Research on the Cooperative Detection of Stochastic Resonance and Chaos for Weak SNR Signals in Measurement While Drilling.

In the process of drilling, severe downhole vibration causes attitude measurement sensors to be erroneous; the errors will accumulate gradually during the inclination calculation. As a result, the ultimate well path could deviate away from the planned trajectory. In order to solve this problem, this paper utilized the stochastic resonance (SR) and chaos phase transition (CPT) produced by the second-order Duffing system to identify the frequency and estimate the parameters of the signal during measurement while drilling. Firstly, the idea of a variable-scale is introduced in order to reconstruct the frequency of the attitude measurement signal, and an SR frequency detection model based on a scale transformation Duffing system is established in order to meet the frequency limit condition of the SR. Then, an attitude measurement signal with a known frequency value is input into the Duffing chaos system, and the scale transformation is used again to make the frequency value meet the parameter requirement of chaos detection. Finally, two Duffing oscillators with different initial phases of their driving signal are combined in order to estimate the amplitude and phase parameters of the measurement signal by using their CPT characteristics. The results of the laboratory test and the field-drilling data demonstrated that the proposed algorithm has good immunity to the interference noise in the attitude measurement sensor, improving the solution accuracy of the inclination in a severe noise environment and thus ensuring the dynamic stability of the well trajectory.

A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics.

Many problems in the study of dynamical systems-including identification of effective order, detection of nonlinearity or chaos, and change detection-can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.