Robust stability analysis of structures with uncertain parameters using mathematical programming approach

This paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties, geometry of element cross section, and loading conditions, all of which are described by an interval model. The proposed method formulates the two cases of interest, namely, worst and best buckling load calculation, into a pair of mathematical programming problems. Two straightforward advantages are exhibited by such formulations. The first advantage is that the proposed formulation can overcome the interference on the sharpness of bounds of the buckling load due to the interval dependence issue. The second benefit is that the information of uncertain parameters causing the extremities of buckling load can always be retrieved as by‐products of the uncertain stability analysis. Some numerical examples are presented to illustrate the capability of the proposed method on various structures and the sharpness of the bounds of the buckling load factors. The efficiency and effectiveness of the proposed method are also demonstrated through comparison with the classical Monte Carlo simulation method. Copyright © 2014 John Wiley & Sons, Ltd.     

Fuzzy analysis for steady-state availability: a mathematical programming approach

Steady-state availability has been widely applied as a measure to evaluate the reliability characteristics of a repairable system. However, it is generally not realistic to make assumptions concerning failure time and repair time distributions. Thus, this article has developed a procedure to construct the membership function for fuzzy steady-state availability. Based on Zadeh’s extension principle, a pair of mathematical programs is formulated to find α-cuts of fuzzy steady-state availability. An explicit closed-form expression for the membership function is derived by taking the inverse function of the $\alpha$-cut. To illustrate the interpretation and practical value of fuzzy availability in real-world applications, several numerical examples are provided and discussed.     

径向驱动式啮合电机结构设计与静态转矩分析

针对机器人系统对驱动电机的启动性能和空间适应性的要求,设计了一种径向驱动式啮合电机结构.该电机利用3个定子和1个转子间磁阻的变化将电能转化为机械能,驱动转子在十字滑块机构约束下绕定子轴线做圆周平动,进而直接带动摆线机构输出低速大扭矩.设计制作了一台物理样机,给出了该电机的控制方法,运用有限元方法分析了在不同转子位置角的...     

Representative static load models for transient stability analysis: development and examination

Load representation has a significant impact on power system analysis and control results. Currently, static load models are still popular in power industry for transient stability analysis. Dynamic load models are recommended in both industry and academia for possible improvement in analysis accuracy. The accuracy of using static (nonlinear) load models with suitably identified parameters for transient stability analysis is examined. Numerical studies conducted using on-line measurement data indicate that static load models, as compared with induction motor load models, are acceptable for modelling real power behaviours during disturbances and hence are adequate for transient stability analysis. Using multiple sets of on-line measurements, representative model parameters of five static nonlinear load models are derived and their performance in modelling dynamic behaviours of both real and reactive powers is compared. A method is presented to determine a representative set of parameters of static (nonlinear) load models for each loading condition     

Harmonics and voltage stability analysis in power systems including thyristor-controlled reactor

In this study, non-sinusoidal quantities and voltage stability, both known as power quality criteria, are examined together in detail. The widespread use of power electronics elements cause the existence of significant non-sinusoidal quantities in the system. These non-sinusoidal quantities can create serious harmonic distortions in transmission and distribution systems. In this paper, harmonic generation of a static VAR compensator with thyristor-controlled reactor and effects of the harmonics on steady-state voltage stability are examined for various operational conditions.     

An integrated approach to path analysis for weighted citation networks

Scientometrics - Profuse growth of scientometrics as a research field owes a discernible attribution to the introduction of citation networks and other scientograms. Centrality analysis, path...     

A stochastic programming approach to determine robust delivery profiles in area forwarding inbound logistics networks

One technique to coordinate the suppliers’ and the producers’ production plans in a supply chain is the use of delivery profiles, which provide fixed delivery frequencies for all suppliers. The selection of a delivery profile assignment has major effects on the cost efficiency and the robustness of a supply chain and thus should be performed carefully. In this work, we consider planning approaches to select delivery profiles for the case of area forwarding-based inbound logistics networks, which are commonly used in several industries to consolidate supplies in an early stage of transport. We present a two-stage stochastic mixed integer linear programming model to determine robust delivery profile assignments under uncertain and infrequent demands and complex tariff systems. The model is embedded into a solution framework consisting of scenario generation and reduction techniques, a decomposition approach, a genetic algorithm, and a standard MILP solver. On the basis of an industrial case study, we show that our approach is computationally feasible and that the planning solutions obtained by our model outperform both a deterministic approach and the planning methodology prevailing in industrial practice.     

A non‐linear programming method approach for upper bound limit analysis

This paper presents a finite element model based on mathematical non‐linear programming in order to determine upper bounds of colapse loads of a mechanical structure. The proposed formulation is derived within a kinematical approach framework, employing two simultaneous and independent field approximations for the velocity and strain rate fields. The augmented Lagrangian is used to establish the compatibility between these two fields. In this model, only continuous velocity fields are used. Uzawa's minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate. The use of this technique allows to bypass the complexity of the non‐linear aspects of the problem, since non‐linearity is addressed as a set of small local subproblems of optimization for each finite element. The obtained model is quite versatile and suitable for solving a wide range of collapse problems. This paper studies 3D strut‐and‐tie structures, 2D plane strain/stress and 3D solid problems. Copyright © 2007 John Wiley & Sons, Ltd.     

A programming approach to the numerical analysis of elastoplastic continua

The extended kinematic minimum principle is used to formulate a quadratic programming solution to the rate problem in elastoplasticity for plane continua. A simple algorithm is presented which involves the minimisation of a continuous functional subject to inequality constraints. The algorithm has been implemented within an incremental finite element formulation which includes equilibrium iterations and predictor-corrector procedures for calculating plastic strain increments. The potential of this algorithm in situations where the plastic zone at failure is small is discussed.     

Exponential stability analysis of travelling waves solutions for nonlinear delayed cellular neural networks

In this paper, the exponential stability of travelling waves solutions for nonlinear cellular neural networks with distribute delays in the lattice is studied. The weighted energy method and comparison principle are employed to derive the sufficient conditions under which the networks proposed are exponentially stable. Following the study [13 X. Liu, P. Weng, and Z. Xu, Existence of traveling wave solutions in nonlinear delayed cellular neural networks, Nonlinear Anal. Real World Appl. 10(1) (2009), pp. 277–286.[Crossref], [Web of Science ®] , [Google Scholar]] on the existence of the travelling wave solutions in nonlinear delayed cellular neural networks, this paper is focused on the exponential stability of these travelling wave solutions.     

Image analysis applications on assessing static stability and flowability of self-consolidating concrete

A digital image processing (DIP) method associated with a MATLAB algorithm is used to evaluate cross sectional images of self-consolidating concrete (SCC). Two new parameters, such as inter-particle spacing of coarse aggregate and average mortar-to-coarse aggregate ratio, defined as average mortar thickness index (MTI), were proposed to quantitatively evaluate the static stability of SCC. Statistical models were developed to predict flowability of SCC mixtures. Test results revealed that the proposed DIP method and MATLAB algorithm can be successfully used to derive inter-particle spacing and MTI and quantitatively evaluate the static stability on hardened SCC samples. A probability density of 60% from histogram analysis appears to be a reasonable threshold for indicating a uniformly distributed SCC mixture. For a given mortar yield stress, a critical mortar viscosity of 1.30 Pa s tends to significantly affect the trend of slump flow changing with MTI. The investigated relationship between parameters measured from DIP method and existing theoretical frames is well correlated. The outcome of this study can be of practical value for providing an efficient and useful tool in designing mixture proportions of SCC.     

Alternative approach for defining the particle population requirements for static image analysis based particle characterization methods

For image based particle characterisation approaches one of the most common discussion points is determining the number of particles required to have statistical confidence that the measurement is able to adequately describe the distribution of the sample. This topic becomes significantly more challenging when applied to the extraction of single component size distributions from multi-component samples.The aim of this work was to propose a means to accurately assess the particle number requirements using a method specific approach. The method applies a sub-sampling method to the original imaged dataset in order to provide an understanding of the impact of sub-sampling on the ability to accurately reproduce the original distribution.The method was applied to understand the particle number requirements for two batches of theophylline anhydrous with varied particle size distributions, using the input size distribution to guide the requirements for the subsequent multi-component samples of both materials.The results demonstrate the utility of the method to determine the appropriate number of particles required to recreate the size distributions. Whilst the minimum number of particles required to be sampled can be estimated, how those particles are sampled can also affect the validity of the measurement and must be taken into consideration.     

The use of stochastic stresses in the static approach of probabilistic limit analysis

In the framework of the structural reliability theory, the probabilistic limit analysis (PLA) represents a powerful tool for the evaluation of the safety of structures with stochastic strengths with respect to the ultimate limit state of plastic collapse. Aim of the PLA is to evaluate the conditional probability of collapse (CPC), that is, the probability of plastic collapse of the structural system for assigned value of the acting loads. In this paper the focus is on the static approach of the limit analysis theory, which is particularly attractive for engineers, because it gives upper bounds of the CPC, that is, safe bounds. The classical static approach, introduced more than 30 years ago, however, cannot in any case evaluate the exact CPC of the structural system, and moreover generally the bounds obtained are not very close, especially in the range of very small probabilities. In this paper an alternative static approach is proposed, which can obtain the exact CPC of the structural system considering a finite number of suitable chosen stochastic stress vectors through the use of the partial admissible domains; moreover, it gives good safe bounds of the CPC considering only a few stochastic stress vectors. Some simple numerical examples show the accuracy and effectiveness of the method. Copyright © 2007 John Wiley & Sons, Ltd.     

Mathematical programming approach for unconfined seepage flow problem

In this paper, a mathematical programming technique for numerical simulation of unconfined flow through porous media is presented. Considering the original free boundary problem as a shape optimization problem, we perform boundary elements discretization. Taking the state variable and free boundary variable as independent variables, we treat the discretized problem as nonlinear mathematical program and apply interior point algorithm to solve it. This simple, accurate and computationaly efficient technique can be easily applied to 2D real size problems and extended to 3D problems. Numerical results for an illustrative 2D test problem of an earth dam are discussed.     

Graph theory and stability analysis of protein complex interaction networks

Protein complexes play an essential role in many biological processes. Complexes can interact with other complexes to form protein complex interaction network (PCIN) that involves in important cellular processes. There are relatively few studies on examining the interaction topology among protein complexes; and little is known about the stability of PCIN under perturbations. We employed graph theoretical approach to reveal hidden properties and features of four species PCINs. Two main issues are addressed, (i) the global and local network topological properties, and (ii) the stability of the networks under 12 types of perturbations. According to the topological parameter classification, we identified some critical protein complexes and validated that the topological analysis approach could provide meaningful biological interpretations of the protein complex systems. Through the Kolmogorov–Smimov test, we showed that local topological parameters are good indicators to characterise the structure of PCINs. We further demonstrated the effectiveness of the current approach by performing the scalability and data normalization tests. To measure the robustness of PCINs, we proposed to consider eight topological‐based perturbations, which are specifically applicable in scenarios of targeted, sustained attacks. We found that the degree‐based, betweenness‐based and brokering‐coefficient‐based perturbations have the largest effect on network stability.Inspec keywords: graph theory, perturbation theory, proteins, molecular configurations, molecular biophysics, pattern clustering, pattern classification, cellular biophysics, biology computingOther keywords: stability analysis, protein complex interaction networks, biological processes, protein complex interaction network, cellular processes, interaction topology, graph theoretical approach, local network topological properties, topological parameter classification, Kolmogorov‐Smirnov test, network structures, data normalisation tests, topological‐based perturbations, highly clustered protein complexes, brokering‐coefficient‐based perturbations, betweenness‐based perturbations     

On the optimal design of radial basis function neural networks for the analysis of nonlinear stochastic systems

In this paper, an iterative selection strategy of Gaussian neurons for radial basis function neural networks (RBFNN) is proposed when the RBFNN method is applied to obtain the steady-state solution of the Fokker–Planck–Kolmogorov (FPK) equation. A performance index is introduced to rank neurons. Top rank neurons are selected, leading to a RBFNN with optimal number and locations of Gaussian neurons for the FPK equation under consideration. The statistical properties of the performance index are studied. It is found that the index assigned to the $j$th neuron is proportional to the probability of the system falling into the small neighborhood of the mean of this neuron as well as proportional to the weight of the neuron. The RBFNN method with the optimally selected neurons is then applied to several challenging examples of nonlinear stochastic systems in 2, 3 and 4 dimensional state space. The RBFNN solutions are also compared with the results of extensive Monte Carlo simulations. It is observed that the RBFNN method with optimally selected neurons by the proposed iterative algorithm is much more efficient than the RBFNN method with uniformly distributed neurons, and is very accurate in terms of the root mean squared (RMS) errors of the FPK equation or the RMS errors of the PDF solution compared with simulation results.     

Smart demand for improving short-term voltage control on distribution networks

Smart grids must involve active roles from end users in order to be truly smart. The energy consumption has to be done in a flexible and intelligent manner, in accordance with the current conditions of the power system. Moreover, with the advent of dispersed and renewable generation, increasing customer integration to aid power system performance is almost inevitable. This study introduces a new type of smart demand side technology, denoted demand as voltage controlled reserve (DVR), to improve short-term voltage control, where customers are expected to play a more dynamic role to improve voltage control. The technology can be provided by thermostatically controlled loads as well as other types of load. This technology is proven to be effective in case of distribution systems with a large composition of induction motors, where the voltage presents a slow recovery characteristic due to deceleration of the motors during faults. This study presents detailed models, discussion and simulation tests to demonstrate the technical viability and effectiveness of the DVR technology for short-term voltage control.