Acoustic　mode　detection　is　attached　great　significance　for　providing　guidance　to　noise　reduction　design　of　commercial　aero-engine　with　high-bypass　ratio.　Compressive　sampling　method　has　been　creatively　employed　in　this　field　due　to　its　notable　performance　on　reducing　the　number　of　microphones　in　acoustic　mode　measurements.　However,　the　classical　e　1-norm　regularized　compressive　sampling　model　tends　to　underestimate　the　dominant　mode　amplitudes　of　interest.　Moreover,　the　traditional　regularization　parameter　selection　strategy　with　fixed　threshold　brings　out　inefficient　and　cumbersome　work.　In　this　paper,　we　propose　a　nonconvex　penalized　compressive　sampling　model　with　adaptive　threshold,　to　seek　the　sparse　and　accurate　solution　of　acoustic　mode　detection　from　limited　measurements,　and　provide　a　sufficiently　efficient　way　to　adaptively　seek　the　optimal　regularization　parameter.　Firstly,　the　reweighted　generalized　minimax-concave　(ReGMC)　regularization　is　employed　to　improve　the　accuracy　of　acoustic　pressure　reconstruction,　which　feasibly　enhances　sparsity　with　maintaining　the　convexity　of　the　cost　function.　Secondly,　the　k-sparsity　strategy　is　introduced　to　set　regularization　parameters　adaptively.　Finally,　the　applicability　of　the　proposed　approach　is　verified　on　a　multi-stage　aero-engine　fan　test　rig.　Experimental　results　demonstrate　that　the　nonconvex　ReGMC　regularized　method　outperforms　the　classical　l(1)-norm,　producing　more　accurate　results　in　mode　detection　with　fewer　measurements　and　being　more　robust　towards　background　noise.　(C)　2021　Elsevier　Ltd.　All　rights　reserved.