The　rapid　development　of　the　Artificial　Intelligence　of　Things　(AIoT)　opens　up　a　new　perspective　for　emerging　service-based　applications,　and　becomes　a　major　driver　of　diverse　Federated　Learning　(FL)　applications.　However,　due　to　the　heterogeneity　of　nodes　and　the　existence　of　free-rider　attacks,　some　device　nodes　may　launch　free-rider　attacks　to　obtain　the　global　model　without　any　contribution,　which　not　only　dampens　the　enthusiasm　of　legitimate　participants　but　also　undermines　the　fairness　of　node　contributions.　In　this　paper,　we　propose　a　free-rider　attack　detection　mechanism　(FRAD)　for　federated　learning　with　deep　autoencoding　gaussian　mixture　model　based　on　contribution　and　reputation.　Specifically,　we　first　model　the　contribution　values　based　on　the　computing　resource,　communication　cost,　and　data　quality　of　each　device　node.　Then,　based　on　PageRank　algorithms,　we　design　an　optimal　reputation-based　model　to　fairly　and　precisely　choose　benign　nodes　to　participate　in　federated　training　under　information　asymmetry.　Furthermore,　we　develop　FRAD　mechanism　via　deep　autoencoding　gaussian　mixture　model　that　combines　historical　contribution　with　reputation　scores.　Simulation　results　validate　that　the　proposed　mechanism　in　this　paper　outperforms　the　state-of-the-art　baselines　(　∼×2.14　and　∼×1.1　on　MNIST　and　CIFAR,　respectively)　in　defending　against　free-rider　attacks,　and　when　the　main　clients　are　free-riders,　i.e.,　50%　or　even　up　to　80%　of　the　free-riders,　FRAD　can　still　maintain　a　high　defense　performance　against　free-rider　attacks.　IEEE