1、December 2014 Translation by DIN-Sprachendienst.English price group 13No 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).I
2、CS 17.040.30!%Zu“2275582www.din.deDDIN EN ISO 16610-71Geometrical product specifications (GPS) Filtration Part 71: Robust areal filters: Gaussian regression filters(ISO 16610-71:2014);English version EN ISO 16610-71:2014,English translation of DIN EN ISO 16610-71:2014-12Geometrische Produktspezifika
3、tion (GPS) Filterung Teil 71: Robuste Flchenfilter: Gausche Regressionsfilter (ISO 16610-71:2014);Englische Fassung EN ISO 16610-71:2014,Englische bersetzung von DIN EN ISO 16610-71:2014-12Spcification gomtrique des produits (GPS) Filtrage Partie 71: Filtres surfaciques robustes: Filtres de rgressio
4、n gaussiens(ISO 16610-71:2014);Version anglaise EN ISO 16610-71:2014,Traduction anglaise de DIN EN ISO 16610-71:2014-12www.beuth.deIn case of doubt, the German-language original shall be considered authoritative.Document comprises 28 pages12.14 DIN EN ISO 16610-71:2014-12 2 A comma is used as the de
5、cimal marker. National foreword This document (EN ISO 16610-71:2014) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” (Secretariat: DS, Denmark) in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical
6、product specification and verification” (Secretariat: AFNOR, France). The responsible German body involved in its preparation was the DIN-Normenausschuss Technische Grundlagen (DIN Standards Committee Technical Fundamentals), Working Committee NA 152-03-03 AA Oberflchen. The DIN Standards correspond
7、ing to the International Standards referred to in this document are as follows: ISO 16610-1 DIN EN ISO 16610-1ISO 16610-30)DIN EN ISO 16610-30)ISO/IEC Guide 98-3 DIN V ENV 13005 ISO/IEC Guide 99 VIM, International vocabulary of metrology (VIM) )In preparation. )Bilingual (German/English), obtainable
8、 from: Beuth Verlag GmbH, 10772 Berlin, Order No. 22472, ISBN 978-3-410-22472-3. DIN EN ISO 16610-71:2014-12 3 National Annex NA (informative) Bibliography DIN EN ISO 8015, Geometrical product specifications (GPS) Fundamentals Concepts, principles and rules DIN EN ISO 14253-1, Geometrical product sp
9、ecifications (GPS) Inspection by measurement of workpieces and measuring equipment Part 1: Decision rules for proving conformity or nonconformity with specifications DIN EN ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts DIN EN ISO 16610-30), Geom
10、etrical product specifications (GPS) Filtration Part 30: Robust profile filters: Basic concepts DIN EN ISO 16610-31), Geometrical product specifications (GPS) Filtration Part 31: Robust profile filters: Gaussian regression filters DIN EN ISO 25178-3, Geometrical Product Specifications (GPS) Surface
11、texture: Areal Part 3: Specification operators DIN EN ISO 80000-2, Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology DIN V 32950, Geometrical product specification (GPS) Masterplan DIN V ENV 13005, Guide to the expression of uncertainty in
12、measurement VIM, International vocabulary of metrology )In preparation. DIN EN ISO 16610-71:2014-12 4 This page is intentionally blank EN ISO 16610-71September 2014 ICS 17.040.20 English VersionGeometrical product specifications (GPS) - Filtration -Part 71: Robust areal filters: Gaussian regression
13、filters(ISO 16610-71:2014)Spcification gomtrique des produits (GPS) - Filtrage - Partie 71: Filtres surfaciques robustes: Filtres de rgression gaussiens (ISO 16610-71:2014) Geometrische Produktspezifikation (GPS) - Filterung -Teil 71: Robuste Flchenfilter: Gausche Regressionsfilter(ISO 16610-71:2014
14、)This European Standard was approved by CEN on 16 August 2014. CEN members 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 ref
15、erences 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, German). A version in any other language made by translation under the responsibility of a C
16、EN 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, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedon
17、ia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey andUnited Kingdom. CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2014 CEN All
18、 rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-71:2014 EEUROPEAN COMMITTEE FOR STANDARDIZATIONCOMIT EUROPEN DE NORMALISATIONEUROPISCHES KOMITEE FR NORMUNGEUROPEAN STANDARDNORME EUROPENNEEUROPISCHE NORMDIN EN ISO 16610-71:2014-1
19、2 EN ISO 16610-71:2014 (E) 2Contents Page Foreword . 3 Introduction . 4 1 Scope . 5 2 Normative references. 5 3 Terms and definitions 5 4 Robust planar Gaussian regression filter 6 4.1 General 6 4.2 Weighting function . 6 4.3 Filter equation . 7 4.4 Transmission characteristics . 9 5 Robust cylindri
20、cal Gaussian regression filter 9 5.1 General 9 5.2 Weighting function . 9 5.3 Filter equation . 10 5.4 Transmission characteristics . 11 6 Nesting Index for planar and cylinder surfaces . 12 7 Filter designation . 12 Annex A (informative) Regression filter 13 Annex B (informative) Examples 15 Annex
21、C (informative) Relationship to the filtration matrix model . 20 Annex D (informative) Relation to the GPS matrix model 22 Bibliography 24 ForewordThis document (EN ISO 16610-71:2014) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verifica
22、tion” 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 by publication of an identical text or by endorse
23、ment, at the latest by March 2015, and conflicting national standards shall be withdrawn at the latest by March 2015. 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
24、 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, Denmark, Estonia, Finland, Former Yugoslav Re
25、public 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. Endorsement notice The text of ISO 16610-71:2014 has be
26、en approved by CEN as EN ISO 16610-71:2014 without any modification. DIN EN ISO 16610-71:2014-12EN ISO 16610-71:2014 (E)3IntroductionThis part of ISO 16610 is a Geometrical Product Specification (GPS) standard and is to be regarded as a Global GPS standard (see ISO/TR 14638). It influences the chain
27、 links 3 and 5 of all chains of standards.The ISO/GPS Masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS system of which this standard is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this standard and the default decision rules given in ISO 14253-1 apply to spec
28、ifications made in accordance with this standard, unless otherwise indicated.For more detailed information of the relation of this document to the GPS matrix model, see Annex C.This part of ISO 16610 specifies the metrological characteristics of robust areal Gaussian regression filters, for the rota
29、tionally symmetric filtration of nominal planar surfaces and the filtration of nominal cylindrical surfaces.The filter is insensitive against specific phenomena in the input data (e.g. spike discontinuities as well as deep valleys and high peaks, etc.). The boundaries of the measured surface are sti
30、ll usable.DIN EN ISO 16610-71:2014-12 EN ISO 16610-71:2014 (E) 41 ScopeThis part of ISO 16610 specifies the characteristics of the robust areal Gaussian regression filter for the evaluation of surfaces that may contain spike discontinuities as well as deep valleys and high peaks. It specifies in par
31、ticular how to separate large scale lateral components and short scale lateral components of a surface.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cit
32、ed 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 16610-30:1), Geometrical product specifications (GPS) Filtration Part 30: Robus
33、t profile filters: Basic conceptsISO/IEC Guide 99, International vocabulary of metrology Basic and general concepts and associated terms (VIM)ISO/IEC Guide 98-3, Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)3 Terms and definitionsFor the purposes
34、 of this document, the terms and definitions given in ISO 16610-1, ISO 16610-30, ISO/IEC Guide 99 and ISO/IEC Guide 98-3 and the following apply.3.1robust planar filternon linear areal filter to separate a planar surface with specific phenomena (e.g. spike discontinuities as well as deep valleys and
35、 high peaks etc.) into large scale lateral components and short scale lateral components3.2robust cylindrical filternon linear areal filter to separate a cylindrical surface with specific phenomena (e.g. spike discontinuities as well as deep valleys and high peaks etc.) into large scale lateral comp
36、onents and short scale lateral components1) To be published. (Revision of ISO/TS 16610-30:2009)DIN EN ISO 16610-71:2014-12EN ISO 16610-71:2014 (E)53.3biweight functionasymmetric influence function defined byBforforucuucucuc,()=1022(1)where c is the real scale parameter and u is a real numberNote 1 t
37、o entry: See ISO 16610-30:, Figure 4.3.4robust areal regression filterweighted Mestimator based on the areal local complete polynomial modelling of the surfaceNote 1 to entry: See ISO 16610-30 for the definition of the weighted M-estimator.Note 2 to entry: See Annex A for the mathematical definition
38、 of the robust areal regression filter.3.5robust areal Gaussian regression filterrobust areal regression filter based on the areal Gaussian weighting function, the biweight influence function and a local complete polynomial modelling of the surface with the degree p=2 as the default caseNote 1 to en
39、try: to entry:See ISO 16610-61 for the definition of the areal Gaussian weighting function.Note 2 to entry: to entry:In case of p=2, the robust areal Gaussian regression filter follows a complete polynomial up to second degree.4 Robust planar Gaussian regression filter4.1 GeneralRobust planar Gaussi
40、an regression filters complying to this document shall conform to sections 4.2 to 4.4.4.2 Weighting functionThe weighting function of the robust planar Gaussian regression filter depends on the surface values (height to the reference surface) and the location of the weighting function on the surface
41、.DIN EN ISO 16610-71:2014-12 EN ISO 16610-71:2014 (E) 64.3 Filter equationThe filter equation is given bywimj nij ijTij ij ijTij=()()=100000 111XSXXSz,., ,., (2)with the surface valuesz =()zzzzmnmnT11 11 (3)The regression function is spanned by the matrix:Xijijij ijmi jmijmi jxyxy xyxyxy xy=111111 1
42、21211212 111112222xyxy xyxyxxyinjinj injmi nj mi nj mi nj (4)wherexkix kmki=()= ,.,1 (5)andyljy lnlj=()= ,.,1 (6)The spatial varying weighting function Sijis given by:Sijijmijmnijnmnij mnssss=11 111111000000midhorizellipsisdownslopeellipsisvertellipsisdownslopeellipsisvertellipsisdownslopeellipsismi
43、dhorizellipsis(7)with the Gaussian weighting function:sxykmlklijcki ljc=+=11122 2222piexp , , ,n (8)The constant is given by:pi= 101W12e ,7309 (9)with the branch W()11u of the “Lambert W” function 7.DIN EN ISO 16610-71:2014-12EN ISO 16610-71:2014 (E)7The weights ijare derived from the biweight funct
44、ion as follows:ijij ijij ijzwczwimjn=()=B, ,11 (10)In the default case, the scale parameter c is given by:c =3121MAD2erf(11)MADis the median absolute deviation of the residuals zwij ij , and erf-1is the inverse error function 6.mnumber of the surface values in x directionnnumber of the surface value
45、s in y directioniindex of the surface values in x direction i = 1,mjindex of the surface values in y direction j = 1,nzijsurface values before filteringwijfiltered surface valuesccut-off wavelengthxsampling interval in x directionysampling interval in y directionNOTE 1 See ISO 16610-30 for the defin
46、ition of MAD.NOTE 2 wijgives the surface values of the large scale lateral components. The short scale lateral components rijcan be obtained by the difference vector rzwij ij ij=.NOTE 3 The definition for the value c is equivalent to 3 of a surface with a Gaussian amplitude distribution.NOTE 4 The n
47、umber of zeros in Formula (2) is equal to pp+()32 (see Annex A).NOTE 5 The values wijare generally calculated by iteration starting with ij01= and updating the weights according to Formula (10). For the calculation of the first updated weights ij1, the default scale parameter c can be increased by a
48、 factor of two.NOTE 6 For surfaces with big pores or peaks at the surface boundaries the robustness can be increased by setting p=0. In this case the nominal form can be eliminated by using the F-operator. The filter equation for p = 0 results in:wszsijklij kl kllnkmklij kllnkm=1111, with pi=ln2(12)DIN EN ISO 16610-71:2014-12 EN ISO 16610-71:2014 (E) 84.4 Transmission characteristicsThe weighting function of the robust planar Gaussian regression filter depends on the surface values and the location on the surface. Therefore no
