Major Assignments

In this work, we propose a generalized framework for real-time tracking of multiple time-varying sinusoidal frequencies of a non-stationary signal. The non-stationary signal is modeled as a time-varying autoregressive (TVAR) process. A non-linear state-space model is formed to truly represent the TVAR process, considering the frequencies as state variables. We have defined the observation and its Jacobian by the modified roots of a polynomial formed by the state variables. Numerical derivatives have been substituted by the analytic form of the Jacobian matrix for improved numerical accuracy. A constrained Kalman filter is then applied for real-time tracking of the frequencies. We have compared the statistical performance of the proposed method with four other established methods using Monte-Carlo simulations. The proposed method is found to have superior error performance under different conditions of chirp-rate, resolution, noise variance, and abrupt changes in frequency. Additionally, we have taken the bat echolocation signal, gravitational waves of a binary black hole merger, and supply frequency of a three-phase squirrel cage induction motor as practical examples to demonstrate the applicability and efficacy of the proposed method in real-world scenarios.

We propose a single vibration sensor-based method for detecting incipient faults in squirrel cage induction motors (SCIM). We consider defects in different parts of the bearing (inner raceway, outer raceway, cage train, and rolling element) as well as in a single bar of the rotor. The vibration signal is dominated by the fundamental rotational frequency and its harmonics. The dominant components result in numerical errors while estimating the relatively indistinct fault-specific spectral components. We precondition the vibration signal by suppressing multiple dominant components using an extended Kalman filter-based method. The suppression of the dominant components reduces the spectral leakage, exposes minute fault components, and improves the overall amplitude estimation. Subsequently, we estimate the fault frequency and amplitude using an accurate and low-complexity Rayleigh-quotient based spectral estimator. The thresholds for fault detection are determined from a small number of healthy data, and an adaptive minimum distance-based detector is used for hypothesis testing. The proposed test improves detection and reduces false alarm under noisy conditions. We test the complete algorithm using data from a 22-kW SCIM lab-setup. The proposed method has achieved 100% accuracy with the publicly available 12 kHz drive-end bearing data from Case Western Reserve University.

The eigenvalue of a symmetric matrix with known eigenvector can be approximated by using the theory of Rayleigh quotients. the eigenvalues of the autocorrelation matrix corresponding to the signal eigenvectors obtained from the Rayleigh quotients can give vital information about the sinusoidal amplitude present. The mean square error (MSE) between the input sinusoidal frequency and the location of the peak obtained from the respective spectral estimator is evaluated by multiple montecarlo simulations. It is inferred that MUSIC and the proposed spectral estimator have slightly higher accuracy for similar data length when compared to DFT. It is found that the performance of the proposed spectral estimator in a noisy environment is quite robust and is equivalent to that of MUSIC and is quite better than DFT. Unlike MUSIC, the Rayleigh-quotient spectrum can estimate the amplitude of constituent frequency components and is also faster than MUSIC, without requiring any information about the model order.

Fault modeling is essential for testing condition monitoring system of the induction motors. This helps in generating conditions that are difficult to emulate in experimental setup and hence can be used to test and validate the fault detector under different operating conditions. In this work we develop a real-time fault simulator of the induction motor from existing mathematical models. For developing the simulator, modeling was carried out with coupled circuit modeling (CCM) technique and was developed in Simulink. Various faults that arise in an actual motor under different operating conditions can be incorporated in this model. This modeling technique is based on winding function approach that can be used for any arbitrary winding layout. The parameters of the motor are derived from geometry and the winding arrangement. An embedded platform is developed for implementation of the fault simulator. This platform is loaded with the DOS based real-time kernel known as Simulink Real-time (SLRT). The mathematical model is developed in Simulink and an executable code is generated from it. Once generated, the executable code was run on a developed platform. Faults like broken rotor bar, broken end ring, and eccentricity were modelled apart from a healthy motor condition. The model is fully functional for all the three type of eccentricity faults: the static, the dynamic and the mixed conditions.

The embedded hardware development has evolved and matured. We started the with a single board computer built inhouse. The system is capable of taking analog signals as input and can display the results in real-time. The real-time kernal of Simulink Realtime was used to implement the algorithms for embedded solutions. For portable solutions we switched to a Raspberry Pi. Eventually, we also used an android-based mobile device to capture the motor vibrations for fault detection using the inbuilt accelerometer. Currently, we are working towards developing an IoT-based solutions for monitoring multiple motors simultanaously. The IoT-based framework is given below: