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.

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.

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.

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.

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.

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.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

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。

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.

Fuzzy Adaptive Tracking Control of Uncertain Strict-Feedback Nonlinear Systems with Disturbances Based on Generalized Fuzzy Hyperbolic Model

In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.

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。

A Hybrid Inexact Optimization Model for Land-use Allocation of China

Land scarcity has become the prominent obstacle on the way to sustainable development for China. Under the constraints of land shortage, how to allocate the finite land resources to the multiple land users in China considering various political, environmental, ecological and economic conditions have become research topics with great significance. In this study, an interval fuzzy national-scale land-use model(IFNLM) was developed for optimizing land systems of China. IFNLM is based on an integration of existing interval linear programming(ILP), and fuzzy flexible programming(FFP) techniques. IFNLM allows uncertainties expressed as discrete interval values and fuzzy sets to be incorporated within a general optimization framework. It can also facilitate national-scale land-use planning under various environmental, ecological, social conditions within a multi-period and multi-option context. Then, IFNLM was applied to a real case study of land-use planning in China. The satisfaction degree of environmental constraints is between 0.69 and 0.97, the system benefit will between 198.25 × 1012 USD and 229.67 × 1012 USD. The results indicated that the hybrid model can help generate desired policies for land-use allocation with a maximized economic benefit and minimized environmental violation risk. Optimized land-use allocation patterns can be generated from the proposed IFNLM.

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.

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。

Design of Model Following Variable Structure Controller for Three-axle Vehicle

An optimal control procedure is developed for the front and rear wheels of a three-axle vehicle moving on a complex typical road based on model following variable structure control strategy. The actual vehicle may be considered as an uncertain system. Cornering stiffness of front and rear wheels and external disturbances are varied in a limited range. The model-following variable structure control method is used to control both front and rear wheels steering operations of the vehicle, so that steering responses of the vehicle follow from those of the reference model. By numerical results obtained from computer simulation, it is demonstrated that the control system model can cope with the effects of parameter perturbations and outside disturbances.

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。

不确定转子系统动力学降阶模型构建与模型散度参数辨识

在航空、航天、船舶等领域的实际工程转子系统中,广泛存在高维复杂的非线性系统。在航空发动机转子系统、燃气轮机转子系统等重点研究领域,通常还难以对高维复杂非线性系统进行直接的数据处理和分析统计。针对不确定性转子系统的模型维度较高等问题,提出了一种模型不确定性动力学降阶计算模型构建和模型散度参数辨识方法。首先,根据确定性动力学模型和静态矩阵降阶方法,完善了确定性动力学降阶模型;然后,基于随机矩阵理论和非参数动力学建模方法,提出了不确定性动力学降阶模型;最后,利用系统确定性模型的一阶临界转速、振型和实验数据,对不确定性动力学模型的散度参数进行了辨识;为了验证散度参数辨识方法的有效性,笔者又在转子实验平台上进行了实验验证。研究结果表明:实验结果与降阶之后振动响应均值的差异性较小,且与不确定性动力学模型相差不超过10%,表明所采用的理论模型在描述转子系统行为方面具备了较高的准确性和可靠性,该模型可以为深入研究模型不确定性转子系统提供参考。

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。