<p>The robust positioning of clamps plays a pivotal role in determining the natural frequency characteristics of clamp-pipe systems (CPSs) in aero-engine applications, where system uncertainties arising from clamp stiffness variations and positional deviations render natural frequency responses as random variables. To address the computational challenges inherent in robust design optimization of such uncertain systems, this study develops a novel method that integrates multiplicative dimensional reduction method (M-DRM) with the sequential Kriging model for enhanced computational efficiency. The proposed approach approximates high-dimensional moment integrals as products of one-dimensional functions, thereby fundamentally overcoming the curse of dimensionality while maintaining accuracy in statistical moment estimation through limited model evaluations. A robust design optimization model is subsequently formulated with clamp positions as design variables, wherein the uncertainty quantification problem is fully decoupled through multiplicative dimensional reduction approximation, transforming the original stochastic optimization into a computationally tractable deterministic procedure. Sequential Kriging surrogate models are integrated to iteratively identify optimal clamp positions that simultaneously maximize the mean natural frequency and minimize its variance, enabling robust design solutions with significantly reduced computational costs. Numerical investigations on L-shaped and spatial CPSs demonstrate the effectiveness and efficiency of the proposed method, showing superior performance compared to conventional approaches. This research provides an efficient and theoretically sound strategy for robust clamp-position design optimization of complex uncertain CPSs, offering significant potential for broader applications in structural dynamic optimization under uncertainty.</p>