Transient landing dynamics analysis for a lunar lander with random and interval fields

This paper presents an objective comparison of random fields and interval fields to propagate spatial uncertainty, based on a finite element model of a lunar lander. The impulse based substructuring method is used to improve the analysis efficiency. The spatially uncertain input parameters are modeled by both random fields and interval fields. The objective of this work is to compare the applicability of both approaches in an early design stage under scarce information regarding the occurring spatial parameter variability. Focus is on the definition of the input side of the problem under this scarce knowledge, as well as the interpretation of the analysis outcome. To obtain an objective comparison between both approaches, the gradients in the interval field are tuned towards the gradients present in the random field. The result shows a very similar dependence and correlation structure between the local properties for both approaches. Furthermore, through the transient dynamic estimation, it is shown that the response ranges that are predicted by the interval field and random field are very close to each other.     

Dynamic load identification for interval structures under a presupposition of ‘being included prior to being measured’

Influences of structural uncertainties in the dynamic load identification are always significant and need to be quantified. In case of insufficient information available, intervals are favorable for modelling uncertainties. To perform the interval propagation in an inverse problem, this paper develops a sequential dual-stage interval identification method under a presupposition that each noisy response, which is an accomplished measurement for reconstructing unknown loads, should be included in the corresponding interval response of the structure exerted by interval loads to be identified. The proposed method transforms the interval identification problem into a classical one at the midpoint of interval parameters and an optimization model for minimizing the radius of each interval load. The effectiveness of the proposed method is validated by a spatial truss subjected to multiple forces due to the inclusion of each unknown load in the corresponding load. Besides, regularized solutions without exact knowledge of the accuracy loss are recommended to be used as few as possible in the interval identification of unknown loads.     

Fast Identification of Parameters in Optical Systems

This paper presents a scheme for fast identification of parameters in systems that yield large-order measurement vectors. The method can be applied to real-time identification and control. In the paper, the scheme is applied to identification and control of an optical model of a space antenna. Both the mathematical models and numerical results are presented.     

Associative memory approach to the identification of structural and mechanical systems

This paper presents a new method for identification of parameters in nonlinear structural and mechanical systems in which the initial guesses of the unknown parameter vectors may be far from their true values. The method uses notions from the field of artificial neural nets and, using an initial set of training parameter vectors, generates in an adaptive fashion other relevant training vectors to yield identification of the parameter vector in a recursive fashion. The simplicity and power of the technique are illustrated by considering three highly nonlinear systems. It is shown that the technique presented here yields excellent estimates with only a limited amount of response data, even when each element of the set comprising the initial training parameter vectors is far from its true value—in fact, sufficiently far that the usual recursive identification schemes fail to converge.     

An algorithm for addressing the real interval eigenvalue problem

In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states.The algorithm that we propose is a subdivision algorithm that exploits sophisticated techniques from interval analysis. The quality of the computed approximation and the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation).     

Fuzzy finite element model updating of the DLR AIRMOD test structure

This article presents the application of finite-element fuzzy model updating to the DLR AIRMOD structure. The proposed approach is initially demonstrated on a simulated mass-spring system with three degrees of freedom. Considering the effect of the assembly process on variability measurements, modal tests were carried out for the repeatedly disassembled and reassembled DLR AIRMOD structure. The histograms of the measured data attributed to the uncertainty of the structural components in terms of mass and stiffness are utilised to obtain the membership functions of the chosen fuzzy outputs and to determine the updated membership functions of the uncertain input parameters represented by fuzzy variables. In this regard, a fuzzy parameter is introduced to represent a set of interval parameters through the membership function, and a meta model (kriging, in this work) is used to speed up the updating. The use of non-probabilistic models, i.e. interval and fuzzy models, for updating models with uncertainties is often more practical when the large quantities of test data that are necessary for probabilistic model updating are unavailable.     

Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzy confidence interval for pH titration curve

In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.     

Feedback flow control employing local dynamical modelling with wavelets

In this paper, we utilize wavelet transform to obtain dynamical models describing the behaviour of fluid flow in a local spatial region of interest. First, snapshots of the flow are obtained from experiments or from computational fluid dynamics (CFD) simulations of the governing equations. A wavelet family and decomposition level is selected by assessing the reconstruction success under the resulting inverse transform. The flow is then expanded onto a set of basis vectors that are constructed from the wavelet function. The wavelet coefficients associated with the basis vectors capture the time variation of the flow within the spatial region covered by the support of the basis vectors. A dynamical model is established for these coefficients by using subspace identification methods. The approach developed is applied to a sample flow configuration on a square domain where the input affects the system through the boundary conditions. It is observed that there is good agreement between CFD simulation results and the predictions of the dynamical model. A controller is designed based on the dynamical model and is seen to be successful in regulating the velocity of a given point within the region of interest.     

A least squares identification algorithm for a state space model with multi-state delays

A parameter estimator is presented for a state space model with time delay based on the given input–output data. The basic idea is to expand the state equations and to eliminate some state variables, and to substitute the state equation into the output equation to obtain the identification model which contains the information vector and parameter vector. A least squares algorithm is developed to estimate the system parameter vectors. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.     

Online Parameter Identification for Traffic Simulation via Lagrangian Sensing

This paper deals with parameter identification for traffic models. We present a method to estimate model parameters based on Lagrangian measurement data that can be used for online traffic simulation. In the context of Lagrangian sensing the sensor placement is reduced to the optimum choice of measurement vehicles currently moving with the traffic flow. Identifiability is investigated using the Fisher Information Matrix (FIM). Simulation results are presented and validated via simulation based on a car-following-model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A survey on OR and mathematical methods applied on gene-environment networks

In this paper, we survey the recent advances and mathematical foundations of gene-environment networks. We explain their interdisciplinary implications with special regard to human and life sciences as well as financial sciences. Special attention is paid to applications in Operational Research and environmental protection. Originally developed in the context of modeling and prediction of gene-expression patterns, gene-environment networks have proved to provide a conceptual framework for the modeling of dynamical systems with respect to errors and uncertainty as well as the influence of certain environmental items. Given the noise-prone measurement data we extract nonlinear differential equations to describe and analyze the interactions and regulating effects between the data items of interest and the environmental items. In particular, these equations reflect data uncertainty by the use of interval arithmetics and comprise unknown parameters resulting in a wide variety of the model. For an identification of these parameters Chebychev approximation and generalized semi-infinite optimization are applied. In addition, the time-discrete counterparts of the nonlinear equations are introduced and their parametrical stability is investigated by a combinatorial algorithm which detects the region of parameter stability. Finally, we analyze the topological landscape of the gene-environment networks in terms of structural stability. We conclude with an application of our analysis and introduce the eco-finance networks.     

A novel recursive subspace identification approach of closed-loop systems

In this paper, a subspace model identification method under closed-loop experimental condition is presented which can be implemented to recursively identify and update the system model. The projected matrices play an important role in this identification scheme which can be obtained by the projection of the input and output data onto the space of exogenous inputs and recursively updated through sliding window technique. The propagator type method in array signal processing is then applied to calculate the subspace spanned by the column vectors of the extended observability matrix without singular value decomposition. The speed of convergence of the proposed method is mainly dependent on the number of block Hankel matrix rows and the initialization accuracy of the projected data matrices. The proposed method is feasible for the closed-loop system contaminated with coloured noises. Two numerical examples show the effectiveness of the proposed algorithm.     

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is made, however, of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported.     

一种面向效率的系统多序参量识别方法

针对社会组织系统演化过程中效率性要求,基于系统演化有效性识别及评估,提出能够反映系统演化过程效率的多序参量识别方法,为提升系统演化过程效率提供可操作的技术参考。通过产出/投入视角分析多序参量形成过程,结合其对系统演化过程的影响,给出基于产出/投入的系统演化过程中多序参量效率原理;应用改进的数据包络分析方法和已有指标体系,建立面向效率的系统演化过程多序参量识别模型。最后,通过算例验证方法的科学有效性。     

Parameter Identification and FE Implementation of a Viscoelastic Constitutive Equation Using Fractional Derivatives

Damping in viscoelastic materials can be described in several ways. In FE codes for transient calculations with direct integration usually Rayleigh‐damping is provided. However, it is known that this model is not qualified to represent the damping properties of viscoelastic material over a broad range of time or frequency. Another approach uses fractional time derivatives of stresses and strains in the constitutive equations. This model requires few parameters, provides good curve fitting properties and is physically proved. In this paper a parameter identification for the fractional 3‐parameter model will be carried out and its implementation into an FE code will be demonstrated.     

Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process

This paper introduces an artificial neural network (ANN) application to a hot strip mill to improve the model’s prediction ability for rolling force and rolling torque, as a function of various process parameters. To obtain a data basis for training and validation of the neural network, numerous three dimensional finite element simulations were carried out for different sets of process variables. Experimental data were compared with the finite element predictions to verify the model accuracy. The input variables are selected to be rolling speed, percentage of thickness reduction, initial temperature of the strip and friction coefficient in the contact area. A comprehensive analysis of the prediction errors of roll force and roll torque made by the ANN is presented. Model responses analysis is also conducted to enhance the understanding of the behavior of the NN model. The resulted ANN model is feasible for on-line control and rolling schedule optimization, and can be easily extended to cover different aluminum grades and strip sizes in a straight-forward way by generating the corresponding training data from a FE model.     

Continuous Data Assimilation Using General Interpolant Observables

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier–Stokes equations. These ideas are motivated by the fact that dissipative dynamical systems possess finite numbers of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages which govern their long-term behavior. Therefore, our algorithm allows the use of any type of measurement data for which a general type of approximation interpolation operator exists. Under the assumption that the observational measurements are free of noise, our main result provides conditions, on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, obtained by our algorithm from the measurement data, converges to the unknown reference solution over time. Our algorithm is also applicable in the context of signal synchronization in which one can recover, asymptotically in time, the solution (signal) of the underlying dissipative system that is corresponding to a continuously transmitted partial data.     

Stress continuity in DEM-FEM multiscale coupling based on the generalized bridging domain method

Concurrent multiscale method is a spatial and temporal combination of two different scale models for describing the micro/meso and macro mixed behaviors observed in strain localization, failure and phase transformation processes, etc. Most of the existing coupling schemes use the displacement compatibility conditions to glue different scale models, which leads to displacement continuity and stress discontinuity for the obtained multiscale model. To overcome stress discontinuity, this paper presented a multiscale method based on the generalized bridging domain method for coupling the discrete element (DE) and finite element (FE) models. This coupling scheme adopted displacement and stress mixed compatibility conditions. Displacements that were interpolated from FE nodes were prescribed on the artificial boundary of DE model, while stresses at numerical integration points that were extracted from DE contact forces were applied on the material transition zone of FE model (the coupling domain and the artificial boundary of FE model). In addition, this paper proposed an explicit multiple time-steps integration algorithm and adopted Cundall nonviscous damping for quasi-static problems. DE and FE parameters were calibrated by DE simulations of a biaxial compression test and a deposition process. Numerical examples for a 2D cone penetration test (CPT) show that the proposed multiscale method captures both mesoscopic and macroscopic behaviors such as sand soil particle rearrangement, stress concentration near the cone tip, shear dilation, penetration resistance vibration and particle rotation, etc, during the cone penetration process. The proposed multiscale method is versatile for maintaining stress continuity in coupling different scale models.     

A numerical method of structure-preserving model updating problem and its perturbation theory

A method is presented to update a special finite element (FE) analytical model, based on matrix approximation theory with spectral constraint. At first, the model updating problem is treated as a matrix approximation problem dependent on the spectrum data from vibration test and modal parameter identification. The optimal approximation is the first modified solution of FE model. An algorithm is given to preserve the sparsity of the model by multiple correction. The convergence of the algorithm is investigated and perturbation of the modified solution is analyzed. Finally, a numerical example is provided to confirm the convergence of the algorithm and perturbation theory.