1、BS EN ISO 16610-28:2016Geometrical productspecifications (GPS) Filtration Part 28: Profile filters: End effects (ISO 16610-28:2016) BSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS EN ISO 16610-28:2016 BRITISH STANDARDNational forewordThis British Standard is the U
2、K implementation of EN ISO 16610-28:2016. It supersedes DD ISO/TS 16610-28:2010 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee TDW/4, Technical Product Realization.A list of organizations represented on this committee can beobtained on request to its s
3、ecretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2017. Published by BSI Standards Limited 2017ISBN 978 0 580 86272 4ICS 17.040.20; 17.040.40Compliance with a British St
4、andard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 January 2017.Amendments/Corrigenda issued since publicationDate Text affectedEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-
5、28 December 2016 ICS 17.040.40 English Version Geometrical product specifications (GPS) - Filtration - Part 28: Profile filters: End effects (ISO 16610-28:2016) Spcification gomtrique des produits (GPS) - Filtrage - Partie 28: Filtres de profil: Effets de bords (ISO 16610-28:2016) Geometrische Produ
6、ktspezifikation (GPS) - Filterung - Teil 28: Profilfilter: Endeffekte (ISO 16610-28:2016) This European Standard was approved by CEN on 19 November 2016. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the sta
7、tus of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, G
8、erman). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croa
9、tia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and U
10、nited Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2016 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No.
11、EN ISO 16610-28:2016 EBS EN ISO 16610-28:2016EN ISO 16610-28:2016 (E) 3 European Foreword This document (EN ISO 16610-28:2016) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” in collaboration with Technical Committee CEN/TC 29
12、0 “Dimensional and geometrical product specification and verification” the secretariat of which is held by AFNOR. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by June 2017, and conflicting nationa
13、l standards shall be withdrawn at the latest by June 2017. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. According to the CEN-CENELE
14、C Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Icel
15、and, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-28:2016 has been approved by CEN as EN ISO 16610-28:2016 without any modi
16、fication. BS EN ISO 16610-28:2016ISO 16610-28:2016(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 End effect correction methods . 24.1 General . 24.2 Extrapolation of the profile Methods . 44.2.1 Zero padding . 44.2.2 Linear extrapolation . 54.2.3 Symmetri
17、c extension 64.3 Moment retainment criterion 85 Recommendations .145.1 Default end correction . 145.2 End correction designations 15Annex A (normative) Filters according to ISO 16610 with automatic correction of end effects.16Annex B (informative) Relationship to the filtration matrix model .18Annex
18、 C (informative) Relationship to the GPS matrix model 19Bibliography .20 ISO 2016 All rights reserved iiiContents PageBS EN ISO 16610-28:2016ISO 16610-28:2016(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies)
19、. The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non
20、-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are describ
21、ed in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to t
22、he possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO
23、 list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as w
24、ell as information about ISOs adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html.This document was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product specifications and
25、verification.This first edition of ISO 16610-28 cancels and replaces ISO/TS 16610-28:2010, which has been technically revised.A list of all parts in the ISO 16610 series can be found on the ISO website.iv ISO 2016 All rights reservedBS EN ISO 16610-28:2016ISO 16610-28:2016(E)IntroductionThis documen
26、t is a geometrical product specification (GPS) standard and is to be regarded as a general GPS standard (see ISO 14638). It influences the chain link C of all chains of standards.The ISO/GPS Matrix model given in ISO 14638 gives an overview of the ISO/GPS system of which this document is a part. The
27、 fundamental rules of ISO/GPS given in ISO 8015 apply to this document and the default decision rules given in ISO 14253-1 apply to specifications made in accordance with this document, unless otherwise indicated.For more detailed information of the relation of this document to the GPS matrix model,
28、 see Annex C.This document develops the concept of handling end effects in the case of linear profile filters. ISO 2016 All rights reserved vBS EN ISO 16610-28:2016BS EN ISO 16610-28:2016Geometrical product specifications (GPS) Filtration Part 28: Profile filters: End effects1 ScopeThis document pro
29、vides methods for treating the end effects of linear profile filters where such effects occur.2 Normative referencesThe following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition ci
30、ted applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic conceptsISO 16610-20, Geometrical product specifications (GPS) Filtration Part 20: Linear
31、profile filters: Basic conceptsISO 16610-21, Geometrical product specifications (GPS) Filtration Part 21: Linear profile filters: Gaussian filtersISO 16610-22, Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filtersISO 16610-31, Geometrical product specifi
32、cations (GPS) Filtration Part 31: Robust profile filters: Gaussian regression filtersISO/TS 16610-32, Geometrical product specifications (GPS) Filtration Part 32: Robust profile filters: Spline filtersISO/IEC Guide 99, International vocabulary of metrology Basic and general concepts and associated t
33、erms (VIM)3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO/IEC Guide 99, ISO 16610-1, ISO 16610-20, ISO 16610-21, ISO 16610-22, ISO 16610-31, ISO/TS 16610-32 and the following apply.ISO and IEC maintain terminological databases for use in standardizati
34、on at the following addresses: IEC Electropedia: available at http:/www.electropedia.org/ ISO Online browsing platform: available at http:/www.iso.org/obp3.1end effectunintentional changes in the filtration response in the end portions of an open profile3.2end effect regionend portion of an open pro
35、file where end effects are significantINTERNATIONAL STANDARD ISO 16610-28:2016(E) ISO 2016 All rights reserved 1BS EN ISO 16610-28:2016ISO 16610-28:2016(E)3.3momentnth moment, n, of a real valued function f(x), defined bynnxfxx=()d3.4moment criterioncriterion applying to the shift invariant filter c
36、lass of a linear profile filter where the weighting function of the filtration operation has vanishing moments up to the nth order, as expressed byxsxx pnp()= =d01,.,wheres(x) is the weighting function of the filter and the definition area of the weighting function4 End effect correction methods4.1
37、GeneralA linear shift invariant profile filter can be implemented as a weighted moving average with a constant weighting function, s(x), e.g. the Gaussian bell curve according to ISO 16610-21. Because the measured profile, z(x), is always finite, s(x) shall have a local support, l1 x l2, which is no
38、rmally much smaller than the traversing length. Therefore, the filter formula for the low-pass filter based on the convolution is defined aswx zx usuu zu sx uulxlllxlxlt()=()()=()()+dd12212, l1(1)wherew(x) is the reference line;z(x) is the measured profile;ltis the measuring length.In contrast to pr
39、ofile z(x), reference line w(x) is only valid for l2 x lt l1. The end effect regions are B2= 0,l2 and B1= lt l1,lt.NOTE 1 For simplicity, only continuous weighting functions s(x) are considered in this document. The methods are also valid for discrete weighting functions.NOTE 2 The procedure can be
40、applied directly to the profile or can modify the filtration operation.EXAMPLE In the case of the standardized Gaussian filter (see ISO 16610-21), the weighting function has a local support, e.g. l1= l2= c/2. As shown in Figure 1, the filter formula cannot be applied over the whole traversing length
41、. In the end effect region, either the left side or the right side of the Gaussian bell curve lies outside the profile.2 ISO 2016 All rights reservedBS EN ISO 16610-28:2016ISO 16610-28:2016(E)KeyB1 l2right end effect regionB2 l1left end effect regionaEnd effect region.Figure 1 End effects using stan
42、dardized Gaussian filterDue to their mathematical definition, the filters specified in ISO 16610-22, ISO 16610-29, ISO/TS 16610-32 (spline filter) and ISO 16610-31 (Gaussian regression filter) have an automatic end effect correction. Annex A presents the corresponding weighting function for differen
43、t positions of the linear spline filter and the linear Gaussian regression filter. ISO 2016 All rights reserved 3BS EN ISO 16610-28:2016ISO 16610-28:2016(E)4.2 Extrapolation of the profile Methods4.2.1 Zero paddingZero padding is a simple method for retaining the traversing length after filtering th
44、e profile. Profile z(x) is padded with zeros over length l2at the left side and over length l1at the right side of the profile:zxlxzx xllxllttt()= 100021forfor(9)At the end effect region, 0 x l2and lt l1 x lt, bp(x) can be calculated by solving the matrix formula:x x xx x xx x xnnnn n0112 112() () (
45、)() () ()() () ()+midhorizellipsismidhorizellipsisvertellipsisvertellipsisdownslopeellipsisvertellipsismidhorizellipsis()()()=bxbxbxn01100vertellipsis vertellipsis(10)withx xu sx uupnppxlxllt()=()()=()+()dmaxmin21002, (11)EXAMPLE 1 Due to its symmetrical weighting function, the standardized Gaussian
46、 filter has one vanishing moment, p = 1. When solving Formula (10), correction function bp(x) at the end effect region results inbx x xbxxx02 11()=() () ()=() ()/, /detdet (12)withdet xxxx()=()()()2012The corresponding weighting function for l1= l2= c/2 at different positions is shown in Figure 8. F
47、or further information, see Reference 5. ISO 2016 All rights reserved 9BS EN ISO 16610-28:2016ISO 16610-28:2016(E)KeyB1 l2right end effect regionB2 l1left end effect regionaEnd effect region.Figure 8 Retained moment condition n = 1, using standardized Gaussian filterDue to the chosen moment conditio
48、n, n = 1, the filter can exactly approximate a tilted profile as shown in Figure 9.10 ISO 2016 All rights reservedBS EN ISO 16610-28:2016ISO 16610-28:2016(E)KeyB1 l2right end effect regionB2 l1left end effect regionaEnd effect region.Figure 9 Retained moment condition n = 1, using standardized Gauss
49、ian filter and tilted profileAs shown in Figure 10, moment condition n = 1 leads also to a good approximation of a profile with an arc. ISO 2016 All rights reserved 11BS EN ISO 16610-28:2016ISO 16610-28:2016(E)KeyB1 l2right end effect regionB2 l1left end effect regionaEnd effect region.Figure 10 Retained moment condition n = 1, using standardized Gaussian filter and profile w
