This paper studies the fault diagnosis of singular stochastic systems. The probability distribution of output is measured by probability density functions (PDFs), which are modeled by a square root B-spline expansion. An adaptive nonlinear observer is proposed to estimate the size of the fault occurring in systems. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Finally, the simulation results are given to indicate the method for diagnosing the fault. © Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2011.