This work concentrates on the first order Sugeno model of the power spectral density (PSD) of a multi degree of freedom system. Two models are introduced, single and multi degree of freedom system. In both models, the relationship between the input-output power spectral densities is modeled using first order Sugeno model. Minimum error model with fewer numbers of rules for the power spectral density for each model is obtained through enumerative search of the clustering parameters. The resulting models with best clustering parameters are then tuned by using adaptive neurofuzzy inference system (ANFIS). This paper is a first attempt in introducing fuzzy systems and some patents in modeling a very important vibration characteristic such as the power spectral density to identify complex mechanical behaviours. We also demonstrate the ability of these models to sense the sudden jump in the vibration amplitude when the system vibrates under a frequency equal to its natural frequency (resonance). Furthermore, these fuzzy models could be used to monitor, on line, the power spectral density of any rotating or non-rotating structures subjected to dynamic loads. This will give the machine operator the ability to stop the process or change the process parameters to avoid the resonance, which could lead to a machine failure or a disaster.
Keywords: Random vibration, Sugeno model, ANFIS, power spectral density (PSD) and multi degree of freedom vibration
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