考虑参数和线型不确定性的水文设计值估计的贝叶斯方法

根据贝叶斯理论,分别对只考虑参数估计或线型选择不确定性、以及同时考虑这2种不确定性情况下的水文频率计算问题进行研究,提出设计值估计及其不确定性评价方法,并提供了分析示例.研究结果表明,对给定的样本条件,仅考虑参数估计或线型选择不确定性的设计值估计方法,都不能对水文频率分析计算的不确定性做出完整描述,应采用同时考虑这2种不确定性的分析方法.提出的基于贝叶斯理论的水文频率分析方法,不仅可以提供设计值的各种点估计,还可以定量评价水文频率分析结果的不确定性.

基于线型选择不确定性的水文频率分析——以黄河某站洪水资料为例

根据贝叶斯理论和贝叶斯因子法,计算样本隶属于某种线型的后验概率;然后,根据全概率公式,以样本隶属于某种线型的后验概率为权重,对各线型的概率密度函数进行加权平均,得到综合各线型的概率密度函数,进而给出各设计频率的设计值。最后,采用皮尔逊Ⅲ型和对数皮尔逊Ⅲ型作为备选线型对黄河某站洪水资料进行水文频率分析,结果表明:①从线型后验概率估计分析,对研究的样本系列,皮尔逊Ⅲ型稍优于对数皮尔逊Ⅲ型;②可以给出考虑线型选择不确定性的设计值,以此减少线型选择的不确定性。

A scenario relaxation algorithm for finite scenario based robust assembly line balancing

A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For the balancing problem for the scenario-based robust assembly line with a finitely large number of potential scenarios, the direct solution methodology considering all potential scenarios is quite time-consuming. A scenario relaxation algorithm that embeds genetic al- gorithm is developed. This new algorithm guarantees termination at an optimal robust solution with relatively short running time, and makes it possible to solve robust problems with large quantities of potential scenarios. Extensive computational results are reported to show the efficiency and effectiveness of the proposed algorithm.

A linear programming model for long-term mine planning in the presence of grade uncertainty and a stockpile

The complexity of an open pit production scheduling problem is increased by grade uncertainty. A method is presented to calculate the cost of uncertainty in a production schedule based on deviations from the target production. A mixed integer linear programming algorithm is formulated to find the min- ing sequence of blocks from a predefined pit shell and their respective destinations, with two objectives： to maximize the net present value of the operation and to minimize the cost of uncertainty. An efficient clustering technique reduces the number of var/ables to make the problem tractable. Also, the parameters that control the importance of uncertainty in the optimization problem are studied. The minimum annual mining capacity in presence of grade uncertainty is assessed. The method is illustrated with an oil sand deposit in northern Alberta.

Design of observer-based discrete repetitive-control system based on 2D model

A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Effective model based fault detection scheme for rudder servo system

The inherent nonlinearities of the rudder servo system(RSS) and the unknown external disturbances bring great challenges to the practical application of fault detection technology. Modeling of whole rudder system is a challenging and difficult task. Quite often, models are too inaccurate, especially in transient stages. In model based fault detection, these inaccuracies might cause wrong actions. An effective approach, which combines nonlinear unknown input observer(NUIO) with an adaptive threshold, is proposed. NUIO can estimate the states of RSS asymptotically without any knowledge of external disturbance. An adaptive threshold is used for decision making which helps to reduce the influence of model uncertainty. Actuator and sensor faults that occur in RSS are considered both by simulation and experimental tests. The observer performance, robustness and fault detection capability are verified. Simulation and experimental results show that the proposed fault detection scheme is efficient and can be used for on-line fault detection.

改进先验概率的贝叶斯法在设计洪水中的应用

贝叶斯模型是降低设计洪水计算过程中线型选择不确定性的主要方法,其中,先验概率的确定对贝叶斯模型的建立至关重要。为了提高先验概率确定方法的普适性,本文以模型评价准则为基础,多方面考虑模型拟合特征,提出综合指数量化线型的拟合情况,并将其作为先验信息应用于贝叶斯模型,以便合理确定各线型的先验概率,进而达到降低线型选择不确定性影响的目的。研究结果表明:基于综合指数值来挖掘样本的先验信息,可获得较为可靠的先验概率值来合理预估后验概率,使得拟合效果较好的线型获得更高的权重;有先验信息的贝叶斯模型相比无先验信息的贝叶斯模型结果更优;耦合多个评价准则的综合指数值为先验概率的求解提供了新思路。

Stability control of steer by wire system based on μ synthesis robust control

The uncertainty influences may result in performance deterioration and instability to the steer by wire(SBW) system. Thus, it must make the control system keep robust stability from uncertainty, and have good robustness. In order to effectively restrain the interference and improve steering stability, this paper presents a μ synthesis robust controller based on SBW system, which considers the effect of model uncertainty and external disturbance on the system dynamics. Taking the ideal yaw rate tracking, interference suppression and excellent robustness as the control objectives, the μ synthesis robust controller is designed using linear fractional transformation theory to deal with the uncertainty. Then, it is testified through time domain and robustness simulation analysis. Simulation results show that the proposed controller can not only ensure robustness and robust stability of the system quite well, but improve handling stability of the vehicle effectively. The results of this study provide certain theoretical basis for the research and application of SBW system.

Identification and robust limit-cycle-oscillation analysis of uncertain aeroelastic system

Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity are obtained in the time domain. Then robust LCO analysis of the identified model set is performed. First, the proper orthonormal basis is constructed based on the on-line dynamic poles of the aeroelastic system. Accordingly, the identification problem of uncertain model is converted to a nonlinear optimization of the upper and lower bounds for uncertain parameters estimation. By replacing the identified memoryless nonlinear operators by its related sinusoidal-input describing function, the Linear Fractional Transformation (LFT) technique is applied to the modeling process. Finally, the structured singular value(μ) method is applied to robust LCO analysis. An example of a two-degree wing section is carded out to validate the framework above. Results indicate that the dynamic characteristics and model uncertainties of the aeroelastic system can be depicted by the identified uncertain model set. The robust LCO magnitude of pitch angle for the identified uncertain model is lower than that of the nominal model at the same velocity. This method can be applied to robust flutter and LCO prediction.

Sequential Estimate for Generalized Linear Models with Uncertain Number of Effective Variables

For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.

Robust linear optimization under matrix completion

Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.