A probabilistic damage identification approach for structures with uncertainties under unknown input

To avoid the false positives of damages in the deterministic identification method induced by uncertainties in measurement noise, a probabilistic method is proposed to identify damages of the structures with uncertainties under unknown input. The proposed probabilistic method is developed from a deterministic simultaneous identification method of structural physical parameters and input based on dynamic response sensitivity. The deterministic simultaneous identification method is first derived. The effect of uncertainties caused by measurement noise on the identified parameters is then investigated. The statistical parameters of the identified structural parameters are calculated. The damage index is derived from the statistical parameters of the physical parameters of intact and damaged structure. The probability of identified damage, defined as the probability of identified structural stiffness smaller than that of intact structure, is further derived using the probability method. A twelve-story building and a nine-bay three-dimensional frame structure are, respectively, analyzed numerically and experimentally using the proposed method. The research results indicate that the probabilistic simultaneous identification method for damage and input can decrease the false positives of damages in contrast with the deterministic method under intensive measurement noise, and it can also achieve an accurate identification for structural unknown input.     

基于概率模型检测的机电系统动态可靠性评价

为克服传统动态可靠性分析方法的不足,提出基于概率模型检测的机电系统动态可靠性评价方法。介绍了概率模型检测的概念及概率模型检测工具PRISM。用形式化建模语言描述系统单元的状态变迁过程,建立了机电系统的形式化模型。利用连续随机逻辑对机电系统可靠性评价指标进行形式化描述,建立了可靠性指标的规约表达式,借助概率模型检测工具自动解算可靠性指标,实现了基于概率模型检测的机电系统动态可靠性评价。所提方法建模过程简单,能有效提高机电系统动态可靠性分析的效率。     

结构可靠性分析的概率和非概率混合模型

在结构可靠性分析中需要合理地定量处理影响结构性能的诸多不确定性。不确定性的模拟既可以是概率的，也可以是非概率的。文中简要介绍结构可靠性分析的概率方法和基于区间模型的非概率可靠性方法。提出结构可靠性分析的概率和非概率混合模型。通过两级功能方程的逐次建立及可靠性分析，给出结构可靠的概率度量。实例分析说明在结构可靠性分析中，应根据不确定性的产生机理及所掌握的数据信息合理地选取分析模型。     

Approche non-probabiliste de fiabilité basée sur les modèles convexes

A knowledge of the variability in structural responses due to uncertainties in manufacturing tolerances, boundary conditions and excitations is essential for design in order to ensure reliable performance. We are interested in making a reliable decision when knowledge of uncertainties is quite limited and when the use of a probabilistic law is unjustified. A non-probabilistic concept of reliability based on the info-gap robustness function allows us to define the three main components of the uncertainty analysis: structural model, uncertainty model represented by info-gap models, and a performance criterion. This article concentrates on the inverse problem which consists in determining the maximal volume in the domain of uncertainty within which the performance criterion is guaranteed. The proposed methodology is illustrated based on two applications in the field of linear elastodynamics.     

Transient dynamics in structures with non-homogeneous uncertainties induced by complex joints

This paper deals with numerical models for the prediction of the transient dynamical response induced by shocks upon structures with complex joints and shows experimental comparisons. The usual numerical methods for analysing such structures in the low- and medium-frequency ranges consist in using reduced matrix models constructed with the elastic modes. The contribution of the higher modes is very sensitive to the model errors and to the data errors. In this paper, a non-parametric probabilistic method is applied to construct the random matrix model allowing model errors and data errors to be taken into account. The paper presents an extension of the non-parametric method for the case of non-homogeneous model errors through the structure. A dynamic substructuring method is then used and the non-parametric probabilistic model of random uncertainties is used in each substructure with its own level of uncertainties. This approach is applied to a dynamical system made of two plates attached by a complex joint. Experiments have been performed and are used to validate the probabilistic predictive model.     

Global finite-time adaptive control for uncalibrated robot manipulator based on visual servoing

The paper addresses the finite-time convergence problem of a uncalibrated camera-robot system with uncertainties. These uncertainties include camera extrinsic and intrinsic parameters, robot dynamics and feature depth parameters, which are all considered as time-varying uncertainties. In order to achieve a better dynamic stability performance of the camera-robot system, a novel FTS adaptive controller is presented to cope with rapid convergence problem. Meanwhile, FTS adaptive laws are proposed to handle these uncertainties which exist both in robot and in camera model. The finite-time stability analysis is discussed in accordance with homogeneous theory and Lyapunov function formalism. The control method we proposed extends the asymptotic stability results of visual servoing control to a finite-time stability. Simulation has been conducted to demonstrate the performance of the trajectory tracking errors convergence under control of the proposed method.     

Improved reliability analysis method based on the failure assessment diagram

With the uncertainties related to operating conditions,in-service non-destructive testing(NDT) measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram(FAD) approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics(PFM) assessment method is proposed.By integrating 2D kernel density estimation(KDE) technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.     

Flight control of a hexa-rotor airship: Uncertainty quantification for a range of temperature and pressure conditions

The present paper is concerned with the dynamic modeling and design of control laws for a small non-rigid multi-rotor airship constituted of an oblate-spheroid helium balloon coupled with an electric-powered hexa-rotor airframe. The vehicle is assumed to operate in windless and low-speed conditions. A six-degree-of-freedom nonlinear dynamic model is derived for it using the Newton–Euler approach and considering, among other efforts, a restoring torque due to the displacement of the balloon’s center of buoyancy above the vehicle’s center of mass and the added-mass effect resulting from the air–structure interaction. Using the derived model and assuming a time-scale separation between the translational and rotational dynamics, the attitude and position control laws are designed separately from each other. Both laws are formulated using feedback linearization combined with control input saturation within appropriate parallelepipedal sets, which are carefully chosen to respect pre-defined bounds on the control torque, control force and maximum inclination angle. The effect of temperature and pressure fluctuations is taken into account through a parametric probabilistic approach, where Maximum Entropy Principle is used to construct a physically consistent stochastic model and Monte Carlo method is used as the stochastic solver to propagate the uncertainties through the system. Extensive simulation results show the effectiveness of the proposed control system and quantify the uncertainty of its performance over a wide range of local temperature and pressure.     

Parametric adaptive estimation and backstepping control of electro-hydraulic actuator with decayed memory filter

Some unknown parameter estimation of electro-hydraulic system (EHS) should be considered in hydraulic controller design due to many parameter uncertainties in practice. In this study, a parametric adaptive backstepping control method is proposed to improve the dynamic behavior of EHS under parametric uncertainties and unknown disturbance (i.e., hydraulic parameters and external load). The unknown parameters of EHS model are estimated by the parametric adaptive estimation law. Then the recursive backstepping controller is designed by Lyapunov technique to realize the displacement control of EHS. To avoid explosion of virtual control in traditional backstepping, a decayed memory filter is presented to re-estimate the virtual control and the dynamic external load. The effectiveness of the proposed controller has been demonstrated by comparison with the controller without adaptive and filter estimation. The comparative experimental results in critical working conditions indicate the proposed approach can achieve better dynamic performance on the motion control of Two-DOF robotic arm.     

Robust updating of uncertain damping models in structural dynamics for low- and medium-frequency ranges

This paper deals with the robust updating of uncertain computational models in the context of structural dynamics in the low- and medium-frequency ranges of composite sandwich panels for which experimental results are available. The uncertain computational model is constructed using the non-parametric probabilistic approach which takes into account model and data uncertainties. The formulation of the robust updating problem includes the effects of uncertainties and consists in minimizing a cost function with respect to an admissible set of updating parameters. Updating is performed in two steps using several cost functions and experimental results. The results of the robust updating problem show that the method proposed is efficient for updating the uncertain computational model in both low- and medium-frequency ranges.     

Probabilistic dynamic distribution of wireless sensor networks with improved distribution method based on electromagnetism-like algorithm

Performance of the Wireless Sensor Networks (WSNs) depends significantly on coverage area which is determined via the effective dynamic distribution of sensors. Making mobile sensors’ dynamic distributions, which determines their positions within the network effectively, improves performances of WSNs by enabling sensors to form the coverage area more efficiently. In this paper, we initially propose the electromagnetism-like (EM) algorithm as the sensor distribution strategy to increase the coverage area of network after random distribution of sensors. Forming more effective coverage area by using mobile and stationary sensors and probabilistic detection model has been aimed by developing the Optimal Sensor Detection Algorithm that is based on the proposed EM algorithm (OSDA-EM). For this purpose, it has been thought that we would attain to more realistic results, with probabilistic detection model by forming the coverage area more effectively. Additionally, performance of the developed OSDA-EM algorithm has been compared with the Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms which was previously used in the dynamic distribution of WSNs. Simulation results have shown that the developed OSDA-EM can be preferred in dynamic distribution of WSNs that performed with probabilistic detection model.     

Dynamic analysis of multi-body systems considering probabilistic properties

A method of dynamic analysis of mechanical systems considering probabilistic properties is proposed in this paper Probabilistic properties that result from manufacturing tolerances can be represented by means and standard deviations (or variances) The probabilistic characteristics of dynamic responses of constrained multi-body systems are obtained by two ways the proposed analytical approach and the Monte Carlo simulation The former necessitates sensitivity information to calculate the standard deviations In this paper, a direct differentiation method is employed to find the sensitivities of constrained multi-body systems To verify the accuracy of the proposed method, numerical examples are solved and the results obtained by using the proposed method are compared to those obtained by Monte Carlo simulation     

Spatial curvilinear path following control of underactuated AUV with multiple uncertainties

This paper investigates the problem of spatial curvilinear path following control of underactuated autonomous underwater vehicles (AUVs) with multiple uncertainties. Firstly, in order to design the appropriate controller, path following error dynamics model is constructed in a moving Serret–Frenet frame, and the five degrees of freedom (DOFs) dynamic model with multiple uncertainties is established. Secondly, the proposed control law is separated into kinematic controller and dynamic controller via back-stepping technique. In the case of kinematic controller, to overcome the drawback of dependence on the accurate vehicle model that are present in a number of path following control strategies described in the literature, the unknown side-slip angular velocity and attack angular velocity are treated as uncertainties. Whereas in the case of dynamic controller, the model parameters perturbations, unknown external environmental disturbances and the nonlinear hydrodynamic damping terms are treated as lumped uncertainties. Both kinematic and dynamic uncertainties are estimated and compensated by designed reduced-order linear extended state observes (LESOs). Thirdly, feedback linearization (FL) based control law is implemented for the control model using the estimates generated by reduced-order LESOs. For handling the problem of computational complexity inherent in the conventional back-stepping method, nonlinear tracking differentiators (NTDs) are applied to construct derivatives of the virtual control commands. Finally, the closed loop stability for the overall system is established. Simulation and comparative analysis demonstrate that the proposed controller exhibits enhanced performance in the presence of internal parameter variations, external unknown disturbances, unmodeled nonlinear damping terms, and measurement noises.     

基于自适应的电液负载模拟器积分鲁棒控制

为提高电液负载模拟器的跟踪精度,针对其存在的大量非线性特性和模型不确定性等问题,建立了系统非线性数学模型,基于传统的误差符号积分鲁棒控制方法,融合自适应控制的思想,设计了一种自适应误差符号积分鲁棒控制方法。该方法无需获知模型不确定性的确切界,其积分鲁棒增益的取值可在线调节,更好地克服了模型不确定性对系统的影响,在舵机运动干扰作用下实现了系统的渐近稳定性能。仿真对比结果验证了该控制方法的优良性能。     

电子产品动态损伤最优估计与寿命预测

针对电子产品寿命预测中存在的不确定性因素影响,提出一种基于粒子滤波的电子产品动态损伤最优估计和寿命预测方法.首先建立了电子产品动态损伤HMM模型;分析了电子产品动态损伤和寿命预测中的不确定性因素;通过贝叶斯滤波模型,将寿命预测的不确定性问题转化为最优估计问题;利用粒子滤波算法求解出电子产品动态损伤的最优估计值,从而进行寿命预测;实验证明,该方法可有效消除系统和测量因素的干扰,明显提高电子产品剩余寿命预测的精度.     

Optimum design of tuned liquid column dampers under stochastic earthquake load considering uncertain bounded system parameters

The Tuned Liquid Column Damper (TLCD) is an effective alternative to the Tuned Mass Damper (TMD) to reduce the response of structures due to dynamic loads. The optimum TLCD parameters are normally obtained based on the implicit assumption that the system parameters involved are deterministic. But, the efficiency of dampers may reduce if the TLCD parameters are not tuned to the vibrating mode it is designed to suppress due to the unavoidable presence of system parameter uncertainty. The study of TMD parameters’ optimization considering random system parameters is noteworthy. But, the same is not the case for liquid dampers. Moreover, though the damper parameters optimization under uncertain parameters in probabilistic framework is powerful; the approach cannot be applied in many real situations when the required detailed information to describe the parameters in probabilistic format is limited. In present work, the TLCD parameters optimization to control vibration of structures subjected to stochastic earthquake load under uncertain system parameters modeled as uncertain but bounded (UBB) type is studied. With the aid of matrix perturbation theory using first-order Taylor series expansion and interval extension of the dynamic response function, the vibration control problem is transformed to appropriate deterministic optimization problems yielding the lower and upper bound solution. Numerical study is performed to elucidate the effect of parameters’ uncertainties on the optimization of damper parameters and the performance of TLCD.     

Structure dynamic reliability: A hybrid approach and robust meta-models

Mathematical modeling of physical systems is essential to understand and, if possible, control such systems. However, insufficient information may be available about the level of uncertainty related to material properties, geometric parameters, boundary conditions and the applied loads. In the context of structural reliability, the uncertainties may be uncontrollable when designing for robustness. These problems in the modeling of the uncertainties are often complicated by the model's inability to describe the physical phenomena that are involved. In this paper, the proposed approach combines a dynamic reliability method and a meta-model (reduced model) to obtain good results in terms of the reliability and optimization of such systems. Using the available information about the uncertain design parameters, we use the hybrid model coupling of the possibility and probability approaches for the propagation of the uncertainties in the model. The proposed method was implemented on theoretical structures with different meta-models. The results are compared with the Monte Carlo simulations. This allowed us to prove the robustness and efficiency of the proposed methodology for reliability calculations of complex dynamic structures.     

An enhancement of selection and crossover operations in real-coded genetic algorithm for large-dimensionality optimization

The present study aims to implement a new selection method and a novel crossover operation in a real-coded genetic algorithm. The proposed selection method facilitates the establishment of a successively evolved population by combining several subpopulations: an elitist subpopulation, an off-spring subpopulation and a mutated subpopulation. A probabilistic crossover is performed based on the measure of probabilistic distance between the individuals. The concept of ‘allowance’ is suggested to describe the level of variance in the crossover operation. A number of nonlinear/non-convex functions and engineering optimization problems are explored to verify the capacities of the proposed strategies. The results are compared with those obtained from other genetic and nature-inspired algorithms.     

Dynamic cell formation and the worker assignment problem: a new model

In this paper a new model is developed to deal with a simultaneous dynamic cell formation and worker assignment problem (SDCWP). Part routing flexibility and machine flexibility and also promotion of workers from one skill level to another are considered. The proposed model is formulated as a single objective nonlinear integer programming which is converted to a linear one. The objective function consists of two separate components. The first part of the objective function is related to machine-based costs such as production cost, intercell material handling cost, machine costs in the planning horizon. The second part is related to human issues and consists of hiring cost, firing cost, training cost and salary. It is the first time that worker assignment and dynamic cell formation are considered simultaneously. To verify the performance of the proposed model, some numerical examples are presented. Computational and sensitivity analysis results imply the significance of SDCWP.