Linear Least-squares Method Research Articles

Detection of structural damages by model updating based on singular value decomposition of transfer function subsets

In this paper, a sensitivity-based finite element (FE) model updating method using singular value decomposition (SVD) of frequency response function (FRF) is introduced. An exact sensitivity equation is proposed by incorporating measured responses of a damaged structure in the mathematical formulations. A set of incompletely measured natural frequencies of a damaged structure and mode shapes of the intact structure are used to deal with incomplete measurement without the implementation of FE model reduction or data expansion algorithms. The insights provided from the variation of SVD of transfer functions are used for the selection of proper updating frequency ranges. The appropriate arrangement and assembly of SVD-based sensitivity equations are discussed to achieve more accurate model updating results. The solution of the developed sensitivity equation is obtained by the linear least-square (LS) method and imposing unbiased side constraints on the design variables. The proposed method was examined numerically on the FE model of a 2D truss model and experimentally on a concrete beam. Low-frequency ranges, including ranges around the first sixth vibration modes for numerical cases and ranges around the first three vibration modes for experimental cases, are successfully implemented for damage detection. The numerical and experimental results prove its high sensitivity for the cases of low severity and distributed damages and its robustness against high levels of measurement, natural frequency, and mass modeling errors.

Unsteady skin-friction field estimation based on global luminescent oil-film image analysis

A global luminescent oil-film (GLOF) image analysis method to estimate unsteady skin-friction fields in an unsteady flow field is proposed and demonstrated. A governing equation describing the dynamics of the oil film (the thin-oil-film equation) is employed for the unsteady oil-film images. The frequency response of the oil-film movement is analyzed, and a cutoff frequency is defined as a function of the oil-film thickness and the kinematic oil viscosity. The estimating skin-friction vector is defined along with a spatiotemporal weighted window and obtained by solving the overdetermined system of the thin-oil-film equation. The system can be solved by using the weighted linear least-squares method, and the time-resolved skin-friction field can be estimated. The time-resolved GLOF image analysis method is demonstrated on an experiment of a junction flow on a flat surface with a square cylinder. The GLOF images in the Karman vortex shedding bounding the flat surface were acquired, and the time-resolved skin-friction fields were obtained. The results showed that fluctuation in the skin-friction vectors corresponds to the shedding frequency, and the vortices bounding the surface were extracted. The averaged skin-friction field is compared with the result of the previous study based on the time-independent model. The normalized skin friction from both methods showed good agreement, which indicates that the quantitative value will be obtained when a calibration process is involved in a future study.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems.

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

Linear and non-linear regression analysis for the sorption kinetics of Tropaeoline 000 onto Nano Talc

ABSTRACTA comparison of linear least-squares method and a trial and error non-linear method of three widely used isotherms, Langmuir, Freundlich, and Temkin, were examined. The batch sorption model, based on a pseudo-second-order mechanism, was applied to predict the rate constant of sorption, the equilibrium capacity and the initial sorption rate with the effects of the initial solution pH (4.5) and adsorbent dose. The calculated adsorption capacity (qe) was qe = 97.6 mg/g. Langmuir isotherm parameters obtained from the Langmuir linear equations were used to fit the adsorption equilibrium data. The adsorption capacity of the adsorbent, obtained from the Langmuir model, was up to 1.78 mol/g−1. In order to optimise the adsorption-isotherm model, correlation coefficient (R2) of 0.991 and 0.841 error functions were employed to facilitate the evaluation of fitting accuracy.

Molecular Dynamics Ensemble Refinement of Intrinsically Disordered Peptides According to Deconvoluted Spectra from Circular Dichroism

We have developed a computational method of atomistically refining the structural ensemble of intrinsically disordered peptides (IDPs) facilitated by experimental measurements using circular dichroism spectroscopy (CD). A major challenge surrounding this approach stems from the deconvolution of experimental CD spectra into secondary structure features of the IDP ensemble. Currently available algorithms for CD deconvolution were designed to analyze the spectra of proteins with stable secondary structures. Herein, our work aims to minimize any bias from the peptide deconvolution analysis by implementing a non-negative linear least-squares fitting algorithm in conjunction with a CD reference data set that contains soluble and denatured proteins (SDP48). The non-negative linear least-squares method yields the best results for deconvolution of proteins with higher disordered content than currently available methods, according to a validation analysis of a set of protein spectra with Protein Data Bank entries. We subsequently used this analysis to deconvolute our experimental CD data to refine our computational model of the peptide secondary structure ensemble produced by all-atom molecular dynamics simulations with implicit solvent. We applied this approach to determine the ensemble structures of a set of short IDPs, that mimic the calmodulin binding domain of calcium/calmodulin-dependent protein kinase II and its 1-amino-acid and 3-amino-acid mutants. Our study offers a, to our knowledge, novel way to solve the ensemble secondary structures of IDPs in solution, which is important to advance the understanding of their roles in regulating signaling pathways through the formation of complexes with multiple partners.

Determination of the drying rate and effective diffusivity coefficients during convective drying of two-phase olive mill waste at rotary dryers drying conditions for their application

Secondary extraction factories in the oil olive production are subjected to high pressures each year due to the treatment of large quantities of olive mill wastes. In return, this sector achieves a biomass by-product and olive pomace oil. Furthermore, these facilities remove a serious environmental problem. To help improve and optimize the drying process of these wastes, we have carried out a study of mass transfer in a convective dryer using the drying conditions in rotary dryers. A design of experiments based on a central composite design in two dimensions, drying air temperature (between 100 °C and 425 °C) and drying air velocity (between 1 m/s and 7 m/s), was used to determine the drying rate and effective diffusivity coefficients. These variables were calculated from the experimental data obtained in isothermal drying test. Polynomial surface models, obtained by the linear least-squares fitting method, allowed to calculate these variables as a function of other such as drying air temperature, drying air velocity and moisture ratio. Drying rate and effective diffusivity values were found between 0.00001915 and 0.028 kgwater/kgsolid·s and 1.917·10−8 and 10.02·10−8 m2/s, respectively. These parameters will contribute to solve the heat and mass transfer phenomena in rotary dryers.

Determination of monomer reactivity ratios and thermal properties of poly(GMA-co-MMA) copolymers

In this study, the free radical copolymerization of glycidyl methacrylate (GMA) and methyl methacrylate (MMA) was investigated for the first time by solution free radical copolymerization in toluene at 80 °C using azobisisobutyronitrile as an initiator. The 1H-NMR spectroscopy has been used for determining the copolymer composition. Monomer reactivity ratios (r values) were calculated by various linear least-square methods. According to the results, using the Kelen–Tudos (KT) and extended Kelen–Tudos (Ex KT) methods the r values were obtained as $$ r_{\text{G}} = 1.528 \pm 0.168 $$ , $$ r_{\text{M}} = 0.789 \pm 0.121 $$ , and $$ r_{\text{G}} = 1.577 \pm 0.186 $$ , $$ r_{\text{M}} = 0.783 \pm 0.129 $$ , respectively. The calculated monomer reactivity ratios showed the higher reactivity for GMA (rG) compared to MMA (rM). Furthermore, the findings demonstrated random or ideal behavior ( $$ r_{\text{G}} \cdot r_{\text{M}} \simeq 1 $$ ) for these copolymers. The monomers sequence distribution as probability of finding the multiple sequence distribution of the GMA and MMA units in copolymers was calculated and showed higher probabilities for GMA sequences. Thermogravimetric analysis of the copolymers had three degradation stages, and the main degradation occurred at third stage (340–456 °C) with 56% weight loss. Also, with regard to initial temperature of degradation and T50, the thermal stability was improved 62% and 2.3%, respectively, by increasing MMA content in copolymer. These studies could uncover the underlying GMA–MMA composition in copolymer, shedding light on the future design of top-performing applications such as UV printing ink and resin industry.

Label-Free Visualization of Early Cancer Hepatic Micrometastasis and Intraoperative Image-Guided Surgery by Photoacoustic Imaging.

The detection of cancer micrometastasis for early diagnosis and treatment poses a great challenge for conventional imaging techniques. The aim of our study was to evaluate the performance of photoacoustic imaging (PAI) in detecting hepatic micrometastases from melanoma at a very early stage and in aiding tumor resection by intraoperative guidance. Methods: In vivo studies were performed by following protocols approved by the Ethical Committee for Animal Research at Xiamen University. First, a mouse model of B16 melanoma metastatic to the liver (n = 10) was established to study the development of micrometastases in vivo. Next, the mice were imaged by a scalable PAI instrument, ultrasound, 9.4-T high-resolution MRI, PET/CT, and bioluminescence imaging. PAI scans acquired with optical wavelengths of 680-850 nm were kept spectrally unmixed by using a linear least-squares method to differentiate various components. Differences in signal-to-background ratios among different modalities were determined with the 2-tailed paired t test. The diagnostic results were assessed with histologic examination. Excised liver samples from patients diagnosed with hepatic cancer were also examined to identify the tumor boundaries. Surgical removal of metastatic melanoma was precisely guided in vivo by the portable PAI system. Results: PAI was able to detect metastases as small as approximately 400 μm at a depth of up to 7 mm in vivo-a size that is smaller than can be detected with ultrasound and MRI. The tumor-to-liver ratio for PAI at 8 d (4.2 ± 0.2, n = 6) and 14 d (9.2 ± 0.4, n = 5) was significantly higher than for PET/CT (1.8 ± 0.1, n = 5, and 4.5 ± 0.2, n = 5, respectively; P < 0.001 for both). Functional PAI revealed dynamic oxygen saturation changes during tumor growth. The limit of detection was approximately 219 cells/μL in vitro. We successfully performed intraoperative PAI-guided surgery in vivo using the portable PAI system. Conclusion: Our findings offer a rapid and effective complementary clinical imaging application to noninvasively detect micrometastases and guide intraoperative resection.

Multireflection grazing-incidence X-ray diffraction: a new approach to experimental data analysis

The multireflection grazing-incidence X-ray diffraction method is used to test surface stresses at depths of several micrometres in the case of metal samples. This work presents new ways of analysing experimental data obtained by this method for Ni samples exhibiting significant elastic anisotropy of crystals. Three different methods of determining biaxial stresses and lattice parameter were compared. In the first approach, the calculations were performed using the linear least-squares method, and then two simplified procedures based on simple linear regression (weighted and non-weighted) were applied. It was found that all the tested methods give similar results, i.e. almost equal values of the determined stresses and lattice parameters and the uncertainties of their determination. The advantage of analyses based on simple linear regression is their simplicity and straightforward interpretation, enabling easy verification of the influence of the crystallographic texture and the presence of shear stresses, as well as graphical determination of the stress-free lattice parameter.

A crank-kinematics-based engine cylinder pressure reconstruction model

A new inverse model is proposed for reconstructing steady-state and transient engine cylinder pressure using measured crank kinematics. An adaptive nonlinear time-dependent relationship is assumed between windowed-subsections of cylinder pressure and measured crank kinematics in a time-domain format (rather than in crank-angle domain). This relationship comprises a linear sum of four separate nonlinear functions of crank jerk, acceleration, velocity and crank angle. Each of these four nonlinear functions is obtained at each time instant by fitting separate m-term Chebyshev polynomial expansions, where the total 4 m instantaneous expansion coefficients are found using a standard (overdetermined) linear least-square solution method. A convergence check on the calibration accuracy shows that this initially improves as more Chebyshev polynomial terms are used, but with further increase, the overdetermined system becomes singular. Optimal accuracy Chebyshev expansions are found to be of degree m = 4, using 90 or more cycles of engine data to fit the model. To confirm the model accuracy in predictive mode, a defined measure is used, namely the ‘ calibration peak pressure error’. This measure allows effective a priori exclusion of occasionally unacceptable predictions. The method is tested using varying speed data taken from a three-cylinder direct-injection spark ignition engine fitted with cylinder pressure sensors and a high-resolution shaft encoder. Using appropriately filtered crank kinematics (plus the ‘calibration peak pressure error’), the model produces fast and accurate predictions for previously unseen data. Peak pressure predictions are consistently within 6.5% of target, whereas locations of peak pressure are consistently within ±2.7 °CA. The computational efficiency makes it very suitable for real-time implementation.

Influence of relative humidity on real-time measurements of particulate matter concentration via light scattering

As the particulate-matter (PM) emission standards in China become increasingly rigorous (their upper limit has decreased to 10 mg/m3 in the power industry), considerable attention has been paid to PM emissions from coal-fired power plants. However, there is a large amount of water vapour in flue gas from power plants, which poses a great challenge to the measurement of the PM mass concentration via light scattering. Although water vapour does not affect the light scattering, changes in the properties of particles caused by water vapour influence it. To investigate the effects of the aerosol relative humidity on the PM mass-concentration measurement via light scattering, a test rig was constructed for wet aerosol light-scattering measurements. Light-scattering and hygroscopic properties, as well as morphological features of fly ash aerosol and pure mineral aerosol (pure powder silica) under different relative-humidity conditions were compared in a laboratory. The linear least-squares method was used to fit the relationship between the scattered light intensity and the PM mass concentration under four different humidity conditions. With increase in relative humidity, the R-squared values and the slopes of the fitted line were 0.9941, 0.9941, 0.9926, and 0.9854 and 35.14, 35.90, 28.59, and 26.91, respectively. Thus, the intensity of light scattering was directly proportional to the PM mass concentration, and the mass sensitivity, i.e. the slope of the fitted curve, changed with respect to relative humidity. From low to high relative-humidity conditions, the enhancement factors at a scattering angle of 20° were 0.868 ± 0.045, 0.814 ± 0.053, and 0.706 ± 0.029 for powder silica and 0.905 ± 0.010, 0.918 ± 0.015, and 0.984 ± 0.019 for fly ash. Thus, humidity had a greater influence on the mass-concentration measurement of powder silica aerosol via light scattering than on that of fly ash aerosol. Scanning electron microscopy results for aerosol particles under different humidity conditions indicated that the agglomeration characteristics of these particles increased with the relative humidity. Considering previous reports on the response characteristics of the hygroscopic particles with respect to their optical properties to relative humidity in the atmosphere, we found that the hygroscopic growth and agglomeration of aerosol particles together determine the measurement accuracy, which is very useful for onsite measurements of the PM mass concentration via the light-scattering method.

Calculating the k-Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC

Geometric sensitivity analyses of the -eigenvalue have many applications in analyses of geometric uncertainty, calculations of differential control rod worth, and searches for critical geometry. The adjoint-weighted first-order geometric sensitivity theory is widely used and has continuously evolved with the Monte Carlo methods. However, the existing adjoint-weighted algorithm can do only uniform isotropic expansions or contractions of surfaces. The adjoint-weighted algorithm also requires computation of adjoint-weighted scattering and fission reaction rates exactly at material interfaces, which has an infinitesimal probability in reality. This paper presents an improved geometry adjoint-weighted perturbation algorithm that is incorporated into the continuous-energy Reactor Monte Carlo (RMC) code. The improvement of the adjoint-weighted algorithm is decomposed into three steps for constructing a cross-section function of geometric parameters using logical expressions, calculating the derivative of the cross-section function, and estimating the adjoint-weighted surface reaction rates. The improved algorithm can accommodate common one-parameter geometric perturbations of internal interfaces or boundary surfaces as well as those of cells as long as the perturbed cells can be described by logical expressions of spatial surface equations. The perturbation algorithm is compared with a direct difference method, the linear least-squares fitting method with central differences, for several typical geometric perturbations including translation, fixed-axis rotation, and uniform isotropic/anisotropic expansion transformations of planar, spherical, cylindrical, and conical surfaces. The differences between the two methods are not more than 3% and not more than 3 for the majority of the test examples. Even though the perturbation algorithm has higher figures of merit than the direct difference method for the majority of the test examples, there is no guarantee that the former can always be more efficient than the latter. The limitation in the efficiency of the perturbation algorithm was demonstrated by the totally reflecting light water reactor pin model.

Logarithmic-Domain Array Interpolation for Improved Direction of Arrival Estimation in Automotive Radars.

In automotive radar systems, a limited number of antenna elements are used to estimate the angle of the target. Therefore, array interpolation techniques can be used for direction of arrival (DOA) estimation to achieve high angular resolution. In general, to generate interpolated array elements from original array elements, the method of linear least squares (LLS) is used. When the LLS method is used, the amplitudes of the interpolated array elements may not be equivalent to those of the original array elements. In addition, through the transformation matrix obtained from the LLS method, the phases of the interpolated array elements are not precisely generated. Therefore, we propose an array transformation matrix that generates accurate phases for interpolated array elements to improve DOA estimation performance, while maintaining constant amplitudes of the array elements. Moreover, to enhance the effect of our interpolation method, a power calibration method for interpolated received signals is also proposed. Through the simulation, we confirm that the array interpolation accuracy and DOA estimation performance of the proposed method are improved compared to those of the conventional method. Moreover, the performance and effectiveness of our proposed method are also verified using data obtained from the commercial radar system. Because the proposed method exhibits better performance when applied to actual measurement data, it can be utilized in commercial automotive radar systems.

Electrical resistivity method for water content and compaction evaluation, a laboratory test on construction material

ABSTRACT The amount of water content (WC) and the density of geotechnical parameters are important because it affects various engineering structures. In the geotechnical test, there is an increased need for the development of efficient methods for measuring the soil WC and the density of structural materials in the construction. These soil parameters are measured by destructive and non-destructive methods. In general, destructive methods are time-consuming and provide limited information, while electrical resistivity (ER) method is a fast, non-invasive and inexpensive method that has a high capability to predict geotechnical parameters such as WC and compaction. Laboratory ER tests on construction materials with different compaction and WC were conducted in this research. The purpose of this exercise was to develop a methodology based on the amount of soil ER in order to formulate a correlation between the amount of gravimetric water content (GWC) and soil compaction as well as the interaction relation between these parameters. The tested soil was GW-GM type and A-1-a type according to USCS and AASHTO respectively (Soil type E base material according to Iranian highway specifications code) and non-plastic. Data analysis shows a linear relationship between ER and compaction and a third degree polynomial relationship between ER and GWC. In addition, the obtained relationships indicate that the third degree polynomial curve fitted on the ER-GWC data (R-square: 0.8716) is more appropriate than the fitted curve on the ER-degree of saturation data (R-square: 0.7471). To find the interactive relationship between the parameters, robust linear least-squares (bisquare) method was used. Finally, a polynomial relationship between ER-GWC-Compaction is established with R-square 0.9142 and RMSE 12.16. The proposed relationship is also compared with Archie's law.

Ellipse Coefficient Map-Based Geomagnetic Fingerprint Considering Azimuth Angles

Geomagnetic fingerprint has been actively studied because of the high signal stability and positioning resolution even when the time has elapsed. However, since the measured three-axis geomagnetism signals at one position are irregular according to the change of the azimuth angle, a large-sized database which is stored magnitudes per angles is required for robust and accurate positioning against the change of the azimuth angle. To solve this problem, this paper proposes a novel approach, an elliptic coefficient map based geomagnetic fingerprint. Unlike the general fingerprint, which stores strength or magnitude of the geomagnetism signals depending on the position, the proposed algorithm minimized the size of databased by storing the Ellipse coefficient map through the ellipse equation derived from the characteristics of 2-D magnetic vectors depending on the position. In addition, the curvature bias of ellipse was reduced by applying the normalized linear least-squares method to 2-D geomagnetic characteristics and the positioning accuracy was improved by applying the weighted geomagnetic signal equalization method.

Data‐driven tuning of feedforward controller structured with infinite impulse response filter via iterative learning control

Iterative learning control (ILC) is an effective approach for tracking control system that performs repeating tasks. However, the performance of ILC is significantly deteriorated when the reference is changed. To obtain high tracking performance for both repeating and varying tasks, a novel data-driven tuning method of feedforward controller structured with infinite impulse response (IIR) filter via ILC is developed in this study. Global optimal parameters of the feedforward controller are obtained by linear least-squares method based on the optimal feedforward control force obtained by ILC, while model information is not required. Additionally, to deal with the possible instability problem of the feedforward controller structured with IIR filter, a stable approximation approach on the basis of zero-phase-error tracking algorithm is presented. The stable approximation approach can convert the approximation problem to a convex optimisation problem. Finally, the proposed approach is compared with the standard ILC and a data-driven feedforward control structured with finite impulse response filter by two simulation studies. Simulation results demonstrate that the proposed data-driven feedforward tuning method can achieve high tracking performance and is insensitive to reference variations.

Response surface methodological optimization of batch Cu(II) sorption onto succinic acid functionalized SiO2 nanoparticles

Functionalizing nanosilica (n-SiO2) particles with suitable active organic moiety leads to the formation of surfaces with precisely controlled physical and chemical characteristics. In this work, a novel nanosorbent (31 ± 2.4 nm), namely succinic acid functionalized nanosilica (n-SiO2@SA), was synthesized via a simple protocol using microwave irradiation to remove Cu(II) ions from aqueous media. The successful functionalization of n-SiO2 was confirmed by FTIR, and the thermal stability of n-SiO2@SA was investigated by TGA study. Other techniques, including HRTEM, DLS and zeta-potential, were utilized to investigate the chemical, surface, and morphological properties of the fabricated n-SiO2@SA. The response surface methodology (RSM) combined with three-level, three-factorial Box–Behnken design (BBD) was applied to optimize the multivariable sorption system using data obtained from 17 batch runs to reach 98.9% of Cu(II) ion removal. The predicted optimal conditions were as follows: contact time = 30 min, pH = 7.1, initial Cu(II) concentration = 317.5 mg L−1, and sorbent dose = 15 mg at which the maximum sorption capacities for n-SiO2 and n-SiO2@SA were 209.3 and 386.4 mg g−1, respectively, at 25 °C, thus supporting the validity of functionalization process. Non-linear regression and linear least-squares methods confirm the suitability of Langmuir model to describe the experimental endothermic, feasible, and chemisorption data, whereas the normalized standard deviation Δq% recommends the pseudo second-order kinetic model to represent the kinetic data. Real Cu-contaminated wastewaters were used to examine n-SiO2@SA nanosorbent for removing Cu(II) ions.

Comparative assessment of linear least-squares, nonlinear least-squares, and Patlak graphical method for regional and local quantitative tracer kinetic modeling in cerebral dynamic 18 F-FDG PET.

Dynamic 18 F-FDG PET allows quantitative estimation of cerebral glucose metabolism both at the regional and local (voxel) level. Although sensitive to noise and highly computationally expensive, nonlinear least-squares (NLS) optimization stands as the reference approach for the estimation of the kinetic model parameters. Nevertheless, faster techniques, including linear least-squares (LLS) and Patlak graphical method, have been proposed to deal with high resolution noisy data, representing a more adaptable solution for routine clinical implementation. Former research investigating the relative performance of the available algorithms lack precise evaluation of kinetic parameter estimates under realistic acquisition conditions. The present study aims at the systematic comparison of the feasibility and pertinence of kinetic modeling of dynamic cerebral 18 F-FDG PET using NLS, LLS, and Patlak method, based on numerical simulations and patient data. Numerical simulations were used to study the bias and variance of K1 and Ki parameters estimation under representative noise levels. Patient data allowed to assess the concordance between the three methods at the regional and voxel scale, and to evaluate the robustness of the estimations with respect to patient head motion. Our findings indicate that at the regional level NLS and LLS provide kinetic parameter estimates (K1 and Ki ) with similar bias and variance characteristics (K1 bias±relative standard deviation [RSD] 0.0±5.1% and 0.1%±4.9% for NLS and LLS respectively, Ki bias±RSD 0.1%±4.5% and -0.7%±4.4% for NLS and LLS respectively). NLS estimates appear, however, to be slightly less sensitive to patient motion. At the voxel level, provided that patient motion is negligible or corrected, LLS offers an appealing alternative solution for local K1 mapping. It yields K1 estimates that are highly correlated, with high correlation with NLS values (Pearson's r=0.95 on actual data) within computations times less than two orders of magnitude lower. Last, Patlak method appears as the most robust and accurate technique for the estimation of Ki values at the regional and voxel scale, with or without head motion. It provides low bias/low variance Ki quantification (bias±RSD -1.5±9.5% and -4.1±19.7% for Patlak and NLS respectively) as well as smooth parametric images suitable for visual assessment.

Rupture characteristics of a small-sized earthquake (MW 4.2), onshore the south Red Sea, Saudi Arabia

The present study is based on the use of Empirical Green's Function (EGF) deconvolution technique to retrieve the slip distribution of the 2014 Mw 4.2 Jizan earthquake, Saudi Arabia. Two datasets of complex Source Time Functions (STFs) were retrieved using two appropriate EGF events. We inverted the STF datasets to recover the slip distribution over both nodal planes, using the Bayesian modeling followed by a linear least-squares method. The inversion was performed assuming both planes as the fault plane and examined the goodness of fit for each nodal plane. Based on a series of finite-source inversions using different rupture velocities, we resolved the rupture velocity at 2.7–2.8 km/s and the fault plane of NNW trending; paralleling the Red Sea rift. Using the estimated rupture velocities and the preferred fault plane, we imaged quite similar slip models, exhibiting two slip patches located to the updip and downdip directions from the hypocentre. The spatiotemporal slip distributions revealed a complex rupture history of such small-sized earthquake is likely to that reported for large-sized earthquakes. A seismic moment of 2.8–3.2E+15 NM and a corresponding moment magnitude of 4.2-4-3 are inferred. The stress drops obtained from the slip distribution models were 2.2–2.5 MPa; indicating a typical value that characterized the plate-boundary earthquakes.

Mitigating the Effect of Incomplete Measurement in Sensitivity-Based FE Model Updating by Enhanced Transfer Function

Finite-element method is widely used for estimation of the structural behavior at various states. The finite-element (FE) models are not, however, a perfect representation of the real-life structures. In order to find a perfect FE model of the structure as well as monitoring of structural parameter changes, the FE model must be updated to match with real-life model. The curse of incomplete measurement is a major challenge for an updating method, especially in frequency domain. This paper proposes and investigates the replacement of the unmeasured degrees of freedom (DOFs) by experimentally enhanced decomposed transfer function (EDTF), in a FRF-based sensitivity equation to mitigate the adverse effects of data incompleteness. The enhanced transfer function is reached by a truncated set of experimentally measured natural frequencies and damping loss factors of real model. To highlight the merits of the EDTF in mitigating the effect of incomplete measurement, it is compared with the dynamic expansion of measured mode shapes. The results of the numerical investigations show that proposed approach is more efficient than dynamic expansion in the presence of high measurement error, large damages (parameter changes) and fewer measured DOFs. Besides, EDTF eliminates the need for modal data measurement up to a frequency much higher than the highest excitation frequency, which is necessary in dynamic expansion method. In this study, linear least-square method bounded with impartial side constraints is used for solving the sensitivity-based error minimization problem needed for model updating. Furthermore, fifty sets of numerically simulated error-contaminated FRF data are adopted to conduct Monte-Carlo analysis of the robustness of model updating results against error. The mean and coefficient of variation of estimated parameters are utilized for results indication and illustration purpose.