1、BS EN ISO 16610-31:2016Geometrical productspecifications (GPS) FiltrationPart 31: Robust profile filters: Gaussianregression filters (ISO 16610-31:2016)BSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS EN ISO 16610-31:2016 BRITISH STANDARDNational forewordThis Briti
2、sh Standard is the UK implementation of EN ISO 16610-31:2016. It supersedes DD ISO/TS 16610-31:2010 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizations represented on this committee can be obtain
3、ed on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2016.Published by BSI Standards Limited 2016ISBN 978 0 580 86273 1 ICS 17.040.20; 17.040.40 Com
4、pliance with a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 December 2016.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dEUROPEAN STANDARD NORME E
5、UROPENNE 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 (ISO 16610-31:2016) Spcification gomtrique des produits (GPS) - Filtrage - Partie 31: Filtres de p
6、rofil 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 are bound to comply with th
7、e 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 to the CEN-CENELEC Managemen
8、t 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 Centre has the same status
9、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, Lithuania, Luxembourg, Malta, N
10、etherlands, 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-1000 Brussels 2016 CEN All
11、rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-31:2016 EBS EN ISO 16610-31:2016EN ISO 16610-31:2016 (E) 3 European foreword This document (EN ISO 16610-31:2016) has been prepared by Technical Committee ISO/TC 213 “Dimensional an
12、d geometrical product specifications and verification” in collaboration with Technical Committee CEN/TC 290 “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
13、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 possibility that some of the elements of this document may be the subject of patent rights. CEN and/or CENELEC
14、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 countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic,
15、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 the United Kingdom. Endorsemen
16、t notice The text of ISO 16610-31:2016 has been approved by CEN as EN ISO 16610-31:2016 without any modification. BS EN ISO 16610-31:2016ISO 16610-31:2016(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 Robust Gaussian regression filter 24.1 Weighting funct
17、ion 24.2 Filter equation . 24.2.1 General 24.2.2 Filter equation for the robust Gaussian regression filter for open profiles 24.2.3 Filter equation for robust Gaussian regression filter for closed profiles 54.2.4 Transmission characteristics 65 Recommendations for nesting index (cutoff values c) 66
18、Filter designation. 6Annex A (informative) Examples 7Annex B (informative) Relationship to the filtration matrix model .10Annex C (informative) Relationship to the GPS matrix model 11Bibliography .12 ISO 2016 All rights reserved iiiContents PageBS EN ISO 16610-31:2016ISO 16610-31:2016(E)ForewordISO
19、(the International 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 comm
20、ittee has 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 electrote
21、chnical 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 drafte
22、d in accordance 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 right
23、s. Details 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 constitut
24、e an endorsement.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/fore
25、word.html.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 foun
26、d on the ISO website.iv ISO 2016 All rights reservedBS EN ISO 16610-31:2016ISO 16610-31:2016(E)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.Fo
27、r more detailed information 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 de
28、fault decision rules given 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 s
29、ubject of this document is the robust Gaussian regression filter of degree p = 2, which has very good robust behaviour and form approximation for functional stratified engineering surfaces. ISO 2016 All rights reserved vBS EN ISO 16610-31:2016BS EN ISO 16610-31:2016Geometrical product specifications
30、 (GPS) Filtration Part 31: Robust profile filters: Gaussian regression filters1 ScopeThis document specifies the characteristics of the discrete robust Gaussian regression filter for the evaluation of surface profiles with spike discontinuities such as deep valleys and high peaks.2 Normative referen
31、cesThe 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 cited applies. For undated references, the latest edition of the referenced document (including any amendments) app
32、lies.ISO 16610-1:2015, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts3 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 16610-30 and the following apply.ISO and IEC mai
33、ntain terminological databases for use in standardization at the following addresses: IEC Electropedia: available at http:/www.electropedia.org/ ISO Online browsing platform: available at http:/www.iso.org/obp3.1robust filterfilter that is insensitive to output data against specific phenomena in the
34、 input data3.2regression filterM-estimator based on the local polynomial modelling of the profile3.3robust Gaussian regression filterregression filter (3.2) based on the Gaussian weighting function and a biweight influence function (3.4)3.4biweight influence functionasymmetric function which is scal
35、e-invariant, expressed by xxxcxcxc()=1022forforwhere c is the scale parameter.INTERNATIONAL STANDARD ISO 16610-31:2016(E) ISO 2016 All rights reserved 1BS EN ISO 16610-31:2016ISO 16610-31:2016(E)4 Robust Gaussian regression filter4.1 Weighting functionThe weighting function of the robust Gaussian re
36、gression 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 from the general discrete regression filter (see Annex A) by setting the degree
37、 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.4.2.2 Filter equation for the robust Gaussian regression filter for open profile
38、sFor 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,.,=()= 1 (3)2 ISO 2016 All rights reservedBS EN ISO 16610-31:2016ISO 16610-31:
39、2016(E)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 = ()1120Wexp1730 9pi, (6)The additional weightslllllllzwczw
40、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 profiles and is the default case. ISO 2016 All rights reserv
41、ed 3BS EN ISO 16610-31:2016ISO 16610-31:2016(E)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 o
42、f dimension n of the profile values of the filter reference line;wkis the value of the filter mean line at position k;cis the cut-off wavelength of the profile filter;x is the sampling interval.NOTE 1 Vector w gives the profile values of the long-wave component (reference line). The short-wave compo
43、nent, r, can be obtained by the difference vector, r = z w.NOTE 2 For surfaces with big pores or peaks at the profile boundaries, the robustness can be increased by setting P = 0. In this case, the nominal form is eliminated by using a pre-filtering technique. The filter equation for P = 0 results i
44、nwsszkkTkk kTklkllnlk l=( )= =XSXXSz111,lln()=1whereXk=11 andln2pi4 ISO 2016 All rights reservedBS EN ISO 16610-31:2016ISO 16610-31:2016(E)4.2.3 Filter equation for robust Gaussian regression filter for closed profilesFor closed profiles, the filter equation for the robust Gaussian regression filter
45、 is given by Formula (9): wkkTkk kTk=()( )1001XSXXSz (9)The regression function is spanned by the matrixtildenosptildenosptildenospvertellipsisvertellipsis vertellipsistildenosptildenospXkkknk nkxxxx=111122,(10)withxlknnnxl nlk,mod, .,=+=221 (11)The space variant weighting function,Sk, is given byti
46、ldenosptildenosptildenospmidhorizellipsistildenosptildenospvertellipsisvertellipsisdownslopeellipsismidhorizellipsistildenosptildenospSkkknk nsss=1122000000,(12)with the Gaussian functionsxlnlklk,.,=112 ccexp pi (13)and the parameter = ()120W1exp1730 9pi, (14)The additional weights llllllzwczw czw=1
47、022forforlcln=, .,1(15)are derived from the biweight influence function with the parameterc =() 312erf 0,5median 4,447 8medianzw zw (16)The definition for c is equivalent to three times Rq of the surface roughness for Gaussian distributed profiles and is the default case. ISO 2016 All rights reserve
48、d 5BS EN ISO 16610-31:2016ISO 16610-31:2016(E)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;zis the vector of dimension n of the profile values before filtering;wis the vector of dimension n of the profile values of the filter reference line;wkis the value of the filter mean line at position k;cis the cut-off wavelength of the profile fi
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