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This paper presents a new fault detection and diagnosis (FDD) algorithm for general stochastic systems. Different from the classical FDD design, the distribution of system output is supposed to be measured rather than the output signal itself. The task of such an FDD algorithm design is to use the measured output probability density functions (PDFs) and the input of the system to construct a stable filter-based residual generator such that the fault can be detected and diagnosed. For this purpose, square root B-spline expansions are applied to model the output PDFs and the concerned problem is transformed into a nonlinear FDD algorithm design subjected to a nonlinear weight dynamical system. A linear matrix inequality based solution is presented such that the estimation error system is stable and the fault can be detected through a threshold. Moreover, an adaptive fault diagnosis method is also provided to estimate the size of the fault. Simulations are provided to show the efficiency of the proposed approach.