Niklas Grip

An Analysis Method for Sampling in Shift-Invariant Spaces

A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted 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 to derive both new results and relatively simple proofs of some previously known results. Among these are 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 x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.

A discrete model for the efficient analysis of time-varying narrowband communication channels

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, we 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.

Simple non-iterative calibration for triaxial accelerometers

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 Earths 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 from just 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° 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-squares error extensions of it for more than six measurements. These simulations compare the sensitivities to noise and cross-axis 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° deviation from horizontality and compensating with more measurements and least-squares fitting.

Non-iterative calibration for accelerometers with three non-orthogonal axes, reliable measurement setups and simple supplementary equipment

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.

A new generation of wavelet shrinkage: adaptive strategies based on composition of Lorentz-type thresholding and Besov-type non-threshold shrinkage

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

Sensitivity-based model updating for structural damage identification using total variation regularization

Abstract 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 unknown 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 compare a well established interpolation-based regularization method against methods based on the minimization of the total variation of the unknown model parameters. These are new regularization methods for structural damage identification. We investigate how using Huber and pseudo Huber functions in the definition of total variation affects important properties of the methods. For instance, for well-localized damages the results show a clear advantage of the total variation based regularization 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 performed first on an undamaged plate, and then repeated after applying four different degrees of damage.

Wavelet compression, data fitting and approximation based on adaptive composition of lorentz-type thresholding and besov-type non-threshold shrinkage

In this study we initiate the investigation of a new advanced technique, proposed in Section 6 of [3], for generating adaptive Besov–Lorentz composite wavelet shrinkage strategies We discuss some advantages of the Besov–Lorentz approach compared to firm thresholding.

Evaluation of prestress losses in prestressed concrete specimens subjected to freeze–thaw cycles

Prestressed concrete structures are considered to be reliable and durable. However, their long-term performance when subjected to frost attack is still unclear. In this work, experiments were carried out to evaluate the prestress losses in post-tensioned prestressed concrete specimens subjected to freeze–thaw cycles (FTCs). Two cases were considered: in one case, a series of specimens were prepared and tested in a freeze–thaw chamber; in the second case, the same series of specimens were tested in an indoor environment (outside the chamber). The difference between the prestress losses of the specimens inside the freeze–thaw chamber and those outside the chamber equalled the prestress losses due to FTCs. When using mathematical models to predict the prestress losses due to the FTCs, it was found that they were relatively small when the concrete was slightly damaged. However, they increased rapidly when the FTCs were repeated. The eccentricity of the prestress wires led to larger prestress losses when subjected to FTCs. Moreover, the same cross section and eccentricity resulted in similar prestress losses due to the FTCs, and the relatively high-strength concrete could withstand more FTCs.

Investigation of changes in modal characteristics before and after damage of a railway bridge: a case study

The linear, time-invariant transfer function has been utilised for the construction of frequency response function , based on the ambient vibration measurements. The results presented here indicated the possibility to identify and localise damages in steel railway bridges from the variations in the modal characteristics of the structure. The comparison between the modal characteristics for the healthy and collapsed bridge confirmed that damage had been existed. The abnormal percentage of change in modal damping, between the healthy and any other condition for a structure, can be regarded as a serious indicator for early stages of damage, while the high percentage of change in modal damping can clearly indicate the existence of damage in that structure. The average ratio of change in the damping ratio from the healthy to the collapsed bridge was about 206% and this ratio could be regarded as an index for the existence of a serious damage in steel bridges, which needs further evaluation in other test cases.

Protecting a five span prestressed bridge against ground deformations

A 50 year-old, 121.5 m long, five span prestressed bridge was situated in the deformation zone close to a mine in Kiruna in northern Sweden. There was a risk for uneven ground deformations so the bridge was analyzed and monitored. Results and measures taken to ascertain the robustness of the bridge are presented. The analysis resulted in an estimate that the bridge could sustain 24 mm in uneven horizontal and 83 mm in uneven vertical displacement of the two supports of a span. To be able to sustain larger deformations, the columns of the bridge were provided with joints, where shims could be inserted to counteract the settlements. To accomplish this, each one of the 18 columns of the bridge was unloaded by help of provisional steel supports. The column was then cut and a new foot was mounted to it. This made it possible to lift each individual column with two jacks, when needed, and to adjust its height by inserting or taking away shim plates. The deformations of the bridge and the surrounding ground were monitored. The eigenmodes of the bridge were studied with accelerometers and by analysis with finite elements (FE) models. Comparison indicated good agreement between the model and the actual bridge, with calculated eigenfrequencies of 2.17, 4.15 and 4.67 Hz, for the first transversal, vertical and torsional modes, respectively. Measurements during winter resulted in higher values due to increased stiffness caused by frozen materials.