The common failure modes of a turbocharger rotor are bearing wear, impeller-casing rub events and shaft cracks due to high thermal currents. A reliable design of such rotors is therefore essential in order to avoid the vibration-based failure incidents during operation. The dynamic response gives vital information about the rotor condition as well as it helps in the inverse modelling to predict the optimum parameters. Present work deals with dynamic analysis and optimum design of a turbocharger rotor system subjected to ideal exhaust gas emission loads. The exhaust emission loads at the turbine in radial direction are modelled as Muszynska’s nonlinear seal forces, while the axial gas emission loads are treated as periodic blade passing excitations. The critical vibration characteristics of the rotor system running at uniform speed are analysed using the finite element model by considering nonlinear floating ring bearing forces and are initially validated with an experimental work performed on a turbocharger test-rig. Furthermore, the effects of gas load as well as floating ring bearing parameters on the critical frequencies and amplitudes are studied in detail. The effective input–output relationships are established using counter-propagation neural network (CPNN) learning scheme. Surrogate model using an improved Cuckoo search optimization in-conjunction with trained CPNN model in function evaluations is employed to predict the optimum values of the bearing parameters and relative emission load data. The relative output frequency response with optimized parameters is presented and effectiveness of the approach over the finite element based function evaluation scheme is illustrated. © 2021, The Brazilian Society of Mechanical Sciences and Engineering.