This paper presents an approach developed to quantify the chaotic behavior for the characterization of electromechanical systems. A technique named Signal Analysis based on Chaos using Density of Maxima (SAC-DM) is presented. This technique uses a simple peak counting algorithm in the time domain of the current signal to detect faults. To demonstrate the potential of SAC-DM, an experiment is presented where a small BLDC motor at different speeds, with a regular and an unbalanced propeller. The results demonstrated that the SAC-DM was able to detect the speed of the BLDC motor in 99.16% of the cases, and to identify the unbalanced system in 99.79% of the cases, when the speed is at 50%.

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.

We propose a dynamical way to set the process error covariance matrix (Q) for a constant velocity (CV) model Kalman filter. We are able to achieve the best possible solution for the estimated state, in the sense of forecast error, while significantly reducing the convergence time at no significant computational cost. No assumptions regarding the statistical nature of the observed process are made and no prior knowledge of the system is required. To achieve this, we adopt a recently proposed performance index for the Kalman filter, we map the best Q for an ample range of model deviations (accelerations) and dynamically set the best possible Q for the CV filter by identifying the average acceleration of the measured signal online. We demonstrate our scheme ability by filtering simulated trajectories with low, medium, and high signal-to-noise ratios. We also track a real erratic target and compare our filter prediction with the best possible a posteriori CV filter.

Brushless Direct Current (BLDC) motors have been used in a wide range of fields. In some critical applications, failures in these machines can cause operational disasters and cost lives if they are not detected in advance. The classical methods for detecting incipient faults in BLDC motors perform processing of the current signal to obtain the required information. In this work, the SAC-DM (Signal Analysis based on Chaos using Density of Maxima) technique is applied for the first time in the diagnosis of failures of electromechanical systems from sound signals. Wavelet Multiresolution Analysis (WMA) is used to separate a chaotic signal component from the sound emitted by the motor. This work demonstrates that it is feasible to perform dynamic eccentricity diagnosis in BLDC motors by identifying variations of the SAC-DM of the sound signal. The technique exposed in this work requires low computational cost and achieves high success rate. To validate the method, tests were carried out on a small BLDC motor normally used in Unmanned Aerial Vehicle (UAV), demonstrating the ability of the method to detect the speed of the motor in 95.89% of the cases and to detect eccentricity problems at a fixed speed in 88.34% of the cases.

The three-phase induction motor (TIM) is present in most industrial processes, being the main responsible for the electromechanical conversion in the sector. The total breakdown of these machines can compromise the production of entire sectors in a manufacturing environment, hence the need for early fault detection. In this context, broken bar failures are the most common on the TIM rotor. The present work analyzes the chaotic behavior of one stator current of a TIM, with different levels of broken rotor bar failures. The characterization of the failure is performed by analyzing the behavior of the chaotic variable called density of maxima. The proposed approach has advantages over classic Motor Current Signature Analysis techniques in that it does not require long acquisition windows (in this work it was possible to perform detection using a range of 0.35 s) and enables fault detection even for motors operating under variable load or with low slip. The technique also has a lower computational cost compared to classical detection methods. The obtained results indicate that the method is also able to identify different severity levels with the TIM under nominal load.