Generalized Algorithm for Finding Outliers in a Regression Model

One of the actively developing areas of modern computational problems is data analysis. The studied data have a different structure, which causes certain difficulties in the process of smoothing and analysis. This fact entails the need to search for new universal algorithms for data processing and create computer programs that analyze data of various nature. Today, a widely used method of data processing is regression modeling. It is used in problems of pattern recognition, classification, dimensionality reduction, and many others. The literature describes various methods of constructing regression models, the basis of which is the optimization of a certain indicator — the quality functional. A very important requirement for the quality of such models is the absence of outliers (outliers) in the data. This article discusses a method for examining a sample for outliers. The obtained algorithm can be applied to regression models estimated by the most common methods (least squares method, least modulus method). The mathematical basis of this procedure is the Legendre transformation, which provides computational accuracy in computer implementation. The adequacy of the obtained algorithm was investigated on a number of test samples. All tests were positive in terms of emissions. The MatLab system is used to develop a set of programs, which allows the building of various regression models and evaluation of the original sample for sharply distinguished observations.

CHOOSING A METHOD FOR ESTIMATING THE PARAMETERS OF LINEAR REGRESSION BASED ON IDENTIFICATION OF ANOMALOUS OBSERVATIONS

Описываются свойства методов оценивания параметров регрессионных моделей - наименьших квадратов, модулей, антиробастного, а также их применения для решения конкретных практических проблем. При этом метод наименьших модулей не реагирует на аномальные наблюдения выборки, метод антиробастного оценивания сильно отклоняет линию регрессии в их направлении, метод наименьших квадратов занимает промежуточное положение. Показано, что если целью построения модели является проведение на ее основе многовариантных прогнозных расчетов значений зависимой переменной, то выбор метода численной идентификации параметров модели следует производить на основе анализа характера выбросов. Если есть основания полагать, что подобные им ситуации могут иметь место в будущем, следует выбрать метод антиробастного оценивания, в противном же случае - метод наименьших модулей. Построена регрессионная модель грузооборота Красноярской железной дороги на основе применения всех трех методов оценивания параметров. Проведен анализ причин, имеющих место в 2010 году в ситуации резкого падения величины грузооборота, которая вполне может характеризоваться как аномальное наблюдение в данных. Сделаны рекомендации по выбору метода оценивания параметров в этом случае The article describes the properties of methods for estimating the parameters of regression models - least squares, moduli, anti-robust - as well as their application for solving specific practical problems. At the same time, the method of least modules does not respond to anomalous observations of the sample, the method of anti-robust estimation strongly deviates the regression line in their direction, the method of least squares occupies an intermediate position. I show that if the purpose of constructing a model is to carry out multivariate predictive calculations of the values of the dependent variable on its basis, then the choice of a method for the numerical identification of model parameters should be based on an analysis of the nature of emissions. If there is a reason to believe that similar situations may occur in the future, the anti-robust estimation method should be chosen, otherwise - the least modulus method. I built a regression model of the freight turnover of the Krasnoyarsk railway on the basis of the application of all three methods of parameter estimation. I carried out the analysis of the reasons for the situation of a sharp drop in the value of cargo turnover in 2010, which may well be characterized as anomalous observation in the data. I give recommendations on the choice of the parameter estimation method in this case

Laboratory Model Test to Explore the Bearing Mechanism of Composite Foundation in the Loess Area

Pile composite foundation can make good use of the bearing capacity of the soil and pile, which is widely used in the Chinese northwest loess area. However, the theory of pile composite foundation is far from sufficient, hindering its long-term development. Aiming at this problem, a laboratory model test of pile composite foundation in the loess area was conducted to explore the common working mechanism and variations of each bearing stage. Besides, the settlement of the single pile composite foundation was calculated by using the modified tangent modulus method, and the result was compared with the experimental data. The main results of this paper are as follows: Both in the single pile and single pile composite foundation, loading-settlement curves showed a trend of “elastic to elastoplastic to plastic,” accompanied by the appearance of plummeting point. Influenced by the pile group effect, the loading-settlement curve of the group pile composite foundation showed a slow-varying trend without an obvious breakdown point. Pile axis stress increased with the growth of upper load. At the beginning of loading, the pile axis stress indicated such a distribution that stress on both ends of the pile was larger than that in the middle of the pile. When reaching a certain load, the location of the biggest pile axis stress transferred to the pile top, and the pile axis stress decreased gradually as the pile became deep. The side friction resistance in the static load test of the single pile was always positive, whereas in the composite foundation of a single pile and a group of piles, negative side resistance appeared in the upper side of the neutral point. Pile-soil stress ratio in the depth of 12 cm changed with the upper load. The outcome calculated by the modified tangent modulus method had a relatively better consistency with experimental data if the upper load was not too large.

Determination of corrugated core sandwich panels elastic constant based on three different experimental methods and effect of structural integrity on flexural properties

This study deals with the investigation of flexural stiffness and transverse shear rigidity in the direction of corrugation of the integrated and non-integrated corrugated core sandwich panels with the rectangular core. The non-integrated sandwich panels were reinforced with conventional 2-D fabrics in which resin provides the bond between core and skins. The integrated sandwich panels were reinforced with 3-D weft knitted fabrics in which bonding of the core wall to skins was carried out by combined efforts of knitted loop and resin. Using weft knitting technical capabilities, samples of the integrated and non-integrated structures were manufactured with the uppermost degree of resemblance in terms of geometry and mass. Flexural stiffness and transverse shear rigidity of the structures based on the known and unknown facing modulus of ASTM D7250 standard and Nordstrand–Carlsson methods were calculated. The estimated elastic constants based on unknown facing modulus and the Nordstrand–Carlsson methods were found to be highly compatible. However, the unknown facing modulus method is prone to disclose the statistical significant differences between the elastic constants of the structures with fewer tests. Regarding the unknown facing modulus method, it was found that the flexural stiffness and transverse shear rigidity of the non-integrated structure in the direction of corrugation were higher than those of the integrated structure. Results also indicated that the load-carrying capacity in the direction of corrugation was significantly higher in case of the non-integrated rectangular core structure compared with that of the integrated structure.

Time-dependent behaviour of concrete

<p>This chapter provides an introduction to the constitutive models commonly specified in design guidelines to describe the time-dependent behaviour of concrete and that can be used for the time-dependent analysis of composite structures. These formulations range from the simplest algebraic methods, such as the Effective Modulus Method that is widely recommended in design guidelines, to more sophisticated approaches that can account for creep and shrinkage effects in advanced modelling. The last part of the chapter provides a brief overview of multi-physics modelling that could be useful in predicting the concrete time-dependent response for composite construction.</p>

Introduction

<p>This chapter provides an introduction to the constitutive models commonly specified in design guidelines to describe the time-dependent behaviour of concrete and that can be used for the time-dependent analysis of composite structures. These formulations range from the simplest algebraic methods, such as the Effective Modulus Method that is widely recommended in design guidelines, to more sophisticated approaches that can account for creep and shrinkage effects in advanced modelling. The last part of the chapter provides a brief overview of multi-physics modelling that could be useful in predicting the concrete time-dependent response for composite construction.</p>

Algorithm For Calculation Of Multi Span Uncut Beams Taking Into Account The Nonlinear Work Of Reinforced Concrete

An algorithm for calculating multi-span continuous beams is developed on the basis of the integral deformation modulus method. This takes into account the nonlinear and nonequilibrium properties of concrete deformation, the rheological equations of the mechanical state.

The Influence of Blade Angle on the Performance of Plastic Centrifugal Pump

In order to obtain the influence of blade placement angle on the performance of plastic centrifugal pumps, this article used the velocity modulus method. Based on the method, the hydraulic design of the flow passage components of the plastic centrifugal pump was carried out, and the two-dimensional model and three-dimensional model diagram of the flow components were established. The flow field of the impeller model under different working conditions was simulated and the results were analyzed by ANSYS CFX. The influence of different fluid loads on the solid structure under design conditions on the structure characteristics of the impeller was studied by ANSYS Workbench. Impeller models with different outlet angles were established to study the influence of the outlet angle on the performance of pump, and fluid-structure interaction for different impeller models was utilized to study the influence of the outlet angle on the structural characteristics of the impeller. According to the Stepanoff velocity modulus method, considered the import prerotation, the wrap angle design method and the blade inlet angle design method were proposed. In order to study the influence of different inlet angles on the performance of pump, the inlet angle was changed to establish multiple sets of impeller models, 3D printing technology was used to print out each impeller, and performance experiments were performed on the pump equipped with the impeller. The result of the experiments showed that working pressure of plastic centrifugal pump exceeding 5 atm would cause impeller structure damage. When the outlet angle was 35°, the plastic centrifugal pump reached the highest efficiency of 81.0161% and the highest H of 35.8029. The maximum deformation caused by the flow field load on the impeller increased with the increase of the outlet angle. With the increase of the inlet angle, the efficiency and H of the plastic centrifugal pump were reduced. Under normal pressure load, the deformation of the impeller first decreased and then increased, and when β1 was 13°, the total deformation of the impeller was the smallest.