On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Simulation of spatially coupling dynamic response of train-track time-variant system

There exist three problems in the calculation of lateral vibration of the train-track time-variant system athome and abroad and the method to solve them is presented. Spatially coupling vibration analysis model of train-track time-variant system is put forward. Each vehicle is modeled as a multi-body system with 26 degrees of freedomand the action of coupler is also considered. The track structure is modeled as an assembly of track elements with 30degrees of freedom, then the spatially coupling vibration matrix equation of the train-track time-variant system is es-tablished on the basis of the principle of total potential energy with stationary value and the "set-in-right-position"rule. The track vertical geometric irregularity is considered as the excitation source of the vertical vibration of thesystem, and the hunting wave of car bogie frame is taken as the excitation source of lateral vibration of the system.The spatially coupling vibration matrix equation of the system is solved by Wilson-θ direct integration method. Theapproximation of the calculated results to the spot test results demonstrates the feasibility and effectiveness of thepresented analysis method. Finally, some other vibration responses of the system are also obtained.

Time-Variant Reliability-Based Multi-Objective Fuzzy Design Optimization for Anti-Roll Torsion Bar of EMU

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit(EMU)car body,it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties.To address this issue,amulti-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar.A hybrid optimization strategy combining the design of experiment(DoE)sampling and non-linear programming by quadratic lagrangian(NLPQL)is presented to deal with the design optimization model.To characterize the effect of time on the structural performance of the torsion bar,the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints.Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar.A physical programming approach is used to improve the designer’s preference and to make the optimization results more consistent with engineering practices.Moreover,the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstem-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine （SVM） was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c andfon reliability index of slopes was taken into discussion and the changing trend was observed.

Time-Variant Reliability Analysis of FPSO Hull Girder Considering Corrosion Based on Statistics

FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at dock like other kinds of ships, the reliability of FPSO hull girder during the whole service should be focused. Based on latest corrosion database and rational corrosion model, the ultimate strength of one FPSO is calculated under the conditions of slight, moderate and severe corrosion. The results not only provide the reliabihty under different corrosion conditions, but also do well for further inspection and maintenance research. The results provide necessary foundation for deciding inspection intervals and maintenance measure, which has practical sense to improve the general safety level of ocean engineering.

Complex Modal Analysis for the Time-Variant Dynamical Problem of Rotating Pipe Conveying Fluid

A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.

Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters,mismatched and matched disturbances.Different from the traditional adaptive results that are applied to dispose of unknown constant parameters only,the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant parameters.Concurrently both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this way.With skillful integration of the backstepping technique and the adaptive control,a synthesized controller framework is successfully developed for electro-hydraulic axis systems,in which the coupled interaction between parameter estimation and disturbance estimation is avoided.Accordingly,this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and disturbances.Also,a nonlinear filter is designed to eliminate the“explosion of complexity”issue existing in the classical back-stepping technique.The stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also assured.Finally,contrastive experiment results validate the superiority of the developed method as well.

Non-uniform thermal behavior of single-layer spherical reticulated shell structures considering time-variant environmental factors: analysis and design

Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temperature variations due to dynamic environmental coupling.These differences can affect structural performance and pose safety risks.Here,a systematic numerical method was developed and applied to simulate long-term temperature variations in such a structure under real environmental conditions,revealing its non-uniform distribution characteristics and time-variant regularity.A simplified design method for non-uniform thermal loads,accounting for time-variant environmental factors,was theoretically derived and validated through experiments and simulations.The maximum deviation and mean error rate between calculated and tested results were 6.1℃ and 3.7%,respectively.Calculated temperature fields aligned with simulated ones,with deviations under 6.0℃.Using the design method,non-uniform thermal effects of the structure are analyzed.Maximum member stress and nodal displacement under non-uniform thermal loads reached 119.3 MPa and 19.7 mm,representing increases of 167.5%and 169.9%,respectively,compared to uniform thermal loads.The impacts of healing construction time on non-uniform thermal effects were evaluated,resulting in construction recommendations.The methodologies and conclusions presented here can serve as valuable references for the thermal design,construction,and control of single-layer spherical reticulated shells or similar structures.

A Distributed Time-Variant Gain Hydrological Model Based on Remote Sensing

提出了一个完全采用遥感数据驱动的分布式时变增益水文模型,该模型通过融雪、产汇流等水文过程计算,给出流量的雪盖、蒸散发、径流等水文要素。在拉萨河流域,该模型采用遥感USGS-SRTM的3秒DEM、遥感TRMM(The Tropical RainfallMeasuring Mission)降水、Modis-LST(Land Surface Temperature)数据,建立分布式水文模型,模拟了2001-2008年日水文过程。模拟结果效率系数接近0.7,相关系数接近0.8,水量平衡误差5%以内。说明完全依靠遥感驱动水文模型进行水文水资源模拟可行。该模型为解决高寒山区无资料或缺资料地区水文水资源问题提供了一个新方法。

Development of distributed time-variant gain model for nonlinear hydrological systems

In this paper, a rainfall-runoff modeling system is developed based on a nonlinear Volterra functional series and a hydrological conceptual modeling approach. Two models, i.e. the time-variant gain model (TVGM) and the distributed time-variant gain model (DTVGM) that are built on the platform of Digital Elevation Model (DEM), Remote Sensing (RS) and Unit Hydro-logical Process were proposed. The developed DTVGM model was applied to two cases in the Heihe River Basin that is located in the arid and semiarid region of northwestern China and the Chaobai River basin located in the semihumid region of northern China. The results indicate that, in addition to the classic dynamic differential approach to describe nonlinear processes in hy-drological systems, it is possible to study such complex processes through the proposed sys-tematic approach to identify prominent hydrological relations. The DTVGM, coupling the advan-tages of both nonlinear and distributed hydrological models, can simulate variant hydrological processes under different environment conditions. Satisfactory results were obtained in fore-casting the time-space variations of hydrological processes and the relationships between land use/cover change and surface runoff variation.

A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification

This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.

Time-Variant Consensus Tracking Control for Networked Planar Multi-Agent Systems with Non-Holonomic Constraints

A time-variant consensus tracking control problem for networked planar multi-agent systems with non-holonomic constraints is investigated in this paper. In the time-variant consensus tracking problem, a leader agent is expected to track a desired reference input, simultaneously, follower agents are expected to maintain a time-variant formation. To solve the time-variant consensus tracking problem of planar multi-agent systems with non-holonomic constraints, a time-variant consensus tracking control strategy is designed on the basis of an unidirectional topology structure. One of main contributions of this paper is the time-variant consensus tracking protocol for general time-variant formations of planar multi-agent systems with non-holonomic constraints, the other main contribution of this paper is an active predictive control strategy, where predictions of agents are generated actively, so that the computational efficiency is improved than passive approaches. The proposed control strategy is verified by two types of time-varying formations of wheeled mobile robots, and the experimental results show that the proposed control strategy is effective for general time-variant consensus tracking problems of planar multi-agent systems with non-holonomic constraints in local and worldwide networked environments.

Time-variant reliability analysis of a continuous system with strength deterioration based on subset simulation

To conduct a reliability analysis for mechanical components, it is necessary to consider the combined influence of strength deterioration and dynamic loads. An efficient method based on subset simulation is proposed in this paper to analyze time-variant reliability by considering the strength deterioration of mechanical components in a continuous system. A gamma process is used to describe the deterioration of system strength. A model for timevariant reliability considering strength deterioration is constructed for a continuous system. A representative example and tubular cantilever structure are assessed to demonstrate the efficiency and accuracy of the proposed method. The reliability probability examples were analyzed using a first-order reliability method and benchmark results for the proposed method were derived using direct Monte Carlo simulation (MCS). The results of the proposed method and MCS are consistent, indicating that the proposed method is an effective reliability analysis method for evaluating small failure probabilities in a continuous system subjected to strength deterioration and dynamic loads.

Two dimensional Wigner-Ville spectrum of the linear random time-variant ocean channel

In this paper, the ocean acoustic channel is considered as a time-variant channel. In order to analyse the conjoint time-shift - frequency-delay distribution or the fading and spread statistical characteristics of the channel. The TDWVS (Two Dimensional Wigner-Ville Spectrum) of the time - variant channel is defined. The relation between the WVS (Wigner-Ville Spectrum) of the input and the output of the channel is discussed and some examples for the specific channel are shown. Finally, the applications on the detection of signals in noise using the WVS and TDWVS are given and the advantage is obvious, when the detected signal is linear frequency-modulation signal.

GRACE time-variable gravity and its application to geoscience:Quantitative analysis of relevant literature

The Gravity Recovery and Climate Experiment(GRACE)is the most important gravity satellite to date in human history.Since its launch in 2002,GRACE time-varying gravity has had an unprecedented impact on earth science and has generated revolutionary changes.Because of natural phenomena such as climate warming,glacial melting,sea level rise,and earthquakes,earth science research has become an increasingly popular discipline in recent years.This article summarizes the importance of GRACE time-varying gravity,its application to geoscience,and its development.We analyzed the historical development and current status of GRACE time-varying gravity as well as research hotspots by searching the literature in the core collection databases of the China National Knowledge Infrastructure and the Web of Science over the past 20 years.The CiteSpace and VOSviewer software packages were applied with reference to the principle of literature metrology.Our investigation and analysis of characteristic indexes,such as the numbers of publications,co-occurrence of keywords,and co-citation of documents,uncovered the wide application and promotion of gravity satellites,especially GRACE time-varying gravity,in earth science.The results showed that the number of publications addressing GRACE data and time-varying gravity theory is increasing annually and that the USA,China,and Germany are the main producers.The Chinese Academy of Sciences,the National Aeronautics and Space Administration of the United States,and the Helmholtz Association of German Research Centres rank among the top three institutions in the world in terms of producing the most publications on this topic.We found that GRACE time-varying gravity plays unique roles in measuring changes in terrestrial water storage changes,ice and snow melting and sea level changes,and(co)seismic gravity changes,as well as in promoting other disciplines.

IDENTIFICATION OF TIME-VARIANT CONTINUOUS SYSTEM BY A QUASI-NEWTON METHOD

A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system of differential equations, that is, to identify the parameter vector q = q(t) appearing in the following system of differential equations, based on the measurement of the state , where is a measurement operator. We give two examples to show the algorithm.

时变可靠性分析的高效近似最大可能轨迹法

现有的时变可靠性分析方法在处理飞行器复杂时变可靠性分析问题时,具有求解效率过低的缺点。在基于近似最大可能轨迹的时变可靠性分析方法的基础上,根据时间离散所得串联系统瞬时可靠度最小的组件决定整个系统可靠度的特点,在最大可能轨迹自适应建模过程中同时考虑轨迹模型的预测误差和预估值增加样本,提出时变可靠性分析的高效近似最大可能轨迹法;采用解析算例验证最大可能轨迹法的有效性,并将该可靠性分析方法应用于水动力涡轮叶片和航天飞机机翼的时变可靠性分析。结果表明:在精度相近的情况下,所提方法对极限状态函数调用次数不高于基于时间离散的可靠性分析方法的3%。

时变指向约束下姿态参数空间离散化路径规划方法

为满足深空探测器在复杂动态环境约束下的姿态机动任务需求,解决时变指向约束下姿态路径规划求解困难、路径优化性能差的问题,提出了一种基于修正罗德里格斯参数(MRP)和动态路径搜索的姿态参数空间离散化路径规划方法。通过MRP空间的笛卡尔网格划分和非奇异空间构建,实现航天器姿态的参数空间离散化和指向约束表征。考虑指向约束的时变动态特性,在三维动态空间中搜索初始到目标姿态的机动路径,并引入路径节点的时间特性,在约束冲突时对路径进行实时修正,设计非奇异空间时变约束路径搜索算法,生成执行路径节点序列。进一步,对生成的路径节点进行插值拟合,基于逆动力学方法计算角速度和控制力矩,完成姿态机动轨迹规划。仿真结果验证了该方法的有效性,可为深空探测器在时变指向约束下规划出姿态机动执行路径。