Noise-free Data Research Articles

Uncertainty analysis using generalized Polynomial Chaos for the identification of structural constraining fixtures

Inverse problem solution is always prone of: (i) noise contamination sensitivity (ii) model uncertainty sensitivity (iii) the sensitivity against variation parameters’ magnitude. Our investigation consists in evaluating the performance of a method for the identification of the dynamic parameters of local constraining supports such as mass, stiffness and damping of multi-supported structure that will operate in the presence of the inevitable model parameters uncertainty. In the present contribution, the robustness of a method, that combine the measured frequency transfer functions and structural modification techniques for the identification of the dynamic parameters of local constraining, is evaluated against uncertainty in the model physical parameters. The contribution of the uncertain physical parameters to the identification procedure when using noise-free data as well as under a realistic noise level is further addressed. Results using the polynomial chaos expansion method are compared with Monte Carlo simulations. It is shown that uncertainty levels in the input data could result in large variation in the dynamic response of the multi-supported system. A sensitivity analysis is applied in order to quantify the influence of the uncertain model parameters on the identified supports parameters.

An adaptive data cleaning framework: a case study of the water quality monitoring system in China

Robust detection of patterns at low signal-to-noise ratios (SNR) is a fundamental challenge of analyzing high-frequency data, particularly in water quality monitoring. When conducting water quality data analysis, an indispensable step is to clean the data noise. In this paper, a new method named ADAPTIVE-EWT-MFE based on empirical wavelet transform (EWT) and multi-scale fuzzy entropy (MFE) is proposed to implement time series data cleaning. EWT-MFE can decompose the spectrum into different inherent mode functions (IMFs). According to different characteristics of the IMFs, an adaptive and adjustable parameter based on MFE, which reflects the intrinsic characteristics is introduced into the threshold function to improve the performance of noise-cleaning. Finally, this hybrid data cleaning method is designed to filter the high-frequency noise on the IMFs. Results show that our proposed method not only has great potential to improve the better noise-cleaning performance but also does not distort noise-free data.

A Mixed Finite Differences Scheme for Gradient Approximation

In this paper, we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective function is costly or the objective function values are affected by some noise. These functionals have been recently considered to estimate the gradient of the objective function by the expected value of the function variations in the space of directions. The expected value is then approximated by a sample average over a proper (random) choice of sample directions in the domain of integration. In this way, the approximation error is characterized by statistical properties of the sample average estimate, typically its variance. Therefore, while useful and attractive bounds for the error variance can be expressed in terms of the number of function evaluations, nothing can be said on the error of a single experiment that could be quite large. This work instead is aimed at deriving an approximation scheme for linear functionals approximating the gradient, whose error of approximation can be characterized by a deterministic point of view in the case of noise-free data. The previously mentioned linear functionals are no longer considered as expected values over the space of directions, but rather as the filtered derivative of the objective function by a Gaussian kernel. By using this new approach, a gradient estimation based on a suitable linear combination of central finite differences at different step sizes is proposed and deterministic bounds that do not depend on the particular sample of points considered are computed. In the noisy setting, on the other end, the variance of the estimation error of the proposed method is showed to be strictly lower than the one of the estimation error of the Central Finite Difference scheme. Numerical experiments on a set of test functions are encouraging, showing good performances compared to those of some methods commonly used in the literature, also in the noisy setting.

An Integrated Surrogate Modeling Method for Fusing Noisy and Noise-Free Data

Abstract Many datasets in engineering applications are heterogeneous mixtures of noise-free data, noisy data with known noise variances, and noisy data with unknown noise variances. This article proposes a data fusion method called the multi-type data fusion (MTDF) model, which fully utilizes the information provided by each of these types of data. To capture the underlying trend implied in the multiple types of data, the method approximately interpolates the noise-free data, while regressing the noisy data. The prediction accuracy of the MTDF model is compared with those of various surrogate models (interpolation models, regression models, and multi-fidelity models) on both numerical and practical engineering problems. In the experiments, the proposed MTDF model demonstrates higher performance than the other benchmark models. The effects of noise level and sample size of the noise-free data on the model performance are investigated, along with the robustness of the MTDF model. The results demonstrate the satisfactory feasibility, practicality, and stability of the MTDF.

Strategies for the Efficient Estimation of Soil Moisture through Spectroscopy: Sensitive Wavelength Algorithm, Spectral Resampling and Signal-to-Noise Ratio Selection

It is found that the remote sensing parameters such as spectral range, spectral resolution and signal-to-noise ratio directly affect the estimation accuracy of soil moisture content. However, the lack of research on the relationship between the parameters and estimation accuracy restricts the prolongation of application. Therefore, this study took the demand for this application as the foothold for developing spectrometry. Firstly, a method based on sensitivity analysis of soil radiative transfer model-successive projection algorithm (SA-SPA) was proposed to select sensitive wavelengths. Then, the spectral resampling method was used to select the best spectral resolution in the corresponding sensitive wavelengths. Finally, the noise-free spectral data simulated by the soil radiative transfer model was added with Gaussian random noise to change the signal-to-noise ratio, so as to explore the influence of signal-to-noise ratio on the estimation accuracy. The research results show that the estimation accuracy obtained through the SA-SPA (RMSEP < 12.1 g kg−1) is generally superior to that from full-spectrum data (RMSEP < 14 g kg−1). At selected sensitive wavelengths, the best spectral resolution is 34 nm, and the applicable signal-to-noise ratio ranges from 150 to 350. This study provides technical support for the efficient estimation of soil moisture content and the development of spectrometry, which comprehensively considers the common influence of spectral range, spectral resolution and signal-to-noise ratio on the estimation accuracy of soil moisture content.

Shear wave velocity estimation based on the particle swarm optimization method of HVSR curve inversion in Bakauheni district, Indonesia

The Nakamura method, known as horizontal to vertical spectral ratio (HVSR), has been used to analyze site effect assessment. Over the past decade, various HVSR curve inversion methods for near-surface geophysical surveys have been developed. Particle swarm optimization (PSO) inversion method has been applied to solve the HVSR inversion curve to estimate the shear wave velocity (Vs) value towards the depth. In this study, the HVSR curve inversion experiment has been applied with two synthetic data: noise-free data and the other is contaminated by 10% random noise. This research aims to find out how the PSO algorithm performs to find the best solution. The result indicated that the PSO algorithm is relatively stable fast in converging and producing the solution closely with the actual model. Finally, we obtained a fit model on actual data inversion that shows the Vs value towards depth from PSO inversion and is able to describe the fault model and sediment layer in Way Baka fault.

NS2NS: Self-Learning for Seismic Image Denoising

Attenuation of incoherent noise is an effective way to improve signal-to-noise ratio (SNR) of seismic data. Recently, supervised deep learning based methods have been widely utilized for seismic image denoising, which often need plenty of noise-free data as training labels. However, noise-free seismic data are often unavailable in field applications. We propose an unsupervised learning method (NS2NS) to train a denoising network by using single noisy seismic data. The proposed model is based on two basic truths of seismic data: (1) High self-similarity of seismic data; (2) Spatially independence of incoherent noise in seismic data. To implement the proposed method, we first build a sampling workflow to generate paired noisy images based on single noisy seismic image. Moreover, we create similar noisy images that are similar but different with the original noisy image by using the proposed self-similar sampler. The original noisy images and generated similar noisy images are then fused by using a suggested Bernoulli sampler to create new paired noisy images. These new paired noisy images are used as the input and target of the denoising model, respectively. Next, an end-to-end convolutional neural network (CNN) is built for seismic image denoising, which aims to learn features of valid signals and suppress unpredictable random noise. Finally, we apply the proposed NS2NS method to both synthetic and field data. The results show that our proposed method can effectively suppress incoherent noise while preserving valid signals.

Similarity-Informed Self-Learning and Its Application on Seismic Image Denoising

Seismic image denoising is essential to enhance signal-to-noise ratio (SNR) of seismic images and facilitate seismic processing and geological structure interpretation. With the development of deep learning (DL), several DL based models have been proposed for seismic image denoising. However, the commonly used supervised DL based denoising models require noise-free data as training labels, yet noise-free data is often difficult to be obtained in field application scenarios. By considering the similarity of seismic images, we propose a similarity informed self-learning (SISL) to address seismic image denoising in the absence of noise-free seismic images. To accurately preserve valid seismic signals when constructing training pairs, we develop a specialized workflow, termed the similar image sampler. In this way, we can fully use the self-similarity of noisy seismic images to build training pairs and then train a denoising model. Moreover, to effectively attenuate random noise, we propose a hybrid loss function with a regularization constraint to availably retain valid seismic events. After comparing with traditional denoising methods and several state-of-the-art unsupervised DL models, the experiment results from synthetic and field data quantitatively and qualitatively demonstrate the effectiveness and the stability of the proposed SISL model for seismic image denoising.

Unsupervised CNN Based on Self-Similarity for Seismic Data Denoising

Convolutional neural network (CNN)-based methods are powerful tools for seismic data denoising. Most methods adopt a supervised learning strategy, which requires noise-free labels to construct an objective function to guide the training of network parameters; however, it is impossible to obtain true noise-free field data. We propose a novel unsupervised random-noise-suppression method that can train a network directly on noisy target data without noise-free labels. The proposed method is inspired by the simple denoising idea of averaging multiple noisy observations, and it requires noise to satisfy two assumptions: it should be zero-mean and independent of the signal. In this method, multiple observations can be used as labels, and the loss function is constructed as the mean square error expected between the network output and these observations. The trained network estimates the expected value of these noise observations (i.e., the clean signal). This unsupervised method theoretically requires multiple noisy observations. Considering the good nonlocal self-similarity of seismic data, we used self-similar blocks to rearrange the data to construct multiple pseudo-observations and finally realize unsupervised training. The proposed method was compared with the traditional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f-x</i> deconvolution, curvelet, and generator CNN method on synthetic and field data, and the experimental results verified the effectiveness of the proposed method.

An Unsupervised Deep Learning Method for Denoising Prestack Random Noise

Deep-learning-based methods have been successfully applied to seismic data random noise attenuation. Among them, the supervised deep-learning-based methods dominate the unsupervised ones. The supervised methods need accurate noise-free data as training labels. However, the field seismic data cannot meet this requirement. To circumvent it, some researchers utilized realistic-looking synthetic data or denoised results via conventional methods as labels. The former ones encounter the problem of weak generalization ability because it requires the same distribution of test and training data. The latter ones encounter the issue of insufficient denoising ability because its denoising ability is difficult to significantly exceed the conventional methods which were used to generate labels. To avoid preparing noise-free labels, we propose a novel deep learning framework for attenuating random noise of prestack seismic data in an unsupervised manner. The prestack seismic data, such as common-reflection-point (CRP) gathers and common-midpoint (CMP) gathers after normal moveout (NMO) correction, have high self-similarity. It is because their events are coherent in the time–space domain and approximately horizontal from shallow to deep layers. The generator convolutional neural network (GCN) first learns self-similar features before any learning. The useful signals are more self-similar than random noise, which is incoherent and randomly distributed. Therefore, the GCN extracts features of useful signals before random noise. We select the specific training iteration and adopt the early stopping strategy to suppress random noise. Both synthetic and field prestack seismic data examples demonstrate the validity of our methods.

Handling noisy data in sparse model identification using subsampling and co-teaching

In this paper, a novel algorithm based on sparse identification, subsampling and co-teaching is developed to mitigate the problems of highly noisy data from sensor measurements in modeling of nonlinear systems. Specifically, sparse identification is combined with subsampling, a method where a fraction of the data set is randomly sampled and used for model identification, as well as co-teaching, a method that mixes noise-free data from first-principles simulations with the noisy measurements to provide a mixed data set that is less corrupted with noise for model training. The proposed method is bench-marked against sparse identification without subsampling as well as subsampling but without co-teaching using two examples, a predator-prey system and a chemical process, both of which are modeled as nonlinear systems of ordinary differential equations. It was shown that the proposed method yields better models in terms of prediction accuracy in the presence of high noise levels.

DETERMINATION OF FIBER ORIENTATION IN HIGH ANGULAR RESOLUTION DIFFUSION IMAGING USING SPHERICAL HARMONICS AND PARTICLE SWARM OPTIMIZATION

The fiber directions in High Angular Resolution Diffusion Imaging (HARDI) with low fractional anisotropy or low Signal to Noise Ratio (SNR) cannot be estimated accurately. In this paper, the fiber directions are estimated using Particle Swarm Optimization and Spherical Deconvolution (PSO-SD). Fiber orientation is modeled as a Dirac delta function in [Formula: see text]. The Spherical Harmonic Coefficients (SHC) of the Dirac delta function in the [Formula: see text] direction are obtained using the rotational harmonic matrix and the SHC of the Dirac delta function in the [Formula: see text]-axis. The PSO-SD method is used to determine ([Formula: see text]). We generated noise-free synthetic data for isotropic regions (FA varied from 0.1 to 0.8) and synthetic data with two crossing fibers for anisotropic regions with SNRs of 20, 15, 10 and 5 (FA [Formula: see text] 0.78). In the noise-free signal (FA [Formula: see text] 0.3), the Success Ratio (SR) and Mean Difference Angle (MDA) of the PSO-SD method were 1∘ and 9.48∘, respectively. In the noisy signal (FA [Formula: see text] 0.78, SNR [Formula: see text] 10, crossing angle [Formula: see text] 40), the SR and MDA of PSO-SD (with [Formula: see text]) were 0.46∘ and 12.3∘, respectively. The PSO-SD method can estimate fiber directions in HARDI with low fractional anisotropy and low SNR. Moreover, it has a higher SR and lower MDA in comparison with those of the super-CSD method.

Estimating the dimensionality of the manifold underlying multi-electrode neural recordings.

It is generally accepted that the number of neurons in a given brain area far exceeds the number of neurons needed to carry any specific function controlled by that area. For example, motor areas of the human brain contain tens of millions of neurons that control the activation of tens or at most hundreds of muscles. This massive redundancy implies the covariation of many neurons, which constrains the population activity to a low-dimensional manifold within the space of all possible patterns of neural activity. To gain a conceptual understanding of the complexity of the neural activity within a manifold, it is useful to estimate its dimensionality, which quantifies the number of degrees of freedom required to describe the observed population activity without significant information loss. While there are many algorithms for dimensionality estimation, we do not know which are well suited for analyzing neural activity. The objective of this study was to evaluate the efficacy of several representative algorithms for estimating the dimensionality of linearly and nonlinearly embedded data. We generated synthetic neural recordings with known intrinsic dimensionality and used them to test the algorithms’ accuracy and robustness. We emulated some of the important challenges associated with experimental data by adding noise, altering the nature of the embedding of the low-dimensional manifold within the high-dimensional recordings, varying the dimensionality of the manifold, and limiting the amount of available data. We demonstrated that linear algorithms overestimate the dimensionality of nonlinear, noise-free data. In cases of high noise, most algorithms overestimated the dimensionality. We thus developed a denoising algorithm based on deep learning, the “Joint Autoencoder”, which significantly improved subsequent dimensionality estimation. Critically, we found that all algorithms failed when the intrinsic dimensionality was high (above 20) or when the amount of data used for estimation was low. Based on the challenges we observed, we formulated a pipeline for estimating the dimensionality of experimental neural data.

Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States.

Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. Given measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, these constants may be inferred by model fitting, but the estimation problems are hard to solve if models are large. Here we show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined from data if metabolic fluxes are known. The estimation method, called model balancing, can handle models with a wide range of rate laws and accounts for thermodynamic constraints between fluxes, kinetic constants, and metabolite concentrations. It can be used to estimate in-vivo kinetic constants, to complete and adjust available data, and to construct plausible metabolic states with predefined flux distributions. By omitting one term from the log posterior—a term for penalising low enzyme concentrations—we obtain a convex optimality problem with a unique local optimum. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in E. coli central metabolism. The example shows what information about kinetic constants can be obtained from omics data and reveals practical limits to estimating in-vivo kinetic constants. While noise-free omics data allow for a reasonable reconstruction of in-vivo and values, prediction from noisy omics data are worse. Hence, adjusting kinetic constants and omics data to obtain consistent metabolic models is the main application of model balancing.

Semi-Supervised Ensemble Learning for Dealing with Inaccurate and Incomplete Supervision

In real-world tasks, obtaining a large set of noise-free data can be prohibitively expensive. Therefore, recent research tries to enable machine learning to work with weakly supervised datasets, such as inaccurate or incomplete data. However, the previous literature treats each type of weak supervision individually, although, in most cases, different types of weak supervision tend to occur simultaneously. Therefore, in this article, we present Smart MEnDR, a Classification Model that applies Ensemble Learning and Data-driven Rectification to deal with inaccurate and incomplete supervised datasets. The model first applies a preliminary phase of ensemble learning in which the noisy data points are detected while exploiting the unlabelled data. The phase employs a semi-supervised technique with maximum likelihood estimation to decide on the disagreement rate. Second, the proposed approach applies an iterative meta-learning step to tackle the problem of knowing which points should be made correct to improve the performance of the final classifier. To evaluate the proposed framework, we report the classification performance, noise detection, and the labelling accuracy of the proposed method against state-of-the-art techniques. The experimental results demonstrate the effectiveness of the proposed framework in detecting noise, providing correct labels, and attaining high classification performance.

Nonlinear Inversion Using Very Fast Simulated Annealing for Horizontal Electric Dipole Time-Domain Electromagnetic Data

A nonlinear stochastic inversion scheme, called very fast simulated annealing (VFSA), was applied to the time-domain electromagnetic data generated from a horizontal electric dipole. The forward formulation of the vertical magnetic field was expressed in the Laplace domain by applying the Hankel integral transform. Time-domain transformation was performed by applying the inverse Laplace transform using the Gaver–Stehfest algorithm. In this study, for noise-free synthetic data, the VFSA scheme yielded the smallest misfit and an inverted resistivity model that resembled the test model. The addition of 5% random noise to the synthetic data produced the same level of misfit and a model that still mimicked the test model. However, the addition of 10% noise to the synthetic data resulted in a misfit value that was three times that of the first two values and a resistivity model with a large discrepancy with the test model, particularly at large depths. These results indicate the efficacy of the VFSA inversion scheme for inferring the subsurface resistivity structure from the electromagnetic data. This inversion scheme was applied to field data measured in a volcanic environment. The general pattern of the resistivity structure inferred by the VFSA inversion is consistent with the structure obtained previously by using a deterministic inversion scheme.

Gender and region detection from human voice using the three-layer feature extraction method with 1D CNN

ABSTRACT Analysing the human voice has always been a challenge to the engineering society for various purposes such as product review, emotional state detection, developing AI, and much more. Two basic grounds of voice or speech analysis are to detect human gender and the geographical region based on accent. This study presents a three-layer feature extraction method from the raw human voice to detect the gender as male or female, as well as the region from where that voice belongs. Fundamental frequency, spectral entropy, spectral flatness, and mode frequency have been calculated in the first layer of feature extraction. On the other hand, Mel Frequency Cepstral Coefficient has been used to extract the features in the second layer and linear predictive coding in the third layer. Regular voice contains some noises which have been removed with multiple audio data filtering processes to get noise-free smooth data. Multi-Output-based 1D Convolutional Neural Network has been used to recognize gender and region from a combined dataset which consists of TIMIT, RAVDESS, and BGC datasets. The model has successfully predicted the gender with 93.01% and region with 97.07% accuracy. This method works better than usual state-of-the-art methods in separate datasets along with the combined dataset on both gender and region classification.

Lagrange Multiplier State-Space Substructuring

In this article a new state-space coupling formulation, named Lagrange Multiplier State-Space Substructuring (LM-SSS), is presented. This method represents an evolution of the classical state-space substructuring method (classical SSS). Likewise the well-known Lagrange Multiplier Frequency Based Substructuring (LM FBS) method, the LM-SSS is achieved by using a dual assembly formulation, which means that the full set of degrees of freedom (DOFs) is retained. The equilibrium and compatibility conditions are established by directly considering the connecting forces. The LM-SSS method has demonstrated to be simple to understand and to implement in a computational environment. Furthermore, since the formulation uses a mapping matrix to enforce the coupling conditions, several substructures can be coupled at same time. Similar to classical SSS, this method is not able to directly compute a minimal-order coupled state-space model. However, two post-processing procedures are presented in order to compute a minimal realization of the obtained coupled state-space models by using these techniques.By coupling numerical data is found that when dealing with state-space models estimated from noise-free data the same solutions are obtained by using the classical SSS or the LM-SSS. However, by comparing both methods is clear that the LM-SSS may have advantages over the classical method when dealing with state-space models estimated from experimental data, since it requires the inversion of only one matrix, thus reducing the instability of the associated numerical problems.

Cuckoo Search Algorithm for model parameter estimation from self-potential data

The use of the Cuckoo Search Algorithm (CSA) is introduced for estimating the model parameters from both synthetic and field self-potential (SP) anomalies in this study. The CSA offers a simple and efficient way to optimization studies as a popular nature-inspired metaheuristic algorithm because it requires only two algorithm-based parameters (the number of population and probability of recognition of the egg), and instead of isotropic random walks, it employs Lévy flights for search. This work presents the first application of the CSA for inversion of SP anomalies in geophysics. The test studies with the synthetic data included the cases of the noise-free and noisy data. Additionally, the Bavarian (Germany), Süleymanköy (Turkey) and Malachite (Colorado, USA) anomalies, which are the well-studied benchmark field data sets in the literature, were tested with the field data. An uncertainty appraisal analysis was performed for each model parameter via the Metropolis-Hastings algorithm. Also, the estimated parameters from the CSA were compared with the previous studies used a variety of metaheuristic methods to invert the same field data sets. According to the results, the CSA can be integrated into the inversion of SP anomalies as an efficient alternative method.

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.