A discussion on the control of grading machine settings ... · A discussion on the control of...

A discussion on the control A discussion on the control of grading machine settings of grading machine settings with regard to EN 14081with regard to EN 14081

Markus Deublein

COST E53

- Meeting WG 3

BFH Hamburg, Germany 14/15th

May 2007

Foto

: M

ichae

l M

eute

r/

LIG

NU

M

Jochen Köhler

René

Steiger

[ 2 ]swiss

project

Development of an efficient scheme for timber machine strength grading

Close collaboration between

duration: 2007 - 2010

Research Team:

Jochen Köhler, ETHRené Steiger, EMPAMarkus Deublein, PhD ETH/EMPA

MiCROTEC

LIGNUM.CH

LIGNUM.CH

[ 3 ]introduction

Forestry

Harvesting Sawmill

Timber

Grading

Graded

Timber

Material

Building Codes and Regulations

Structural

Design

Timber

Research

Code Authorities

Reliability

based

Code Calibration

Grading

Rules

Extended

Requirements:

-

probabilistic

models

for

timber

material properties

Derived

Requirements:

-

sufficient

strength

-

sufficient

stiffness

- …

[ 4 ]outline

Control method given in EN14081

Alternative approach: Probabilistic modeling of timber material properties

Conclusions

[ 5 ]EN14081

EN 14081, part 1: “General requirements” … (visual strength grading)

EN 14081, part 2: “Machine grading – additional requirements for initial type testing.”

EN 14081, part 3: “Machine grading – additional requirements for factory production control.”

EN 14081, part 4: “Machine grading – grading machine settings for machine controlled systems.”

1. Output control: Continuous control by testing the grading machines‘

output.

2. Machine control: Extensive calibration process prior to the operation phase of the grading machine.

Both systems require a visual override inspection to cater for strength-reducing characteristics that are not automatically sensed by the machine.

[ 6 ]EN14081 –

machine control

Related and important standards

EN338: “Structural timber – Strength classes”

EN384: “Structural timber – Determination of characteristic values of mechanical properties and density”

EN408: “Timber structures – Structural timber and glued laminated timber – Determination of some physical and mechanical properties”

[ 7 ]

Production

Settings

Assessment of production settings

Applied GradingStrategy (settings)

Assigned Grades

Fulfills criterion(Cost matrix)

no

yes

EN14081 –

machine control

Indicating Property

Optimum Grades

Sample Data

[ 8 ]

Optimum grade

EN14081 –

machine control

[ 9 ]EN14081 –

machine control

Assigned grade

Settings shall be determined by considering all other sub-samples.

Mean value of the sub-sample settings for calculation of production settings.

Production settings for grading each piece into defined strength class.

A B C D

B A C D

C A B D

D A B C

sub-sample

setting

A

sub-sample

setting

B

sub-sample

setting

C

sub-sample

setting

D

production

settings

grades

sub-samples

[ 10 ]EN14081 –

machine control

Optimum

grade

Assigned grade

C35 C27 C22 reject

C35 207 32 16 2 257

C27 10 168 12 1 191

C22 4 13 84 2 103

reject 0 2 2 24 28

221 215 114 29 579

Size-Matrix

[ 11 ]EN14081 –

machine control

Cost

(upgrading) = 10*(βtarget

–

β)

,3

,

1m opt

m ass

MOEMOE

−Cost

(downgrading) = 10 *

Costs

for

wronly

upgraded

specimen:

Costs

for

wronly

downgraded

specimen:

[ 12 ]EN14081 –

machine control

Assigned

gradeOptimum

grade

Elementary

cost

matrix

given

in EN14081

[ 13 ]EN14081 –

machine control

Optimum

grade

Assigned grade

C35 C27 C22 reject

C35 207 32 16 2 257

C27 10 168 12 1 191

C22 4 13 84 2 103

reject 0 2 2 24 28

221 215 114 29 579

Optimum

grade

Assigned grade

C35 C27 C22 reject

C35 0.0 0.06 0.13 0.20

C27 0.04 0.0 0.05 0.08

C22 0.04 0.05 0.0 0.13

reject 0.0 0.04 0.05 0.0

Global Cost-Matrix

Size-Matrix

_elementary size

size∑global =

Factor

from

the

elementary

cost

matrix: 0.76

*

Cost

criterion: wrongly

upgraded

values

≤

0.2!

[ 14 ]data set

Sample size:1020 specimen;

Species:Spruce

Origins:North-, South- & Central-SwedenFinland

Cross Sections [mm]: 45 x 7045 x 14543 x 17045 x 190

Device & measured Indicator: Frequency-Device (Indicating Property)

Assessed Properties:- Bending Strength- Bending Young’s Modulus- Density- Moisture Content

[ 15 ]example

-

material properties

n = 152 n = 199 n = 518 n = 151 n = 1020

Bending strength

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

bending strength [Mpa]

cum

ulat

ive

dist

ribu

tion

func

tion

north sweden south sweden central sweden finland model_total sample

[ 16 ]example

-

material properties

n = 152 n = 199 n = 518 n = 151 n = 1020

Modulus

of elasticity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5000 10000 15000 20000 25000

modulus of elasticity [Mpa]

cum

ulat

ive

dist

ribu

tion

func

tion


[ 17 ]example

-

material properties

n = 152 n = 199 n = 518 n = 151 n = 1020

Density

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

250 300 350 400 450 500 550 600 650

density [kg/m^3]

cum

ulat

ive

dist

ribu

tion

func

tion


[ 18 ]results

–

EN14081

IP yield strength MOE density

C30 ≥

7000 475 31.8 14775 380

C24 < 7000 ≥

6400295 26.3 11948 369

C14 < 6400 ≥

4300249 17.8 9873 354

reject <4300 1 12.2* 6375* 367*

*=minimum value

Bending strength Modulus

of elasticity Density

C30 30 12.000 380

C24 24 11.000 350

C14 14 7000 290

Characteristic

values

given

in EN338

Characteristic

values

of the

grades according

to EN14081 (n=1020)

Production settings and characteristic values

[ 19 ]outline



Conclusions

[ 20 ]probabilistic

modeling

-

concept

Data

Fitting

PriorSelection

and quality

controlscheme

Posterior

Lower

tailconsideration

Considerationof all data

Indicators

Population

Grades

[ 21 ]probabilistic

modeling

Data

Fitting

PriorSelection

and quality

controlscheme

Posterior

Lower

tailconsideration


Indicators

Population

Grades

[ 22 ]

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80 90 100


F

sample model_lowertail model_total

example

lower

tail

fitting

Lower

tail

fitting

fitted

to data

lower

30%

fitted

to all data

sample

values

[ 23 ]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20 25 30 35 40 45 50


F

sam ple m odel_lowertail m odel_total

example

lower

tail

fitting

Lower

tail

fitting

–

larger scale

fitted

to data

lower

30%

fitted

to all data

sample

values

[ 24 ]probabilistic

modeling

Data

Fitting

PriorSelection

and quality

controlscheme

Posterior

Lower

tailconsideration


Indicators

Population

Grades

[ 25 ]probabilistic

modeling

–

regression

analysis

3000

4000

5000

6000

7000

8000

9000

10000

0 20 40 60 80 100

bending

strength

[Mpa]

indic

atin

gpro

per

ty[-

]

n = 1020

εσ +⋅+= CaaI 10

Regression coefficients Normal distributed, with

µε

=0 and σε

[ 26 ]probabilistic

modeling

–

probability

of acceptance

An acceptance criteria may be formulated in form of

With the information from the regression analysis we assess the probability of acceptance P(AC

|σC

) by

{ }ULC bIbA ≤≤=where bL

and

bU

are lower and upper bounds for the Indicator of a particular grade.

)()( 10 UCLCC baabPAP ≤+⋅+≤= εσσ

2000

4000

6000

8000

10000

12000

14000

10 20 30 40 50 60 70 80 90

Property of Interest

Indi

cato

r

bL

bU

[ 27 ]probabilistic

modeling

–

Bayes

rule

)()(1)( CCCCC APfc

AfCC

σσσ σσ ⋅′=′′

Posterior

distribution

function

with

application

of the

Bayes

rule.

[ 28 ]

0

0.02

0.04

0.06

0 40 80 120 160Bending Strength [MPa]

Prob

abili

ty D

ensi

ty

probabilistic

modeling

–

Bayes

rule

)()(1)( CCCCC APfc

AfCC


Prior

Prior

[ 29 ]probabilistic

modeling

–

Bayes

rule

Prior Likelihood

0

0.02

0.04

0.06


Prob

abili

ty D

ensi

ty

Prior Likelihood

)()(1)( CCCCC APfc

AfCC


[ 30 ]

0

0.02

0.04

0.06


Prob

abili

ty D

ensi

ty

probabilistic

modeling

–

Bayes

rule

Prior Likelihood

Normalizing factor

Posterior

Prior Likelihood

Posterior

)()(1)( CCCCC APfc

AfCC


[ 31 ]results

IP yield strength MOE density

EN model EN model EN model EN model EN model

C30 ≥

7000 ≥

7000 475 475 31.8 31.8 14775 14775 380 380

C24 < 7000 ≥

6400< 7000 ≥

5950295 429 26.3 24.5 11948 11577 369 366

C14 < 6400 ≥

4300< 5950 ≥

4250250 116 17.8 16.0 9873 8816 354 347

reject <4300 <4250 1 0 12.2* - 6375* - 367* -

*=minimum value

Characteristic values of the grades according to EN14081 and the

probabilistic model (total n=1020 specimens)

[ 32 ]outline



Conclusions

[ 33 ]

The probabilistic approach does not only concentrate on the test sample

but rather allows for a model extrapolation to the whole population.

It is a central requirement that timber material properties can be probabilistically assessed.

The grading procedure has to be considered in probabilistic modeling.

Current grading practice does not allow an explicit consideration of the grading procedure in probabilistic modeling.

The probabilistic approach is more feasible and consistent.

Uncertainties have not to be calculated afterwards (by cost-matrices) but are included in the model.

Alternative and more straight forward methods exist and it should be discussed how future codes and regulations could be advanced.

Summary

Thank you!Thank you!

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