Dynamic uncertainty evaluation of dynamic time series based on mixture density network

The dynamic measurement uncertainty is an important indicator to characterize dynamic measurement precision. A dynamic uncertainty evaluation method based on mixture density network (MDN) was proposed. The MDN is formed by combining the forward network which realizes the model parameters with the Gaussian mixture model. The dynamic measurement uncertainties were evaluated by taking a simulated stationary time series and the self-developed two-dimensional (2D) accelerometer as examples. A simulated stationary time series was input into the MDN model to verify the effectiveness of the proposed method. The predicted mean and standard deviation are basically consistent with the simulated mean and standard deviation. The mixed density network was also used to evaluate the dynamic mean and uncertainty of an accelerometer output signal. Time was used as the network input and the measured signal of the accelerometer was used as the network output to predict the change trend of the measured signal. Then，the dynamic measurement uncertainty model of the accelerometer was obtained. The mean values of the uncertainties for the X-axis and Y-axis are 0.0095 mm/s² and 0.0038 mm/s², respectively. The measured signals of X-axis and Y-axis are 97.6% and 98.4% within the envelope of uncertainty, respectively. The simulated results and the experimental results show that the proposed method for dynamic uncertainty evaluation can reliably evaluate the dynamic measurement uncertainty.