125 years after Bertha Benz completed the first overland journey in automotive history, the Mercedes Benz S-Class S 500 INTELLIGENT DRIVE followed the same route from Mannheim to Pforzheim, Germany, in fully autonomous manner. The autonomous vehicle was equipped with close-to-production sensor hardware and relied solely on vision and radar sensors in combination with accurate digital maps to obtain a comprehensive understanding of complex traffic situations. The historic Bertha Benz Memorial Route is particularly challenging for autonomous driving. The course taken by the autonomous vehicle had a length of 103 km and covered rural roads, 23 small villages and major cities (e.g. downtown Mannheim and Heidelberg). The route posed a large variety of difficult traffic scenarios including intersections with and without traffic lights, roundabouts, and narrow passages with oncoming traffic. This paper gives an overview of the autonomous vehicle and presents details on vision and radar-based perception, digital road maps and video-based self-localization, as well as motion planning in complex urban scenarios.

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Making Bertha Drive?An Autonomous Journey on a Historic Route

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Sensitivity Analysis of Discrete Structural Systems

A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

A study of mathematical programming methods for structural optimization. Part I: Theory

A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods

Recent developments are reviewed in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented. In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications. In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. In addition to reviewing recent contributions in this area, the paper raises the issue of differentiability and continuity associated with the occurrence of repeated eigenvalues.

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Recent developments in structural sensitivity analysis

Numerical Methods with Applications

An algorithm for domain decomposition in finite element analysis

A fast, accurate Choleski method for the solution of symmetric systems of linear equations is presented. This direct method is based on a variable-band storage scheme and takes advantage of column heights to reduce the number of operations in the Choleski factorization. The method employs parallel computation in the outermost DO-loop and vector computation via the 'loop unrolling' technique in the innermost DO-loop. The method avoids computations with zeros outside the column heights, and as an option, zeros inside the band. The close relationship between Choleski and Gauss elimination methods is examined. The minor changes required to convert the Choleski code to a Gauss code to solve non-positive-definite symmetric systems of equations are identified. The results for two large-scale structural analyses performed on supercomputers, demonstrate the accuracy and speed of the method.

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A parallel-vector algorithm for rapid structural analysis on high-performance computers

A direct linear equation solution method based on the Choleski factorization procedure is presented which exploits both parallel and vector features of supercomputers. The new equation solver is described, and its performance is evaluated by solving structural analysis problems on three high-performance computers. The method has been implemented using Force, a generic parallel FORTRAN language.

Duc T. Nguyen

Papers

Numerical Methods with Applications

An algorithm for domain decomposition in finite element analysis

A parallel-vector algorithm for rapid structural analysis on high-performance computers

Parallel-vector solution of large-scale structural analysis problems on supercomputers

A FE model updating technique based on SAP2000-OAPI and enhanced SOS algorithm for damage assessment of full-scale structures