Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

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Wavelet deconvolution technique for impact force reconstruction: mutual deconvolution approach

Science & Technology Development Journal - Engineering and Technology ◽

10.32508/stdjet.v3isi2.507 ◽

2021 ◽

Vol 3 (SI2) ◽

pp. first

Author(s):

Hai Tran ◽

Tat-Hien Le

Keyword(s):

Indirect Method ◽

Impact Force ◽

Impulse Response Function ◽

Reconstruction Process ◽

Deconvolution Technique ◽

Force Reconstruction ◽

History Of ◽

Ill Posed ◽

And Shifts ◽

Large Magnification

In the field of impact engineering, one of the most concerned issues is how to exactly know the history of impact force which often difficult or impossible to be measured directly. In reality, information of impact force apply to structure can be identified by means of indirect method from using information of corresponding output responses measured on structure. Namely, by using the output responses (caused by the unknown impact force) such as acceleration, displacement, or strain, etc. in cooperation with the impulse response function, the profile of unknown impact force can be rebuilt. A such indirect method is well known as impact force reconstruction or impact force deconvolution technique. Unfortunately, a simple deconvolution technique for reconstructing impact force has often encountered difficulty due to the ill-posed nature of inversion. Deconvolution technique thus often results in unexpected reconstruction of impact force with the influences of unavoidable errors which is often magnified to a large value in reconstructed result. This large magnification of errors dominates profile of desired impact force. Although there have been some regularization methods in order to improve this ill-posed problem so far, most of these regularizations are considered in the whole-time domain, and this may make the reconstruction inefficient and inaccurate because impact force is normally limited to some portions of impact duration. This work is concerned with the development of deconvolution technique using wavelets transform. Based on the advantages of wavelets (i.e., localized in time and the possibility to be analyzed at different scales and shifts), the mutual reconstruction process is proposed and formulated by considering different scales of wavelets. The experiment is conducted to verify the proposed technique. Results demonstrated the robustness of the present technique when reconstructing impact force with more stability and higher accuracy.

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Determination of Cellular Tractions on Elastic Substrate Based on an Integral Boussinesq Solution

Journal of Biomechanical Engineering ◽

10.1115/1.3118767 ◽

2009 ◽

Vol 131 (6) ◽

Cited By ~ 31

Author(s):

Jianyong Huang ◽

Xiaoling Peng ◽

Lei Qin ◽

Tao Zhu ◽

Chunyang Xiong ◽

...

Keyword(s):

Inverse Problem ◽

Green’S Function ◽

Green's Function ◽

Cardiac Myocyte ◽

Image Correlation ◽

Area Element ◽

Cell Functions ◽

Force Reconstruction ◽

Ill Posed ◽

Boussinesq Solution

Cell-substrate interaction is implicated in many physiological processes. Dynamical monitoring of cellular tractions on substrate is critical in investigating a variety of cell functions such as contraction, migration, and invasion. On account of the inherent ill-posed property as an inverse problem, cellular traction recovery is essentially sensitive to substrate displacement noise and thus likely produces unstable results. Therefore, some additional constraints must be applied to obtain a reliable traction estimate. By integrating the classical Boussinesq solution over a small rectangular area element, we obtain a new analytical solution to express the relation between tangential tractions and induced substrate displacements, and then form an alternative discrete Green’s function matrix to set up a new framework of cellular force reconstruction. Deformation images of flexible substrate actuated by a single cardiac myocyte are processed by digital image correlation technique and the displacement data are sampled with a regular mesh to obtain cellular tractions by the proposed solution. Numerical simulations indicate that the 2-norm condition number of the improved coefficient matrix typically does not exceed the order of 100 for actual computation of traction recovery, and that the traction reconstruction is less sensitive to the shift or subdivision of the data sampling grid. The noise amplification arising from ill-posed inverse problem can be restrained and the stability of inverse solution is improved so that regularization operations become less relevant to the present force reconstruction with economical sampling density. The traction recovery for a single cardiac myocyte, which is in good agreement with that obtained by the Fourier transform traction cytometry, demonstrates the feasibility of the proposed method. We have developed a simple and efficient method to recover cellular traction field from substrate deformation. Unlike previous force reconstructions that numerically employ some regularization schemes, the present approach stabilizes the traction recovery by analytically improving the Green’s function such that the intricate regularizations can be avoided under proper conditions. The method has potential application to a real-time traction force microscopy in combination with a high-efficiency displacement acquisition technique.

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Inverse Infiltration Modeling of Dike Covers Made of Dredged Material Using PEST and AMALGAM

Geosciences ◽

10.3390/geosciences11020041 ◽

2021 ◽

Vol 11 (2) ◽

pp. 41

Author(s):

Tim Jurisch ◽

Stefan Cantré ◽

Fokke Saathoff

Keyword(s):

Large Scale ◽

Measurement Data ◽

Fine Grained ◽

Dredged Materials ◽

Measurement Results ◽

Large Scale Field ◽

Eigenvalue Ratio ◽

Ill Posed ◽

Materials Used ◽

Installation Technology

A variety of studies recently proved the applicability of different dried, fine-grained dredged materials as replacement material for erosion-resistant sea dike covers. In Rostock, Germany, a large-scale field experiment was conducted, in which different dredged materials were tested with regard to installation technology, stability, turf development, infiltration, and erosion resistance. The infiltration experiments to study the development of a seepage line in the dike body showed unexpected measurement results. Due to the high complexity of the problem, standard geo-hydraulic models proved to be unable to analyze these results. Therefore, different methods of inverse infiltration modeling were applied, such as the parameter estimation tool (PEST) and the AMALGAM algorithm. In the paper, the two approaches are compared and discussed. A sensitivity analysis proved the presumption of a non-linear model behavior for the infiltration problem and the Eigenvalue ratio indicates that the dike infiltration is an ill-posed problem. Although this complicates the inverse modeling (e.g., termination in local minima), parameter sets close to an optimum were found with both the PEST and the AMALGAM algorithms. Together with the field measurement data, this information supports the rating of the effective material properties of the applied dredged materials used as dike cover material.

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Impact force reconstruction and localization using nonconvex overlapping group sparsity

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2021.107983 ◽

2022 ◽

Vol 162 ◽

pp. 107983

Author(s):

Junjiang Liu ◽

Baijie Qiao ◽

Yuanchang Chen ◽

Yuda Zhu ◽

Weifeng He ◽

...

Keyword(s):

Impact Force ◽

Group Sparsity ◽

Overlapping Group Sparsity ◽

Force Reconstruction

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Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽

10.3390/proceedings2019033021 ◽

2019 ◽

Vol 33 (1) ◽

pp. 21

Author(s):

Fabrizia Guglielmetti ◽

Eric Villard ◽

Ed Fomalont

Keyword(s):

Inverse Problem ◽

Image Plane ◽

Source Distribution ◽

Bayesian Probability ◽

Model Parameters ◽

Uncertain Information ◽

Source Detection ◽

Component Mixture ◽

Ill Posed ◽

Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

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Experimental force reconstruction on plates of arbitrary shape using neural networks

INTER-NOISE and NOISE-CON Congress and Conference Proceedings ◽

10.3397/in-2021-2397 ◽

2021 ◽

Vol 263 (3) ◽

pp. 3407-3416

Author(s):

Tyler Dare

Keyword(s):

Neural Network ◽

Neural Networks ◽

Inverse Problem ◽

Artificial Neural Network ◽

Rectangular Plate ◽

Arbitrary Shape ◽

Impulsive Force ◽

Force Reconstruction ◽

Output Space ◽

Arbitrary Shapes

Measuring the forces that excite a structure into vibration is an important tool in modeling the system and investigating ways to reduce the vibration. However, determining the forces that have been applied to a vibrating structure can be a challenging inverse problem, even when the structure is instrumented with a large number of sensors. Previously, an artificial neural network was developed to identify the location of an impulsive force on a rectangular plate. In this research, the techniques were extended to plates of arbitrary shape. The principal challenge of arbitrary shapes is that some combinations of network outputs (x- and y-coordinates) are invalid. For example, for a plate with a hole in the middle, the network should not output that the force was applied in the center of the hole. Different methods of accommodating arbitrary shapes were investigated, including output space quantization and selecting the closest valid region.

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