ASTM_E_3076_-_18.pdf

Designation:E307618Standard Practice forDetermination of the Slope in the Linear Region of a TestRecord1This standard is issued under the fixed designation E3076;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.1.Scope1.1 This practice presents an automated,objective linear-fitting method for determining the slope of the linear portion ofa test record.The method assumes that there is a linear regionearly in the test record where the value of the y variableincreases roughly in proportion to the x variable and the slopeof the record decreases after the linear region.The practicedetermines the best linear fit to the data based on the leastnormalized residual and provides metrics for evaluating thequality of the test record and the quality of the resultant fit.1.2 Data quality metrics are applied that evaluate the levelof noise and the digital resolution of the data to determine if thetest record is adequate for a linear regression analysis.Fitquality metrics use analysis of residuals in the vicinity of the fitrange to determine if the test record is adequately linear and thefit range is sufficiently large.1.3 For test records that meet the data and fit quality metrics,the practice determines a repeatable slope without the need foroperator input that is independent of operator judgment.Fortest records that fail one or more of the quality metrics,it isrecommended that the analyst evaluate the fit to determine if itis acceptable.1.4 This practice represents a general purpose approach thatis applicable for any test standard or method in which a linearfit is desired.It is intended that this practice can be called uponby standard test methods when slope must be determined.1.5 This standard does not purport to address all of thesafety concerns,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety,health,and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade(TBT)Committee.2.Referenced Documents2.1 ASTM Standards:2E1942 Guide for Evaluating Data Acquisition Systems Usedin Cyclic Fatigue and Fracture Mechanics TestingE2443 Guide for Verifying Computer-Generated Test Re-sults Through The Use Of Standard Data Sets2.2 ASTM Data Set:3E3076-DS1(2018)File 01 Benchmark Data Set to EvaluateComputer Implementation of the Algorithm in StandardE3076.3.Terminology3.1 Definitions:3.1.1 digital resolution,nthe precision of stored informa-tion resulting from a discrete digital representation of analogdata.3.1.2 linear region,na region of the test record where theunderlying physics indicate that the dependent variable wouldincrease in proportion to the independent variable if there wereno noise in the test record.3.1.3 normalized,ndata with global minima of 0 andglobal maxima of 1 in x and y.3.1.4 residual,nthe difference between the linear fit andthe original test record y-values at a given x-value.3.1.5 test record,nthe basic raw data from a data set4.Summary of Practice4.1 This practice is intended for the analysis of test recordswhere the y variable increases roughly in proportion to the xvariable over a region early in the test record.4.2 The linear-fitting algorithm utilizes analysis of residualscoupled with computational effort to numerically determine the1This practice is under the jurisdiction ofASTM Committee E08 on Fatigue andFracture and is the direct responsibility of Subcommittee E08.03 on AdvancedApparatus and Techniques.Current edition approved Nov.15,2018.Published April 2019.DOI:10.1520/E3076182For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.3This data set is available for download from ASTM at https:/www.astm.org/COMMITTEE/E08.htm,under the heading,Additional Information.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade(TBT)Committee.1 most linear region in a given test record.4The analysis ofresiduals methodology is more robust than conve