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An enhanced method for solving multi-input systems is presented which builds on the concepts of partial coherence using conditioned input analysis and virtual coherence using principal component analysis. Conditioned source analysis expands the definition of partially coherent inputs to include partially coherent input arrays. Each input array may describe a complex multi-dimensional source. The cross correlated input array is replaced by its equivalent principal component decomposition and conditioned from subsequent inputs/arrays using the techniques for determining partial coherence. The extension of existing theory to include conditioned source analysis is described and the method is illustrated on a lumped-parameter model. A practical application of the technique is also presented where the component of noise and vibration in an engine which is statistically related to combustion is separated from mechanically induced sources.