In this work a two step approach to efficiently carrying out hyper parameter optimisation, required for building kriging and gradient enhanced kriging metamodels, is presented. The suggested approach makes use of an initial line search along the hyper-diagonal of the design space in order to find a suitable starting point for a subsequent gradient based optimisation algorithm. During the optimisation an upper bound constraint is imposed on the condition number of the correlation matrix in order to keep it from being ill conditioned. Partial derivatives of both the condensed log likelihood function and the condition number are obtained using the adjoint method, the latter has been derived in this work. The approach is tested on a number of analytical examples and comparisons are made
An approach to solving multidisciplinary design optimisation problems using approximations built in subspaces of the design variable space is proposed. Each approximation is built in the sub-space significant to the corresponding discipline while the optimisation problem is solved in the full design variable space. Since the approximations are built in a space of reduced dimensionality, the computational budget associated with building them can be reduced without compromising their quality. The method requires the designer to make assumptions on which design variables are significant to each discipline. If such assumptions are deficient, the resulting approximations suffer from errors that are not possible to reduce by additional sampling. Therefore a recovery mechanism is proposed that updates the values of the insignificant variables at the end of each iteration to align with the current best point. The method is implemented within a trust region based optimisation framework and demonstrated on a multidisciplinary optimisation of a thin-walled beam section subject to stiffness and impact requirements.
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