In this thesis, after introducing the fault diagnosis methods based on the vibration analysis in three domain (time, frequency, time-frequency), we use these techniques on the helicopter intermediate gearbox. In the time domain, Eigenvalues of the covariance matrix from accelerometer (in three axis) using Principle Component Analysis (PCA), Histograms of autocorrelation functions, and high order statistical moments extracted as the meaningful features and these features used in the feature vector to justify; TEXT-INDENT: 14.2pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-layout-grid-align: none" A method of detecting transients in mechanical systems by matching wavelets with associated signal is proposed, leading to a development of joint time-frequency-scale distribution. The three variables, the time, frequency and scale, have maximized the chance for finding similar signal segments from a system under iection. The Fourier transform (FT) represents a signal by a family of complex exponents with infinite time duration. Therefore, FT is useful in identifying harmonic signals. However, due to its constant time and frequency resolutions, it is weak in analyzing transitory signals. So, the time-frequency analysis is more sensitive and more exact than time domain and frequency domain analysis to detect transient signals due to breakage shock pulses. Also we analyze the vibration signals based on the Short Time Fourier Transform (STFT) and Wigner – Ville Distribution WVD. The results show that Daubuchi bases in the wavelet packet transform is better than morlet bases because of the orthogonality advantages of the Daubuchi bases rather than morlet bases. Also, the results show that Daubuchi 33 and Daubuchi 44 wavelets are the best mother wavelets to analyze the gearbox vibration signals. After feature extraction, we use Principle Component Analysis to decrease the dimensionality of the feature space. Finally, the feature vectors justify; TEXT-INDENT: 14.2pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-layout-grid-align: none" The SVM tries to orient the boundary such that the distance between the boundary and the nearest data point in each left; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" align=left Keywords: Fault Diagnosis, Vibration Analysis, Wavelet Packet Transform, Support Vector Machine .