From　a　practical-theoretic　viewpoint,　there　is　a　need　to　develop　rigorous　design　and　analysis　tools　for　the　control,　fault　diagnosis,　and　security　of　wastewater　quality.　However,　sludge　bulking　remains　a　widespread　problem　in　the　operation　of　activated　sludge　processes,　which　leads　to　severe　economic　and　environmental　consequences.　Sludge　volume　index　(SVI)　monitoring　is　a　key　challenge　that　will　become　even　more　crucial　in　the　years　ahead　to　quantify　sludge　bulking.　This　brief　presents　a　system　that　consists　of　online　sensors　and　an　SVI　predicting　plant.　The　SVI　predicting　plant　uses　a　hierarchical　radial　basis　function　(HRBF)　neural　network　to　predict　SVI　in　a　wastewater　treatment　process　(WWTP).　Then,　an　approach　named　extended　extreme　learning　machine　(EELM)　is　proposed　for　training　the　weights　of　HRBF.　Unlike　conventional　single-hidden-layer　feedforward　networks,　this　EELM-HRBF　is　based　on　the　hierarchical　structure　which　is　capable　of　hierarchical　learning　of　sequential　information　online,　and　one　may　only　need　to　adjust　the　output　weights　linking　the　hidden　and　the　output　layers.　In　such　EELM-HRBF　implementations,　the　EELM　provides　better　generalization　performance　during　the　learning　process.　Moreover,　the　convergence　of　the　proposed　algorithm　is　analyzed.　To　illustrate　the　methodology,　the　proposed　predicting　plant　with　the　EELM-HRBF　has　been　tested　and　compared　with　other　methods　by　applying　it　to　the　problem　of　predicting　SVI　in　a　simplified　and　real　WWTP.　Experimental　results　show　that　the　EELM-HRBF　can　be　used　to　predict　the　wastewater　quality　online.　The　results　demonstrate　its　effectiveness.