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.

Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model

An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.

Uncertain optimal model and solving method to platform scheduling problem in battlefield

The platform scheduling problem in battlefield is one of the important problems in military operational research.It needs to minimize mission completing time and meanwhile maximize the mission completing accuracy with a limited number of platforms.Though the traditional certain models obtain some good results,uncertain model is still needed to be introduced since the battlefield environment is complex and unstable.An uncertain model is prposed for the platform scheduling problem.Related parameters in this model are set to be fuzzy or stochastic.Due to the inherent disadvantage of the solving methods for traditional models,a new method is proposed to solve the uncertain model.Finally,the practicability and availability of the proposed method are demonstrated with a case of joint campaign.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Research on Credit Risk Measurement Based on Uncertain KMV Model

Regarding KMV model identification credit risk profile of small and medium-sized listed companies, at present, domestic scholars has made some achievements in the process of the KMV model combined with China’s national conditions. In this paper, we will amend the model by using uncertain interest rate instead of fixed rate on the basis of existing research. Comparing the uncertain KMV model to traditional KMV model with ST-listed companies and non-ST-listed companies in Shanghai and Shenzhen stock exchange, we find that it performs slightly better as a predictor in uncertain KMV model and in out of sample forecasts.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Nonlinear Uncertain HIV-1 Model Controller by Using Control Lyapunov Function

In this paper, we introduce a new Control Lyapunov Function (CLF) approach for controlling the behavior of nonlinear uncertain HIV-1 models. The uncertainty is in decay parameters and also external control setting. CLF is then applied to different strategies. One such strategy considers input into infected cells population stage and the other considers input into a virus population stage. Furthermore, by adding noise to the HIV-1 model a realistic comparison between control strategies is presented to evaluate the system’s dynamics. It has been demonstrated that nonlinear control has effectiveness and robustness, in reducing virus loading to an undetectable level.

基于报童模型的供应链网络均衡决策研究

在不确定性需求下构建了基于报童模型的两层供应链网络,供应链网络是由原料供应商、产品生产商和需求市场构成。针对不确定性需求引入报童模型到供应链网络均衡模型中,用于供应链网络中厂商的产量和价格决策。模型构建了基于报童模型的变分不等式来表达供应链网络在不确定性需求下的均衡条件。最后,通过数值案例给出了需求均匀分布下,方差对于产品价格、原料供应商产品流量的影响分析。

不确定大数据流分类的决策树模型构建仿真

在不确定大数据流分类过程中,受噪声和孤立点的干扰,导致处理效果和分类精度无法达到预期要求。为解决上述问题,提出一种基于决策树模型的不确定大数据流分类算法。通过采用在线字典学习算法,对不确定大数据流去噪处理,消除噪声对分类过程产生的干扰。构建决策树,在剪枝过程中通过特征过滤算法,滤除不确定大数据流中掺杂的孤立点。将去噪后的不确定大数据流,输入决策树模型中,完成分类工作。实验结果表明,所提算法处理后的不确定大数据流振幅明显减小,且分类精度高,具有一定的应用价值。

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

重大传染病疫情下基于服务水平的疫苗分配及储备研究

为缓解重大传染病疫情下疫苗的短缺现状,本文结合传染病模型(susceptible-infected-recovered-deceased,SIRD)考虑疫苗需求与疫区医院收治容量的关系,以期望短缺数最小为目标建立疫苗分配模型,推导分析了最佳服务水平和储备量,并给出了不同情形下疫苗的最优分配方案。此外,通过数值模拟,进一步探究了紧急调配成本、资金预算、需求变化、疫区数量以及疫区间相关性等外生变量带来的影响,验证了模型推导结果,为疫苗分配和储备策略提供了科学依据。研究发现:疫苗接种有助于促进病毒感染曲线平坦化和降低疫情峰值,从而减轻医疗系统超负荷运转的现象,降低因感染而死亡的人数;在不考虑储备疫苗的情况下,无论需求的不确定性程度如何,为每个地区提供同等的服务水平有利于最小化疫苗期望短缺量;考虑储备疫苗的情况下,向需求波动幅度较大的疫区提供更高的服务水平可以减少期望短缺,但疫区数量较多时,为每个疫区提供同等服务水平更具公平性,即使会导致疫苗的次优覆盖;是否考虑储备疫苗取决于紧急调配成本、预算的高低以及疫区需求情况等。

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

动态径流系数法和基于城市功能区的SWMM参数率定方法研究

城市雨洪模型是研究城市内涝形成规律及演进过程的重要手段,但在我国城市化进程加速、雨水内涝监测能力不足的背景下,模型参数率定和应用面临挑战。为解决缺乏实测雨洪数据条件下城市雨洪模型参数校准的难题,本文提出了根据地理和气候特征计算雨水径流量的动态径流系数法和基于城市功能区的Storm Water Management Model(SWMM)参数率定方法。在福建省三明市的应用表明:动态径流系数法与规范和经验公式结果一致,与传统方法相比则能反映降雨产流随雨强、下渗等因素变化的规律,更符合城市降雨产流的实际过程。基于城市功能区的参数率定方法结果与研究区城市化水平和下垫面特征相符。率定后雨水径流过程NSE值达到0.80,雨水总径流量误差处于6%以内,洪峰时间误差小于3分钟。本文提出的方法可为缺乏实测雨洪数据地区的城市雨洪模拟提供参考。

损失依赖保费下的稳健最优投资和再保险策略

探究了在最大化终端期望指数效用准则下保险人的稳健最优投资和再保险问题.其中,保险人采用了损失依赖保费原则,而再保险人由于信息不对称仍采用期望保费原则,风险投资由GBM模型刻画.通过动态规划原理处理稳健优化问题后可得到稳健最优投资和再保险策略以及相应的值函数.最后,用数值模拟验证参数对最优策略的影响.

基于扰动观测器的动态供应链系统模型预测控制

针对不确定市场需求供应链系统(supply chain system)的生产-库存预测控制问题,设计了一种模型预测控制(model predictive control,MPC)和扰动观测器(disturbance observer,DOB)结合的供应链系统生产控制策略。首先,对三级供应链系统进行分析,构建三级动态供应链的生产-库存数学模型;其次,设计基于扰动观测器的前馈补偿机制,补偿不确定性需求对供应链系统的影响;最后,考虑供应链系统存在的实际约束条件,设计模型预测控制方案,并证明系统的渐进稳定性。算例仿真验证了该方法的有效性。

基于不确定参数的变电站碳储量预估方法

设备资产运维精益管理系统(power production management system,PMS)SF6气体量数据不全且误差较大,无法为电网企业核算碳储量以及实现待建变电站碳规划提供基础数据。针对上述情况,研究了计及母线和断路器的变电站碳储量核算方法,并结合宁夏电网现场实测数据,通过MIC法筛选神经网络输入参数,构建了6输入参数的GA-BP、PSO-BP、HPO-BP神经网络模型,结果表明HPO-BP神经网络模型的评估指标及预估结果相对误差(6.28%)均优于其余2种神经网络模型,可以准确核算断路器SF6气体量。针对参数不确定情况,根据PCCs法分析不同参数之间的线性关系,构建了3输入参数的HPO-BP神经网络模型,预估结果相对误差为9.72%。通过遍历输出方式,在参数不确定情况下输出多组断路器SF6气体量预估数据,利用求和累积方法获取变电站总SF6气体量,并量化为变电站碳储量,从而为电网企业实现“双碳”目标提供数据支撑。

需求正态分布条件下基于报童模型的供应链网络均衡模型

针对不确定性需求引入报童模型到供应链网络均衡模型中,用于供应链网络中厂商的产量和价格决策。考虑到在实际生活中正态分布的更为常见性和重要性,在需求正态分布条件下运用博弈理论、网络均衡理论、报童模型以及变分不等式等方法建立了需求正态分布条件下基于报童模型的供应链网络均衡模型,研究了当需求服从正态分布条件下供应链与供应链之间的竞争行为和竞争结果。

考虑源荷储不确定性的新型电力系统随机生产模拟方法

新型电力系统可再生能源占比不断增加,给电力系统的安全稳定带来新的挑战,对新能源出力不确定性进行随机生产模拟对电力系统的规划和运行具有指导意义。首先,对新能源出力和负荷预测的不确定性进行建模。然后通过主成分聚类分析方法对新能源出力和负荷数据的时序性相关性进行处理,并结合等效变量函数法进行随机生产模拟;最后,通过某省实际电力系统算例进行了验证,证明了所提出的理论方法的正确性,可为新型电力系统随机生产模拟提供新的思路和方法。

基于源荷谐波耦合模型的数据驱动概率谐波潮流计算

随着新能源及负荷中电力电子装置的广泛应用,电力系统谐波畸变程度不断增加。同时,新能源及负荷显著的不确定特征,进一步增加了谐波分析难度。为有效评估系统不确定谐波状态,充分挖掘源荷实际运行特征,提出一种数据驱动的概率谐波潮流(probabilistic harmonic power flow,PHPF)计算方法。首先,基于实测数据,建立考虑时变特性的源荷动态谐波耦合矩阵模型(dynamic harmonic coupling matrix model,DHCMM),揭示不同时段内谐波电压与谐波电流的相互耦合关系。然后,利用实测数据挖掘源荷时变不确定特征,采用改进点估计法提取统计特性,克服变量间相互影响引起的估计偏差。最后,提出针对源荷不确定性的PHPF计算方法,对系统中时变不确定谐波进行评估。实验结果表明,基于实测数据的谐波耦合矩阵模型能够有效分析谐波源时变特性,结合源荷时变不确定功率状态,所提PHPF计算方法能够对电力系统谐波进行准确评估。