The off-line fault detection, isolation and identification of multiplicative actuator faults using sensors providing measurements affected by unknown nonlinear distortions and bounded noises are addressed. The only assumption about the unknown functions modeling the sensor distortions is their monotonicity. Bounded disturbances are also considered as unknown inputs of the system time-varying dynamics. Polytopic faulty parameter sets resulting from the search of robust output pairs and from zonotope computations are the basis for a decision scheme which makes use of multi-scale temporal windows. A numerical example modeling part of a distillation column illustrates the off-line diagnosis of three multiplicative actuator faults from a single low-cost noisy sensor with unknown nonlinear distortion and constant bias.