Discrete and continuous time signals Reactor noise and causality analysis BWR stability and dynamics a b s t r a c t This paper presents a first application of a novel Continuous and Structural Autoregressive Moving Average (CSARMA) modeling approach to BWR noise analysis. The CSARMA approach derives a unique representation of the system dynamics by more robust and reliable canonical models as basis for signal analysis in general and for reactor diagnostics in particular. In this paper, a stability event that occurred in a Swiss BWR plant during power ascension phase is analyzed as well as the time periods that preceded and followed the event. Focusing only on qualitative trends at this stage, the obtained results clearly indicate a different dynamical state during the unstable event compared to the two other stable periods. Also, they could be interpreted as pointing out a disturbance in the pressure control system as primary cause for the event. To benchmark these findings, the frequency-domain based signal transmission-path (STP) method is also applied. And with the STP method, we obtained similar relationships as mentioned above. This consistency between both methods can be considered as being a confirmation that the event was caused by a pressure control system disturbance and not induced by the core. Also, it is worth noting that the STP analysis failed to catch the relations among the processes during the stable periods, that were clearly indicated by the CSARMA method, since the last uses more precise models as basis.
We often use a discrete time vector autoregressive (DVAR) model to analyse continuous time, multivariate, linear Markov systems through their time series data sampled at discrete time steps. However, the DVAR model has been considered not to be structural representation and hence not to have bijective correspondence with system dynamics in general. In this paper, we characterize the relationships of the DVAR model with its corresponding structural vector AR (SVAR) and continuous time vector AR (CVAR) models through finite difference approximation of time differentials. Our analysis shows that the DVAR model of a continuous time, multivariate, linear Markov system bijectively corresponds to the system dynamics. Further we clarify that the SVAR and the CVAR models are uniquely reproduced from their DVAR model under a highly generic condition. Based on these results, we propose a novel Continuous time and Structural Vector AutoRegressive (CSVAR) modeling approach for continuous time, linear Markov systems to derive the SVAR and the CVAR models from their DVAR model empirically derived from the observed time series. We demonstrate its superior performance through some numerical experiments on both artificial and real world data.
A vector autoregressive model in discrete time domain (DVAR) is often used to analyze continuous time, multivariate, linear Markov systems through their observed time series data sampled at discrete timesteps. Based on previous studies, the DVAR model is supposed to be a noncanonical representation of the system, that is, it does not correspond to a unique system bijectively. However, in this article, we characterize the relations of the DVAR model with its corresponding Structural Vector AR (SVAR) and Continuous Time Vector AR (CTVAR) models through a finite difference method across continuous and discrete time domain. We further clarify that the DVAR model of a continuous time, multivariate, linear Markov system is canonical under a highly generic condition. Our analysis shows that we can uniquely reproduce its SVAR and CTVAR models from the DVAR model. Based on these results, we propose a novel Continuous and Structural Vector Autoregressive (CSVAR) modeling approach to derive the SVAR and the CTVAR models from their DVAR model empirically derived from the observed time series of continuous time linear Markov systems. We demonstrate its superior performance through some numerical experiments on both artificial and real-world data.
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