PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES

Kadir Kıran

doi:10.54365/adyumbd.997113

TR EN

ÖLÇÜLEN 2B PROFİLLERE GEOMETRİ UYDURULMASINDA GRADYAN TEMELLİ DOĞRU BOYUNCA ARAMA ŞARTLARI DİKKATE ALINARAK EN DİK İNİŞ YÖNTEMİNİN PERFORMANS DEĞERLENDİRMESİ

Öz

Bu çalışmada ölçülen 2B profillere geometri uydurulmasında doğru boyunca aramada kullanılan adım uzunluğu hesaplama yöntemlerinin en dik iniş yönteminin performansına etkisinin ortaya çıkarılmasına odaklanılmaktadır. Bu amaçla, zayıf Wolfe, güçlü Wolfe ve tam olarak minimize eden adım uzunluğunu bulan olmak üzere üç adım uzunluğu hesaplama yöntemi ya da doğru boyunca arama şartları geometri uydurma sürecinde kullanılmıştır. Doğru boyunca arama şartlarının performansını test etmek amacıyla, daire, kare, üçgen, elips ve dikdörtgen geometrilerini içeren bir 2B temel geometri seti kullanılmıştır. Bu geometrilerin profilleri yüksek hassasiyet ile koordinat ölçme cihazı ile elde edilmiştir. Performans değerlendirmeleri için ilgili en dik iniş yöntemi-doğru boyunca arama şartı kombinasyonu istenen tolerans değerini sağladığında ortaya çıkan toplam fonksiyon kullanım sayısı kullanılmıştır. Doğru boyunca arama şartlarının güvenilir ve verimli bir şekilde performans değerlendirilmesini yapmak için bu veriler vasıtasıyla performans profilleri oluşturulmuştur. Sonuçlar adım uzunluğu hesaplama tekniklerinin en dik iniş yöntemi performansında önemli bir rol oynadığını göstermektedir. Performans profillerine dayanarak, en hızlı doğru boyunca arama şartı zayıf Wolfe olarak saptanmıştır. Bunun yanı sıra, çalışmada geometri uydurma süreci için optimum yöntemin tam olarak minimize eden adım uzunluğunu bulan yöntem olduğu ortaya çıkarılmıştır.

Anahtar Kelimeler

En dik iniş yöntemi , Performans profilleri , Doğru boyunca arama , Geometri uydurma , Optimizasyon

PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES

Abstract

This paper focuses on exploring effect of the step length, used in the line search, computation techniques on the performance of steepest descent (SD) method in the geometry fitting of the 2D measured profiles. To this end, the three step length computation techniques or line search conditions accommodating Weak Wolfe (WWC), Strong Wolfe (SWC) and the exact minimizer finder have been implemented during the fitting process. To test the line search conditions performances, the 2D primitive geometry test set consisting of five different geometries such as circle, square, triangle, ellipse and rectangle have been employed. The 2D profiles of those geometries have been extracted using coordinate measuring machine (CMM) with high precision. For performance assessments, the total number of function evaluations when the SD method-line search condition combination satisfies the required converge tolerance have been used. By means of those data, the performance profiles have been created to conduct reliable and efficient assessments on the line search conditions. The results have shown that the step length computation technique plays a crucial role for the SD method performance. Based on the performance profiles, it has been determined that the fastest line search condition is the WWC. Besides that, it has been revealed that the optimum technique is the exact minimizer finder for the geometry fitting process in the study.

Keywords

Steepest descent method , Performance profiles , Line search , Geometry fitting , Optimization

References

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Kadir Kıran ^*
0000-0002-6109-435X
Türkiye

Publication Date

December 31, 2021

Submission Date

September 17, 2021

Acceptance Date

November 10, 2021

Published in Issue

Year 1970 Volume: 8 Number: 15

DOI

https://doi.org/10.54365/adyumbd.997113

IZ

https://izlik.org/JA67GG43LA

APA

Kıran, K. (2021). PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, 8(15), 515-524. https://doi.org/10.54365/adyumbd.997113

AMA

1.Kıran K. PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2021;8(15):515-524. doi:10.54365/adyumbd.997113

Chicago

Kıran, Kadir. 2021. “PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8 (15): 515-24. https://doi.org/10.54365/adyumbd.997113.

EndNote

Kıran K (December 1, 2021) PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8 15 515–524.

IEEE

[1]K. Kıran, “PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES”, Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, vol. 8, no. 15, pp. 515–524, Dec. 2021, doi: 10.54365/adyumbd.997113.

ISNAD

Kıran, Kadir. “PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8/15 (December 1, 2021): 515-524. https://doi.org/10.54365/adyumbd.997113.

JAMA

1.Kıran K. PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2021;8:515–524.

MLA

Kıran, Kadir. “PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, vol. 8, no. 15, Dec. 2021, pp. 515-24, doi:10.54365/adyumbd.997113.

Vancouver

1.Kadir Kıran. PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2021 Dec. 1;8(15):515-24. doi:10.54365/adyumbd.997113

Cited By

Performance evaluation of a conjugate gradient method considering step length computation techniques in geometry fitting of coordinate measuring machine data

Measurement

https://doi.org/10.1016/j.measurement.2022.111202