sudoku and geotechnical solutions lessons from a parallel … · 2017-05-19 · 24/04/2015 1 sudoku...

24/04/2015

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Sudoku and Geotechnical SolutionsLessons from a Parallel Universe

of Limited Data

Dr Burt Look

Risk Informed

decision making

Project

constraints

Data available

Time

Budget

Complexity of

problem

Reliability of

tools & data

Analytical tools

EA Gold Coast Region - April 2015

The Parallel Universe

• Geotechnical engineering relies on data to reduce risk. We infer, interpolate, and extrapolate based on often limited data with time and cost constraints also at work

• Similarly, solving a Sudoku puzzle relies on seeing data relationships• ,…. but what about time and cost constraints

• This presentation is based on a 2014 paper

Look B (2014). Sudoku and Geotechnical Solutions: Lessons from a Parallel Universe of Limited Data, Geostrata ASCE Geo-Institute, pp 56 - 60


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Elements of The Parallel Universe

Geotechnical

Engineering

Often incomplete data

Establish relationships

•Historical Field Lab Design

Connections to other disciplines

GE1 GE2 GE3

Time and $ constraint

Sudoku

Limited Data

Establish number relationships

Any solution must have no conflicts

with other “boxes, rows or columns

Easy Medium Hard Harder

Apply time constraint

Quality – Cost – Time Relationship

• This relationship says that if we change one of the three, the other two must be affected as well

• A client expects high quality at the least cost

• Ideal Relationship – perfectly balanced

b. Ideal for client

CostQuality

c. Time as the Pivot Point

CostQuality

a. Ideally well balanced


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Quality – Cost – Time – Changing one

• If a shift in time, then either • reduced quality or higher cost is the outcome

• With no change in time, any reduction in cost must be offset by a reduction in quality

High

CostQuality

d. Reduced Time High Costs

Reduced Time

CostQuality

e. Reduced Time Low Quality

Reduced Time

f. Cost Reduces Quality Reduces

Cost

Cost

Quality

Quality


Sudoku Puzzles

• A Sudoku puzzle is a logic numbers game, which consists of • a 9 X 9 square grid,

• further sub-divided into another nine 3 X 3 sub-grids

• Some of the squares already contain numbers• objective is to fill in the remaining squares

so that

• every row and every column contains each of the numbers 1 to 9 only once

9 Rows9 X 9


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Geotechnical

Investigations

0.001%

Sampled

Solving Techniques

• By trial and error • Assume a number and progress around the grids to see if any conflict results• Works only for easy puzzles

• Easy ~ 35 knowns 46 unknowns• Single position / Single Candidate

• Medium• Candidate Line / Double Pair / Multi – line

• Hard• Naked Pairs / Hidden Pairs / Triples

• Extreme• X- Wing / Swordfish / Forcing Chains

https://www.sudokuoftheday.com/techniques/


~ 35 knowns (43%): 46 unknowns




Sudoku Puzzle – Easy Example

5 1 7 6

6 7 4

3 7 5 9 8

9 8 4

4 9 8 2

8 6 2 5 9

7 3 9 2 1

4 3 7

5 7 2 9


5 1 7 4 6

6 7 4

3 4 7 5 9 8

9 8 4

4 9 8 2

8 6 2 5 9

7 3 9 2 1

4 3 7

5 7 2 4 9

5 1 7 4 6

6 7 4

3 4 7 5 9 8

7 9 8 4

4 9 7 8 2

8 6 2 5 9 7

7 3 9 2 1

4 3 7

5 7 2 4 9

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The Metaphor Journey

• Quality in this metaphor is accuracy in solving the puzzle.

• Solving correctly means considering interactions • Inside our Box Across Up Down The Big Picture

• What happens if the objective is to solve the puzzle in as little time as possible? • If one tries to beat the clock, the error rate goes up (quality is reduced) analogous to meeting a

daily schedule.

• And when a more difficult puzzle occurs with time constraints?• Like when difficulty / costs change in a project What is effect on error / quality

• The lessons learnt from solving puzzles with different degrees of difficulty can be used to illustrate how we can compromise quality and introduce errors in our day-to-day work.


The Sudoku Puzzle – Need to always connect in several ways

XAcross

Up

Do

wn


We will

examine a few

eXamples

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The meaning of Factor of safety


• Factor of safety = Factor of Ignorance

• An output for judgement. It is one component in a decision making process

• Example for a given geometry and loading

o Lower bound parameters : Say c´ = 5 kPa, Ø´ = 25⁰

Calculated FS (say 1.4)

o Typical parameters: Say c´ = 20 kPa, Ø´ = 30⁰

Calculated FS (say 1.5)

Is a calculated Factor

of safety =1.5 safer

than FS = 1.4 ?

The Sudoku Puzzle Factor of Safety– Need to always connect in several ways

FS =

1.5Consequences

Likelih

oo

d


Input

Factor of safety

has meaning

only when

related to input

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Lesson 1 from Sudoku puzzles

• Consider interaction effects

• QRA Example• If likelihood is likely should we be

always concerned ?

• Severe consequences = $ + Time

• Insignificant = $ + Time

Likelihood Consequence Risk


Desc

rip

tio

n

Ap

pro

x.

An

nu

al

Pro

bab

ilit

y Consequences

Catastrophic

200%

Major

60%

Medium

20%

Minor

5%

Insignificant

0.5%

Almost

Certain

10 -1

Likely 10 -2 VH VL

Possible 10 -3

Unlikely 10 -4

Rare 10 -5

Barely

Credible

10 -6

Is FS = 1.5 appropriate

for all consequences?

The Sudoku Puzzle Factor of Safety– Need to always connect in several ways

FS =

1.5Consequences

Likelih

oo

d


Input

Factor of safety

has meaning only

when related to

Input

+ Likelihood

+ Consequences

Ownership

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Risk perception of varying asset owners

Owner of Consequences Comment

Road Major – Medium Alternative route available

Pipeline Catastrophic - Major No alternative route

Farmland Insignificant Undulating cow paddock


FS = 1.4 to 1.5

Decision trees to rationalise FS

70.0% 0.0%

-5000000 -$5,000,000

FALSE Chance

0 -$3,500,000

30.0% 0.0%

0 $0

TRUE Decision to minimise cost - accept risk

0 -$1,250,000

5.0% 5.0%

-5000000 -$6,000,000

TRUE Chance

-1000000 -$1,250,000

95.0% 95.0%

0 -$1,000,000

Decision for further work

-1250000

0.1% 0.0%

-4000000 -$7,500,000

FALSE Chance

-2500000 -$3,504,000

99.9% 0.0%

0 -$3,500,000

FALSE Decision to accept cost - minimise risk

-1000000 -$6,000,300

0.01% 0.0%

-3000000 -$9,000,000

TRUE Chance

-5000000 -$6,000,300

99.99% 0.0%

0 -$6,000,000

Pipeline Failure Occurs

No Pipeline failure


No Pipeline failure

Esk Kilcoy Landslide - Chainage 6+720

Improve Factor of Safety

FS = 1.4

FS = 1.5

Minimal Work

Accept Risk


No Pipeline failure

FS = 1.3 (temporary)


No Pipeline failure

QTMR Design requirement

FS= 1.5

Cost Effective

to do nothing

- Take the Risk

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Number

Wrong

0 1 to 2 2 to 5 6 to 10 10 to 20 > 20

With time

constraint

How accurate are you ?

• If I give you 100 easyproblems to solve: How many will you get wrong ?


Number

Wrong

0 1 to 2 2 to 5 6 to 10 10 to 20 > 20

Albert Einstein Quote

“When you are courting a nice girl an hour seems like a second.

When you sit on a red-hot cinder a second seems like an hour.

That's relativity“


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Introducing Time

SudokuTime

Limit

What

happens?

Sudoku Addiction Getting Bored Start the clock


Easy Sudoku - Lessons

Easy

Accuracy 91.0%

Error 9.0%

Best Time (mins) 3

Worst Time (mins) 10

No. in Test 67

With no time constraint, my accuracy 100% accuracy.

Inaccuracies due to either boredom or disturbance (e.g.,

wife interrupted me time to do grocery shopping);

+ Time 1-in-11 chance of inaccuracy;

The more quickly one tries to do the puzzle, the more

likely there will be an error;

I am more likely to get a puzzle wrong after scoring a

best time; and

For an easy puzzle, there’s an over-confidence bias due

to less self-checking


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Easy Sudoku – Engineering Lessons

Easy

Accuracy 91.0%

Error 9.0%

Best Time (mins) 3

Worst Time (mins) 10

No. in Test 67

As a frequent Sudoku player, a 9 percent inaccuracy

disturbs me because the puzzles were easy

Suggests that in my day-to-day geotechnical

engineering, 100 percent accuracy may not be

achieved, because time constraints do occur

This “inaccuracy” could range from a typographical

mistake to a critical calculating error.


Introduction to Engineering Statistics


1. Statistics

Basics

2. Everyday

Application

3.Engineering

Application

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Statistics Basics: Symbols

Sample Statistic Population Parameter

Arithmetic Mean μ

Standard Deviation s σ

Number of items n N


• Sample mean is a point estimate

• Sum of all scores divided by the number of items

𝑥

𝑥 = 𝑥

𝑛

Variability

• Range • Difference between highest and lowest

• Standard Deviation• Data scatter about the mean for small samples : (n-1)= degrees of freedom

• 𝑠 = 𝑖=1

𝑛(𝑥𝑖−𝑥)

𝑛−1

• For n ≥ 30 samples or whole population being studied

• σ = (𝑥 − 𝜇)

𝑁


𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛

𝐶𝑂𝑉 =𝑠

𝑥

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Central Limit Theorem

• Distribution of a sample follows a normal curve

• Applies for large samples n ≥ 30

• Standard Error of the Mean (S.E.) = 𝑠√𝑛

• Smaller the standard error the greater the precision

• The greater the number of samples, the standard error reduces

• For sample size samples (n< 30): Use the Student t-distribution as the arithmetic mean is not normally distributed


Design values based on probability of failure

1 in

2 c

han

ce

20

% to

30

% C

ha

nce

Modera

tely

conserv

ative

5%

to

10

% C

ha

nce

Factor of Safety

Note that design value is

lower than most

unfavourable value

Most

Pro

bable

Desig

n V

alu

e

Partial Factor

0.1

% C

han

ceU

nfa

voura

ble

V

alu

e

Chara

cte

ristic V

alu

e

Design value based on factor of safety chosen so

that probability of failure is acceptable small

Partial factor of safety should (in theory)

produce similar design value - but does not in

practice


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The statistics of 2012 Olympics

Australia No 44 Australia No 30

Australia 7 Gold 16 silver 12 bronzeEA Gold Coast Region - April 2015

The Queensland statistics of 2012 Olympics

Aug 18 2012


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Examples of Continuous Distribution Functions


Sleeper, 2010 Webinar on Why Be Normal ?

Probability Distribution Function – Easy Sudoku


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Times for Easy to Hard Puzzles

Easy Medium Hard

Accuracy 91.0% 82.1% 54.5%

Error 9.0% 17.9% 45.5%

Best Time (mins) 3 5 15

Worst Time (mins) 10 15 88

No. in Test 67 67 66


Over 100 hrs

data

gathering !!

Probability Distribution Function – Hard Sudoku


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Lessons from using a normal distribution

• The normal distribution is typically used by many engineers, and if used here would indicate:• 10 percent chance of completing a puzzle in 13.2 minutes (my best time out of

66 attempts was 15 minutes)

• 5 percent probability of achieving a time of 5 minutes

• 1 percent probability chance of achieving a time of -10.3 minutes (The negative is not a mis -print)


“Assumed” Normality does not always apply

1 in

2 c

han

ce

20

% to

30

% C

ha

nce

Modera

tely

conserv

ative5%

to

10

% C

ha

nce

Non Normal distribution

Most

Pro

bable

Desig

n V

alu

e

0.1

% C

han

ce

With the assumption of “normal”

distribution over design can take place -

the most common error which affects our

design value


1 in

2 c

han

ce

20

% to

30

% C

ha

nce

Modera

tely

conserv

ative

5%

to

10

% C

ha

nce

Factor of Safety

Note that design value is lower

than most unfavourable value

Most

Pro

bable

Desig

n V

alu

e

Partial Factor

0.1

% C

han

ceU

nfa

voura

ble

Valu

e

Chara

cte

ristic V

alu

e

24/04/2015

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Distributions for the diametral Is (50)


X 7

Pier 6 Pile Layout


Bridge Structure spans 1.6km between abutments

– Bridge has 17 Piers of varying height with pier

heights varying from 17m to 54m

– Central River span ~ 260m

– Main span at Piers 6 and 7

• 24 Bored piles

• 1.5m diameter

• Compressive loads up to 36MN

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Distribution Models at the 24 locations

Pier 6

Pile #

Diametral Is (50) Statistics 10% Characteristic (MPa)

Mean (MPa) COV No. of points Normal Log Normal

P6-5 0.85 39 % 10 0.46 n/a

P6-6 1.01 151% 10 0.26 0.43

P6-7 0.57 56% 15 0.15 0.19

P6-8 0.74 68% 15 0.12 0.30

P6-21 0.94 37% 16 0.48 0.51

P6-22 0.81 113% 17 (-0.13) 0.20

P6-23 0.81 40% 13 0.40 0.45

P6-24 0.61 87% 18 (-0.12) 0.12

P6-ALL 0.82 91% 330 0.03 0.24


Look and Wijeyakulasuriya (2009)

Lesson 2: Do not assume normal distribution applies

1 in

2 c

han

ce

20

% to

30

% C

ha

nce

Modera

tely

conserv

ative5%

to

10

% C

ha

nce


Most

Pro

bable

Desig

n V

alu

e

0.1

% C

han

ce

You may end up with to

low a value or,

A negative design

number sometimes, then

Say statistics is waste of

time

when you are actually

wasting time on the

incorrect PDF


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Lesson 3: Delivering above or below time

1 in

2 c

han

ce

20

% to

30

% C

ha

nce

Modera

tely

conserv

ative5%

to

10

% C

ha

nce


Most

Pro

bable

Desig

n V

alu

e

0.1

% C

han

ce

If we deliver projects

below time and cost,

Outcome will be

nominally less,

But when we do not

meet the project

schedule, the overrun

can be significant


Lesson Summary on PDF


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Smith Street


Bridge

Site

Range of Is (50) Values

DW Rock SW Rock

Average

(MPa)

Coefficient of

Variation

Lower

Characteristic

Value (MPa)

Average

( MPa)

Coefficient of

Variation

Lower

Characteristic

Value (MPa)

A 2.03 121% 0.23 2.05 79% 1.48

B 0.57 123% ( - ) 1.94 54% 1.42

C 0.98 30% 0.49 Insufficient data

D 2.20 58% 1.50 2.60 36% 1.96

E 1.50 135% ( - ) 2.57 71% ( - )

Look (2001)

Point Load Index test results with weathering grade

Question 2 – What is design

characteristic value ?


Strongest

Weakest

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Design Values for Bored piers

Look, 2001

Bridge Site Ultimate Resistance of Bored Piers

DW Rock SW Rock

A 5000 kPa 10,000 kPa

B 5000 kPa 10,000 kPa

C 5000 kPa 10,000 kPa

D 5000 kPa 10,000 kPa

E 5000 kPa 10,000 kPa

o Geotechnical report produced same design values at all sites

o Difficult to argue against the benefit of “local experience ”.

o The designer can be excused for wondering what is the value of carrying out so many tests on the rock

and not using the data


Lesson 4: Guessing Sudoku

With Guessing You will get a wrong solution !!

Arguably “conservative” with “experience”,

But most likely not cost effective


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Guessing….. And hoping a miracle occurs


Variability in selecting design values


Facts (Data)Rules for

assessmentConclusion

Look and Campbell (2013)

2%2%

2%3%

3%

3%

3%5%

5%

5%

5%7% 7%7%

7%

10% 10%10%

15%15%

0%

20%

40%

60%

80%

100%

Project

Manager

Civil +

Structural

Geotechnical Other

15%

10%

7%

5%

3%

2%

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Pavement Cost vs Design Risk


$500

$700

$900

$1,100

$1,300

$1,500

$1,700

$1,900

$2,100

$2,300

$2,500

2 3 5 5 10 15

Cost $

Th

ou

san

ds

CBR %

Lowest 10% 20% 20% 40% Average

Percentage Defective

Full

R & R

Full

R & R

Main

ten

an

ce $

Main

ten

an

ce $

Change in Design CBR


Think you

know ! ..

Least likely

to change

mind

Greatest

initial error

Did not

seem to

consider

cost ?

Most

likely to

change

24/04/2015

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Design CBR Selection


The Sudoku Puzzle Design CBR– Need to always connect in several ways

CBR

= ?Cost $

Main

ten

an

ce $

$

R &

R


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Times Easy to Hard Puzzles - COV

Easy Medium Hard

Accuracy 91.0% 82.1% 54.5%

Error 9.0% 17.9% 45.5%

Best Time (mins) 3 5 15

Worst Time (mins) 10 15 88

No. in Test 67 67 66

COV 25% 38% 64%


Ranges of Soil Property Variation

Geotechnical

Parameter

Property

Variability

COV

(%)Comment

Undrained

Shear Strength

Low

Medium

High

10–30

30–50

50–70

Good quality direct lab or field measurement

Indirect correlations w/ good data except for SPT

Indirect/empirical correlations w/ SPT data

Quality of

Concrete

Excellent

Good

Satisfactory

Bad

≤ 10

10-15

15-20

≥ 20

Concrete is a “uniform” material

(Phoon and Kulhawy, 2008).


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Quality

• Quality is measured in relation to characteristics of the product that a customer expects to find

• Quality comes at a cost

• Cost of Quality (COQ) is contentious• Cost of non conformance (how much it costs company) is a one side argument

• Need to assess cost incurred in preventing non conformance, and

• Cost to improve product


Lesson 5: On reducing error - Review

Error for difficult puzzles > 40 % : Error for Easy = 9%

This outcome is metaphorically a GE3 engineering problem, and this high error is unacceptable

Independent review required

Required Review to reduce to 1%

1 Reviewer (RPEQ / CPENG) + Independent Reviewer ( 2 No.) + External Reviewer (3 No.)

Geotechnical Equivalent

GE1 GE2 GE3

Error Rate

9% 18% 45%

Sudoku Level of Difficulty

Easy Medium Hard


11% Increase in Knowns

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Swiss Cheese Model

http://www.ask.com/wiki/Swiss_cheese_model?o=2802&qsrc=999&ad=doubleDown&an=apn&ap=ask.com

In the Swiss Cheese model, an organization's

defences against failure are modelled as a

series of barriers, represented as slices of

cheese.

Holes in the slices =weaknesses in individual

parts of the system and are continually

varying in size and position across the slices.

System produces failures when hole in each

slice momentarily aligns, permitting (in

Reason's words) "a trajectory of accident

opportunity", so that a hazard passes

through holes in all slices, leading to failure


Review 1 Review 2 Review 3

Points so far

1) Statistics can produce different conclusions depending on the way the data is “normalised” Queensland is the Olympic champion ??

2) Selecting design values is not a guessing game

3) More Tests More Confidence a safer product Piling Example to follow

In piling code: [ = 0.8 (FS of 1.25) with testing] [ = 0.4 (FS = 2.5) no testing]


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Pile Redundancy

High

Redundancy

Pile groups

with 4 or

more piles

Piled rafts

Large pile

groups

under

large caps

High Redundancy

• Pile cap connects pile

• Load shedding

Low Redundancy

• Pile used as column

without a pile cap


Pile Testing Requirements for Serviceability

Very high

ARR > 4.5 10%

High

ARR = 4.0 – 4.49 5%

Moderate to high

ARR =3.50 – 3.99 3%

Moderate

ARR =3.00 – 3.49 2%

Low to moderate

ARR =2.50 – 2.99 1%

Overall risk category

Average Risk Rating (ARR) % of pile to be tested for serviceability

FS = 2.5

FS = 1.5

FS = 1.3

FS = 2.1


24/04/2015

30

Design geotechnical strength (AS 2159)

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Test

ing

Ben

efit

Fact

or

(K)

% of Piles Tested + OK

Static or Rapid Load Dynamic

FS = 1.25


Increased Data

Pile Testing summary (AS 2159) for high risk

No Pile Testing (BH Data only)

• = 0.4

• FS = 2.5

With Pile Testing

• = 0.8

• FS = 1.25


With Pile test data

24/04/2015

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Low FS due to data reliability

Property

Variability

COV

(%)

Low

Medium

High

10–30

30–50

50–70

(Phoon and Kulhawy, 2008).

EA Gold Coast Region - April 2015Look (2015)

Final Sudoku Lesson

Sudoku may be entertaining, but the game can also teach us many lessons.Incomplete data increases the likely error. The same is true in geotechnical engineering. More data Less error Less cost to project

Stop Guessing !

Estimates of times can be skewed (Non normal distribution). Below-average time events may take nominally less, while time estimates that are above average, will have a significant error. Hence when we get it wrong, it will be wrong in a big way

Stop Using Normal Distribution !

And Sudoku’s most important final lesson is — take a break! Constantly pushing to get a solution faster increases both stress and errors

Take time to Enjoy what you do !


sudoku and geotechnical solutions lessons from a parallel … · 2017-05-19 · 24/04/2015 1 sudoku...

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