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Lightly-damped mechanical systems exhibit strong resonant behaviour which could potentially result in life-threatening situations. To prevent these situations from happening, frequency response function measurements are essential to accurately characterise the resonant modes of the mechanical system. Unfortunately, these measurements are distorted by leakage and (long) transient phenomena. Local modelling techniques have been introduced in the past to resolve these complications but either they do not use the correct model structure or they introduce a bias. This paper proposes a local rational modelling technique which completely removes the bias from the estimation procedure and is applicable to large-scale multiple-input, multiple-output systems. The developed technique uses the bootstrapped total least squares estimator which provides unbiased estimates for the local rational model and generates accurate uncertainty bounds for the obtained non-parametric frequency response function. The proposed technique is successfully verified using a simulation example of a large-scale system which contains 100 resonances and has 100 inputs and 100 outputs. Its practical applicability is illustrated by characterising the resonant behaviour of the tailplane of a glider.