1、March 2017 English price group 11No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 17.040.40!%bo(“2637605www.din.deDI
2、N EN ISO 16610-31Geometrical product specifications (GPS) Filtration Part 31: Robust profile filters: Gaussian regression filters (ISO 1661031:2016);English version EN ISO 1661031:2016,English translation of DIN EN ISO 16610-31:2017-03Geometrische Produktspezifikation (GPS) Filterung Teil 31: Robust
3、e Profilfilter: Gausche Regressionsfilter (ISO 1661031:2016);Englische Fassung EN ISO 1661031:2016,Englische bersetzung von DIN EN ISO 16610-31:2017-03Spcification gomtrique des produits (GPS) Filtrage Partie 31: Filtres de profil robustes: Filtres de rgression gaussiens (ISO 1661031:2016);Version a
4、nglaise EN ISO 1661031:2016,Traduction anglaise de DIN EN ISO 16610-31:2017-03www.beuth.deDocument comprises 21 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.02.17 DIN EN ISO 16610-31:2017-03 2 A comma is used as the decimal
5、marker. National foreword This document (EN ISO 16610-31:2016) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specification and verification” (Secretariat: DS, Denmark) in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product
6、 specification and verification” (Secretariat: AFNOR, France). The responsible German body involved in its preparation was DIN-Normenausschuss Technische Grundlagen (DIN Standards Committee Technical Fundamentals), Working Committee NA 152-03-03 AA Oberflchen. The DIN Standards corresponding to the
7、International Standards referred to in this document are as follows: ISO 3274 DIN EN ISO 3274 ISO 8015 DIN EN ISO 8015 ISO 14253-1 DIN EN ISO 14253-1 ISO 14638 DIN EN ISO 14638 ISO 16610-1 DIN EN ISO 16610-1 ISO 16610-20 DIN EN ISO 16610-20 ISO 16610-301)DIN EN ISO 16610-30 ISO/IEC Guide 99 VIM, Int
8、ernational vocabulary of metrology2)1)In preparation. 2)Obtainable from: Beuth Verlag GmbH, 10772 Berlin, Order no. 22472, ISBN 978-3-410-22472-3. DIN EN ISO 16610-31:2017-03 3 National Annex NA (informative) Bibliography DIN EN ISO 3274, Geometrical product specifications (GPS) Surface texture: Pro
9、file method Nominal characteristics of contact (stylus) instruments DIN EN ISO 8015, Geometrical product specifications (GPS) Fundamentals Concepts, principles and rules DIN EN ISO 14253-1, Geometrical product specifications (GPS) Inspection by measurement of workpieces and measuring equipment Part
10、1: Decision rules for proving conformity or nonconformity with specifications DIN EN ISO 14638, Geometrical Product Specifications (GPS) Matrix model DIN EN ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts DIN EN ISO 16610-20, Geometrical product s
11、pecifications (GPS) Filtration Part 20: Linear profile filters: Basic concepts DIN EN ISO 16610-30, Geometrical product specifications (GPS) Filtration Part 30: Robust profile filters: Basic concepts VIM, International vocabulary of metrology DIN EN ISO 16610-31:2017-03 4 This page is intentionally
12、blank EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-31 November 2016 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration -Part 31: Robust profile filters: Gaussian regression filters(ISO16610-31:2016) Spcification gomtrique des produits (GPS) - Filtra
13、ge -Partie 31: Filtres de profil robustes: Filtres de rgression gaussiens (ISO 16610-31:2016) Geometrische Produktspezifikation (GPS) - Filterung - Teil 31: Robuste Profilfilter: Gausche Regressionsfilter (ISO 16610-31:2016) This European Standard was approved by CEN on 22 October 2016. CEN members
14、are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application t
15、o the CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). 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
16、Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lith
17、uania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey andUnited Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-
18、1000 Brussels 2016 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-31:2016 EForeword 4Introduction 51 Scope . 62 Normative references 63 Terms and definitions . 64 Robust Gaussian regression filter 74.1 Weighting function
19、 74.2 Filter equation . 74.2.1 General 74.2.2 Filter equation for the robust Gaussian regression filter for open profiles 74.2.3 Filter equation for robust Gaussian regression filter for closed profiles .104.2.4 Transmission characteristics .115 Recommendations for nesting index (cutoff values c) .1
20、16 Filter designation11Annex A (informative) Examples .12Annex B (informative) Relationship to the filtration matrix model .15Annex C (informative) Relationship to the GPS matrix model 16Bibliography .17Contents PageEN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 2European foreword .3European f
21、oreword This document (EN ISO 16610-31:2016) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the secreta
22、riat 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 May 2017, and conflicting national standards shall be withdrawn at the latest by May 2017. Attention is drawn to the
23、 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-CENELEC Internal Regulations, the national standards organizations of the following countr
24、ies 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, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Pola
25、nd, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-31:2016 has been approved by CEN as EN ISO 16610-31:2016 without any modification. EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 3 ForewordISO (the In
26、ternational Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). 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 h
27、as been established has the right to be represented on that committee. International organizations, governmental and non-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
28、 standardization.The procedures used to develop this document and those intended for its further maintenance are described 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 ac
29、cordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the 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. Deta
30、ils of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO 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 en
31、dorsement.For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well 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.ht
32、ml.The committee responsible for this document is ISO/TC 213, Dimensional and geometrical product specifications and verification.This first edition of ISO 16610-31 cancels and replaces ISO/TS 16610-31, which has been technically revised.A list of all parts in the ISO 16610 series can be found on th
33、e ISO website.EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 4 IntroductionThis document 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.For more detailed informatio
34、n of the relation of this document to the GPS matrix model, see Annex C.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 fundamental rules of ISO/GPS given in ISO 8015 apply to this document and the default decision rules given
35、 in ISO 14253-1 apply to specifications made in accordance with this document, unless otherwise indicated.This document develops the concept of the discrete robust Gaussian regression filter. The robust process reduces the influence of the deep valleys and high peaks. The subject of this document is
36、 the robust Gaussian regression filter of degree p = 2, which has very good robust behaviour and form approximation for functional stratified engineering surfaces.EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 5 1 ScopeThis document specifies the characteristics of the discrete robust Gaussian
37、 regression filter for the evaluation of surface profiles with spike discontinuities such as deep valleys and high peaks.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 refe
38、rences, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 16610-1:2015, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts3 Terms and definitionsFor the purposes of this do
39、cument, the terms and definitions given in ISO/IEC Guide 99, ISO 16610-1, ISO 16610-20, ISO 16610-30 and the following apply.ISO and IEC maintain terminological databases for use in standardization at the following addresses: IEC Electropedia: available at http:/www.electropedia.org/ ISO Online brow
40、sing platform: available at http:/www.iso.org/obp3.1robust filterfilter that is insensitive to output data against specific phenomena in the input data3.2regression filterM-estimator based on the local polynomial modelling of the profile3.3robust Gaussian regression filterregression filter (3.2) bas
41、ed on the Gaussian weighting function and a biweight influence function (3.4)3.4biweight influence functionasymmetric function which is scale-invariant, expressed by xxxcxcxc()=1022forforwhere c is the scale parameter.EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 6 4 Robust Gaussian regressio
42、n filter4.1 Weighting functionThe weighting function of the robust Gaussian regression filter depends on the profile values (distance to the reference line) and the location of the weighting function along the profile.4.2 Filter equation4.2.1 GeneralThe robust Gaussian regression filter is derived f
43、rom the general discrete regression filter (see Annex A) by setting the degree to p = 2, using the biweight influence function and the Gaussian weighting function according to ISO 16610-21. In the case of p = 2, the robust Gaussian regression filter follows form components up to the second degree.4.
44、2.2 Filter equation for the robust Gaussian regression filter for open profilesFor open profiles, the filter equation for the robust Gaussian regression filter is given by Formula (1):wkkTkk kTk=( )1001XSXXSz (1)The regression function is spanned by the matrixXkkknk nkxxxx=111122, (2)wherexlkx lnlk,
45、.,=()= 1 (3)EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 7 The space variant weighting function, Sk, is given by Formula (4):Skkknk nsss=1122000000,midhorizellipsisvertellipsisvertellipsisdownslopeellipsismidhorizellipsis(4)with the Gaussian functionsxlnlklk,=112ccexp pi(5)and the parameter
46、= ()1120Wexp1730 9pi, (6)The additional weightslllllllzwczw czw c=1022forfor=, ,ln1(7)are derived from the biweight influence function with the parameterc =() 312erf 0,5median 4,447 8medianzzww (8)The definition for c is equivalent to three times Rq of the surface roughness for Gaussian distributed
47、profiles and is the default case.EN ISO 16610-31:2016 (E) DIN EN ISO 16610-31:2017-03 8 whereW(X) is the “Lambert W” function;erf1(x)is the inverse error function;n is the number of values in the profile;k is the index of the profile ordinate k = 1, , n;z is the vector of dimension n of the profile values before filtering;w is the vector of dimension n of the profile values of the filter reference lin
