Least-squares Approach Research Articles

Strain-based forward modeling and inversion of seismic moment tensors using distributed acoustic sensing (DAS) observations

This study used a waveform inversion of distributed acoustic sensing (DAS) data, acquired in two horizontal monitoring wells, to estimate the moment tensor (MT) of two induced microearthquakes. An analytical forward model was developed to simulate far-field tangential strain generated by an MT source in a homogeneous and anisotropic medium, averaged over the gauge length along a fiber of arbitrary orientation. To prepare the data for inversion, secondary scattered waves were removed from the field observations, using f-k filtering and time-windowing. The modeled and observed primary arrivals were aligned using a cut-and-paste approach. The MT parameters were inverted via a least-squares approach, and their uncertainties were determined through bootstrap analysis. Using simulated data with additive noise derived from the field data and the same fiber configuration as the monitoring wells, the inversion method adequately resolved the MT. Despite the assumption of Gaussian noise, which underlies the least-squares inversion approach, the method was robust in the presence of heavy-tailed noise observed in field data. When the inversion was applied to field data, independent inversion results using P-waves, S-waves, and both waves together yielded results that were consistent between the two events and for different wave types. The agreement of the inversion results for two events resulting from the same stress field illustrated the reliability of the method. The uncertainties of the MT parameters were small enough to make the inversion method useful for geophysical interpretation. The variance reduction obtained from the data predicted for the most probable MT was satisfying, even though the polarity of the P-waves was not always correctly reproduced.

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

Geometrical dimensions in nanostructures can be determined through indirect optical measurements carried out by a scatterometer. This includes solving a non-linear regression task in which a physical model is fitted to the observed optical diffraction pattern. We developed a virtual experiment which produces simulated diffraction patterns in coherent Fourier scatterometry measurements including perturbations due to various error sources. We utilize this virtual experiment to assess the suitability of data analysis and uncertainty quantification methods employed in scatterometry. In addition to investigating relevant physical parameters we explore the impact of deviations between the regression model utilized for the analysis and the scatterometry model used to produce the virtual diffraction pattern. We choose coverage probabilities of interval estimates of the geometrical dimensions as the main metric for the assessment. One of our findings is that the discretization level, expressed as the number of retained Fourier orders, can be relaxed up to order 9 in our case study, which is relevant as calculation times strongly depend on this parameter. Another result is that the least-squares approach considered here for solving the regression task in combination with the propagation of variances yields uncertainties which have somewhat lower coverage probabilities than the envisaged 95%. It turned out that it was critically important to model the oxide layer in order to get proper estimates of the width, or ‘critical dimension’, of the sample, while the uncertainty of the side wall angle had the largest impact on the uncertainty of the measurands. Our findings can help establishing traceability of Fourier scatterometry and underline the usefulness of high-quality virtual experiments in connection with complex measurement principles. At the same time the presented case study can be seen as a generic approach that could be followed for assessing uncertainty quantifications in other applications as well.

Stability of classification performance on an adaptive neuro fuzzy inference system for disease complication prediction

It is crucial to detect disease complications caused by metabolic syndromes early. High cholesterol, high glucose, and high blood pressure are indicators of metabolic syndrome. The aim of this study is to use adaptive neuro fuzzy inference system (ANFIS) to predict potential complications and compare its performance to other classifiers, namely random forest (RF), C4.5, and naïve Bayesian classification (NBC) algorithms. Fuzzy subtractive clustering is used to construct membership functions and fuzzy rules throughout the clustering process. This study analyzed 148 different data sets. Cholesterol, random glucose, systolic, and diastolic blood pressure are all included in the data collection. This learning process was conducted using a hybrid algorithm. The consequent parameters are adjusted forward using the leastsquare approach, while the premise parameters are adjusted backward using the gradient-descent process. The performance of a system is determined by the following indicators: accuracy, sensitivity, specification, precision, area under the curve (AUC), and root mean squared error (RMSE). The results of the training prove that ANFIS is an "excellent classification" classifier. ANFIS has proven to have very good stability across the six performance parameters. The adaptive properties used in ANFIS training and the implementation of fuzzy subtractive clustering strongly support this stability.

High-Precision Measuring System for Internal Deformation Monitoring Pipeline of Rockfill Dams: Design and Validation

The monitoring of internal deformation in rockfill dams using pre-buried flexible pipelines is a promising technique; however, achieving precise measurements over a long-range pipeline is crucial and challenging. In this paper, we present a high-precision pipeline measuring system for monitoring internal deformation in rockfill dams, which can simultaneously measure the pipeline centerline and cross-section geometry. The system leverages the inertial measurement principle to perform positioning by fusing an inertial measurement unit (IMU) with odometers. It utilizes a Kalman filter and Rauch-Tung-Striebel (RTS) smoothing to estimate the optimal 3D curves of the pipeline. The pipeline’s inner diameter is measured using three wheel swing arms and a set of load-bearing wheels, and the pipeline cross-section geometry is fitted using a direct least-square ellipse fitting approach. Finally, we validated the measuring system through both model and on-site experiments and compared the measurements with the Leica AT-960LR absolute tracker and hydraulic overflow settlement gauge. The results indicate that the measuring system has excellent accuracy for measuring pipeline curves and deformation, and the settlement trend is consistent with the hydraulic overflow settlement gauge. We also assessed the cross-section deformation of the deformation monitoring pipeline in the Lianghekou dam for six months, and the results showed that if deployed in strict accordance with the design requirements, the monitoring pipeline buried inside the rockfill dam would not deform significantly. These findings provide a tremendous incentive for the continued development of rockfill dam internal deformation monitoring.

Establishment of a design study for comprehensive hydrodynamic optimisation in the preliminary stage of the ship design

ABSTRACT An automated practical multi-objective optimisation scheme is proposed for ship hull modification. A shift transformation and a self-blending method are sequentially performed based on resistance objectives at multi-design speeds. The Lackenby variation alters hull forms and produces initial designs. Subsequently, self-blending method combines obtained ships to cover design space. All processes are automated by MATLAB coding that connects the ©Maxsurf modeller and ©Maxsurf Resistance in the case of panel method resistance calculation. After whole shape optimisation, the platform defines ship portions in the stern and bow regions. Particularly, an approximation modelling Least-Square approach is investigated to construct a surrogate model. Optimisation results indicate 11.26% cost function reduction contributes to 16.23% resistance reduction at lower speed and 6.12% resistance reduction at higher speed for a passenger catamaran boat. Thus, the developed in-house optimisation code provides an optimal and cost-effective solution for hydrodynamic optimisation in the preliminary stage of ship design.

Examination of the Bi-LSTM Based 5G-OFDM Wireless Network Over Rayleigh Fading Channel Conditions

Fifth generation (5G) wireless networks’ system performance is dependent on having perfect knowledge of the channel state information (CSI). Deep learning (DL) has helped improve both the end-to-end reliability of 5G and beyond fifth generation (B5G) networks and the computational complexity of these networks. This work uses the Bi-linear long short-term memory (Bi-LSTM) scheme to examine the overall performance of the 5G orthogonal frequency division multiplexing (OFDM) technology. The least squares (LS) channel estimation scheme is a famous scheme employed to estimate the fading channel coefficients due to their lower complexity without the prior CSI. However, this scheme has an exceedingly high CSI error. Using pilot symbols (PS) and loss functions, this work has proposed the Bi-LSTM 5G OFDM estimators to improve the channel estimation obtained by the LS approach. All simulation analysis uses convex optimization (CO) software (CVX software) and stochastic gradient descent (SGD). When combined with many PS (72) and a cross-entropy loss function, the proposed Bi-LSTM outperforms the long-short-term memory (LSTM) cross-entropy, LS, and minimum mean square error (MMSE) estimators in low, medium, and high signal-to-noise ratio (SNR) regimes. The computational and training times of Bi-LSTM and LSTM DL estimators are also compared. Because of its DNN design, it can evaluate massive datasets, find hidden statistical patterns and characteristics, establish underlying relationships, and transfer what it has learnt to other contexts. Statistical analysis of the bit error rate (BER) reveals that Bi-LSTM outperforms the MMSE in terms of accurate channel prediction.

Observability-Aware Online Multi-Lidar Extrinsic Calibration

Accurate and robust extrinsic calibration is necessary for deploying autonomous systems which need multiple sensors for perception. In this paper, we present a robust system for real-time extrinsic calibration of multiple lidars in vehicle base frame without the need for any fiducial markers or features. We base our approach on matching absolute GNSS (Global Navigation Satellite System) and estimated lidar poses in real-time. Comparing rotation components allows us to improve the robustness of the solution than traditional least-square approach comparing translation components only. Additionally, instead of comparing all corresponding poses, we select poses comprising maximum mutual information based on our novel observability criteria. This allows us to identify a subset of the poses helpful for real-time calibration. We also provide stopping criteria for ensuring calibration completion. To validate our approach extensive tests were carried out on data collected using Scania test vehicles (7 sequences for a total of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\approx$</tex-math></inline-formula> 6.5 Km). The results presented in this paper show that our approach is able to accurately determine the extrinsic calibration for various combinations of sensor setups.

Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats

An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the “curse of dimensionality” can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favorable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent neural network based methods.

Model-Robust Estimation of Multiple-Group Structural Equation Models

Structural equation models (SEM) are widely used in the social sciences. They model the relationships between latent variables in structural models, while defining the latent variables by observed variables in measurement models. Frequently, it is of interest to compare particular parameters in an SEM as a function of a discrete grouping variable. Multiple-group SEM is employed to compare structural relationships between groups. In this article, estimation approaches for the multiple-group are reviewed. We focus on comparing different estimation strategies in the presence of local model misspecifications (i.e., model errors). In detail, maximum likelihood and weighted least-squares estimation approaches are compared with a newly proposed robust Lp loss function and regularized maximum likelihood estimation. The latter methods are referred to as model-robust estimators because they show some resistance to model errors. In particular, we focus on the performance of the different estimators in the presence of unmodelled residual error correlations and measurement noninvariance (i.e., group-specific item intercepts). The performance of the different estimators is compared in two simulation studies and an empirical example. It turned out that the robust loss function approach is computationally much less demanding than regularized maximum likelihood estimation but resulted in similar statistical performance.

A new hybrid method with data-characteristic-driven analysis for artificial intelligence and robotics index return forecasting

Forecasting returns for the Artificial Intelligence and Robotics Index is of great significance for financial market stability, and the development of the artificial intelligence industry. To provide investors with a more reliable reference in terms of artificial intelligence index investment, this paper selects the NASDAQ CTA Artificial Intelligence and Robotics (AIRO) Index as the research target, and proposes innovative hybrid methods to forecast returns by considering its multiple structural characteristics. Specifically, this paper uses the ensemble empirical mode decomposition (EEMD) method and the modified iterative cumulative sum of squares (ICSS) algorithm to decompose the index returns and identify the structural breakpoints. Furthermore, it combines the least-square support vector machine approach with the particle swarm optimization method (PSO-LSSVM) and the generalized autoregressive conditional heteroskedasticity (GARCH) type models to construct innovative hybrid forecasting methods. On the one hand, the empirical results indicate that the AIRO index returns have complex structural characteristics, and present time-varying and nonlinear characteristics with high complexity and mutability; on the other hand, the newly proposed hybrid forecasting method (i.e., the EEMD-PSO-LSSVM-ICSS-GARCH models) which considers these complex structural characteristics, can yield the optimal forecasting performance for the AIRO index returns.

An AI-Based Newly Developed Analytical Formulation for Discharging Behavior of Supercapacitors with the Integration of a Review of Supercapacitor Challenges and Advancement Using Quantum Dots

A supercapacitor is a type of electrical component that has larger capacitance, due to asymmetric behavior with better power density, and lower ESR (effective series resistance) than conventional energy-storage components. Supercapacitors can be used with battery technology to create an effective energy storage system due to their qualities and precise characterization. Studies have shown that the use of quantum dots as electrodes in supercapacitors can significantly increase their effectiveness. In this research article, we have used a Drude model based on free electrons (asymmetric nature) to describe the supercapacitor’s discharging characteristics. Commercially available Nippon DLA and Green-cap supercapacitors were used to verify the Drude model by discharging them through a constant current source using a simple current mirror circuit. The parameters of both the fractional-order models and our suggested method were estimated using the least-squares regression fitting approach. An intriguing finding from the Drude model is the current-dependent behavior of the leakage-parallel resistance in the constant current discharge process. Instead of using the traditional exponential rule, supercapacitors discharge according to a power law. This work reflects the strong symmetry of different aspects of designing a hybrid supercapacitor with high efficiency and reliability.

Moving least squares approximation using variably scaled discontinuous weight function

Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.

Orientation estimation of cryo-EM images using projected gradient descent method

Orientation estimation is an important task in three-dimensional cryo-EM image reconstruction. By applying the common line method, the orientation estimation task can be formulated as a least squares (LS) problem or a least un-squared deviation (LUD) problem with orthogonality constraint. However, the non-convexity of the orthogonality constraint introduces numerical difficulties to the orientation estimation. The conventional approach is to reformulate the orthogonality constrained minimization problem into a semi-definite programming problem using convex relaxation strategies. In this paper, we consider a direct way to solve the constrained minimization problem without relaxation. We focus on the weighted LS problem because the LUD problem can be reformulated into a sequence of weighted LS problems using the iteratively re-weighted LS approach. As a classical approach, the projected gradient descent (PGD) method has been successfully applied to solve the convex constrained minimization problem. We apply the PGD method to the minimization problem with orthogonality constraint and show that the constraint set is a generalized prox-regular set, and it satisfies the norm compatibility condition. We also demonstrate that the objective function of the minimization problem satisfies the restricted strong convexity and the restricted strong smoothness over a constraint set. Therefore, the sequence generated by the PGD method converges when the initial conditions are satisfied. Experimental results show that the PGD method significantly outperforms the semi-definite relaxation methods from a computation standpoint, and the mean square error is almost the same or smaller.

Enhancing Localization Efficiency and Accuracy in Wireless Sensor Networks

Accuracy is the vital indicator in location estimation used in many scenarios, such as warehousing, tracking, monitoring, security surveillance, etc., in a wireless sensor network (WSN). The conventional range-free DV-Hop algorithm uses hop distance to estimate sensor node positions but has limitations in terms of accuracy. To address the issues of low accuracy and high energy consumption of DV-Hop-based localization in static WSNs, this paper proposes an enhanced DV-Hop algorithm for efficient and accurate localization with reduced energy consumption. The proposed method consists of three steps: first, the single-hop distance is corrected using the RSSI value for a specific radius; second, the average hop distance between unknown nodes and anchors is modified based on the difference between actual and estimated distances; and finally, the least-squares approach is used to estimate the location of each unknown node. The proposed algorithm, named Hop-correction and energy-efficient DV-Hop (HCEDV-Hop), is executed and evaluated in MATLAB to compare its performance with benchmark schemes. The results show that HCEDV-Hop improves localization accuracy by an average of 81.36%, 77.99%, 39.72%, and 9.96% compared to basic DV-Hop, WCL, improved DV-maxHop, and improved DV-Hop, respectively. In terms of message communication, the proposed algorithm reduces energy usage by 28% compared to DV-Hop and 17% compared to WCL.

A New RF Sensing Framework for Human Detection Through the Wall

A recent trend for human activity recognition, fall detection, health-care applications, etc., which is using the non-contact radio-frequency (RF) signals, is known as the RF sensing. State-of-the-art radar and Wi-Fi based human sensing systems utilize high bandwidth and require high computational burden. In this paper, a machine learning (ML) framework is proposed for device-free through-the-wall (TTW) human detection using narrow-band continuous RF signals that are transmitted and captured by low-cost software-defined radio (SDR) modules. To be more realistic the double TTW scenario, where both transmitter and receiver are placed outside the walls of the monitored area, is considered. Three different classes are defined as empty (human-free), moving human, and additionally the static human (only breathing, not moving) which addresses the unconscious or sleeping person. In this framework, the variance of the respiratory rate (RR) estimates of the subject and overall signal variances are used as distinguishing features. RR estimates are obtained using nonlinear least-squares (NLS) approach. It is shown in the experiments conducted with real measurements from different environments that the proposed ML framework achieves over 99% classification accuracy using a Decision Tree (DT) classifier. In addition, it is also shown that the proposed framework achieves over 95% accuracy in a completely different environment where the model is not trained. This indicates that the proposed ML framework can be applied generally without requiring specific re-training for different environments and conditions.

Approximating the span of principal components via iterative least-squares

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the variance is maximized, its first introduction by Pearson at 1901 was done through defining a non-linear least-squares minimization problem of fitting a plane to scattered data points. Thus, it seems natural that PCA and linear least-squares regression are somewhat related, as they both aim at fitting planes to data points. In this paper, we present a connection between the two approaches. Specifically, we present an iterated linear least-squares approach, yielding a sequence of subspaces, which converges to the space spanned by the leading principal components (i.e., principal space).

Relative Performance Evaluation and Strategic Differentiation

ABSTRACTI predict that relative performance evaluation (RPE) CEOs avoid strategic differentiation and increase the correlation of their firms’ returns with that of their peers. This prediction follows from a moral hazard model integrating strategic differentiation decisions: Differentiation enhances performance but exposes firms to risks not shared with peers, and the weakening RPE’s risk-shielding effect. Consistent with my prediction, I find evidence that changes in peer-group correlation are higher for RPE than non-RPE firms. This effect is more pronounced if benefits from differentiation are low, RPE benchmarks are industry specific, or RPE grants are large. Additional analyses provide direct evidence that RPE CEOs differentiate strategies less from industry-common strategies than non-RPE CEOs. To address endogeneity concerns, I present a two-stage least-squares approach exploiting variance in RPE usage induced by compensation consultants’ distinct styles. My analyses suggest strategic differentiation decisions to help explain why many boards do not completely filter peer performance from CEO compensation.Data Availability: All data are obtained from commercially available databases, including Compustat, CRSP, Execucomp, I/B/E/S, and ISS Incentive Lab.JEL Classifications: M12; M21; M41; M52.

Os efeitos da infraestrutura e do investimento público na elasticidade do investimento privado: uma investigação empírica para o Brasil

ABSTRACT This study estimates the determinants of the elasticities of private investment and total investment for the Brazilian economy for the period between 1960 and 2013. It uses a Bayesian model averaging and weighted-average least-squares approach with a flexible accelerator model of investment equation and Kalman filtering techniques. We conclude that the aggregate infrastructure index (taken from the main component analysis) and public investment crowd-in private investment. The results indicate that private investment is constrained by the availability of bank credit. Furthermore, we find that infrastructure stock and public investment are two of the main determinants of the elasticities of private investment. This demonstrates that public investment, mainly in infrastructure, is of great importance in raising the sensitivity of private investment in the Brazilian economy.

Simulating Theta and Gamma of American Options

This article derives explicit expressions to simulate theta and gamma for American options using the pathwise derivative method. Although the pathwise derivative formulas for delta, rho, and vega of American options have been studied in the literature, no correct explicit results for theta and gamma exist. In addition, we propose a simulation-based least-square method to compute the optimal stopping boundary for American options. The optimal stopping boundary is needed to evaluate our pathwise derivative expression for gamma and can be used in the integral method to calculate the price and Greeks of American options. Our proposed least-square approach to compute the optimal stopping boundary provides an alternative to the traditional recursive method of solving a system of equations. We also incorporate a Brownian bridge in the computation of the Greeks and extend the application of our results to American basket options.

Weather model based atmospheric corrections of Sentinel-1 InSAR deformation data at Turkish volcanoes

SUMMARYOne of the main constraints on the use of satellite radar data for monitoring natural hazards is the existence of atmospheric signals. In particular, volcanic deformation can be difficult to identify because atmospheric phase delays can mask or even mimic ground deformation signals. Eliminating atmospheric signals is particularly crucial for high-relief volcanoes such as Ağrı, Tendürek, Acigöl, Göllüdağ and Hasandağ in the Eastern and Central Anatolia. To overcome the atmospheric effects, we use high-resolution ECMWF weather models coupled with an empirical phase-elevation approach for correcting Sentinel-1 interferograms. We apply these methods to two areas of Turkey, the first of which covers three volcanoes in Central Anatolia (Acigöl, Göllüdağ, Hasandağ) between January 2016 and December 2018 and the second covers two volcanoes in Eastern Anatolia (Ağrı, Tendürek) between September 2016 and December 2018. The reduction in standard deviation (quality factor) is calculated for both ascending and descending tracks and the atmospheric corrections are found to perform better on descending interferograms in both cases. Then, we use a least-squares approach to produce a time-series. For Central Anatolia, we used 416 ascending and 415 descending interferograms to create 144 and 145 cumulative displacement maps, respectively, and for Eastern Anatolia, we used 390 ascending and 380 descending interferograms to produce 137 and 130 cumulative displacement maps, respectively. We find that the temporal standard deviation before atmospheric corrections ranges between 0.9 and 3.7 cm for the five volcanoes in the region and is consistently higher on ascending track data, which is acquired at the end of the day when solar heating is greatest. Atmospheric correction reduces the standard deviation to 0.5–2.5 cm. Residual signals might be due to the ice-cap at Ağrı and agriculture near Acigöl. We conclude that these volcanoes did not experience significant magmatic deformation during this time period, despite the apparent signals visible in individual uncorrected interferograms. We demonstrate that atmospheric corrections are vital when using InSAR for monitoring the deformation of high-relief volcanoes in arid continental climates such as Turkey.