scholarly journals Evaluation of a Straight-Ray Forward Model for Bayesian Inversion of Crosshole Ground Penetrating Radar Data

Electronics ◽  
2019 ◽  
Vol 8 (6) ◽  
pp. 630 ◽  
Author(s):  
Hui Qin ◽  
Xiongyao Xie ◽  
Yu Tang
Keyword(s):  
Ground Penetrating Radar ◽  
Computational Cost ◽  
Measurement Data ◽  
Forward Model ◽  
Bayesian Inversion ◽  
Inversion Method ◽  
Model Parameters ◽  
Model Structure ◽  
Modeling Error ◽  
Ground Penetrating

Bayesian inversion of crosshole ground penetrating radar (GPR) data is capable of characterizing the subsurface dielectric properties and qualifying the associated uncertainties. Markov chain Monte Carlo (MCMC) simulations within the Bayesian inversion usually require thousands to millions of forward model evaluations for the parameters to hit their posterior distributions. Therefore, the CPU cost of the forward model is a key issue that influences the efficiency of the Bayesian inversion method. In this paper we implement a widely used straight-ray forward model within our Bayesian inversion framework. Based on a synthetic unit square relative permittivity model, we simulate the crosshole GPR first-arrival traveltime data using the finite-difference time-domain (FDTD) and straight-ray solver, respectively, and find that the straight-ray simulator runs 450 times faster than its FDTD counterpart, yet suffers from a modeling error that is more than 7 times larger. We also perform a series of numerical experiments to evaluate the performance of the straight-ray model within the Bayesian inversion framework. With modeling error disregarded, the inverted posterior models fit the measurement data nicely, yet converge to the wrong set of parameters at the expense of unreasonably large number of iterations. When the modeling error is accounted for, with a quarter of the computational burden, the main features of the true model can be identified from the posterior realizations although there still exist some unwanted artifacts. Finally, a smooth constraint on the model structure improves the inversion results considerably, to the extent that it enhances the inversion accuracy approximating to those of the FDTD model, and further reduces the CPU demand. Our results demonstrate that the use of the straight-ray forward model in the Bayesian inversion saves computational cost tremendously, and the modeling error correction together with the model structure constraint are the necessary amendments that ensure that the model parameters converge correctly.

Ü-Net: Deep-Learning Schemes for Ground Penetrating Radar Data Inversion

2020 ◽  
Vol 25 (2) ◽  
pp. 287-292
Author(s):  
Longhao Xie ◽  
Qing Zhao ◽  
Chunguang Ma ◽  
Binbin Liao ◽  
Jianjian Huo
Keyword(s):  
Neural Network ◽  
Dielectric Constant ◽  
Data Compression ◽  
Ground Penetrating Radar ◽  
Quantitative Imaging ◽  
Inversion Method ◽  
Output Unit ◽  
Data Inversion ◽  
Ground Penetrating ◽  
Constant Distribution

Electromagnetic (EM) inversion is a quantitative imaging technique that can describe the dielectric constant distribution of a target based on the EM signals scattered from it. In this paper, a novel deep neural network (DNN) based methodology for ground penetrating radar (GPR) data inversion, known as the Ü-net is introduced. The proposed Ü-net consists of three parts: a data compression unit, U-net, and an output unit. The novel inversion approach, based on supervised learning, uses a neural network to generate the dielectric constant distribution from GPR data. The GPR data can be compressed and reshaped the size using data compression unit. The U-net maps the object features to the dielectric constant distribution. The output unit meshes the dielectric constant distribution more finely. A novel feature of the proposed methodology is the application of instance normalization (IN) to the DNN EM inversion method and a comparison of its performance to batch normalization (BN). The validity of this technique is confirmed by numerical simulations. The Mean-Square Error of the test data sets is 0.087. These simulations prove that the instance normalization is suitable for GPR data inversion. The proposed approach is promising for achieving quality dielectric constant images in real-time.

scholarly journals A Non-Iterative Method Combined with Neural Network Embedded in Physical Model to Solve the Imaging of Electromagnetic Inverse Scattering Problem

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3104
Author(s):  
Hongsheng Wu ◽  
Xuhu Ren ◽  
Liang Guo ◽  
Zhengzhe Li
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Computational Cost ◽  
Inverse Scattering Problem ◽  
Forward Model ◽  
Inversion Method ◽  
Generative Adversarial Network ◽  
Simple Method ◽  
Adversarial Network ◽  
Electromagnetic Inverse Scattering

The main purpose of this paper is to solve the electromagnetic inverse scattering problem (ISP). Compared with conventional tomography technology, it considers the interaction between the internal structure of the scene and the electromagnetic wave in a more realistic manner. However, due to the nonlinearity of ISP, the conventional calculation scheme usually has some problems, such as the unsatisfactory imaging effect and high computational cost. To solve these problems and improve the imaging quality, this paper presents a simple method named the diagonal matrix inversion method (DMI) to estimate the distribution of scatterer contrast (DSC) and a Generative Adversarial Network (GAN) which could optimize the DSC obtained by DMI and make it closer to the real distribution of scatterer contrast. In order to make the distribution of scatterer contrast generated by GAN more accurate, the forward model is embedded in the GAN. Moreover, because of the existence of the forward model, not only is the DSC generated by the generator similar to the original distribution of the scatterer contrast in the numerical distribution, but the numerical of each point is also approximate to the original.

scholarly journals Sparse low-rank separated representation models for learning from data

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180490
Author(s):  
Christophe Audouze ◽  
Prasanth B. Nair
Keyword(s):  
Computational Cost ◽  
Approximation Problem ◽  
Coordinate Descent ◽  
Low Rank ◽  
Learning Problems ◽  
Model Parameters ◽  
Model Structure ◽  
Training Algorithms ◽  
Coordinate Descent Algorithm ◽  
Separated Representation

We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity constraints to ensure the well posedness of the approximation problem. We propose two fast training algorithms to estimate the model parameters: (i) a cyclic coordinate descent algorithm and (ii) a block coordinate descent (BCD) algorithm. While the first algorithm is not provably convergent owing to the non-convexity of the optimization problem, the BCD algorithm guarantees convergence to a Nash equilibrium point. The computational cost of the proposed algorithms is shown to scale linearly with respect to all of the parameters in contrast to methods based on ALS. Numerical studies on synthetic and real-world regression datasets indicate that the proposed SSR model structure holds significant potential for machine learning problems.

scholarly journals Particle Filter Based Monitoring and Prediction of Spatiotemporal Corrosion Using Successive Measurements of Structural Responses

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3909 ◽  
Author(s):  
Sang-ri Yi ◽  
Junho Song
Keyword(s):  
Particle Filter ◽  
Progress Monitoring ◽  
Measurement Data ◽  
Steel Plates ◽  
Bayesian Inversion ◽  
Inversion Method ◽  
Structural Deterioration ◽  
Recent Developments ◽  
Structural Responses ◽  
Inspection Data

Prediction of structural deterioration is a challenging task due to various uncertainties and temporal changes in the environmental conditions, measurement noises as well as errors of mathematical models used for predicting the deterioration progress. Monitoring of deterioration progress is also challenging even with successive measurements, especially when only indirect measurements such as structural responses are available. Recent developments of Bayesian filters and Bayesian inversion methods make it possible to address these challenges through probabilistic assimilation of successive measurement data and deterioration progress models. To this end, this paper proposes a new framework to monitor and predict the spatiotemporal progress of structural deterioration using successive, indirect and noisy measurements. The framework adopts particle filter for the purpose of real-time monitoring and prediction of corrosion states and probabilistic inference of uncertain and/or time-varying parameters in the corrosion progress model. In order to infer deterioration states from sparse indirect inspection data, for example structural responses at sensor locations, a Bayesian inversion method is integrated with the particle filter. The dimension of a continuous domain is reduced by the use of basis functions of truncated Karhunen-Loève expansion. The proposed framework is demonstrated and successfully tested by numerical experiments of reinforcement bar and steel plates subject to corrosion.

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