Statistical Analysis Of Residuals Research Articles

Spatio-temporal microstructure of sprays: data science-based analysis and modelling

Abstract

Physics‐based probabilistic seismic hazard and loss assessment in large urban areas: A simplified application to Istanbul

AbstractA set of 3D physics‐based numerical simulations (PBS) of possible earthquakes scenarios in Istanbul along the North Anatolian Fault (Turkey) is considered in this article to provide a comprehensive example of application of PBS to probabilistic seismic hazard (PSHA) and loss assessment in a large urban area. To cope with the high‐frequency (HF) limitations of PBS, numerical results are first postprocessed by a recently introduced technique based on Artificial Neural Networks (ANN), providing broadband waveforms with a proper correlation of HF and low‐frequency (LF) portions of ground motion as well as a proper spatial correlation of peak values also at HF, that is a key feature for the seismic risk application at urban scale. Second, before application to PSHA, a statistical analysis of residuals is carried out to ensure that simulated results provide a set of realizations with a realistic within‐ and between‐event variability of ground motion. PBS results are then applied in a PSHA framework, adopting both the “generalized attenuation function” (GAF) approach, and a novel “footprint” (FP)‐based approach aiming at a convenient and direct application of PBS into PSHA. PSHA results from both approaches are then compared with those obtained from a more standard application of PSHA with empirical ground motion models. Finally, the probabilistic loss assessment of an extended simplified portfolio of buildings is investigated, comparing the results obtained adopting the different approaches: (i) GMPE, (ii) GAF, and (iii) FP. Only FP turned out to have the capability to account for the specific features of source and propagation path, while preserving the proper physically based spatial correlation characteristics, as required for a reliable loss estimate on a building portfolio spatially distributed over a large urban area.

Erratum toRegional Stochastic GMPEs in Low‐Seismicity Areas: Scaling and Aleatory Variability Analysis—Application to the French Alps

We generate stochastic ground‐motion prediction equations (GMPEs) for a wide magnitude range ( M w 3–8) that are adapted to the French Alps. Based on inversions of source, path, and site terms from weak‐motion accelerometric data (Drouet et al. , 2010), we build seismological stochastic models to use in conjunction with the simulation program Stochastic‐Method SIMulation (SMSIM) to stochastically simulate ground‐motion response spectral amplitudes. All the input parameters are considered random variables, and the uncertainty is propagated through simulations by random sampling of the corresponding distributions. Constant and magnitude‐dependent stress parameter models are compared with variable large‐magnitude stress levels. Stochastic simulations are performed for periods between 0.01 and 3 s, M w from 3 to 8, epicentral distances from 1 to 250 km, and two site conditions: rock ( V S 30=800 m/s) and hard rock ( V S 30=2000 m/s). These synthetic data are then regressed to produce stochastic GMPEs using an up‐to‐date regression form, the parameterization of which can be defined in terms of different distance metrics (i.e., epicentral, hypocentral, Joyner–Boore, or rupture distance). The impact of the uncertainty on each input parameter on the GMPE standard deviation is determined through sensitivity analysis. The major contributors to the uncertainty are the site model, both V S 30 and κ (the high‐frequency parameter), which affect the within‐event standard deviation, and the uncertainty on the stress parameter, which affects the between‐event term. The GMPEs are compared to real data using statistical analysis of residuals. Two sets of strong‐motion data are considered (the Reference Database for Seismic Ground Motion in Europe [RESORCE] and the worldwide Next Generation Attenuation databases), as well as weak‐motion data recorded in France. The results show that the magnitude‐dependent stress parameter models (for magnitudes below 4.6) fit the French data better, and a large‐magnitude constant stress parameter of 10 MPa gives a better fit to strong‐motion data. Online Material: Tables of ground‐motion prediction equation coefficients.

Application of the Simple Linear Regression Model in the Experiment

The paper presents the results of experiments and measurements of the stress of a pipeline located on a pipe bridge. The experiment was carried out by means of resistance strain gages for two modes, which were the stress changes upon pressure changes in the pipes and at the driving in of sheet pilings in the immediate vicinity of the pipeline. On the basis of measurements, the impact of these changes on the operational safety of the pipeline in the renovation process of old above ground and the realization of new underground pipeline solutions. Polynomial regression models were applied for the prediction and a statistical analysis of residuals was applied for the quality assessment of selected models.

Motion Detection in Diffusion MRI via Online ODF Estimation

The acquisition of high angular resolution diffusion MRI is particularly long and subject motion can become an issue. The orientation distribution function (ODF) can be reconstructed online incrementally from diffusion-weighted MRI with a Kalman filtering framework. This online reconstruction provides real-time feedback throughout the acquisition process. In this article, the Kalman filter is first adapted to the reconstruction of the ODF in constant solid angle. Then, a method called STAR (STatistical Analysis of Residuals) is presented and applied to the online detection of motion in high angular resolution diffusion images. Compared to existing techniques, this method is image based and is built on top of a Kalman filter. Therefore, it introduces no additional scan time and does not require additional hardware. The performance of STAR is tested on simulated and real data and compared to the classical generalized likelihood ratio test. Successful detection of small motion is reported (rotation under 2°) with no delay and robustness to noise.

Quality analysis of digital terrain models for the test area Zlatibor

Digital terrain models (DTM) have recently become products which substitute standard methods for the terrain relief presentation. As a part of a Geographic Information Systems (GIS) they represent not only a data base related to heights that are used for terrain visualization by the means of interpolation routines for the generation of contours, or terrain presentation by the 3D meshes, but also a useful data base in many GIS and other applications. Numerous users of DTMs should also be supplied with information of DTM quality. This is obtained by the statistical analysis of residuals between generated height and heights of the control points called ground truth. The results of this analysis might be compulsorily part of metadata base for all DTMs products.

ESTIMA – an integrated software tool for nonlinear parameter estimation

System identification is an iterative model building process to obtain an accurate mathematical description from measured system responses. It involves two characteristically different aspects, the first being the choice of computationally intensive parameter estimation procedure and the second being the mandatory tasks such as preparation of experimental data, statistical analysis of residuals and model validation through time history plots and system analysis. In the first case, a variety of efficient parameter estimation algorithms is necessary to cover the broad spectrum of applications. The second aspect requires availability of user friendly pre- and post-processing graphical tools to rapidly determine the model quality. ESTIMA, an integrated software tool developed at the DLR Institute of Flight Systems, provides a well proven developmental environment to researchers and engineers to accelerate efficient model development process. This paper highlights the capabilities of this universally applicable package for system identification and simulation of general nonlinear dynamic systems. A few typical examples of parameter estimation and post-processing capabilities are demonstrated. A short description of related software tools KONVERT and MeDaLib for format conversion and preparation of measured data is presented.

CPLET computer program for evaluation of colligative property equilibrium data

Abstract Colligative property equilibrium data, in particular vapour-pressure osmometry, can be evaluated with the CPLET program using the general least squares method whilst applying pit-mapping, simplex, Davidon-Fletcher-Powell and Monte Carlo minimizing routines. From the measurement of colligative property as a function of the reactant concentrations, the “best” set of complexes and corresponding equilibrium constants are found. The stoichiometry of the species can be directly searched for via simultaneous regression estimation of equilibrium constants and stoichiometric indices. A correction of the analytical concentration of the compound under study and/or calculation of the impurity concentration are also possible. The program, written in Fortran 77 for PCs includes a complete statistical analysis of residuals.

Some properties of, and relationships among, several uncorrelated and homoscedastic residual vectors

In this paper we examine the properties of four types of residual vectors, arising from fitting a linear regression model to a set of data by least squares. The four types of residuals are (i) the Stepwise residuals (Hedayat and Robson, 1970), (ii) the Recursive residuals (Brown, Durbin, and Evans, 1975), (iii) the Sequentially Adjusted residuals (to be defined herein), and (iv) the BLUS residuals (Theil, 1965, 1971). We also study the relationships among the four residual vectors. It is found that, for any given sequence of observations, (i) the first three sets of residuals are identical, (ii) each of the first three sets, being identical, is a member of Thei’rs (1965, 1971) family of residuals; specifically, they are Linear Unbiased with a Scalar covariance matrix (LUS) but not Best Linear Unbiased with a Scalar covariance matrix (BLUS). We find the explicit form of the transformation matrix and show that the first three sets of residual vectors can be written as an orthogonal transformation of the BLUS residual vector. These and other properties may prove to be useful in the statistical analysis of residuals.

Computation in kinetics I. A general program KILET for simulation and evaluation of kinetic experimental data in multicomponent systems

A general regression program KILET written in FORTRAN IV for an IBM PC and other computers (MV 4000 Eclipse and EC 1033) enables (i) to model multicomponent kinetic data (ii) to load the smooth curves with random noise of required level (iii) to evaluate rate constants and/or simultaneously concentrations. Complete statistical analysis of residuals is performed. The program can be used for the discrimination of chemical kinetic models and for analytical purposes.

Complexation equilibria of some sulphoazoxines. Part VIII. Complexes of SNAZOXS with copper(II), lead(II) and cadmium(II) ions evaluated by regression analysis of potentiometric data

The reactions of oligomers of the sulphoazoxine SNAZOXS with H+, Pb2+, Cd2+ and Cu2+ ions were studied potentiometrically at 298 K in aqueous solutions. The protonation constants of the ligand oligomers L2H42–, L2H33–, L2H24– and L2H5– and the formation constants of several metal complexes were calculated with the aid of the program MINIQUAD. The chemical models were selected on the basis of a critical evaluation of the least-squares results and of a goodness-of-fit test by the statistical analysis of residuals. Whereas Cu2+ and Cd2+ ions form CuL–, CuLH, CuL24– and CuL2H3– complexes (Cu can be replaced with Cd), the Pb2+ ion forms PbLH, PbL24–, PbL2H3– and Pb2L35– complexes.