Membrane　fouling　caused　by　many　direct　and　indirect　triggering　factors　has　become　an　obstacle　to　the　application　of　membrane　bioreactors　(MBRs).　The　nonlinear　relationship　between　those　factors　is　subject　to　complex　causality　or　affiliation,　which　is　difficult　to　clarify　for　the　diagnosis　of　membrane　fouling.　To　solve　this　problem,　this　paper　proposes　a　compressible　diagnosis　model　(CDM)　based　on　transfer　entropy　to　facilitate　the　fault　diagnosis　of　the　root　cause　for　membrane　fouling.　The　novelty　of　this　model　includes　the　following　points:　Firstly,　a　framework　of　a　CDM　between　membrane　fouling　and　causal　variables　is　built　based　on　a　feature　extraction　algorithm　and　mechanism　analysis.　The　framework　can　identify　fault　transfer　scenarios　following　the　changes　in　operating　conditions.　Secondly,　the　fault　transfer　topology　of　a　CDM　based　on　transfer　entropy　is　constructed　to　describe　the　causal　relationship　between　variables　dynamically.　Thirdly,　an　information　compressible　strategy　is　designed　to　simplify　the　fault　transfer　topology.　This　strategy　can　eliminate　the　repetitious　affiliation　relationship,　which　contributes　to　diagnosing　the　root　causal　variables　speedily　and　accurately.　Finally,　the　effectiveness　of　the　proposed　CDM　is　verified　by　the　measured　data　from　an　actual　MBR.　The　results　of　experiments　demonstrate　that　the　proposed　CDM　fulfills　the　diagnosis　of　membrane　fouling.