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which determine the centre coordinate Fig1 work Architecture Applications of HDANN in Simultaneous Diagnosis of Multiple Faults Typical faults of rotating machines such as unbalance, rubbing, shaft crack, misalignment, oil whirl, rubbing whirl, bearing inaccuracy, and their posed forms of double and triple faults are considered in this section. Fault Data The various fault data were obtained by introducing physical faults on an test rig rotor system driven by an electric motor. The rotor is supported by journal bearings, and data are collected at the bearings in both the horizontal and vertical directions using displacement sensors. The rotor was held at a constant speed of 3000 rpm during sampling, and data was collected at a sampling frequency of KHz, with 1024 points being collected in each time sample. 1o 2o mo 1x 2x 3x mx Training and Testing Patterns for Neural Networks Taking the energy distribution of eight different frequency intervals from vibration spectra as feature vectors to calibrate various fault classes, the standard training patterns for Net1 are shown in Table 1. *F1–F7 denote the fault class of unbalance, rubbing, axis crack, misalignment, oil whirl, rubbing whirl and bearing inaccuracy, respectively. Much research has indicated that a work’s ability to generalise is seriously impaired if the input space is of high dimensionality, particularly when small amounts of training data are available. Much research has indicated that a work’s ability to generalise is seriously impaired if the input space is of high dimensionality, particularly when small amounts of training data are available. However, in condition monitoring applications largeamounts of fault data are extremely rare. The approach used here to deal with this problem is to assume that training samples to which random noise has been added are drawn from a kernel or Parzen–Rosenb estimate of the true training vector density function. Using this approach 200 groups of patterns for seven fault types were produced for training and testing of the works Network Training In HDANN, all subworks are ellipsoidal unit works with eight input units, the number of output units of various subworks is determined according to assigned fault classed. Each subwork is trained independently with 100 groups of patterns selected randomly from the 200 patterns for each fault type, using the learning algorithm described. Network Testing Results The testing process was carried out using the fault patterns not used during training. The total number of patterns for testing were therefore 7100 single fault patterns,21100