Optimisation of passive and semi-active heavy vehicle suspensions

An investigation into the potential for reducing road damage by optimising the design of heavy vehicle suspensions is described. In the first part of the paper two simple mathematical models are used to study the optimisation of conventional passive suspensions. Simple modifications are made to the steel spring suspension of a tandem axle trailer and it is found experimentally that RMS dynamic tyre forces can be reduced by 15% and theoretical road damage by 5.2%. A mathematical model of an air-sprung articulated vehicle is validated, and its suspension is optimised according to the simple models. This vehicle generates about 9% less damage than the leaf-sprung vehicle in the unmodified state and it is predicted that, for the operating conditions examined, the road damage caused by this vehicle can be reduced by a further 5.4%. Finally, it is shown experimentally that computer-controlled semi-active dampers have the potential to reduce road damage by a further 5-6%, compared to an air suspension with optimum passive damping. © Copyright 1994 Society of Automotive Engineers, Inc.

Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.