Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects

This study explores the use of generalized polynomial chaos theory for modeling complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. The polynomial chaos framework has been chosen because it offers an efficient computational approach for the large, nonlinear multibody models of engineering systems of interest, where the number of uncertain parameters is relatively small, while the magnitude of uncertainties can be very large (e.g., vehicle-soil interaction). The proposed methodology allows the quantification of uncertainty distributions in both time and frequency domains, and enables the simulations of multibody systems to produce results with “error bars”. The first part of this study presents the theoretical and computational aspects of the polynomial chaos methodology. Both unconstrained and constrained formulations of multibody dynamics are considered. Direct stochastic collocation is proposed as less expensive alternative to the traditional Galerkin approach. It is established that stochastic collocation is equivalent to a stochastic response surface approach. We show that multi-dimensional basis functions are constructed as tensor products of one-dimensional basis functions and discuss the treatment of polynomial and trigonometric nonlinearities. Parametric uncertainties are modeled by finite-support probability densities. Stochastic forcings are discretized using truncated Karhunen-Loeve expansions. The companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part II: Numerical Applications” illustrates the use of the proposed methodology on a selected set of test problems. The overall conclusion is that despite its limitations, polynomial chaos is a powerful approach for the simulation of multibody systems with uncertainties.     

A linearized input–output representation of flexible multibody systems for control synthesis

In this paper, a linearized input–output representation of flexible multibody systems is proposed in which an arbitrary combination of positions, velocities, accelerations, and forces can be taken as input variables and as output variables. The formulation is based on a nonlinear finite element approach in which a multibody system is modeled as an assembly of rigid body elements interconnected by joint elements such as flexible hinges and beams. The proposed formulation is general in nature and can be applied for prototype modeling and control system analysis of mechatronic systems. Application of the theory is illustrated through a detailed model development of an active vibration isolation system for a metrology frame of a lithography machine.     

Efficient coupling of multibody software with numerical computing environments and block diagram simulators

Simulation of complex mechatronic systems like an automobile, involving mechanical components as well as actuators and active electronic control devices, can be accomplished by combining tools that deal with the simulation of the different subsystems. In this sense, it is often desirable to couple a multibody simulation software (for the mechanical simulation) with external numerical computing environments and block diagram simulators (for the modeling and simulation of nonmechanical components).     

A quantitative foundation for defining and manipulating deals to facilitate automated e-commerce

We propose a goal programming framework that aims at automating e-commerce transactions. This framework consists of three basic layers: deal definition—defining the deal’s parameters and associated constraints (e.g., item, price, delivery dates); deal manipulation—a collection of procedures for shaping deals to attain desired goals (e.g., earliest delivery and minimum price) and an applications layer that employs these procedures within some negotiations settings (e.g., an auction-related application presents a “better offer” while bidding on a contract). Our proposed foundation is rich enough to support a wide array of applications ranging from 1-1 and 1-n negotiations (auctions) to deal valuation and deal splitting. Whereas the techniques are appropriate to a multitude of settings, we shall mainly present them in the context of business-to-business (B2B) commerce where we see the greatest short term benefits. O. Shmueli’s work is partially supported by the Fund for the Promotion of Research at the Technion.     

Flexible Multibody Dynamics: Review of Past and Recent Developments

In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynamics, control-structure interaction, use of modal identification and experimental methods in flexible multibody simulations, application of flexible multibody techniques to computer graphics, numerical issues, and large deformation problem. Establishing the relationship between different flexible multibody formulations is an important issue since there is a need to clearly define the assumptions and approximations underlying each formulation. This will allow us to establish guidelines and criteria that define the limitations of each approach used in flexible multibody dynamics. This task can now be accomplished by using the absolute nodal coordinate formulation which was recently introduced for the large deformation analysis of flexible multibody systems.     

Deadlock detection in distributed database systems: a new algorithm and a comparative performance analysis

This paper attempts a comprehensive study of deadlock detection in distributed database systems. First, the two predominant deadlock models in these systems and the four different distributed deadlock detection approaches are discussed. Afterwards, a new deadlock detection algorithm is presented. The algorithm is based on dynamically creating deadlock detection agents (DDAs), each being responsible for detecting deadlocks in one connected component of the global wait-for-graph (WFG). The DDA scheme is a “self-tuning” system: after an initial warm-up phase, dedicated DDAs will be formed for “centers of locality”, i.e., parts of the system where many conflicts occur. A dynamic shift in locality of the distributed system will be responded to by automatically creating new DDAs while the obsolete ones terminate. In this paper, we also compare the most competitive representative of each class of algorithms suitable for distributed database systems based on a simulation model, and point out their relative strengths and weaknesses. The extensive experiments we carried out indicate that our newly proposed deadlock detection algorithm outperforms the other algorithms in the vast majority of configurations and workloads and, in contrast to all other algorithms, is very robust with respect to differing load and access profiles. Received December 4, 1997 / Accepted February 2, 1999     

Multidisciplinary Optimization of Multibody Systems with Application to the Design of Rail Vehicles

A methodology for the design optimization of multibody systems is presented. The methodology has the following features: (1) multibody dynamics is employed to model and simulate complex systems; (2) multidisciplinary optimization (MDO) methods are used to combine multibody systems and additional systems in a synergistic manner; (3) using genetic algorithms (GAs) and other effective search algorithms, the mechanical and other design variables are optimized simultaneously. The methodology is shown to handle the conflicting requirements of rail vehicle design, i.e., lateral stability, curving performance, and ride quality, in an effective manner. By coordinating these conflicting requirements at the system level, three multibody models corresponding to each of these requirements for a rail vehicle are optimized simultaneously.     

Two approaches for feedforward control and optimal design of underactuated multibody systems

An underactuated multibody system has less control inputs than degrees of freedom. For trajectory tracking, often a feedforward control is necessary. Two different approaches for feedforward control design are presented. The first approach is based on a coordinate transformation into the nonlinear input–output normal-form. The second approach uses servo-constraints and results in a set of differential algebraic equations. A comparison shows that both feedforward control designs have a similar structure. The analysis of the mechanical design of underactuated multibody systems might show that they are nonminimum phase, i.e., they have unstable internal dynamics. Then the feedforward control cannot be computed by time integration and output trajectory tracking becomes a very challenging task. Therefore, based on the two presented feedforward control design approaches, it is shown that through the use of an optimization procedure underactuated multibody systems can be designed in such a way that they are minimum phase. Thus, feedforward control design using the two approaches is significantly simplified.     

Integration of micro-mechatronics in automotive applications

 Micro-Mechatronics and System Integration is a multidisciplinary field, which offers low cost system solutions based on the principle of homogenizing system components and consequent elimination of at least one material component or packaging level from the system. These system approaches show, compared to the existing solutions, a higher functionality, more intelligence and better reliability performance. The number of interconnects necessary to link a motor, or sensor, or an actuator to the digital bus decreases, as the smartness of the devices increases. The paper presents system solutions and manufacturing technology for mechatronic systems, developed at Fraunhofer IZM. To reduce package volume, advanced packaging technologies as Flip Chip and CSP are used, for increased reliability and additional mechanical functionality encapsulation processes as transfer-molding, a combination of transfer- and injection-molding or modular packaging toolkit based on LTCC are selected. The first system is a multi-chip-module for motor control used for automotive applications as window-lifts or sun-roofs. For the module at least three interconnection layers were eliminated using novel concepts as intelligent leadframes and integrated plugs. The package resists harsh environment as present in automotive applications. Another mechatronic package called TB-BGA or StackPac respectively, is a 3-D solution, containing a pressure sensor and the complete electronics necessary for control and data transfers. This package involves CSP-technologies on flex, with an increase of functionality per volume unit by direct CSP-to-CSP mounting, eliminating substrate layers and large signal distances of unamplified signals from sensor output. The mechatronic packages will be discussed in detail. Especially cost, reliability performance and according “Design for Reliability” show the potential of micro-mechatronic solutions in automotive and industrial applications.     

Intrinsic deformable joints

This paper addresses the problem of reducing the constitutive behavior of relatively complex mechanical systems to lumped deformable components that connect two nodes of a multibody system. It is common practice, both in finite element and multibody system dynamics analysis, to refer the constitutive properties of lumped components to one of the nodes they connect. It is shown that this practice, here termed “attached,” could result in either underestimating or overestimating the couplings related to the finiteness of the relative rotation between the connected nodes. This work proposes an alternative formulation, here termed “intrinsic” that allows to correlate very well the behavior of general lumped deformable components with that resulting from the nonlinear finite element analysis of three-dimensional models of the components. Numerical examples, including the analysis of components that are widely used in the mechanical and aerospace industry, show how the proposed formulation can easily and accurately account for nonlinear geometrical effects, and thus deliver compact and accurate models suitable for the analysis of the global behavior of rather complex components.     

Vertical dynamic behavior of three-piece bogie suspensions with two types of friction wedge

There are two common types of friction wedge in the suspension system of a three-piece bogie—the “constant damping” wedge and the variable damping wedge. A generic wagon–track dynamics interaction model has been developed to investigate the dynamic behavior of suspension systems with these two wedge types. The model differs from usual approaches in two aspects: (1) the mass of the wedge is considered in the model and, (2) the track is modeled as a flexible element with multiple degrees of freedom modeling sleepers, ballast and subgrade. The dynamic response characteristics of the two suspension-wedge systems are simulated, compared and discussed for different wedge friction conditions and track input frequencies.     

A comparative study between the augmented Lagrangian method and the complementarity approach for modeling the contact problem

The increasing demand for real-time high-fidelity multibody dynamics simulations in several modern fields such as robotics and computer game industries has motivated many researches to propose novel approaches to model multibody systems with several contacts. The possibility of different contact conditions in a system with several contacts yields a combinatorial problem of potentially large size. Rigid contact model which is the most common model used for real-time simulations yields a non-smooth dynamic formulation. The solution of such a system can be governed using different methods. In this paper a comparison between the complementarity approaches and the augmented Lagrangian based formulations to deal with non-smooth contact models is presented via numerical examples, and the advantages and shortcomings of each method are discussed.     

Simulation of a helicopter’s main gearbox semiactive suspension with bond graphs

This paper presents a bond graph model of a helicopter’s semiactive suspension and the associated simulations. The structural and modular approach proposed with bond graph permits a systematic modeling of mechatronic multibody systems. This approach was carried out thanks to the use of the singular perturbation method, which is a variant of penalty formulation. The model is then built as an assembly of components or modules (rigid bodies and compliant kinematic joints) by following the structure of the actual system.The bond graph model of the passive suspension with fixed flapping masses has been verified with another multibody tool for three different excitations (pumping, roll, and yaw). Next, the passive model, augmented with electrical actuators and controllers, is called the semiactive suspension model. Simulations on the semiactive suspension model have been conducted.     

Detecting global predicates in distributed systems with clocks

Summary. This paper proposes a framework for detecting global state predicates in systems of processes with approximately-synchronized real-time clocks. Timestamps from these clocks are used to define two orderings on events: “definitely occurred before” and “possibly occurred before”. These orderings lead naturally to definitions of 3 distinct detection modalities, i.e., 3 meanings of “predicate held during a computation”, namely: (“ possibly held”), (“ definitely held”), and (“ definitely held in a specific global state”). This paper defines these modalities and gives efficient algorithms for detecting them. The algorithms are based on algorithms of Garg and Waldecker, Alagar and Venkatesan, Cooper and Marzullo, and Fromentin and Raynal. Complexity analysis shows that under reasonable assumptions, these real-time-clock-based detection algorithms are less expensive than detection algorithms based on Lamport's happened-before ordering. Sample applications are given to illustrate the benefits of this approach. Received: January 1999 / Accepted: November 1999     

Process mining: a two-step approach to balance between underfitting and overfitting

Process mining includes the automated discovery of processes from event logs. Based on observed events (e.g., activities being executed or messages being exchanged) a process model is constructed. One of the essential problems in process mining is that one cannot assume to have seen all possible behavior. At best, one has seen a representative subset. Therefore, classical synthesis techniques are not suitable as they aim at finding a model that is able to exactly reproduce the log. Existing process mining techniques try to avoid such “overfitting” by generalizing the model to allow for more behavior. This generalization is often driven by the representation language and very crude assumptions about completeness. As a result, parts of the model are “overfitting” (allow only for what has actually been observed) while other parts may be “underfitting” (allow for much more behavior without strong support for it). None of the existing techniques enables the user to control the balance between “overfitting” and “underfitting”. To address this, we propose a two-step approach. First, using a configurable approach, a transition system is constructed. Then, using the “theory of regions”, the model is synthesized. The approach has been implemented in the context of ProM and overcomes many of the limitations of traditional approaches.     

Efficient design/simulation algorithms for simultaneous switching noise in leadframe packages

 Two new modeling and simulation approaches for Simultaneous Switching Noise (SSN) are described and compared to “brute force” simulation by SPICE. Both simulation accuracy and simulation run-time are considered. The two new approaches are: 1) the “effective inductance” method, in which an approximate, very efficient method of extracting an SSN L _eff  is utilized; and 2) the “macromodel” method, in which the complex inductance network responsible for SSN is represented by only a few dominant poles in the frequency domain and the time domain response is obtained by an efficient convolution algorithm. Both approaches are shown to be accurate and fast, but only the effective inductance algorithm is robust in numerical convergence. Received: 19 March 1997 / Accepted: 25 March 1997     

Layered evaluation of interactive adaptive systems: framework and formative methods

The evaluation of interactive adaptive systems has long been acknowledged to be a complicated and demanding endeavour. Some promising approaches in the recent past have attempted tackling the problem of evaluating adaptivity by “decomposing” and evaluating it in a “piece-wise” manner. Separating the evaluation of different aspects can help to identify problems in the adaptation process. This paper presents a framework that can be used to guide the “layered” evaluation of adaptive systems, and a set of formative methods that have been tailored or specially developed for the evaluation of adaptivity. The proposed framework unifies previous approaches in the literature and has already been used, in various guises, in recent research work. The presented methods are related to the layers in the framework and the stages in the development lifecycle of interactive systems. The paper also discusses practical issues surrounding the employment of the above, and provides a brief overview of complementary and alternative approaches in the literature.     

MDA Tool Components: a proposal for packaging know-how in model driven development

As the Model Driven Development (MDD) and Product Line Engineering (PLE) appear as major trends for reducing software development complexity and costs, an important missing stone becomes more visible: there is no standard and reusable assets for packaging the know-how and artifacts required when applying these approaches. To overcome this limit, we introduce in this paper the notion of MDA Tool Component, i.e., a packaging unit for encapsulating business know-how and required resources in order to support specific modeling activities on a certain kind of model. The aim of this work is to provide a standard way for representing this know-how packaging unit. This is done by introducing a two-layer MOF-compliant metamodel. Whilst the first layer focuses on the definition of the structure and contents of the MDA Tool Component, the second layer introduces a language independent way for describing its behavior. An OMG RFP (Request For Proposal) has been issued in order to standardize this approach. This work is supported in part by the IST European project “MODELWARE” (contract no 511731) and extends the work presented in the paper entitled “MDA Components: A Flexible Way for Implementing the MDA Approach” edited in proceedings of the ECMDA-FA’05 conference.     

Trust structures

A general formal model for trust in dynamic networks is presented. The model is based on the trust structures of Carbone, Nielsen and Sassone: a domain theoretic generalisation of Weeks’ framework for credential based trust management systems, e.g., KeyNote and SPKI. Collections of mutually referring trust policies (so-called “webs” of trust) are given a precise meaning in terms of an abstract domain-theoretic semantics. A complementary concrete operational semantics is provided using the well-known I/O-automaton model. The operational semantics is proved to adhere to the abstract semantics, effectively providing a distributed algorithm allowing principals to compute the meaning of a “web” of trust policies. Several techniques allowing sound and efficient distributed approximation of the abstract semantics are presented and proved correct. BRICS: Basic Research in Computer Science (www.brics.dk) funded by the Panish National Research Foundation.