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.

Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

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 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.

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.

Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression

The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.

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.

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.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay,this paper explors the control capability of linear active disturbance rejection control(LADRC).Firstly,the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion,and the stable time-delay interval starting from zero is accurately obtained,which reveals the limitations of general LADRC on large time-delay.Then in view of the large time-delay,an LADRC controller is developed and verified to be effective,along with the robustness analysis.Finally,numerical simulations show the accuracy of critical time-delay,and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.

Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

Effects of Physical Parameters and Time-Delay Coefficients on the Amplitude and Frequency Bandwidth of Saturation Controller for a Beam Vibration

In this paper, the influence of physical parameters on the width of saturated control frequency band and the influence of time delay parameters on the stability of saturated control system are studied. The analytical solution of the motion equation of the system when the main resonance and the 1:2 internal resonance occur simultaneously is obtained by multiple scale method, experimentally measured natural frequencies of nonlinear beams. The effects of excitation amplitude, delay feedback coefficients and nonlinear coefficients on saturation control are investigated. The results of the study show that the bandwidth of the saturation control can be increased by increasing the value of the external excitation, the nonlinear coefficients enhance the nonlinear phenomena of the system.

Modeling of temperature-humidity for wood drying based on time-delay neural network

The temperature-humidity models of wood drying were developed based on Time-delay neural network and the identification structures of Time-delay neural network were given. The controlling model and the schedule model, which revealed the relation between controlling signal and temperature-humidity and the relation between wood moisture content and temperature-humidity of wood drying, were separately presented. The models were simulated by using the measured data of the experimental drying kiln. The numerical simulation results showed that the modeling method was feasible, and the models were effective.

Distributed Platooning Control of Automated Vehicles Subject to Replay Attacks Based on Proportional Integral Observers

Secure platooning control plays an important role in enhancing the cooperative driving safety of automated vehicles subject to various security vulnerabilities.This paper focuses on the distributed secure control issue of automated vehicles affected by replay attacks.A proportional-integral-observer(PIO)with predetermined forgetting parameters is first constructed to acquire the dynamical information of vehicles.Then,a time-varying parameter and two positive scalars are employed to describe the temporal behavior of replay attacks.In light of such a scheme and the common properties of Laplace matrices,the closed-loop system with PIO-based controllers is transformed into a switched and time-delayed one.Furthermore,some sufficient conditions are derived to achieve the desired platooning performance by the view of the Lyapunov stability theory.The controller gains are analytically determined by resorting to the solution of certain matrix inequalities only dependent on maximum and minimum eigenvalues of communication topologies.Finally,a simulation example is provided to illustrate the effectiveness of the proposed control strategy.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

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.

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.

Behavioral modeling of RF power amplifiers with time-delay feed-forward neural networks

A novel behavioral model using three-layer time-delay feed-forward neural networks （TDFFNN）is adopted to model radio frequency （RF）power amplifiers exhibiting memory nonlinearities. In order to extract the parameters, the back- propagation algorithm is applied to train the proposed neural networks. The proposed model is verified by the typical odd- order-only memory polynomial model in simulation, and the performance is compared with different numbers of taped delay lines（TDLs） and perceptrons of the hidden layer. For validating the TDFFNN model by experiments, a digital test bench is set up to collect input and output data of power amplifiers at a 60 × 10^6 sample/s sampling rate. The 3.75 MHz 16-QAM signal generated in the vector signal generator（VSG） is chosen as the input signal, when measuring the dynamic AM/AM and AM/PM characteristics of power amplifiers. By comparisons and analyses, the presented model provides a good performance in convergence, accuracy and efficiency, which is approved by simulation results and experimental results in the time domain and frequency domain.