosing rules yields some improvement on the ordinary welfare criterion, especially when the shocks hitting the system are unknown.     

Optimal experiment design for autoregressive model with output power constraints

The output power constraint problem of optimal experiment design for an autoregressive model is considered. It is shown that besides the known minimum variance control law design, aD- optimal experiment consisting of sinusoidai input test signals without feedback can be obtained by solving a set of nonlinear equations. Two examples are also given to illustrate this design methodology.