Probabilistic Behavioural Modelling of Non-Linear Devices

Abstract

Behavioural device models are black-box models which depend only on measured data and are independent of the underlying physics behind the working of the device. Behavioural device models are widely used to model non-linear devices due to their computational convenience. Accurate models are useful for circuit and system designs to help minimise the design time and maximise the utility of simulations. In most of the behavioural models, the measured data are assumed to be ideal, while in actuality these measured data are subjected to errors. These errors can influence the modelling of the device and result in inaccurate predictions. In many cases, the measurement system can be designed to minimise measurement uncertainty and measurement errors, but measurements will also be subject to random errors due to environmental conditions. In the existing studies which include measurement errors in modelling, point estimates are estimated for the output responses of the Device Under Test (DUT). However, these point estimates do not reflect the reality that the input data are measured in the presence of uncertainties. In this work, a method to model non-linear devices with random errors is proposed. This method is based on the Bayesian probabilistic approach which gives probabilistic distributions for the model parameters and output responses of the DUT. Probabilistic distributions and credible regions for X-parameters are established by deriving probability distributions for the output responses of the DUT rather than point responses. Finally, the potential to use Bayesian Neural Networks (BNN) to achieve increased accuracy is proposed and examined.