1、Beuth Verlag GmbH, Berlin, has the exclusive right of sale for German Standards (DIN-Normen) 01.95 DIN EN 705 Engl. Price group 12 SalesNo. 1112 DEUTSCHE NORM August 1994 GI ass-rei nforced thermosetting plastics (G R P) pipes and fittings - I EN 705 Methods for regression analyses and their use Eng
2、lish version of DIN EN 705 ICs 23.040.20; 23.040.45 Descriptors: Pipework, plastic pipe, glass reinforced plastics, regression analysis, fitting. Kunststoff-Rohrleitungssysteme; Rohre und Formstcke aus glasfaserverstrkten duroplastischen Kunststoffen (GFK); Verfahren zur Regressionsanalyse und deren
3、 Anwendung European Standard EN 705: 1994 has the status of a DIN Standard. A comma has been used as the decimal marker. National foreword This standard has been prepared by CENITC 155. The responsible German body involved in the preparation of this standard was the Normenausschu Kunststoffe (Plasti
4、cs Standards Committee), Technical Committee 505.1. International Patent Classification F 16 L 009/12 G O1 D G O1 N 033/44 EN comprises 44 pages. EUROPEAN STANDARD NORME EUROPENNE EUROPAISCHE NORM EN 705 April 1994 UDC 621.643.2-036.067.5:621.643.06:620.1 1519.2 Descriptors: Pipework, plastic pipe,
5、glass reinforced plastics, regression analysis, fitting English version Plastics piping systems G lass-rei nforced thermosetting plastics (G RP) pipes and fittings Methods for regression analyses and their use Systmes de canalisations plastiques; tubes et raccords plastiques thermodur- cissables ren
6、forcs de verre et raccords (PRV); mthodes pour une analyse de rgression et leurs utilisations Kunststoff-Rohrleitungssysteme; Rohre und Formstcke aus glasfaserverstrkten duroplastischen Kunststoffen (GFK); Verfahren zur Regressionsanalyse und deren Anwendung This European Standard was approved by CE
7、N on 1994-04-1 1. CEN members are bound to comply with the CENKENELEC 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
8、 be obtained on application to the Central Secretariat 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 Cent
9、ral Secretariat has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom. CEN European
10、Committee for Standardization Comit Europen de Normalisation Europisches Komitee fr Normung Central Secretariat: rue de Stassart 36, 8-1050 Brussels O 1994. Copyright reserved to all CEN members. Ref. No. EN 705:1994 E Page 2 EN 705 : 1994 Content 8 Foreword 3 Introduction 1 Scope 2 Principle 3 Proc
11、edure8 for determining the functional relation8hip8 3.1 Linear relationships - Methods A and B 3.2 Second order polynomial relationships - Method C 4 4.1 General 4.2 Design 4.3 Examples for validation of calculation procedures 4.4 Procedures for verifying conformance to product design 4.5 Examples f
12、or validation of calculation procedures for Application of methods to product deeign and testing or design and performance values design or product performance verification Annex A (informative) Mathematical procedures A.l Matrix system A.? Subititution nyntem 4 5 5 6 6 17 11 21 23 27 32 37 42 42 43
13、 Page 3 EN 705 : 1994 Foreword This standard was prepared by CEN/TC 155 “Plastics piping systems and ducting systems“. This standard is based on document N 197 “Glass-reinforced thermosetting plastics (GRP) pipes and fittings - Standard extrapolation procedures and their use* prepared by working gro
14、up 1 of subcommittee 6 of technical committee 138 of the International Organization for Standardization (ISO). It is a modification of ISO/TC 138/SC 6/WG 1 N 197 for reasons of possible applicability to other test conditions and alignment with textB of other standards on test methods. The modificati
15、ons are: - examples have been introduced to enable validation of alternative calculation facilities; - material-dependent requirements are not given; - editorial changes have been introduced. The material-dependent test parameters and/or performance requirements are incorporated in the referring sta
16、ndard. Annex A, which is informative, describes procedures for solving the given set of equations (see 3.2.3) on a mathematical basis using the example shown in 3.2.6. No existing European Standard is superseded by this standard. This standard is one of a series of standards on test methods which su
17、pport System Standards for plastics piping systems and ducting systems. 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 October 1994, and conflicting national standards shall be withdrawn at the l
18、atest by October 1994. According to the CEN/CENELEC Internal Regulations, the following countries are bound to implement this European Standard: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland
19、, United Kingdom. Page 4 EN 705 : 1994 Introduction This standard has been prepared to describe the procedures intended for analysing the regression of test data. usually with respect to time, and the use of the results in design and assessment of conformity with performance requirements. Its zpplic
20、ability has been limited to use with data obtained from tests carried out on samples. The referring standards require estimates to be made 31 the long-term properties of the pipe for such parameters as circumferential tensile strength, deflection and creep. The committee investigated a range of scat
21、istical techniques that could be used to analyse the test data Frociuced by tests that were destructive. Many of these simple techniques requirscl the logarithms of the data to a) be normally distributed: b) produce a regression line having a negative slope; and c) have a sufficiently hign regressio
22、n correlation (see table 1) hjilst the last two conditions can be satisfied, analysis has shown that there is a skew to the distribution and hence this primary condition is not satisfied. Further investigation into techniques that can handle skewed distributions resulted in the adoption of the covar
23、iance method for analysis of such data for this standard. The results from non-destructive tests. such as creep or changes in deflection with time. often satisfy these three conditions and hence simpler procedures, using time as the independent variable, can also be used in accordance with this stan
24、dard. Page 5 EN 705 : 1994 1 scope This standard specifies procedures suitable for the analysis of data which, when converted into logarithms of the values, have either a normal or a skewed distribution. It is intended for use with the test methods and referring standards for glass-reinforced plasti
25、cs pipes or fittings for the analysis of properties as a function of, usually, time. However it can be used for the analysis of any other data. For use depending upon the nature of the data, three methods are specified. The extrapolation using these techniques typically extends the trend from data g
26、athered over a period of approximately 10000 h, to a prediction of the property at 50 years. 2 Principle Data are analysed for regression using methods based on least squares analysis which can accommodate the incidence of a skew and/or a normal distribution and the applicability of a first order or
27、 a second order polynomial relationship. The three methods of analysis used comprise the following: - method A: covariance using a first order relationship; - method 8: least squares with time as the independent variable using a first order relationship; - method C: least squares with time as the in
28、dependent variable using a second order relationship. The methods include statistical tests for the correlation of the data and the suitability for extrapolation. Page 6 EN 705 : 1994 3 Procedures for determining the functional relationships 3-1 Linear relationships - Methods A and B 3.1.1 Procedure
29、s coiunon to methods A and B Use method A (see 3.1.2) or method 3 the form y=a+bx where : see 3.1.3) to fit a straight line of .I. (1) i. is the logarithm (16) of :he croperty being investigated; a is the intercept on the v axis: b is the slope; s is the logarithm (lg) of Ehe time. in hours. 3.1.2 M
30、ethod A - Covariance method 3.1.2.1 General For method A calculate the following variables as necessary in accordance with 3.1.2.2 to 3.1.2.5: . (2) C(y, - YI2 n O:, = C(x, - .U)2 Q, = n . (3) . (4) where : is the sum of the squared residuals parallel to the y axis divided by n: is the sum of the sq
31、uared residuals parallel to the x axis divided by n: is the sum of the squared residuals perpendicular to the line, divided by n: Q, QX Q, Y is the arithmetic mean of the y data, i.e. CV n y=L- Page 7 EN 705 : 1994 .Y is the arithmetic mean of the x data, i.e. xi. si are. individual values; n is the
32、 total number of results (pairs of readings for xi, ri). WTE: is 3ositive and if the value of o, is less than zero then the slope is negative. If the value of Q, is greacer than zero the slope of the line 3.1.2.2 Suitability of data Calculate the squared, r2, and the linear coefficient of correlatio
33、n, t, using the following equations: If the value of r2 or r is less than the applicable minimum value given in table 1 as a function of n. consider the data unsuitable for analysis. Page 8 EN 705 : 1994 Table 1: Minimum values for the squared, s, and linear coefficient of correlation, r, for accept
34、able data from n pairs of data =- . . . (17) b T- (variance of b I:. If the absolute value IT1 ( 2.0423. The estimated mean values for V at various times are given in table 4 and shown in figure 1. Page 14 EN 705 : 1994 Table 4: Estimated mean values, V, for V time h v, 1000 10000 100000 438000 45.7
35、6 42.39 39,28 36.39 33,71 ?1,23 28.94 27.55 Values 50 Frvations A 27.56 Regession I l I I 1 I 10-1 1 O0 101 102 io3 1 o4 io5 106 Time Figure 1: Regression line from the results in table 4 3.1.3 Method B - Regression with time as the independent variable 3.1.3.1 General For method B calculate the fol
36、lowing variables: s, = ay, - YI2 . . . (18) (The sum of the squared residuals parallel to the y axis) s, = C(X, - X)2 . . . (19) (The sum of the squared residuals parallel to the x axis) Page 15 EN 705 : 1994 sw = C( (Xi - .u(Y, - Y) 1 . . . (20) (The sum of the squared residuals perpendicular to th
37、e line) where : t is -the arithmetic mean of the y data, i.e. -1 is the arithmetic mean of the x data, i. sl. yr are individual values : il is the total number of results (pairs of readings for xi, ri- YOTE: is positive and ir the ralue of Sr-, is less than zero then the slope is negative. If the va
38、lue or L7 is greacer chan zero the slope of the line - 3.1.3.2 Suitability of i. :onsider the data unsuitable for analysis. 3.1.3.3 F.rmctional relationships Calculate a and b for the functional yelationship line ;see equation (I), using the following equations: %. SIC b- . (23) . . . (24) a = Y - b
39、9 Page 16 EN 705 : 1994 3.1.3.4 Check for the suitability of data for extrapolation If it is intended to extrapolate the line, calculate M using the following equation: where : . . . (25) t., is the applicable value for StuLfnts t determined from table 2. If .Y is equal to or less than zero consider
40、 the data unsuitable for extrapolation. 3.1.3.5 Validation of statistical procedures by an example caldation Use the data given in table 3 for the calculation procedures described in 3.1.3.2 to 3.1.3.4 to ensure cnat the statistical procedures to be used in conjunction with this method will give res
41、ults for r, 9, a, b and V, to within t 0,l 99 of the values given in this example. Table 5: Basic data for example calculation and statistical validation n Time h 1 2 3 4 5 6 7 9 10 11 12 13 14 15 a 0.10 0,27 0,50 l,oo 3.28 7,2a 20.0 45.9 72.0 166 219 384 504 3000 10520 - 1.0000 -0.5686 -O. 3010 O O
42、. 5159 1 0.8621 i. 3010 L. 6618 1,8373 1 2.2201 2,3404 2,5843 2,7024 3,4771 4,0220 V 7114 6935 6698 6533 6453 6307 6199 6133 5692 6824 5508 5393 5364 5200 4975 3, a521 3, a341 3, a259 3, aisi 3,8410 3,8098 3,7999 3,7923 3,7877 3,7552 3,7410 3,7318 3,7295 3,7160 3,6968 Means : .Y = 1,4450 Y = 3,7819
43、Page 17 EN 705 : 1994 Sums of squares S, = 31,6811; 5 = 0.0347; 5. .Cl = -1,0242 Coefficient of correlation rz = 0.9556; r = 0,9775. Functional relationships (see 3.1.3.3) a = 3,8286; 5 = -0,0323. Check of the suitability for extrapolation (see 3.1.3.4) t., - 2,1604; .Y = 9rC2.21. Table 6: Estimated
44、 mean values, r-, for Y Time lh 0.1 1.0 100. o 1 1 1000 10000 100000 438000 7259 6739 6256 5808 5391 JO05 46G h423 3.2 Second order polynomial relationships - Hethod C 3.2.1 General This method fits a curved line of the form y = c + dx + esi -. . (26) where : y is the logarithm (lg) of the property
45、being investigated; C is the intercept on the y axis; Page 18 EN 705 : 1994 d. e are the coefficients to the two orders of x; :z is the logarithm (ig) of the time, in hours. 3.2.2 Variables For method C calculate the following variables: t cum of all individual x data) ; sum of all squared x data);
46、isum of all x data to the third power); (sum of all x data to the fourth power); (cum of all individual y data); (squared sum of all individual y data); (sum of all squared y data); (sum of all products xiy,); isum of all products xi2yi); isum of the squared residuals parallel to the x axis for the
47、linear part); (sum of the squared residuals parallel to the x axis for the quadratic part); (sum of the squared residuals parallel to Che y axis) ; (sum of the squared residuals perpendicular to the line for the linear part 1 : (sum of the squared residuals perpendicular to the line for the quadrati
48、c part). where : 5 is the arithmetic mean of the y data, i.e. Vi y*-; n X is the arithmetic mean of the x data, i.e. Page 19 EN 705 : 1994 3.2.3 Solution system Determine c, d and e (see 3.2.1) using the following matrix: Zy = cn + dcXi + eBi2 . . . (27a) ,ki2y; = ccXi2 + db.: + eXxi* . . . (27c) .V
49、E: in annex -4. Examples showing the procedures that can be used are detailed 3.2.4 Suitability of data Calculate the squared. r2. ond the linear coefficient of correlation, r, using the following equations: . . . (28) If the value of rz, or r. is less than Che applicable minimum value given in table 1 as a function of II. consider the data unsuitable for analysis. 3.2.5 Check for the suitability of Lxi2 = 62,989; “ti3 = 180,623; q4 - 584,233; ZY i = 56,728; (z.yi)2 = 3218,og; c “iYi = 80,932 ; Zyi2yi = 235,175; “I = 31.681; 3 P =? = 0,347; - 386,638; n “ s.
