Difference mode decomposition for adaptive signal decomposition

•Difference mode decomposition (DMD) is proposed to decompose a mixed signal into concerned components, reference components, and noise.•Proposed DMD is based on optimized weights and it has a solid mathematical basis.•Optimized weights are generated by using a sum of weighted normalized Fourier spectrum.•Proposed DMD can adaptively extract repetitive fault transients caused by gear and bearing faults.