对乘法模型的一种方法进行了实验阐述

Hrihorii Larionov, Yu.V. Zemlyanaya
{"title":"对乘法模型的一种方法进行了实验阐述","authors":"Hrihorii Larionov, Yu.V. Zemlyanaya","doi":"10.15407/geotm2022.162.029","DOIUrl":null,"url":null,"abstract":"Description of functions in the vicinity of a point within the domain of a function is most often used for problems solution of mathematical physics as the Taylor series approximation. The reason for this approximation seems to be the application of function derivatives. The greater the order of derivatives, the more accurately the function in vicinity of the selected point could be presented. However, there is a necessity exists to define functions at the point of the mathematical models during experimental studies in a variety field of science. Mostly, two types of the models are used - additive and multiplicative ones. The multiplicative model is distinguished by the practical sense as well as widespread use. The fact is that the nature of a particular function research for technology industrial problems consists in the sequential change of its parameters. The study of function change upon condition of a single parameter change involves the retention of other parameters of certain pre-selected values, i.e. at a certain point in the functional space of parameters. It is not always clear that the result of the experimental study is finding the values of the function exceptionally in the vicinity of this point, not within the function domain. Neglecting this circumstance along with attempts to find the values of the function far out beyond the vicinity of selected point leads to the values of the function with inappropriate error. The approximate representation of scalar functions in the multiplicative form in the vicinity of the point has a wide range of applications, especially for geomechanics. It turned out that the approximate representation of scalar functions in a multiplicative form at a point within the domain could be extended to the whole domain. Moreover, the maximum error of a representation at the boundary of the domain for geotechnical problems, as a rule, does not exceed 5-7%, which is acceptable for engineering calculations. To test an efficiency of the successive approximations method an applied geomechanical problem has been solved. The conclusion on the efficiency of method for geomechanical problem is made. Keywords: mathematical model, successive approximations method, active experimental study, function.","PeriodicalId":222378,"journal":{"name":"Geo-Technical Mechanics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On one method of multiplicative models elaboration during experiments\",\"authors\":\"Hrihorii Larionov, Yu.V. Zemlyanaya\",\"doi\":\"10.15407/geotm2022.162.029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Description of functions in the vicinity of a point within the domain of a function is most often used for problems solution of mathematical physics as the Taylor series approximation. The reason for this approximation seems to be the application of function derivatives. The greater the order of derivatives, the more accurately the function in vicinity of the selected point could be presented. However, there is a necessity exists to define functions at the point of the mathematical models during experimental studies in a variety field of science. Mostly, two types of the models are used - additive and multiplicative ones. The multiplicative model is distinguished by the practical sense as well as widespread use. The fact is that the nature of a particular function research for technology industrial problems consists in the sequential change of its parameters. The study of function change upon condition of a single parameter change involves the retention of other parameters of certain pre-selected values, i.e. at a certain point in the functional space of parameters. It is not always clear that the result of the experimental study is finding the values of the function exceptionally in the vicinity of this point, not within the function domain. Neglecting this circumstance along with attempts to find the values of the function far out beyond the vicinity of selected point leads to the values of the function with inappropriate error. The approximate representation of scalar functions in the multiplicative form in the vicinity of the point has a wide range of applications, especially for geomechanics. It turned out that the approximate representation of scalar functions in a multiplicative form at a point within the domain could be extended to the whole domain. Moreover, the maximum error of a representation at the boundary of the domain for geotechnical problems, as a rule, does not exceed 5-7%, which is acceptable for engineering calculations. To test an efficiency of the successive approximations method an applied geomechanical problem has been solved. The conclusion on the efficiency of method for geomechanical problem is made. Keywords: mathematical model, successive approximations method, active experimental study, function.\",\"PeriodicalId\":222378,\"journal\":{\"name\":\"Geo-Technical Mechanics\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geo-Technical Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15407/geotm2022.162.029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geo-Technical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15407/geotm2022.162.029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在函数的定义域内对点附近的函数的描述最常用于数学物理问题的求解,如泰勒级数近似。这种近似的原因似乎是函数导数的应用。导数阶数越大,表示所选点附近的函数越准确。然而,在各种科学领域的实验研究中,有必要在数学模型的点上定义函数。通常使用两种类型的模型:加性模型和乘性模型。乘法模型具有实用意义和广泛应用的特点。事实上,技术产业问题的特定函数研究的本质在于其参数的顺序变化。研究单参数变化条件下的函数变化,涉及到其他参数保持一定的预选值,即在参数函数空间的某一点上。我们并不总是很清楚,实验研究的结果是在这一点附近,而不是在函数域内,找到异常的函数值。忽略这种情况,并试图在远超出所选点附近的地方寻找函数值,会导致函数值具有不适当的误差。标量函数在点附近以乘法形式的近似表示具有广泛的应用,特别是在地质力学中。结果表明,标量函数在定义域内一点处的近似乘法表示可以推广到整个定义域。此外,对于岩土工程问题,域边界表示的最大误差通常不超过5-7%,这对于工程计算是可以接受的。为了验证逐次逼近法的有效性,解决了一个应用地质力学问题。对该方法求解地质力学问题的有效性进行了总结。关键词:数学模型,逐次逼近法,主动实验研究,函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On one method of multiplicative models elaboration during experiments
Description of functions in the vicinity of a point within the domain of a function is most often used for problems solution of mathematical physics as the Taylor series approximation. The reason for this approximation seems to be the application of function derivatives. The greater the order of derivatives, the more accurately the function in vicinity of the selected point could be presented. However, there is a necessity exists to define functions at the point of the mathematical models during experimental studies in a variety field of science. Mostly, two types of the models are used - additive and multiplicative ones. The multiplicative model is distinguished by the practical sense as well as widespread use. The fact is that the nature of a particular function research for technology industrial problems consists in the sequential change of its parameters. The study of function change upon condition of a single parameter change involves the retention of other parameters of certain pre-selected values, i.e. at a certain point in the functional space of parameters. It is not always clear that the result of the experimental study is finding the values of the function exceptionally in the vicinity of this point, not within the function domain. Neglecting this circumstance along with attempts to find the values of the function far out beyond the vicinity of selected point leads to the values of the function with inappropriate error. The approximate representation of scalar functions in the multiplicative form in the vicinity of the point has a wide range of applications, especially for geomechanics. It turned out that the approximate representation of scalar functions in a multiplicative form at a point within the domain could be extended to the whole domain. Moreover, the maximum error of a representation at the boundary of the domain for geotechnical problems, as a rule, does not exceed 5-7%, which is acceptable for engineering calculations. To test an efficiency of the successive approximations method an applied geomechanical problem has been solved. The conclusion on the efficiency of method for geomechanical problem is made. Keywords: mathematical model, successive approximations method, active experimental study, function.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信