Integrated measurement system using accelerometers and gyros as peripheral sensors to estimate the motional state of an elastic beam

Integrated navigation devices for vehicle guidance are the most common example of an integrated motion measurement system combining the signals from an inertial measurement unit (IMU consisting of three accelerometers and three gyros) and a GPS receiver with a single antenna. For this, the vehicle is traditionally assumed to be a single rigid body with six motional degrees of freedom to be determined. During periods of low vehicle dynamics the common integrated navigation systems show, however, stability problems. Nevertheless, the stability of the system can be guaranteed by distributing sensors over the vehicle structure. In this case the rigid body assumption has to be expanded to take the distributed sensors and the flexibility of the structure into account. Integrated systems in general are fusing different measuring signals by combining their benefits and blinding out their disadvantages. For instance, gyros and accelerometers are used to obtain reliable signals with a good time resolution. On the other hand, aiding sensors like radar units and strain gauges are known to be long-term accurate. Furthermore, the kernel of such integrated systems consists of an extended Kalman filter that estimates the motion state of the structure. Besides the sensor signals, the basis for the filter is an additional kinematical model of the structure which has to be developed individually. The example of the motion of an elastic beam being considered here is meant to be an approach to obtain motional measurements of a wing of a large airplane during flight. By means of a modal approach, a kinematical model of the beam was developed. This paper will compare integrated systems utilising accelerometers as peripheral sensors with systems using gyros and systems with a combination of both peripheral sensor types. Based on simulation the paper shows this approach, different sensor configurations, and estimated motion results of an elastic beam. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integrated motion measurement of rigid multibody systems

During the last years, integrated navigation systems based on gyros, accelerometers, and GPS receivers became powerful devices for the guidance of aircraft and ships. Comparable equipment using especially wheel sensors exists for cars. The kernel of such systems is a Kalman filter estimating the relevant vehicle motion. The filter design in turn requires a kinematical model to settle on the motion components considered and to describe the mechanical meaning of the measurements employed. Until now, usual models consider only one to six degrees of freedom of a single rigid body. The assumption of a solitary rigid body is not a consequence of the basic concept of integrated navigation; it reflects merely classical navigation requirements. In principle, determining the motion of multibody systems, representing certain vehicle types of varying shape, is possible if appropriate kinematical models and sensor arrangements are available. Based on the theory of integrated navigation systems, the paper outlines the fundamentals of designing integrated motion measurement systems for rigid multibody structures. The example of a double pendulum with a movable inertial support and with equipment of microelectromechanical inertial sensors and of small radar units illustrates this approach. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An elastic beam approach to predictive vehicle motion planning

Vehicle guidance systems are among the latest automotive developments. Examples are A daptive C ruise C ontrol (ACC), lane departure warning and active lane keeping. However, the rapid development of environmental sensor systems such as radar, lidar and video technologies in combination with data fusion of the single sensor signals enables further applications as for example lane changing assistance, collision avoidance or even autonomous driving. For all of these functions, trajectories have to be planned and, depending on the application, to be communicated to the driver. Recently, methods originally developed in robotics as for example so-called elastic bands are adapted for road vehicle applications. Here an virtual elastic beam is proposed to guide the vehicle. The beam is deflected by virtual potential fields generated by obstacles in the traffic space. In doing so, the elastic beam avoids obstacles and provides collision-free trajectories, while its bending stiffness counteracts the curvature of the trajectory. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simplified modelling of joints and beam-like structures for BIW optimization in a concept phase of the vehicle design process

The paper proposes an engineering approach for the replacement of beam-like structures and joints in a vehicle model. The final goal is to provide the designer with an effective methodology for creating a concept model of such automotive components, so that an NVH optimization of the body in white (BIW) can be performed at the earliest phases of the vehicle design process. The proposed replacement methodology is based on the reduced beam and joint modelling approach, which involves a geometric analysis of beam-member cross-sections and a static analysis of joints. The first analysis aims at identifying the beam center nodes and computing the equivalent beam properties. The second analysis produces a simplified model of a joint that connects three or more beam-members through a static reduction of the detailed joint FE model.In order to validate the proposed approach, an industrial case-study is presented, where beams and joints of the upper region of a vehicle's BIW are replaced by simplified models. Two static load-cases are defined to compare the original and the simplified model by evaluating the stiffness of the full vehicle under torsion and bending in accordance with the standards used by automotive original equipment manufacturer (OEM) companies. A dynamic comparison between the two models, based on global frequencies and modal shapes of the full vehicle, is presented as well.     

Design of optimal utility of wireless rechargeable sensor networks via joint spatiotemporal scheduling

In wireless rechargeable sensor networks, how to optimize energy resources for maximizing the sensor data is a challenging problem. In this paper, mobile charging vehicle scheduling, sensor charging time splitting and rate control with battery capacity constraints are considered together to maximize network utility. However, they are considered independently in exist works even though these problems are interdependent. In order to improve network performance through collaborative optimization of three problems, a joint optimization problem is formulated firstly. Then, a multistage approach is developed to jointly optimize the three subproblems iteratively. Furthermore, an accelerated distributed algorithm is integrated to improve the convergence speed of rate control. The results of extended experiments demonstrate that proposed approach can obtain higher network utility and charging efficiency compared to other charging scheduling methods.     

Digital stochastic control of distributed-parameter systems

This paper presents a method for discrete-time control and estimation of flexible structures in the presence of actuator and sensor noise. The approach consists of complete decoupling of the modal equations and estimator dynamics based on the independent modal-space control technique and modal spatial filtering of the system output. The solution for the Kalman filter gains reduces to that of independent second-order modal estimators, thus permitting real-time digital control of distributed-parameter systems in a noisy environment. The method can be used to control and estimate any number of modes without computational restraints and is theoretically free of observation spillover. Two examples, the first using nonlinear, quantized control and the second using linear, state feedback control are presented.This work was supported by the National Science Foundation, Grant No. PFR-80-20623.     

A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics

Ideally, NVH simulations become available already in the concept phase of vehicle development. The initial computer-aided design (CAD) can then be improved (by already including countermeasures), and the feasibility to balance NVH with other performance attributes is increased. In this early design stage, when exact geometrical information is not or scarcely available, conventional virtual prototyping techniques based on detailed CAD and FE models are not directly applicable. A state-of-the-art overview of concept NVH simulation methods in vehicle industry is given.This paper then presents a “Reduced Beam and Joint Modeling” approach to analyze and optimize the global bending and torsion modes of a vehicle body. Concept modifications in the body beam-like sections and in the joints are analyzed using the body reduced modal model. This small-sized model can be used to quickly and accurately optimize the low-frequency vehicle performance. The modifications are considered with respect to the existing (predecessor) model. Equivalent beam properties are estimated from the body FE model; modifications in the beam-like sections are then implemented with beam elements from a standard FE library. The joint modifications are considered through static superelements: stiffness formulations between the end points of the joint connected to the beam layout. The validity of the approach is first demonstrated on simple example models. An industrial vehicle BIW application case is subsequently presented. A beam and joint layout is created, and used for a fast sensitivity analysis to identify suitable modifications to improve the global modes. Next, two application cases are presented. First, a fast optimization analysis is performed to optimize the global body modes. Subsequently, suitable physical modifications are identified and applied to the full FE model; it is shown that the effect of these physical modifications is accurately predicted with the fast sensitivity analysis.     

Geometric mechanics of many-body systems

Geometric mechanics for many-body systems is first reviewed, and then applied to jointed cylinders with twist-free condition in order to obtain equations of motion under vanishing total angular momentum condition. The resultant equations are integrated numerically to set the system to turn a somersault.     

Dynamics of a two-layer beam with layer slip

A possible type of structural damping in mechanical systems when there is a distinct dependence of the oscillation decrement on the amplitude is investigated, using the example of the solution of a model problem on the oscillations of a two-layer beam. It is assumed that layer slip only occurs along the beam axis and that the layers together in the transverse direction. The interaction between the layers is of an elastic-friction form. The equations of motion of the beam in Timoshenko's form are numerically integrated using Godunov's difference scheme.     

Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example

Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system’s solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system’s solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system’s dynamic behavior on the vehicle’s structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle.     

Free vibration characteristics of a functionally graded beam by finite element method

This paper presents the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law. The present model is more effective for replacing the non-uniform geometrical beam with axially or transversally uniform geometrical graded beam. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Numerical results are presented in both tabular and graphical forms to figure out the effects of different material distribution, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of the beam.     

选址-库存-路径问题模型及其集成优化算法

设施选址、库存控制和车辆路径安排是物流系统优化中的三个关键问题,三者之间存在相互依赖的关系,应该根据这种关系来相应地进行综合优化与管理物流活动。以典型的单一生产基地、单一产品、采用不断审查的(Q, r)库存策略的供应链二级分销网络为研究对象,建立了一个随机型选址-库存-路径问题优化模型;在将非线性混合整数规划转化为线性整数集合覆盖模型的基础上,采用列生成算法来获得一个近似最优解,再用分支定价法对初始解进行改进,以实现对整个问题“完全集成”的优化。最后,用随机生成的方式,产生了10至160个客户的计算实例,分析了运输费用和库存费用对总成本的影响,算法运算时间表明本文给出的算法能较快地求解这一复杂问题。     

Fast algorithms for designing variable FIR notch filters

The paper presents fast algorithms for designing finite impulse response (FIR) notch filters. The aim is to design a digital FIR notch filter so that the magnitude of the filter has a deep notch at a specified frequency, and as the notch frequency changes, the filter coefficients should be able to track the notch fast in real time. The filter design problem is first converted into a convex optimization problem in the autocorrelation domain. The frequency response of the autocorrelation of the filter impulse response is compared with the desired filter response and the integral square error is minimized with respect to the unknown autocorrelation coefficients. Spectral factorization is used to calculate the coefficients of the filter. In the optimization process, the computational advantage is obtained by exploiting the structure of the Hessian matrix which consists of a Toeplitz plus a Hankel matrix. Two methods have been used for solving the Toeplitz‐plus‐Hankel system of equations. In the first method, the computational time is reduced by using Block–Levinson's recursion for solving the Toeplitz‐plus‐Hankel system of matrices. In the second method, the conjugate gradient method with different preconditioners is used to solve the system. Comparative studies demonstrate the computational advantages of the latter. Both these algorithms have been used to obtain the autocorrelation coefficients of notch filters with different orders. The original filter coefficients are found by spectral factorization and each of these filters have been tested for filtering synthetic as well as real‐life signals. Copyright © 2007 John Wiley & Sons, Ltd.     

Systematic dynamic modelling of mechanical systems containing kinematic loops

In this tutorial paper a systematic procedure is presented to obtain the dynamic models of mechanical systems containing kinematic loops, with a main emphasis on efficiency and with particular regard to robotic systems. The procedure retains a minimal set of generalized coordinates for the corresponding open loop structure, obtained by removing some additional constraints closing loops in the original structure, while adopting an efficient Newton-Euler formulation of the equations of motion. Two methods for including the loop closure equations are then discussed: the Lagrange multipliers method and the method based on an explicit solution of the constraint equations. In the first case the dynamic model is given in the form of an implicit Differential Algebraic Equations (DAE) system, while in the second case an Ordinary Differential Equations (ODE) system could be obtained.     

New Approach to Model Validation and Fault Diagnosis

The paper presents a new approach to model validation and fault diagnosis problems for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint. The new approach is developed by applying methods from linear quadratic optimal control theory. This leads to a method for model validation and fault diagnosis which is based around a robust Kalman filter type structure.     

Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load

This work deals with a study of the vibrational properties of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs) under the actions of moving load. Timoshenko and Euler-Bernoulli beam theories are used to evaluate dynamic characteristics of the beam. The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The primary contribution of the present work deals with the global elastic properties of nano-structured composite beams. The system of equations of motion is derived by using Hamilton’s principle under the assumptions of the Timoshenko beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. In order to evaluate time response of the system, Newmark method is also used. Numerical results are presented in both tabular and graphical forms to figure out the effects of various material distributions, carbon nanotube orientations, velocity of the moving load, shear deformation, slenderness ratios and boundary conditions on the dynamic characteristics of the beam. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam and it is believed that new results are presented for dynamics of FG nano-structure beams under moving loads which are of interest to the scientific and engineering community in the area of FGM nano-structures.     

Decentralized State-Estimation of Interconnected Systems with Unknown Nonlinearities

An efficient state-estimation scheme is developed within the LMI framework for robust decentralized state estimation of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints. The procedure utilizes a general linear estimator structure, and consists of two steps, the first giving a block-diagonal Lyapunov matrix together with the robustness degree, and the second determining the filter parameters. Extension to the case of additive filter gain perturbations is established and numerical examples are provided to illustrate the applicability of the method.     

A filtered no arbitrage model for term structures from noisy data

We consider an affine term structure model of interest rates, where the factors satisfy a linear diffusion equation. We assume that the information available to an agent comes from observing the yields of a finite number of traded bonds and that this information is not sufficient to reconstruct exactly the factors. We derive a method to obtain arbitrage-free prices of illiquid or non traded bonds that are compatible with the available incomplete information. The method is based on an application of the Kalman filter for linear Gaussian systems.     

Vibration analysis of Euler–Bernoulli nanobeams by using finite element method

In the present study, an efficient finite element model for vibration analysis of a nonlocal Euler–Bernoulli beam has been reported. Nonlocal constitutive equation of Eringen is proposed. Equations of motion for a nonlocal Euler–Bernoulli are derived based on varitional statement. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Vibration characteristics, such as fundamental frequencies, are illustrated in graphical and tabulated form. Numerical results are presented to figure out the effects of nonlocal parameter, slenderness ratios, rotator inertia, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of nanobeams.