Stall Warning Strategy Based On Fast Wavelet Analysis in a Multi-Stage Axial Flow Compressor

As a reliable stall warning strategy, the fast wavelet method was introduced to successfully predict the aerodynamic instability of a multi-stage axial flow compressor. One single sensor installed at each stage is proved to be sufficient to predict the stability status in a three-stage axial flow compressor. The whole prediction strategy includes the dynamic pressure signal capture, disturbance extraction using decomposition and reconstruction via fast wavelet transform, and stall warning index calculation based on statistical probability distribution. On this premise, the first occurrence of the stall in this three-stage axial flow compressor is predicted to be within the first stage, which is consistent with the stall route captured by the eight transducers around the casing wall. Thereafter, the stall warning index is used to monitor the stability status during the continuous throttling process. Furthermore, the validation using tip air injection and inlet radial distortion indicated that the stall warning index decreases as the compressor's stability improves. Conversely, the deterioration of stability causes the increase of the stall warning index. Thus, experimental results demonstrate that the stall warning method based on fast wavelet analysis can predict the aerodynamic instability in actual application.

3D image compression during ultrasound phased diagnostics based on wavelet subband coding planar scans

The proposed compression method is based on the application of a two-dimensional discrete fast wavelet transform (FWT) to planar scans of 3D ultrasound images in order to simultaneously reduce redundancy and suppress speckle at a fixed quota of bits. The main idea of the method is to fuse three rules for threshold processing the wavelet coefficients of the scans, uniform and non-uniform quantizers, and bit quota distributions over subbands of the scan FWT based on the proposed cost function. The simulation results have shown that at the encoding rate of up to 1 bit/pixel, the quantity of artefacts were decreased up to 5-7 % of the original quantity under a signal-to-speckle ratio more than 16 dB, and the structural similarity index (SSIM) increased to 0.94-0.97 for defects of rectangular, triangular and oval shapes. The paper also presents the results proving the effectiveness of the proposed method in comparison with some variants of the solution according to the scheme “pre-filtering + codec”.

Correction to: Detecting differentially methylated regions using a fast wavelet-based approach to functional association analysis

A Correction to this paper has been published: https://doi.org/10.1186/s12859-021-03979-y

A fast wavelet-based functional association analysis replicates several susceptibility loci for birth weight in a Norwegian population

Background Birth weight (BW) is one of the most widely studied anthropometric traits in humans because of its role in various adult-onset diseases. The number of loci associated with BW has increased dramatically since the advent of whole-genome screening approaches such as genome-wide association studies (GWASes) and meta-analyses of GWASes (GWAMAs). To further contribute to elucidating the genetic architecture of BW, we analyzed a genotyped Norwegian dataset with information on child’s BW (N=9,063) using a slightly modified version of a wavelet-based method by Shim and Stephens (2015) called WaveQTL. Results WaveQTL uses wavelet regression for regional testing and offers a more flexible functional modeling framework compared to conventional GWAS methods. To further improve WaveQTL, we added a novel feature termed “zooming strategy” to enhance the detection of associations in typically small regions. The modified WaveQTL replicated five out of the 133 loci previously identified by the largest GWAMA of BW to date by Warrington et al. (2019), even though our sample size was 26 times smaller than that study and 18 times smaller than the second largest GWAMA of BW by Horikoshi et al. (2016). In addition, the modified WaveQTL performed better in regions of high LD between SNPs. Conclusions This study is the first adaptation of the original WaveQTL method to the analysis of genome-wide genotypic data. Our results highlight the utility of the modified WaveQTL as a complementary tool for identifying loci that might escape detection by conventional genome-wide screening methods due to power issues. An attractive application of the modified WaveQTL would be to select traits from various public GWAS repositories to investigate whether they might benefit from a second analysis.

Detecting differentially methylated regions using a fast wavelet-based approach to functional association analysis

Background We present here a computational shortcut to improve a powerful wavelet-based method by Shim and Stephens (Ann Appl Stat 9(2):665–686, 2015. 10.1214/14-AOAS776) called WaveQTL that was originally designed to identify DNase I hypersensitivity quantitative trait loci (dsQTL). Results WaveQTL relies on permutations to evaluate the significance of an association. We applied a recent method by Zhou and Guan (J Am Stat Assoc 113(523):1362–1371, 2017. 10.1080/01621459.2017.1328361) to boost computational speed, which involves calculating the distribution of Bayes factors and estimating the significance of an association by simulations rather than permutations. We called this simulation-based approach “fast functional wavelet” (FFW), and tested it on a publicly available DNA methylation (DNAm) dataset on colorectal cancer. The simulations confirmed a substantial gain in computational speed compared to the permutation-based approach in WaveQTL. Furthermore, we show that FFW controls the type I error satisfactorily and has good power for detecting differentially methylated regions. Conclusions Our approach has broad utility and can be applied to detect associations between different types of functions and phenotypes. As more and more DNAm datasets are being made available through public repositories, an attractive application of FFW would be to re-analyze these data and identify associations that might have been missed by previous efforts. The full R package for FFW is freely available at GitHub https://github.com/william-denault/ffw.

A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method

In this paper, we present an ecient modication of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This -analytical method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.

Fast wavelet decomposition of linear operators through product-convolution expansions

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately, computing the decomposition is itself a hard problem which is oftentimes out of reach for large-scale problems. The objective of this work is to design fast decomposition algorithms based on another representation called product-convolution expansion. This decomposition can be evaluated efficiently, assuming that a few impulse responses of the operator are available, but it is usually less efficient than the wavelet decomposition when incorporated in iterative methods. The proposed decomposition algorithms, run in quasi-linear time and we provide some numerical experiments to assess its performance for an imaging problem involving space-varying blurs.