Cost optimized Timber Machine Strength Grading

Transcription

1 Cost optimized Timber Machine Strength Grading Markus Sandomeer René Steiger Jochen Köhler COST E53 conference, October 2009, Lisbon, Portugal Eidgenössische Technische Hochschule Zürich Swiss Federal Institute of Technology Zürich Institute of Structural Engineering Group Risk and Safety Materials Science & Technology motivation 2 development of efficient grading models requires cost and reliability considerations incorporate all types of uncertainties (aleatory, epistemic) utilize all available information efficiently (grading machine measurements) optimize combination of strength grades according to material properties of ungraded input material react on different material qualities within the timber material supply (flexible settings) fit into the overall production process seamlessly 1

2 overview 3 maximum benefit efficiency sufficient reliability customer's demands overview 4 2

3 overview 5 overview 6 3

4 existing data sampling and testing sampling grading non-destructive indicating property (IP) testing destructive grade determining property (GDP) 7 RELATIONSHIP MiCROTEC existing data regression analysis regression equation 8 tension strength = β + β IP + ε 1 2 with β N( µ, σ ) 1 2 β 1 1 β N( µ, σ ) β β β 2 2 ε N( µ = 0, σ ) ε ε 1 st regression coefficient 2 nd regression coefficient error term σ N( µ, σ ) ε σ σ ε ε standard dev. of error term 4

5 existing data description of material properties assessment of prior probability density functions 9 overview 10 5

6 grading process various information monitoring of grading machine data 11 source: GoldenEye (MiCROTEC) Sylvatest (CBS-CBT) MiCROTEC Timbergrader (Brookhuis) ETHZ ETHZ ETHZ grading process 12 monitoring of indicating property real-time measurements of the grading device for every graded board no additional costs arise since boards are graded anyway utilization of the gathered information for description of input material quality until now this information is not used for the grading concepts 6

7 grading process monitoring of indicating property 13 Ranta-Maunus A., Denzler J. (2009); paper , CIB-W18 meeting, Zurich, Switzerland grading process PROBLEM: varying input material qualities what to do? 1. control of output additional testing actualization of grading model adjustment of grading machine settings combination of strength grades remains constant analysis of the input timber material quality real-time assessment of prior probability distribution of IP predictive benefit optimized grade combination for maximized benefit optimization of strength grade combination 7

8 overview 15 optimization routine 16 INPUT (what has to be known?) market values of strength classes, costs of grading machine, maintenance, personnel constrains = requirements of EN 338 observations of the indicating property belonging to the current sub-sample (prior probability distribution) relationship between IP and GDP OUTPUT (what is desired?) optimized acceptance criteria = grading machine settings (sufficient reliability, maximum benefit, efficiency) 8

9 optimization routine definition of objective function 17 prior probability distribution of input timber material particular grading procedure monetary benefit (market values) T B ( f ( s), A, GP) = V C T σ C grade C benefit of graded timber acceptance criteria (settings) volumes in particular grades optimization routine 18 optimization of the grading machine settings max B ( f ( s), A, GP) A c T σ C C subject to: N, C req grade constrains (requirements EN 338) grading costs 9

10 optimization routine optimization of the grading procedure 19 comparison of different grading machines or grading strategies (mechanical, visual,...) éæ ö ù çê max max BT ( f σ ( s), A, ) ( ) C C GP CG GP GP - A c êç çè subject to: Nreq, C ú grade ë ø û maximized benefit costs for - machine - maintenance - personnel... optimization routine 20 simplex algorithm algorithm for numerically solving of linear programming problems minimization of negative values objective function 10

11 21 1 st example 1. example simulated data 22 strength classes according to EN 338 relative market values C40 C35 C30 C24 C18 reject

12 1. example simulated data 23 varying mean value coefficient of variation = 0.33 and coefficient of correlation = ,8 40 C40 C40 1,6 1,4 strength class [-] C24 C18 C24 C35 1,2 1 0,8 0,6 benefit [-] 10 0 lower grade higher grade benefit bending strength mean value of sub-sample [MPa] 0,4 0, example simulated data 24 varying coefficient of variation mean value = 45 MPa and coefficient of correlation = ,8 40 C35 C40 C40 1,6 1,4 Strength Class [-] C30 C24 C30 1,2 1 0,8 0,6 benefit [-] 10 lower grade higher grade benefit 0,4 0, ,1 0,2 0,3 0,4 0,5 0,6 coefficient of variation of sub-sample [MPa] 0 12

13 1. example simulated data 25 varying coefficient of correlation mean value = 45 MPa and coefficient of variation = ,18 40 C40 C40 1,16 1,14 Strength Class [-] C24 C18 C30 C24 C24 C30 1,12 1,1 1,08 1,06 benefit [-] 10 lower grade higher grade benefit 1,04 1, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Coefficient of correlation between IP and bending strength [MPa] nd example 13

14 2. example real data 27 GoldenEye 706 dataset: o o o Norway spruce, Central Europe tested in tension n=1162; 8 sub-samples (A-H) assessment of prior distributions at total sample (n=1162) Bayesian regression analysis at total sample (n=1162) observations of indicating properties at individual sub-samples (A-H) given market values for the strength grades predictive calculation of optimized grading machine settings for each sub-sample 2. example real data 28 assessment of prior probability density functions tension strength indicating property 14

15 2. example real data Bayesian regression analysis between tension strength and indicating property transformation of IP and GDP values into logarithm 29 tension strength = β + β IP + ε 1 2 normal distributed random variables correlation β1 β2 σ ε ρ n=500 µ = β β 1 σ = µ = β β 2 σ = µ σ ε = σ σ ε = ρ, = β1 β2 2. example real data 30 Bayesian regression analysis between tension strength and indicating property simulated data (n=500) 15

16 2. example real data Bayesian regression analysis between tension strength and indicating property 31 simulated data (n=500) 2. example real data 32 sample characteristics of bending strength and interrelation with indicating property (CoC) sample n [-] mean [MPa] CoV [-] CoC [-] all A B C D E F G H

17 2. example real data 33 results of grading and optimization routine sample higher grade [-] lower grade [-] predicted benefit [-] all C40 C A C35 C B C40 C C C40 C D C40 C E C40 C F C40 C G C35 C H C40 C average benefit of sub-samples: conclusions 34 real-time assessment of input timber material quality by continuous monitoring of indicating property predictive computation of grading output with given settings, market values and constrains maximization of grading benefit by optimization of strength grade combinations sufficient reliability, high efficiency future investigations o model extension also to MOE and density o implementation into overall grading concept 17

18 obrigado! contact: Contributions by MiCROTEC (Brixen, Italy) are acknowledged for allowing us to publish the results of machine grading by the grading device GoldenEye706. Eidgenössische Technische Hochschule Zürich Swiss Federal Institute of Technology Zürich Institute of Structural Engineering Group Risk and Safety Materials Science & Technology 36 18

19 37 grading process 38 grade 1 grade 2 grade 3 grade determining property (GDP) regression model IP 1 IP 2 indicating property (IP) 19