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In this paper we derive and compare several different vibration analysis techniques for automatic detection of local defects in bearings.Based on a signal model and a discussion on to what extent a good bearing monitoring method should trust it, we present several analysis tools for bearing condition monitoring and conclude that wavelets are especially well suited for this task. Then we describe a large-scale evaluation of several different automatic bearing monitoring methods using 103 laboratory and industrial environment test signals for which the true condition of the bearing is known from visual inspection. We describe the four best performing methods in detail (two wavelet-based, and two based on envelope and periodisation techniques). In our basic implementation, without using historical data or adapting the methods to (roughly) known machine or signal parameters, the four best methods had 9-13% error rate and are all good candidates for further finetuning and optimisation. Especially for the wavelet-based methods, there are several potentially performance improving additions, which we finally summarise into a guiding list of suggestion. r

A subspace V of L 2 (R) is called shift-invariant if it is the closed linear span of integershifted copies of a single function.As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method for deriving both new results and relatively simple proofs of some previously known results. Among these are both some results of rather general nature and some more specialized results for B-spline wavelets.The main problem under study is to find a shift x 0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f (x 0 + k + δ k )) k∈Z , either when all δ k = 0 or in the irregular sampling case with an upper bound sup k |δ k | < δ.

We prove some reiteration formulas for the Cobos-Peetre polygon method for n 1-tuples that consists of spaces A i where A i is of class i with respect to a compatible pair X Y Y . If i is suitably chosen the J-and K-method coincides and is equal to a space X Y Y #Yq . For arbitrarily chosen i the J-and K-spaces will not, in general, coincide. In particular we show that interpolation of Lorentz spaces over the unit square yields that the K-space is the sum of two Lorentz spaces whereas the J-space is the intersection of the same two Lorentz spaces.

We give necessary and sufficient conditions on a general cone of positive functions to satisfy the Decomposition Property (DP) introduced in [5] and connect the results with the theory of interpolation of cones introduced by Sagher [9]. One of our main result states that if Q satisfies DP or equivalently is divisible, then for the quasi-normed spaces £ 0 and £,, (2n £", en £,).., = en(£?. £?),.,.where £« = {/; Qf e £} with Qf = inf{ 9 6 Q; \f\ < g\.According to this formula, it yields that the interpolation theory for divisible cones can be easily obtained from the classical theory.1991 Mathematics subject classification: 46M35.