The role of sparsity in the analysis of large systems

An application of computer-aided design is to the design or optimization ofa physical problem which, if not already a network-type problem, can often be mathematically modelled as such. The c.a.d. aspect is, in part, concerned with the analysis of this network. Efficient and fast techniques are outlined for achieving this analysis and examples are given of application. These techniques are based on the Gauss elimination technique for solving the simultaneous equations describing the system's behaviour. These software techniques can form an integral part of the overall c.a.d. problem.The paper was presented at a one-day symposium on Networks, organized by the Computer-Aided Design specialist group of the British Computer Society and held on the 18th March 1974.     

Design sensitivity analysis of elastic mechanical systems

Adjoint variable methods are employed to develop efficient numerical methods of computing design derivatives of performance measures of elastic mechanical systems. Taking advantage of symmetry in finite element matrices and differential operators, a sensitivity analysis method is developed and demonstrated on a variety of static and dynamic structures and on vibration and impact absorbers. Where direct numerical comparisons are possible, the method is shown to be five to ten times faster than methods previously employed.     

Feedback properties of multivariable systems: The role and use of the return difference matrix

For linear time-invariant multivariable feedback systems, the feedback properties of plant disturbance attenuation, sensor noise response, stability margins, and sensitivity to plant and sensor variation are quantitatively related to the Bode magnitude versus frequency plots of the singular values of the return difference matrixI + Land of the associated inverse-return difference matrixI + L^{-1}. Implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed. The penalty function in the stochastic linear quadratic Gaussian (LQG) optimal control problem is found to be a weighted-sum of the singular values, with the weights determined by the quadratic cost and noise intensity matrices. This enables systematic "tuning" of LQG cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties. The theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft.     

Transfer matrix analysis of asymmetric frame-shear wall systems

Frame-shear wall systems are common high-rise structural forms resisting efficiently lateral forces. High redundancy complicates their three-dimensional analysis by traditional methods. In this paper an efficient and reliable such analysis based on the transfer matrix technique is presented. It yields the coupled linear static as well as the free vibrational response of tall asymmetric buildings of quite general form. The application of the method to various frame-shear wall geometries produced results in good agreement with experimental data and other theoretical predictions. The developed analysis was also found to be applicable to a wider range of geometries than simplified methods would allow while condensing the overall problem to a size depending on the degrees of freedom of a single level of the structure.     

Nonlinear kinematic tolerance analysis of planar mechanical systems

This paper presents a nonlinear kinematic tolerance analysis algorithm for planar mechanical systems comprised of higher kinematic pairs. The part profiles consist of line and circle segments. Each part translates along a planar axis or rotates around an orthogonal axis. The part shapes and motion axes are parameterized by a vector of tolerance parameters with range limits. A system is analyzed in two steps. The first step constructs generalized configuration spaces, called contact zones, that bound the worst-case kinematic variation of the pairs over the tolerance parameter range. The zones specify the variation of the pairs at every contact configuration and reveal failure modes, such as jamming, due to changes in kinematic function. The second step bounds the worst-case system variation at selected configurations by composing the zones. Case studies show that the algorithm is effective, fast, and more accurate than a prior algorithm that constructs and composes linear approximations of contact zones.     

Optimization-based motion prediction of mechanical systems: sensitivity analysis

In this study, we derive sensitivity equations for the problem of optimization-based motion prediction of a mechanical system using the inverse recursive Lagrangian formulation. The simulation and sensitivity formulations are based on Denavit–Hartenberg transformation matrices. External forces and moments are taken into account in the formulation. The sensitivity information is needed in the optimization-based simulation process. The proposed formulation is demonstrated by calculating sensitivities for the optimal time trajectory planning problem of a two-link manipulator. In addition, sensitivities obtained using the proposed algorithm are compared to those obtained using the closed-form equations of motion. The two sensitivities match quite closely. The lifting motion of the two-link manipulator with external loads is also optimized by using the algorithm developed in this paper. More complex applications of the proposed formulation to digital human motion prediction are presented elsewhere.     

The stiffness matrix in elastically articulated rigid-body systems

Discussed in this paper is the Cartesian stiffness matrix, which recently has received special attention within the robotics research community. Stiffness is a fundamental concept in mechanics; its representation in mechanical systems whose potential energy is describable by a finite set of generalized coordinates takes the form of a square matrix that is known to be, moreover, symmetric and positive-definite or, at least, semi-definite. We attempt to elucidate in this paper the notion of “asymmetric stiffness matrices”. In doing so, we show that to qualify for a stiffness matrix, the matrix should be symmetric and either positive semi-definite or positive-definite. We derive the conditions under which a matrix mapping small-amplitude displacement screws into elastic wrenches fails to be symmetric. From the discussion, it should be apparent that the asymmetric matrix thus derived cannot be, properly speaking, a stiffness matrix. The concept is illustrated with an example.     

Performance analysis of mass storage service alternatives fordistributed systems

The authors consider the performance of alternative mass-storage services for a client-server-style distributed system. Some qualitative arguments are presented on the ramifications of implementations of mass-storage services at various levels of the storage semantics hierarchy. The authors concentrate, in particular, on contrasting disk and file services. The functionalities of disk and file services are distinguished by their primitive operations: individual disk-block access for the disk service, and individual file-block access for the file service. This difference results in different partitionings of the computation between the client and server, as well as different network communication requirements. To understand the ramifications of such differences between the services, the authors present performance estimates for basic disk and file services. Performance estimates for several design alternatives are presented     

The role of the interactor matrix in multivariable stochastic adaptive control

This paper is concerned with the extension of the well-known minimum variance control strategy to the multi-input-multi-output case. It is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case. We develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm. We also explore the properties of the algorithm in detail. We also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori.     

The role of information support systems in the joint optimization of work systems

Sociotechnical approach preaches the affinity of the social and the technical organization but divides organizations into social and technical subsystems. Thus, it has failed to anticipate the possibilities of new technologies within the social system. The social subsystem of a modern sociotechnical system does not consist of mere human beings but combines people and the technological artifacts they use. In this article, we discuss one such technology, information support, and how it can be used to expand functional redundancy of a sociotechnical system, even the cognitive redundancy of individual people. However, such technologies have often been applied specifically to limit functional redundancy of the sociotechnical system, that is, to reduce communication, learning, and utilization of human talent. The discussion is based on findings from case studies on multimedia‐based interactive task support systems used in lightweight assembly industry in Finland and in Denmark. The case studies provide both justification to the information support approach and questions to be addressed in the future. For example, why did the introduction of so many interactive task support systems fail? © 2000 John Wiley & Sons, Inc.     

Uncertainty analysis of rule-based expert systems with Dempster-Shafer mass assignments

This article extends Dempster-Shafer Theory (DST) mass probability assignments to Boolean algebra and considers how such probabilities can propagate through a system of Boolean equations, which form the basis for both rule-based expert systems and fault trees. the advantage of DST mass assignments over classical probability methods is the ability to accommodate when necessary uncommitted probability belief. This paper also examines rules in the context of a probabilistic logic, where a given rule itself may be true with some probability in the interval [0,1]. When expert system knowledge bases contain rules which may not always hold, or rules that occasionally must be operated upon with imprecise information, the DST mass assignment formalism is shown to be a suitable methodology for calculating probability assignments throughout the system.     

The role of the industrial engineer in developing expert systems

The most popular area of Artificial Intelligence application today is in expert systems. This paper contains a discussion of expert systems, otherwise known as knowledge-based systems and knowledge systems. The principal components of an expert system, and the evolution of expert systems are presented. The suitability of a task to an expert system is proposed. When a task is suitable for an expert system application, the system must be developed by a knowledge engineer. The methodology that the knowledge engineer must go through to develop an expert system is demostrated. Industrial engineers have formal training in many areas which can be useful when assumming the role of knowledge engineer. These areas of industrial engineering and how they are beneficial is discussed. What the future may hold in store is also pondered.     

The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem

Multibody System Dynamics - In this article we analyze the following problem: given a mechanical system subject to (possibly redundant) bilateral and unilateral constraints with set-valued...     

Stability analysis of non-autonomous linear systems by a matrix decomposition method

A matrix decomposition method is used to study the stability of the equilibrium state of non-autonomous linear systems. This technique systematically provides sufficient stability and asymptotic stability conditions for such systems, Several criteria regarding the stability of linear systems with time-varying coefficients are developed. A few examples illustrating the procedure are discussed. These examples include a system governed by the Mathieu equation, and a parametrically excited multidegree-of-freedom system.     

The spring paradigm in tracking control of simple mechanical systems

An intrinsic formulation of geometric proportional–derivative tracking control for fully actuated mechanical systems is developed. The region of stability is determined directly from the size of the system’s injectivity radius and, for a restricted set of control problems, the system’s locus of cut points about a desired reference point. Exponential stability is obtained under certain boundedness conditions. For controlled motion along a geodesic, the proffered scheme yields a particularly simple and elegant manifestation of the underlying use of the mass–spring–damper paradigm in the control design methodology.