Data derived continuous time model for the Dst dynamics

Abstract

Understanding space weather and forecasting geomagnetic storms are the most important applications of solar‐terrestrial physics. Geomagnetic storms are complex sequences of physical processes, which include both microprocesses, (e.g., magnetic reconnection) and macroprocesses (relaxation of the ring current around the Earth, which is the main contributor to the geomagnetic storms). To derive a mathematical description of the magnetospheric dynamics from first principles the models of all processes involved should be conjugated into a global model. This goal will ultimately be accomplished. However the present level of understanding means that this will not happen in the foreseeable future. An alternative approach used here is based on system identification. A physically interpretable continuous time model capturing the magnetospheric dynamics has been identified directly from measurements of the solar wind and geomagnetic Dst index. It is shown that such a model can provide reliable forecasts of geomagnetic disturbances.

Data derived NARMAX Dst model

“…The average results from the 32 data sets for the NRMSE for the model (2) are not as good, however, the NRMSE for the data section shown in Fig. 3 returns better results than Zhu et al (2006), a NRMSE of 0.3375 for the MPO and 0.1420 for the OSA. The Temerin and Li (2006) model has an excellent MPO correlation coefficient of 0.956.…”

“…This gives an OSA correlation coefficient of 0.9899 which is higher than that of the model by Boaghe et al (2001). The model by Zhu et al (2006) was again only analysed on one data section of 1000 data points and returned the very good results of a NRMSE of 0.4194 for the MPO and 0.1755 for the OSA. The average results from the 32 data sets for the NRMSE for the model (2) are not as good, however, the NRMSE for the data section shown in Fig.…”

“…The Boaghe et al (2001) approach was generalized for multi input single output (MISO) models by Zhu et al (2007) and continuous time models by Zhu et al (2006).…”

Studying robot-environment interaction via transparent controllers

“…We argue that system identification, mathematical modeling of the dynamic behaviour of a robot, can be called in to scatter some of the shroud of mist on this complex interplay. Even though in other fields it has been applied prosperously to characterize many physical processes ( [12], [13], [14]), in robotics we see system identification used mainly in the area of robot calibration ( [16], [15]). However the potential is vast; for instance analyzing robot trajectories, or expressing input-output relationships for sensor-motor couplings, mapping motor commands to behaviour or even estimating robot position.…”

Multi‐input data derived Dst model

“…The most important parameter that affects the D st index is the product of the solar wind velocity and the southern component of the magnetic field V B s . Therefore if in the study of D st dynamics the magnetosphere is treated as a single‐input single‐output (SISO) dynamical system with D st as the output, it is the V B s parameter that is considered as the only system input [ Burton et al , 1975; O'Brien and McPherron , 2000; Boaghe et al , 2001; Zhu et al , 2006; Klimas et al , 1996]. Previously, the NARMAX approach has been implemented to derive both discrete and continuous time models [ Boaghe et al , 2001; Zhu et al , 2006].…”