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Random load identification (including load localization and reconstruction) plays a great significance in structural optimization design and safety evaluation. However, conventional methods perform the identification on the premise of an entire knowledge on excitation locations which is hard to be predetermined in practice. Meanwhile, these methods usually contain complex iterative processes in the identification, and thus encounter the challenge of heavy calculation burden. To this end, this study develops an innovative method with strong applicability and high efficiency for random load identification, which is composed of the transmissibility of power spectral density (PSD) and an improved adaptive multiplicative regularization. Firstly, the transmissibility among different response PSDs is used to measure the localization errors for any specified load location, by which the target load location can be identified via a principle of local minimum error. Then, an improved adaptive multiplicative regularization is developed to construct a new optimization function through defining a global regularization term. On this basis, only a single iterative process is enough to realize the load reconstruction, and the corresponding regularization parameter can be adaptively determined. This treatment simplifies the iterative process in conventional methods and thus reduces the computational cost. Finally, the effectiveness of the proposed method is validated numerically and experimentally. The results demonstrate that it can accurately locate random loads and exhibits a high efficiency in the reconstruction. [ABSTRACT FROM AUTHOR]