The paper deals with a method of constructing orthonormal bases of coordinates which maximize, through redundant dictionaries (frames) of biorthogonal bases, a class separability index or distances among classes. The method proposes an algorithm which consists of biorthogonal expansions over two redundant dictionaries. Embedded classes are often present in multiclassification problems. It is shown how the biorthogonality of the expansion can really help to construct a coordinate system which characterizes the classes. The algorithm is created for training wavelet networks in order to provide an efficient coordinate system maximizing the Cross Entropy function between two complementary classes. Sine and cosine wavelet packets are basis functions of the network. Thanks to their packet structure, once selected the depth of the tree, an adaptive number of basis functions is automatically chosen. The algorithm is also able to carry out centering and dilation of the basis functions in an adaptive way. The algorithm works with a preliminary extracted feature through shrinkage technique in order to reduce the dimensionality of the problem. In particular, our attention is pointed out for time-frequency monitoring, detection and classification of transients in rail vehicle systems and the outlier problem. In the former case the goal is to distinguish transients as inrush current and no inrush current and a further distinction between the two complementary classes: dangerous inrush current and no dangerous inrush current. The proposed algorithm is used on line in order to recognize the dangerous transients in real time and thus shut-down the vehicle. The algorithm can also be used in a general application of the outlier detection. A similar structure is used in developed algorithms which are currently integrated in the inferential modeling platform of the unit responsible for Advanced Control and Simulation Solutions within ABB's (Asea Brown Boveri) industry division. It is shown how impressive and rapid performances are achieved with a limited number of wavelets and few iterations. Real applications using real measured data are included to illustrate and analyze the effectiveness of the proposed method.