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

For high precision measurements, accelerometers need recalibration between different measurement occasions. In this paper we derive a simple calibration method for triaxial accelerometers with orthogonal axes. Just like previously proposed iterative methods, we compute the calibration parameters (biases and gains) from measurements of the Earth gravity for six different unknown orientations of the accelerometer. However, our method is non-iterative, so there are no complicated convergence issues depending on input parameters, round-off errors etc.The main advantages of our method are that only from the accelerometer output voltages it gives a complete knowledge of whether it is possible, with any method, to recover the accelerometer biases and gains from the output voltages, and when this is possible, we have a simple explicit formula for computing them with a smaller number of arithmetic operations than in previous iterative approaches. Moreover, we show that such successful recovery is guaranteed if the six calibration measurements deviate with angles smaller than some upper bound from a natural setup with two horizontal axes. We provide an estimate from below of this upper bound that, for instance, allows 5 degree deviations in arbitrary directions for the Colibrys SF3000L accelerometers in our lab. Similar robustness is also confirmed for even larger angles in Monte Carlo simulations of both our basic method and two different least square error extensions of it for more than six measurements. These simulations compare the sensitivities to noise and crossaxis interference. For instance, for 0.5 % cross-axis interference the basic method with six measurements, each with two horizontal axes, gave higher accuracy than allowing 10 degree deviation from horizontality and compensating with more measurements and least squares fitting.

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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.

Sensitivity-based Finite Element Model Updating (FEMU) is one of the widely accepted techniques used for damage identification in structures. FEMU can be formulated as a numerical optimization problem and solved iteratively making automatic updating of the uncertain model parameters by minimizing the difference between measured and analytical structural properties. However, in the presence of noise in the measurements, the updating results are usually prone to errors. This is mathematically described as instability of the damage identification as an inverse problem. One way to resolve this problem is by using regularization. In this paper we investigate regularization methods based on the minimization of the total variation of the uncertain model parameters and compare this solution with a rather frequently used regularization based on an interpolation technique. For well-localized damages the results show a clear advantage of the proposed solution in terms of the identified location and severity of damage compared with the interpolation based solution.For a practical test of the proposed method we use a reinforced concrete plate. Measurements and analysis were repeated first on an undamaged plate, and then after applying four different degrees of damage.

This article is a systematic overview of compression, smoothing and denoising techniques based on shrinkage of wavelet coefficients, and proposes (in Sections 5 and 6) an advanced technique for generating enhanced composite wavelet shrinkage strategies.

The input–output relationship of an accelerometer depends on parameters that are sensitive to temperature and air humidity. High accuracy field measurements therefore require simple in-field estimation of these parameters. We present an extension of a simple non-iterative six-parameter calibration method for triaxial accelerometers with orthogonal input axes to a nine-parameter method that also handles non-orthogonal axes and cross-axis interference. The method is based on measurements of the Earth gravity with the accelerometer placed at rest in at least nine different orientations. The main difference from previous work is that we derive necessary and sufficient conditions on the accelerometer output that tell whether calibration is possible, model the joint effect of non-orthogonal axes and cross-axis interference, provide closed form expressions for computing the parameter values and do a closer investigation and comparison of different ways to choose the accelerometer orientations for successful calibration. We compare two different setups, one called A90 − 450, which is based on 90° and 45° rotations of the accelerometer and one called Amax sep0 that has the maximized smallest angle between any two of the orientations. For the A90 − 450 setup we have constructed simple test equipment for quick positioning of the accelerometer. For the Amax sep0 setup, similar equipment is more complicated to construct, but equally simple to use. In Monte Carlo simulations with accelerometer orientations deviating at most D degrees from the desired A90 − 450 or Amax sep0 setup, equipment with D < 10° was enough for reliable calibration. For noise standard deviation typical for field measurements and for D up to 18°, our simulations showed slightly smaller errors for the Amax sep0 than for the A90 − 450 setup. The measurement errors after nine-parameter calibration were about 100 times smaller than those for six-parameter calibration both for the Amax sep0 setup and, as long as D ⩽ 13°, for the A90 − 450 setup. For the A90 − 450 setup, however, we found that combinations of large noise levels and/or large D can make six-parameter calibration the better choice.

We derive an efficient numerical algorithm for the analysis of certain classes of Hilbert-Schmidt operators that naturally occur in models of wireless radio and sonar communications channels.We show that many narrowband finite lifelength systems such as wireless radio communications can be well modelled by smooth and compactly supported spreading functions. Further, we exploit this fact to derive a fast algorithm for computing the matrix representation of such operators with respect to well time-frequency localized Gabor bases (such as pulseshaped OFDM bases). Hereby we use a minimum of approximations, simplifications, and assumptions on the channel. Moreover, ve use a multivariate setting to allow for applications to, for example, antenna arrays.The derived algorithm and software can be used, for example, for comparing how different system settings and pulse shapes affect the diagonalization properties of an OFDM system acting on a given channel.