On weak unsteady signal detection using statistical tests

Two statistical tests, namely the Jarque–Bera and the D’Agostino tests, originally adopted for checking data normality are used to recover the initialization of an exponentially growing wave embedded inside a stationary background noise in the present investigation both numerically and experimentally. Such type of signal is very important especially in building services engineering where the early detection of very small alien signals in the systems is crucial to the smooth operation of a heavily serviced building. The effects of the background noise magnitude on the accuracy of the recovery process are examined. The numerical simulation results show that these statistical tests are very sensitive to the change incurred by the wave to the background noise statistics and they are very helpful in locating the instant of the wave initialization even when the signal-to-noise ratio drops to −30 dB. A new parameter derived from the parameters of these two statistical tests, which is easy to compute, is proposed and its performance is found to be better than those of the two tests. It is also demonstrated that the performance of the new parameter does not depend much on the background noise. The experimental results are in line with the numerical simulations.

► Two statistical normality tests are used to analyse exponentially growing waves embedded in a stationary background noise.
► The effects of the background noise magnitude on the accuracy of the analysis are examined.
► The tests are helpful in locating the wave initialization instant even when the signal-to-noise ratio drops to −30 dB.
► A new parameter is derived and its performance is found to be better than those of the two tests.
► Experimental results are in line with numerical simulations.