Non-negative Least-square Algorithm Research Articles

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

Accelerated construction of projection-based reduced-order models via incremental approaches

We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov–Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.

Myelin water imaging at 0.55 T using a multigradient-echo sequence.

To investigate the prospects of a multigradient-echo (mGRE) acquisition for in vivo myelin water imaging at 0.55 T. Scans were performed on the brain of four healthy volunteers at 0.55 and 3 T, using a 3D mGRE sequence. The myelin water fraction (MWF) was calculated for both field strengths using a nonnegative least squares (NNLS) algorithm, implemented in the qMRLab suite. The quality of these maps as well as single-voxel fits were compared visually for 0.55 and 3 T. The obtained MWF values at 0.55 T are consistent with previously reported ones at higher field strengths. The MWF maps are a considerable improvement over the ones at 3 T. Example fits show that 0.55 T data is better described by an exponential model than 3 T data, making the assumed multi-exponential model of the NNLS algorithm more accurate. This first assessment shows that mGRE myelin water imaging at 0.55 T is feasible and has the potential to yield better results than at higher fields.

A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing

Abstract. Optical remote sensing (ORS) combined with the computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over an area under investigation. Whereas medical CT usually uses a beam number of hundreds of thousands, ORS-CT usually uses a beam number of dozens, thus severely limiting the spatial resolution and the quality of the reconstructed map. The smoothness a priori information is, therefore, crucial for ORS-CT. Algorithms that produce smooth reconstructions include smooth basis function minimization, grid translation and multiple grid (GT-MG), and low third derivative (LTD), among which the LTD algorithm is promising because of the fast speed. However, its theoretical basis must be clarified to better understand the characteristics of its smoothness constraints. Moreover, the computational efficiency and reconstruction quality need to be improved for practical applications. This paper first treated the LTD algorithm as a special case of the Tikhonov regularization that uses the approximation of the third-order derivative as the regularization term. Then, to seek more flexible smoothness constraints, we successfully incorporated the smoothness seminorm used in variational interpolation theory into the reconstruction problem. Thus, the smoothing effects can be well understood according to the close relationship between the variational approach and the spline functions. Furthermore, other algorithms can be formulated by using different seminorms. On the basis of this idea, we propose a new minimum curvature (MC) algorithm by using a seminorm approximating the sum of the squares of the curvature, which reduces the number of linear equations to half that in the LTD algorithm. The MC algorithm was compared with the non-negative least square (NNLS), GT-MG, and LTD algorithms by using multiple test maps. The MC algorithm, compared with the LTD algorithm, shows similar performance in terms of reconstruction quality but requires only approximately 65 % the computation time. It is also simpler to implement than the GT-MG algorithm because it directly uses high-resolution grids during the reconstruction process. Compared with the traditional NNLS algorithm, it shows better performance in the following three aspects: (1) the nearness of reconstructed maps is improved by more than 50 %, (2) the peak location accuracy is improved by 1–2 m, and (3) the exposure error is improved by 2 to 5 times. Testing results indicated the effectiveness of the new algorithm according to the variational approach. More specific algorithms could be similarly further formulated and evaluated. This study promotes the practical application of ORS-CT mapping of atmospheric chemicals.

Developments in waveform unfolding of PMT signals in future IceCube extensions

Waveform unfolding, in which photomultiplier tube signals are expressed as a linear combination of single-photoelectron waveforms, is a useful processing method both for analysis and for data compression in the IceCube Neutrino Observatory. This processing is currently only possible with a cluster of computers on the surface, but improvements in embedded technology will make it possible to move this unfolding inside the digital optical modules for planned extensions of IceCube such as IceCube-Gen2. In order to meet power constraints, waveform unfolding is most efficiently implemented with field programmable gate arrays (FPGA). A non-negative least squares (NNLS) algorithm developed for use with FPGAs was modified to reproduce the results of the Lawson-Hanson NNLS algorithm that is currently used for waveform unfolding in IceCube. High Level Synthesis (HLS) tools were used to synthesize firmware directly from C code. This proceeding discusses the structure and performance of the modified NNLS algorithm that was developed, and demonstrates what can be accomplished with new FPGA synthesis tools.

SGSD: A novel Sequential Gamma-ray Spectrum Deconvolution algorithm

A novel approach for analyzing complex gamma-ray spectra using a sequential algorithm is introduced. The developed Sequential Gamma-ray Spectrum Deconvolution (SGSD) algorithm produces a sequence of spectra converging to the best estimation of output spectrum of a gamma-ray detector. In each point of sequence, an isotope of unknown gamma-ray source is identified and the respective response of the detector to unknown source is reconstructed. Effectiveness of the developed algorithm is demonstrated by two empirical and simulation studies. In the case of empirical study, a number of recorded gamma-ray spectra related to a mixed gamma-ray source including different combinations of 5 isotopes (Co-60, Cs-137, Na-22, Eu-152 and Am-241) are analyzed using whole information of spectra. Furthermore, a number of simulated gamma-ray spectra related to a mixed gamma-ray source including different combinations of 30 isotopes are analyzed in simulation study. Both man-made and natural radioisotopes like Ba-133, Co-60, Ir-192, Cs-137, K-40, Th-232 series, U-238 series, Ac-227 series, etc. are used for Monte Carlo simulations. The numerical results of the SGSD algorithm are compared with those of the conventional Non-Negative Least Squares (NNLS) algorithm. Based on the results, the identification procedure of the SGSD algorithm has a remarkable superiority over the NNLS algorithm.

A method for inversion of 1D vertical soundings of gravity anomalies

We have developed a method to interpret potential fields, which obtains 1D models by inverting vertical soundings of potential field data. The vertical soundings are built through upward continuation of potential field data, measured on either a profile or a surface. The method assumes a forward problem consisting of a volume partitioned in layers, each of them homogeneous and horizontally finite, but with the density changing versus depth. The continuation errors, increasing with the altitude, are automatically handled by determining the coefficients of a third-order polynomial function of the altitude. Due to the finite size of the source volume, we need a priori information about the total horizontal extent of the volume, which is estimated by boundary analysis and optimized by a Markov chain process. For each sounding, a 1D inverse problem is independently solved by a nonnegative least-squares algorithm. Merging of the several inverted models finally yields approximate 2D or 3D models that are, however, shown to generate a good fit to the measured data. The method is applied to synthetic models, producing good results for either perfect or continued data. Even for real data, i.e., the gravity data of a sedimentary basin in Nevada, the results are interesting, and they are consistent with previous interpretation, based on 3D gravity inversion constrained by two gamma-gamma density logs.

Process Analytical Approach towards Quality Controlled Process Automation for the Downstream of Protein Mixtures by Inline Concentration Measurements Based on Ultraviolet/Visible Light (UV/VIS) Spectral Analysis.

Downstream of pharmaceutical proteins, such as monoclonal antibodies, is mainly done by chromatography, where concentration determination of coeluting components presents a major problem. Inline concentration measurements (ICM) by Ultraviolet/Visible light (UV/VIS)-spectral data analysis provide a label-free and noninvasive approach to significantly speed up the analysis and process time. Here, two different approaches are presented. For a test mixture of three proteins, a fast and easily calibrated method based on the non-negative least-squares algorithm is shown, which reduces the calibration effort compared to a partial least-squares approach. The accuracy of ICM for analytical separations of three proteins on an ion exchange column is over 99%, compared to less than 85% for classical peak area evaluation. The power of the partial least squares algorithm (PLS) is shown by measuring the concentrations of Immunoglobulin G (IgG) monomer and dimer under a worst-case scenario of completely overlapping peaks. Here, the faster SIMPLS algorithm is used in comparison to the nonlinear iterative partial least squares (NIPALS) algorithm. Both approaches provide concentrations as well as purities in real-time, enabling live-pooling decisions based on product quality. This is one important step towards advanced process automation of chromatographic processes. Analysis time is less than 100 ms and only one program is used for all the necessary communications and calculations.

Hyperspectral and panchromatic image fusion through an improved ratio enhancement

The goal of ratio enhancement for hyperspectral (HS) image pansharpening is to obtain an enhancement ratio between a simulated low-resolution panchromatic (Pan) image and an original high-resolution Pan image. However, the simulated low-resolution Pan image often suffers from gray-level distortion. To solve these problems, the original HS bands are synthesized to a smaller number of reduced HS bands, then the pixels of Pan and HS images are divided into different groups according to the linearity between the Pan band and the reduced bands. For each pixel group, a nonnegative least-squares algorithm is utilized to calculate the weights of reduced HS bands, so that the simulated Pan image is obtained by weighted summation of reduced HS bands. Finally, the HS image is sharpened by a ratio enhancement. The experiments demonstrated that the proposed method had a good performance on fusion quality.

TNT-NN: A Fast Active Set Method for Solving Large Non-Negative Least Squares Problems

In 1974 Lawson and Hanson produced a seminal active set strategy to solve least-squares problems with non-negativity constraints that remains popular today. In this paper we present TNT-NN, a new active set method for solving non-negative least squares (NNLS) problems. TNT-NN uses a different strategy not only for the construction of the active set but also for the solution of the unconstrained least squares sub-problem. This results in dramatically improved performance over traditional active set NNLS solvers, including the Lawson and Hanson NNLS algorithm and the Fast NNLS (FNNLS) algorithm, allowing for computational investigations of new types of scientific and engineering problems.For the small systems tested (5000 × 5000 or smaller), it is shown that TNT-NN is up to 95 × faster than FNNLS. Recent studies in rock magnetism have revealed a need for fast NNLS algorithms to address large problems (on the order of 105 × 105 or larger). We apply the TNT-NN algorithm to a representative rock magnetism inversion problem where it is 60× faster than FNNLS. We also show that TNT-NN is capable of solving large (45000 × 45000) problems more than 150 × faster than FNNLS. These large test problems were previously considered to be unsolvable, due to the excessive execution time required by traditional methods.

A New Strategy for Fast MRI-Based Quantification of the Myelin Water Fraction: Application to Brain Imaging in Infants.

The volume fraction of water related to myelin (fmy) is a promising MRI index for in vivo assessment of brain myelination, that can be derived from multi-component analysis of T1 and T2 relaxometry signals. However, existing quantification methods require rather long acquisition and/or post-processing times, making implementation difficult both in research studies on healthy unsedated children and in clinical examinations. The goal of this work was to propose a novel strategy for fmy quantification within acceptable acquisition and post-processing times. Our approach is based on a 3-compartment model (myelin-related water, intra/extra-cellular water and unrestricted water), and uses calibrated values of inherent relaxation times (T1c and T2c) for each compartment c. Calibration was first performed on adult relaxometry datasets (N = 3) acquired with large numbers of inversion times (TI) and echo times (TE), using an original combination of a region contraction approach and a non-negative least-square (NNLS) algorithm. This strategy was compared with voxel-wise fitting, and showed robust estimation of T1c and T2c. The accuracy of fmy calculations depending on multiple factors was investigated using simulated data. In the testing stage, our strategy enabled fast fmy mapping, based on relaxometry datasets acquired with reduced TI and TE numbers (acquisition <6 min), and analyzed with NNLS algorithm (post-processing <5min). In adults (N = 13, mean age 22.4±1.6 years), fmy maps showed variability across white matter regions, in agreement with previous studies. In healthy infants (N = 18, aged 3 to 34 weeks), asynchronous changes in fmy values were demonstrated across bundles, confirming the well-known progression of myelination.

Does hydration status affect MRI measures of brain volume or water content?

To determine whether differences in hydration state, which could arise from routine clinical procedures such as overnight fasting, affect brain total water content (TWC) and brain volume measured with magnetic resonance imaging (MRI). Twenty healthy volunteers were scanned with a 3T MR scanner four times: day 1, baseline scan; day 2, hydrated scan after consuming 3L of water over 12 hours; day 3, dehydrated scan after overnight fasting of 9 hours, followed by another scan 1 hour later for reproducibility. The following MRI data were collected: T2 relaxation (for TWC measurement), inversion recovery (for T1 measurement), and 3D T1 -weighted (for brain volumes). Body weight and urine specific gravity were also measured. TWC was calculated by fitting the T2 relaxation data with a nonnegative least-squares algorithm, with corrections for T1 relaxation and image signal inhomogeneity and normalization to ventricular cerebrospinal fluid. Brain volume changes were measured using SIENA. TWC means were calculated within 14 tissue regions. Despite indications of dehydration as demonstrated by increases in urine specific gravity (P = 0.03) and decreases in body weight (P = 0.001) between hydrated and dehydrated scans, there was no measurable change in TWC (within any brain region) or brain volume between hydration states. We demonstrate that within a range of physiologic conditions commonly encountered in routine clinical scans (no pretreatment with hydration, well hydrated before MRI, and overnight fasting), brain TWC and brain volumes are not substantially affected in a healthy control cohort. J. Magn. Reson. Imaging 2016;44:296-304.

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis

ObjectTo assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg–Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. Materials and MethodsMRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. ResultsThe NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10−3mm2/s), D*=28±9 (10−3mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10−3mm2/s), D*=63±145 (10−3mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. ConclusionThe IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior.

Source process and tectonic implication of the January 20, 2007 Odaesan earthquake, South Korea

The source process for the 20th of January 2007, Mw 4.5 Odaesan earthquake in South Korea is investigated in the low- and high-frequency bands, using velocity and acceleration waveform data recorded by the Korea Meteorological Administration Seismographic Network at distances less than 70km from the epicenter. Synthetic Green functions are adopted for the low-frequency band of 0.1–0.3Hz by using the wave-number integration technique and the one dimensional velocity model beneath the epicentral area. An iterative technique was performed by a grid search across the strike, dip, rake, and focal depth of rupture nucleation parameters to find the best-fit double-couple mechanism. To resolve the nodal plane ambiguity, the spatiotemporal slip distribution on the fault surface was recovered using a non-negative least-square algorithm for each set of the grid-searched parameters. The focal depth of 10km was determined through the grid search for depths in the range of 6–14km. The best-fit double-couple mechanism obtained from the finite-source model indicates a vertical strike-slip faulting mechanism. The NW faulting plane gives comparatively smaller root-mean-squares (RMS) error than its auxiliary plane. Slip pattern event provides simple source process due to the effect of Low-frequency that acted as a point source model. Three empirical Green functions are adopted to investigate the source process in the high-frequency band. A set of slip models was recovered on both nodal planes of the focal mechanism with various rupture velocities in the range of 2.0–4.0km/s. Although there is a small difference between the RMS errors produced by the two orthogonal nodal planes, the SW dipping plane gives a smaller RMS error than its auxiliary plane. The slip distribution is relatively assessable by the oblique pattern recovered around the hypocenter in the high-frequency analysis; indicating a complex rupture scenario for such moderate-sized earthquake, similar to those reported for large earthquakes.

A non-monotonic method for large-scale non-negative least squares

We present a new algorithm for solving the non-negative least-squares (NNLS) problem. Our algorithm extends the unconstrained quadratic optimization algorithm of Barzilai and Borwein (BB) [J. Barzilai and J. M. Borwein; Two-Point Step Size Gradient Methods. IMA J. Numer. Anal. 1988.] to handle nonnegativity constraints. Our extension differs from other constrained BB variants in simple but crucial aspects, the most notable being our modification to the BB stepsize itself. Our stepsize computation takes into account the nonnegativity constraints, and is further refined by a stepsize scaling strategy. These changes, in combination with orthogonal projections onto the nonnegative orthant, yield an effective NNLS algorithm. We compare our algorithm with several competing approaches, including established bound-constrained solvers, popular BB-based methods, and also a specialised NNLS algorithm. On several synthetic and real-world datasets our method displays highly competitive empirical performance.

Evaluating the performance of the horizontal radial plume mapping technique for locating multiple plumes

This paper evaluated the feasibility of using the horizontal radial plume mapping (HRPM) technique to locate multiple emission sources via computational simulation. Seventy-two test maps, each having two Gaussian distributions, were generated in a two-dimensional domain. The HRPM technique with the non-negative least square (NNLS) algorithm was then applied to reconstruct the plumes, assuming a nine-beam scanning beam geometry. The NNLS algorithm successfully reconstructed the source locations of 68 of the 72 test maps. However, when one of the plumes was near the origin, the NNLS did not always identify the peak locations correctly. Furthermore, when the two plumes were spaced closely, the NNLS tended to reconstruct a wide plume covering both plumes instead of separating them due to the resolution limitation of the current nine-beam geometry. In the sensitivity analysis, five sets of random error (1%, 5%, 10%, 20%, and 30%) were added in the path-integrated concentration (PIC) from the 72 test maps, and thus, an additional 360 reconstructions were implemented. Robust results were obtained when the noise added was less than 20%. The results generally support the implementation of the NNLS algorithm in the HRPM technique as described in the U.S. Environmental Agency (EPA) Other Test Method 10 (OTM-10). Implications: The methodology evaluated in this paper provides near-real-time estimates about the locations of multiple emission sources. The involved optical remote sensing instruments can monitor large spatial areas (e.g., landfills) in a cost-effective way. Supplementary Materials: Supplementary materials are available for this paper. Go to the publisher's online edition of the Journal of the Air & Waste Management Association for three failed cases of narrow plumes and examples of the translated grids.

Comparisons of radial plume mapping algorithms for locating gaseous emission sources

This paper presents the simulation and field evaluation results for two mathematical algorithms applied in the horizontal radial plume mapping (HRPM) technique with optical remote sensing instruments. In the simulation study, 450 test maps with skewed distributions (i.e., bivariate lognormal distribution) were generated in a two-dimensional domain. The HRPM techniques with the smooth basis function minimization (SBFM) algorithm and non-negative least square (NNLS) algorithm were then applied to reconstruct the plumes, assuming a nine-beam scanning beam geometry. The SBFM algorithm was able to identify the peak locations better than the NNLS algorithm when the plumes were near the origin. On the other hand, the NNLS performed better when the plumes were away from the origin. In the field validation study, four experiments were conducted in an open space with the same nine-beam geometry. In each experiment, two tracer gases were released simultaneously at two different locations, and an OP-FTIR was set up to collect the IR spectra. The collected path-integrated concentration data were then used to reconstruct the source locations. The results confirm the conclusions obtained in the simulation study of a better performance from the SBFM algorithm than from the NNLS algorithm for plumes near the origin. We also developed a screening criterion to determine which algorithm results should be chosen as the final estimates in future field applications.

Monitoring of Biochemical Changes through the C6 Gliomas Progression and Invasion by Fourier Transform Infrared (FTIR) Imaging

We have investigated the spatial distribution of molecular changes associated with C6 glioma progression using Fourier transform infrared (FT-IR) microspectro-imaging in order to determine spectroscopic markers for early diagnosis of tumor growth. Our results showed that at day 7 after tumor implantation, FTIR investigations displayed a very small abnormal zone associated with the proliferation of C6 cells in the caudate putamen. From this day, rats developed solid and well-circumscribed tumors and invasive areas. The volume of peritumoral areas increased rapidly until day 19. The maturation of the tumor was accompanied by a diminution in its proliferative and invasive area. The presence of necrotic areas was visible from day 15. A non-negative least-squares algorithm was used to quantify spatial distribution of molecular changes in tissues (lipids, nucleic acids, and proteins) associated with glioma progression. Compared to those in normal brain, statistical tests on fit coefficients showed that the concentrations of sphingomyelin (SMY), nucleic acids, phosphatidylserine (PS), and galactocerebroside (GalC) were significantly affected during C6 glioma development. These constituents can be used as spectroscopic markers for C6 glioma progression. Indeed, the concentration of DNA decreased significantly from tumor to invasion, to normal brain tissues, the necrotic area has higher concentrations of the Galc than other areas. The PS content was significantly higher in the peritumoral zone and decreased in the tumor zones matter.

Poster - Thurs Eve-28: New brain diffusion analysis method: White matter grey matter dissasociation.

Diffusion MR studies are often used to investigate the physical properties of brain tissues (1, 2). It is known that a full characterisation of the diffusion decay for brain could give valuable information about the structural organisation of cerebral tissue. The significance of the present diffusion decay study lies in the combination of three novel procedures to provide a better characterization of the diffusion decay: i) the acquisition of a large number of b-values (96 b-values up to 10,000 s/mm2 ), ii) the application of a noise correction technique (3) to the acquired data, and iii) the use of a Non Negative Least Squares (NNLS) fitting algorithm to evaluate the diffusion coefficients. The presence of noise in magnitude MR images can affect the calculation of the diffusion parameters (4) and therefore a noise correction technique (3) is applied. The NNLS algorithm is used to fit the corrected data instead of the more commonly used Levenberg-Marquardt algorithm since the NNLS algorithm does not require the number of components to be specified, nor does it need initial estimates of the fitting parameters as input; thus giving it more versatility as a fitting tool for the diffusion decay. The results indicate that the diffusion decays in grey and white matter have one and two components, respectively. Consequently, the short diffusion component in white matter (Fig. 1.c) can be used as a tool in the disassociation of white and grey matter tissues.

On the estimation of target spectrum for filter-array based spectrometers

Miniature spectrometers have been drawn researchers much attention due to its wide variety of possible applications. In this paper, we show the achievability of a fine spectrometer on-a-chip based on a low-performance, low-cost filter-array. A low quality filter-array is augmented with digital signal processing techniques. A series of estimators for recovering target spectrum is introduced. By exploiting non-negative nature of spectral content, a non-negative least-square algorithm is found particularly useful for spectrum recovery. The concept is verified in a hardware implementation.