Multiply-distorted　images,　that　is,　distorted　by　different　types　of　distortions　simultaneously,　are　so　common　in　real　applications.　This　kind　of　images　contain　multiple　overlaying　stages　(e.g.,　acquisition,　compression　and　transmission　stage).　Each　stage　will　introduce　a　certain　type　of　distortion,　for　example,　sensor　noise　in　acquisition　stage　and　compression　artifacts　in　compression　stage.　However,　most　current　blind/no-reference　image　quality　assessment　(NR-IQA)　methods　are　specifically　designed　for　singly-distorted　images,　thus　resulting　in　their　deficiency　in　handling　multiply-distorted　images.　Motivated　by　the　hypothesis　that　human　visual　system　(HVS)　is　adapted　to　the　structural　information　in　images,　we　attempt　to　assess　multiply-distorted　images　based　on　structural　degradation.　To　this　end,　we　use　both　first-and　high-order　image　structures　to　design　a　novel　referenceless　quality　metric　for　multiply-distorted　images.　Specifically,　we　leverage　the　quality-aware　features　extracted　from　both　the　gradient-magnitude　map　and　contrast-normalized　map,　and　further　improve　the　performance　by　making　use　of　redundancy　of　features　with　random　subspace　method.　Experimental　results　on　popular　multiply-distorted　image　databases　verify　the　outstanding　performance　of　the　proposed　method.　(c)　2018　Elsevier　B.V.　All　rights　reserved.