On weighted total least-squares with linear and quadratic constraints

A weighted total least-squares (WTLS) approach with linear and quadratic constraints is developed. This method is according to the traditional Lagrange approach to optimize the target function of this problem. The WTLS and constrained total least-squares (CTLS) approach had been distinctively investigated, however, these two problems have not been simultaneously considered yet; furthermore, among the contributions on the CTLS problem, only Schaffrin and Felus considered linear and quadratic constraints together; nevertheless, in many practical examples, some elements of the design/coefficient matrix are fixed and should not be modified and this approach cannot deal with these cases. The main necessity of this research appears after the desirable property of the WTLS approach in preserving the structure of the design matrix was proven by Mahboub. In other words, currently, the WTLS approach is one of the most efficient methods for solving the so-called errors-in-variables model and an attempt for equipping it with constraints seems necessary. Also it is demonstrated that the additional constraints have a ’regularization role’ for ill-conditioned problems and the unconstrained solution suffers from ill-conditioning effects which give it an added advantage over the unconstrained WTLS algorithm. Four geodetic applications indicate the significant of this problem in the presence of colored and white noise in the data.     

Multi-level Optimization of Reservoir Scheduling Using Multi-resolution Wavelet-Based Up-scaled Models

This paper presents a multi-level procedure for production and injection scheduling through a numerical model-based optimization of well control variables. To calculate the net present value (NPV), the objective function of optimization, this procedure uses a number of discretized systems for a reservoir model with different degrees of up-scaling prepared according to a multi-resolution wavelet technique. These up-scaled models were incorporated into optimization based on a probability function. In early optimization iterations, due to the necessity to explore the search space quickly, the coarsest grid model has a higher chance for selection than the others; however, by a selection (with a low probability) of the finest up-scaled grid model in these iterations, solutions and objective function were tuned. In the later iterations of optimization, the finest up-scaled grid model probability was the highest in order to ensure the reliability of the final solution. The optimization algorithm is an adaptive simulated annealing algorithm coupled with a polytope. This procedure was evaluated in two case studies. The first case study was a horizontal 2D oil model with water flooding. The second case study was a vertical 2D oil model with gas injection. The results show that the proposed optimization procedure provides approximately the same accuracy compared to the situation in which the fine grid model is used for all the optimization iterations. Also, the run-time for the proposed optimization procedure is comparable to the run-time of the optimization in which only the coarsest grid model is used to calculate objective function. Moreover, the superiority of the wavelet-based up-scaling over an analogous multiple grid system optimization using uniformly up-scaled models is presented.

     

Intensity measures for the assessment of the seismic response of buried steel pipelines

To estimate the demand of structures, investigating the correlation between engineering demand parameters and intensity measures (IMs) is of prime importance in performance-based earthquake engineering. In the present paper, the efficiency and sufficiency of some IMs for evaluating the seismic response of buried steel pipelines are investigated. Six buried pipe models with different diameter to thickness and burial depth to diameter ratios, and different soil properties are subjected to an ensemble of 30 far-field earthquake ground motion records. The records are scaled to several intensity levels and a number of incremental dynamic analyses are performed. The approach used in the analyses is finite element modeling. Pipes are modeled using shell elements while equivalent springs and dashpots are used for modeling the soil. Several ground motion intensity measures are used to investigate their efficiency and sufficiency in assessing the seismic demand and capacity of the buried steel pipelines in terms of engineering demand parameter measured by the peak axial compressive strain at the critical section of the pipe. Using the regression analysis, efficient and sufficient IMs are proposed for two groups of buried pipelines separately. The first one is a group of pipes buried in soils with low stiffness and the second one is those buried in soils with higher stiffness. It is concluded that for the first group of pipes, \(\sqrt {{\text{VSI}}[\upomega_{1} ({\text{PGD}} + {\text{RMS}}_{\text{d}} )]}\) followed by root mean square of displacement (RMS_d) are the optimal IMs based on both efficiency and sufficiency; and for the second group, the only optimal IM is PGD²/RMS_d.     

Assessment of Relationship Between Grouted Values and Calculated Values in the Bazoft Dam Site

Seepage through foundation and abutments of a dam can potentially result in a waste of the water stored in dam reservoir, erosion of foundation materials, and development of uplift pressure in dam foundation which, consequently, threatens the long-term stability of the dam. In this study, the grout volume is estimated based on parameters such as joint aperture, the maximum penetration length of the grout, and calculated grout take in Bazoft dam site. Bazoft Dam is a hydroelectric supply and double-curvature arch dam with a height of 211 m located in Chaharmahal and Bakhtiari Province of Iran. The bedrock of Bazoft dam site consists of Asemari Formation (limy marl and marly lime), in the middle and upper parts of left abutment, and Jahrom Formation (limestone and dolomite) in the right abutment, river bed, and lower part of left abutment. The joint apertures were calculated based on the permeability and the joint spacing. Next, the maximum penetration length of the grout and grout volume were calculated. Using a statistical analysis, the relationship of the joint aperture, maximum penetration length, and the calculated grout volume with real grout take was also investigated. The results show that the grout take can be predicted with appropriate accuracy based on the calculated grout volume.     

Aquifer vulnerability assessment using GIS and fuzzy system: a case study in Tehran–Karaj aquifer,Iran

Aquifer vulnerability assessment techniques have been developed to predict which areas are more likely than others to become contaminated as a result of activities at or near the land surface. This research focuses on the evaluation of groundwater vulnerability to pollution in an urban area. Among several assessment methods, DRASTIC has been selected for this study. ArcGIS has been used to overlay and calculate different layers and obtain the vulnerability map. In order to show the importance of fuzzy algorithms in classification, both Boolean and fuzzy algorithms were used and compared. The fuzzy algorithm could recognize the areas with low and negligible vulnerability potentials whereas the Boolean model classified them as moderate. Two sensitivity tests, the map removal sensitivity analyses and single-parameter sensitivity analysis, were performed to show the importance of each parameter in the index calculation.     

Ellipsoidal Stokes Boundary-Value Problem with Ellipsoidal Corrections in the Boundary Condition

We would like to solve the Stokes boundary-value problem taking into consideration the ellipsoidal corrections in the boundary condition in ellipsoidal coordinates The original problem, i.e., the ellipsoidal Stokes boundary-value problem has been solved by Martinec and Grafarend (1997) We use the same philosophy expressed by Martinec (1998) to solve the spherical Stokes boundary-value problem with ellipsoidal corrections in the boundary condition We wish to show the magnitude of the integration kernel describing the effect of the ellipsoidal corrections in the boundary condition in a cap around the computational point.     

Geoid Determination Through Ellipsoidal Stokes Boundary-Value Problem by Splitting Its Solution to the Low-Degree and the High-Degree Parts

The ellipsoidal Stokes boundary-value problem is used to compute the geoidal heights. The low degree part of the geoidal heights can be represented more accurately by Global Geopotential Models (GGM). So the disturbing potential is splitted into a low-degree reference potential and a higher-degree potential. To compute the low-degree part, the global geopotential model is used, and for the high-degree part, the solution of the ellipsoidal Stokes boundary-value problem in the form of the surface integral is used. We present an effective method to remove the singularity of the high-degree of the spherical and ellipsoidal Stokes functions around the computational point. Finally, the numerical results of solving the ellipsoidal Stokes boundary-value problem and the difference between the high-degree part of the solution of the ellipsoidal Stokes boundary-value problem and that of the spherical Stokes boundary-value problem is presented.     

Soil moisture from operational meteorological satellites

In recent years, unforeseen advances in monitoring soil moisture from operational satellite platforms have been made, mainly due to improved geophysical retrieval methods. In this study, four recently published soil-moisture datasets are compared with in-situ observations from the REMEDHUS monitoring network located in the semi-arid part of the Duero basin in Spain. The remotely sensed soil-moisture products are retrieved from (1) the Advanced Microwave Scanning Radiometer (AMSR-E), which is a passive microwave sensor on-board NASA’s Aqua satellite, (2) European Remote Sensing satellite (ERS) scatterometer, which is an active microwave sensor on-board the two ERS satellites and (3) visible and thermal images from the METEOSAT satellite. Statistical analysis indicates that three satellite datasets contribute effectively to the monitoring of trends in surface soil-moisture conditions, but not to the estimation of absolute soil-moisture values. These sensors, or rather their successors, will be flown on operational meteorological satellites in the near future. With further improvements in processing techniques, operational meteorological satellites will increasingly deliver high-quality soil-moisture data. This may be of particular interest for hydrogeological studies that investigate long-term processes such as groundwater recharge.     

Landslide susceptibility assessment in the Anfu County,China: comparing different statistical and probabilistic models considering the new topo-hydrological factor (HAND)

The present study is aimed at producing landslide susceptibility map of a landslide-prone area (Anfu County, China) by using evidential belief function (EBF), frequency ratio (FR) and Mahalanobis distance (MD) models. To this aim, 302 landslides were mapped based on earlier reports and aerial photographs, as well as, carrying out several field surveys. The landslide inventory was randomly split into a training dataset (70%; 212landslides) for training the models and the remaining (30%; 90 landslides) was cast off for validation purpose. A total of sixteen geo-environmental conditioning factors were considered as inputs to the models: slope degree, slope aspect, plan curvature, profile curvature, the new topo-hydrological factor termed height above the nearest drainage (HAND), average annual rainfall, altitude, distance from rivers, distance from roads, distance from faults, lithology, normalized difference vegetation index (NDVI), sediment transport index (STI), stream power index (SPI), soil texture, and land use/cover. The validation of susceptibility maps was evaluated using the area under the receiver operating characteristic curve (AUROC). As a results, the FR outperformed other models with an AUROC of 84.98%, followed by EBF (78.63%) and MD (78.50%) models. The percentage of susceptibility classes for each model revealed that MD model managed to build a compendious map focused at highly susceptible areas (high and very high classes) with an overall area of approximately 17%, followed by FR (22.76%) and EBF (31%). The premier model (FR) attested that the five factors mostly influenced the landslide occurrence in the area: NDVI, soil texture, slope degree, altitude, and HAND. Interestingly, HAND could manifest clearer pattern with regard to landslide occurrence compared to other topo-hydrological factors such as SPI, STI, and distance to rivers. Lastly, it can be conceived that the susceptibility of the area to landsliding is more subjected to a complex environmental set of factors rather than anthropological ones (residential areas and distance to roads). This upshot can make a platform for further pragmatic measures regarding hazard-planning actions.