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This proposed work is presenting the approximation of higher-order (HO) underwater robotic vehicle (URV) controller with the help of multi-point matching technique by incorporating greywolf optimization algorithm (GWOA). The performance of URV system is affected by external and internal dynamics. The proper momentum of URV system is achieved by designing a controller. The URV can be effectively operated by control action of controller. The URV controller is approximated to comparatively lower-order (LO) to propose an efficient, effective and economical controller for HOURV system. The approximation is accomplished with the help of expansion parameters of HOURV controller and its desired LOURV controller. The errors between these expansion parameters of HOURV controller and its desired LOURV controller are minimized using multi-point matching. The multi-point matching is depicted in the form of objective function (OF). The constructed OF is minimized by exploiting GWOA by fulfilling the steady-state matching condition and Hurwitz stability criterion, as constraints. The effectiveness of proposed approach of multi-point matching is verified by comparing the proposed LOURV model with LOURV models obtained with the help of other approximation approaches. The applicability of proposed LOURV controller is evaluated and validated by analyzing responses and tabulated data obtained in the results. Additionally, the statistical data of performance error values (PEVs) are provided in tabulated form along with its bar plot.

This paper is devoted to an overview of the basic properties of the Padé transformation and its generalizations. The merits and limitations of the described approaches are discussed. Particular attention is paid to the application of Padé approximants in the mechanics of liquids and gases. One of the disadvantages of asymptotic methods is that the standard ansatz in the form of a power series in some parameter usually does not reflect the symmetry of the original problem. The search for asymptotic ansatzes that adequately take into account this symmetry has become one of the most important problems of asymptotic analysis. The most developed technique from this point of view is the Padé approximation.

In simulations of three-dimensional transient physics filled through a numerical approach, the order of the equation set of high-fidelity models is extremely high. To eliminate the large dimension of equations, a model order reduction (MOR) technique is introduced. In the existing MOR methods, the block Arnoldi algorithm-based MOR method is numerically stable, achieving a passively reduced order model. Nevertheless, this method performs poorly when it is applied to very wide-frequency transients. To eliminate this deficiency, multipoint MOR methods are emerging. However, it is hard to directly apply an existing multipoint MOR method to a 3-D transient field equation set. The implementation issues in a reduction process (such as the selection of expansion points, the number of moments matched at a point and the error bound) have not been explored in detail. In this respect, an adaptive multipoint model reduction model based on the Arnoldi algorithm is proposed to obtain the reduced-order models of a 3-D temperature field. The originality of this study is the proposal of a novel adaptive algorithm for selecting expansion points, matching moments automatically, using a posterior-error estimator based on temperature response coupled with a network topological method (NTM). The computational efficiency and accuracy of the proposed method are evaluated by the numerical results from solving the temperature field of a prototype insulated-gate bipolar transistor (IGBT).

Models used for reservoir prediction are subject to various types of uncertainty, and interpretational uncertainty is one of the most difficult to quantify due to the subjective nature of creating different scenarios of the geology and due to the difficultly of propagating these scenarios into uncertainty quantification workflows. Non-uniqueness in geological interpretation often leads to different ways to define the model. Uncertainty in the model definition is related to the equations that are used to describe the modelled reality. Therefore, it is quite challenging to quantify uncertainty between different model definitions, because they may include completely different model parameters. This paper is a continuation of work to capture geological uncertainties in history matching and presents a workflow to handle uncertainty in the geological scenario (i.e. the conceptual geological model) to quantify its impact on the reservoir forecasting and uncertainty quantification. The workflow is based on inferring uncertainty from multiple calibrated models, which are solutions of an inverse problem, using adaptive stochastic sampling and Bayesian inference. The inverse problem is solved by sampling a combined space of geological model parameters and a space of reservoir model descriptions, which represents uncertainty across different modelling concepts based on multiple geological interpretations. The workflow includes building a metric space for reservoir model descriptions using multi-dimensional scaling and classifying the metric space with support vector machines. The proposed workflow is applied to a synthetic reservoir model example to history match it to the known truth case reservoir response. The reservoir model was designed using a multi-point statistics algorithm with multiple training images as alternative geological interpretations. A comparison was made between predictions based on multiple reservoir descriptions and those of a single one, revealing improved performance in uncertainty quantification when using multiple training images.

A multi-point geostatistical method for ore grade estimation is introduced in order to fully utilize existing sampling information. A block model is used to construct a new three-dimensional training image instead of a variogram. Data events and pattern matching is improved, and the directionality of the data template is considered in the matching. The inverse distance weighted method is used to make up for the lack of multi-point geostatistics. The research improves the reliability of multi-point geostatistical estimation. Optimal estimation results for Li2O and Ta2O5 come from the inverse distance weighted, ordinary Kriging, and multi-point geostatistical methods. Multi-point geostatistical estimation results are compared with those of the inverse distance weighted and ordinary Kriging methods. Deviation, trend, and variogram analyses are used to assess the effect of multipoint geostatistical estimation. This study shows that reducing the samples participating in the estimation can reduce the maximum and minimum deviation of the estimated grade to a certain extent. The grade distribution pattern is the primary factor affecting minimum and maximum deviation. This study proves the reliability and accuracy of the multipoint geostatistical method for ore grade estimation.

We present a model order reduction algorithm for linear time-invariant descriptor systems of arbitrary derivative order that incorporates sensitivity analysis for network parameters in respect to design parameters. It is based on implicit moment matching via rational Krylov subspace methods with adaptive choice of expansion points and number of moments based on an error indicator. Additionally, we demonstrate how parametric reduced order models can be obtained at nearly no extra costs, such that parameter studies are extremely accelerated. The finite element model of a yaw rate sensor MEMS device has been chosen as a numerical example, but our method is also applicable to systems arising in modeling and simulation of electromagnetics, electrical circuits, machine tools, heat conduction and other phenomena.