A system for detecting faults of an electric machine during operation of the electric machine, comprising: an interface configured to acquire signals via sensors with respect to the machine for an input time domain; a memory to store computer-implemented programs including a signal sampling program, a matrix formation program, an optimization formation program, a matrix pencil program, optimization solvers and lookup data including predetermined system parameters related to the faults; and a processor configured to perform the computer-implemented programs in connection with the interface and the memory, the system being characterized in that the processor in configured to perform: generating a signal Hankel matrix based on the acquired signals for the input time domain; forming an optimization problem with a low-rank constraint using the optimization formation program which generates a convex robust parameter estimation, CRPE, optimization problem or a non-convex robust parameter estimation, NRPE, optimization problem; demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of the optimization solvers; extracting parameters of damped exponentials from the low-rank matrix using the matrix pencil program; and determining the faults with respect to the electric machine by identifying each of measured system parameters of the electric machine based on the lookup data. an interface configured to acquire signals via sensors with respect to the machine for an input time domain; a memory to store computer-implemented programs including a signal sampling program, a matrix formation program, an optimization formation program, a matrix pencil program, optimization solvers and lookup data including predetermined system parameters related to the faults; and a processor configured to perform the computer-implemented programs in connection with the interface and the memory, the system being characterized in that the processor in configured to perform: generating a signal Hankel matrix based on the acquired signals for the input time domain; forming an optimization problem with a low-rank constraint using the optimization formation program which generates a convex robust parameter estimation, CRPE, optimization problem or a non-convex robust parameter estimation, NRPE, optimization problem; demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of the optimization solvers; extracting parameters of damped exponentials from the low-rank matrix using the matrix pencil program; and determining the faults with respect to the electric machine by identifying each of measured system parameters of the electric machine based on the lookup data. generating a signal Hankel matrix based on the acquired signals for the input time domain; forming an optimization problem with a low-rank constraint using the optimization formation program which generates a convex robust parameter estimation, CRPE, optimization problem or a non-convex robust parameter estimation, NRPE, optimization problem; demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of the optimization solvers; extracting parameters of damped exponentials from the low-rank matrix using the matrix pencil program; and determining the faults with respect to the electric machine by identifying each of measured system parameters of the electric machine based on the lookup data.