The Application Of Singular Value Decomposition In Weak Signal Detection

In the early fault stage of mechanical equipment, the damage caused by fault isweak, thus, vibration signals obtained by sensors generally consist of feeble featuresignal of failure and abundant of interference noise. Unfortunately, the disturbance ofstrong noise makes the extraction of feature signal rather difficult. Consequently, thisthesis conducts research on techniques of detecting and extracting weak characteristicsignal in the incipient phase of device failure.Singular value decomposition (SVD) is a nonlinear filtering method and isextensively applied to de-noise and detection of signal. Signal component is reservedwhile noise component is largely eliminated with the use of SVD to reduce dimensionof signal matrix. However, this method requires that the first kth singulars selected toform reduced matrix correspond precisely to signal component. If this correspondencefails, regular SVD will therefore lose its efficacy. To deal with the problem of losingeffectiveness of SVD in extremely low Signal-to-Noise ratio (SNR), this thesispresents a new method of SVD based on component signal. This method firstconstructs one-dimensional signal into high-dimensional space, then differentdistribution patterns of correlation matrix of can be achieved. According to standarddeviations of singular vectors, subspace which preserves relatively large concentrationof signal part and reduces noise part markedly can be found. Hence, the goal of noisereduction and signal detection is accomplished. Simulation validates the effectivenessof this method.Stochastic resonance (SR) is occurred in the nonlinear system and utilizessynergistic effect of signal, noise and nonlinear system to enhance the weak signal, sosignal is detected with improved SNR. However, nonlinear system used in stochasticresonance has a range requirement of SNR, that is to say, if the SNR is lower thanthreshold of nonlinear system, then it’s impossible to realize SR. For this issue, amethod based on component signal and stochastic resonance is proposed. This methodprocesses component signals using bi-stable system so as to gain SR response. Withinthe response, the detection of weak characteristic signal submerged in a heavybackground noise is realized.Rolling bearing is one of the components where failures tend to happen inmechanical equipment. Actually, when operating, the bearing is accompanied byheavy background noise, that is to say, bearing failure is unlikely to be discovered until it develops to a certain degree. This is harmful for equipment’s normal operating.For purpose of diagnosing incipient fault of a rolling bearing, an approach using themethod of component-envelope signal is presented. Component signals are firstlycalculated by SVD and then Hilbert Transform is applied to each component signal toobtain envelope spectrum. From envelope spectrum, the incipient fault feature ofrolling bearing can be detected obviously. Both simulation and engineeringexperimental results prove the effectiveness of the proposed method.