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This paper is devoted to investigating the observer-based fault detection (FD) filters for nonlinear distributed processes described by hyperbolic partial differential equations (PDEs). To this end, the PDE systems are first approximated by the Takagi-Sugeno fuzzy models with spatiotemporal uncertainties. Then, the fuzzy FD filter is developed for the hyperbolic PDE systems to guarantee that the residual signal is robust against process inputs including disturbances. The dynamic threshold is designed to ensure the real-time detection of potential faults. It is worth mentioning that the distributed weighting factors are used to weigh the residual signal such that the overall fault detectability can be optimized.