8.problem_solving_methods

8/7/2019 8.problem_solving_methods

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Chapter 3

Problem Solving Methods


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Engineers Solve Problems

Problem solving is a powerful human activity.

Computers are useful tools in problem solving,but it is the human who actually solves theproblem.

It is impossible to teach specific facts that willalways lead to a solution. The ability to solve problem comes from doing it.

Many things must pull together to solve aproblem.


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Problem Solving Problem solving is a combination of

experience, knowledge, process, andart

Design process is a series of logicalsteps that when followed produce an

optimal solution given time andresources as two constraints


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Problem Solving; cont

Aproblem is a situation, quantitative or

otherwise, that confronts an individualor group of individuals, that requires

resolution, and for which the individual

sees no apparent path to the solution.


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Problem Solving; cont

Problem solving is a process, an

activity whereby a best value isdetermined for an unknown, subject to a

specific set of conditions. It is a means

by which an individual uses previously

acquired knowledge, skills andunderstanding to satisfy the demands of

an unfamiliar situation.


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What skills must be used when

solving a problem?

Knowledge

MotivationExperience

Communication Skills

Learning SkillsGroup Skills


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Problem Analysis A distinguishing characteristic of a qualified

engineer is the ability to solve technical

problems; both art and science Science; knowledge of mathematics,

chemistry, physics, etc

Art; proper judgment, experience, commonsense, and know-how; to know when and

how rigorously science should be appliedand whether the resulting answerreasonably satisfies the original problem isan art


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Techniques for Error Free

Problem Solving

Always draw a picture of the physicalsituation,if possible.

State any assumptions made.

Indicate all given properties on thediagram with their units.

Convert units to a given unit system.Label unknown quantities with aquestion mark.


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Problem Solving

From the text, write the main equation

which contains the unknown quantity.Or

derive the desire algebraic equation by

solving integral or differential equations.Algebraically manipulate the equation to

isolate the desired quantity.


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Problem Solving

Write subordinate equations for the unknown

quantities in the main equation. Indent to

indicate that the equation is subordinate. It

may be necessary to go through several

levels of subordinate equations before all the

quantities in the main equation are known.

Once all algebraic manipulations and

substitutions are made, insert numerical

values with their units.


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Problem Solving

Insure that all units cancel.

Check one last time for sign error. Computethe answer.

Clearly mark the final answer. Indicateunits!

Insure that the final answer makes physicalsense!

Insure that all questions have beenanswered.


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Skills used in Implementing

Problem Solving Strategies

Analysis

Use logic to: Identify the system to be analyzed

Identify the objective Identify relationships

Divide the system into parts


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Synthesis

Use creativity to: Develop ideas via brainstorming

Evaluate the ideas by analysis when

enough ideas have been generated


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Decision Making

Use logic to

compare the various ideas and

select the best one(s)

Generalization - Going from the

specific to the broad use abstraction to:Aid in analysis, synthesis, and decisionmaking


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3.1T

ypes of Problems

Research Problems

Knowledge Problems Troubleshooting Problems

Mathematics Problems

Resource Problems

Social Problems

Design Problems


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T

ypes of Problems; cont

Research Problems

A hypothesis be proven or disproved Example; CFC may destroy the earths

ozone layer is a hypothesis. Design an

experiment that either proves or disproves

the hypothesis


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Types of Problems; cont

Knowledge Problems When a person encounters a situation that

he doesnt understand Example;

A chemical engineer noticed that thechemical plant produces more product

when it rains Further study showed that heat exchanger

cooled by rain increasing product


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Types of Problems;

cont Troubleshooting Problems

When equipment or software behaves in

unexpected or improper ways Example

During vibration test of an aluminum beam,the amplitude of the response is higher at

all exciting frequencies Troubleshooting shows that 60 cps of AC

current was close to the natural frequencyof the beam


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Types of Problems; cont Troubleshooting Problems; cont

e.g. an electronic amplifier has a loudhum when it is in a room withfluorescent lights.


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Mathematics Problems Describe physical phenomena with

mathematical models Engineers can unleash the extraordinary

power of mathematics, with the rigorouslyproven theorems and algorithms

Example; Isaac Newtons sine square lawcan be applied to hypersonic flow

e.g. find x such that 4x + 5 = 0.


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T


Resource Problems

There is never enough time, money, orequipment to accomplish the task

Engineers who can get the job done in

spite of resource limitations are highly

prized and awardede.g. how will we get the money to build our

new factory?


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Social Problems

For example, if a factory is relocated towhere there is shortage of skilled worker,

engineers should set up training program

for employees

e.g. how can we improve education?


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T


Design Problems

Require creativity, teamwork, and broadknowledge

Example; design a new car

Economy car? SUV?

Design goal and parameters


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Team Exercise

If you have enough money to buy a car,

what kind of car do you like to buy? If you are a car design engineer, identify

design goal and design parameters

from your teams preference


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Team Exercise Well Posed Design Problem: Design a

new car that can:

1. Go from 0 - 60 mph in 6 seconds

2. Gets 50 miles/gal

3. Costs less than $10,000 to the consumer

4. Does not exceed government pollutionstandards

5. Appeals to aesthetic tastes


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Team Exercise 1. Identify Problem e.g. we need to

build a new car since we are losing

market share

2. Synthesis (integrating parts to for awhole) e.g. we can combine an

aerodynamic body with a fuel efficientengine to make a new car with veryhigh fuel efficiency


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Team Exercise3. Analysis

identify relationships,

distinguish fact from opinion, detect logic information,

make conclusions from evidence,

select relevant information,

TRANSLA

TER

EAL-WOR

LD PROB

LEMINTO

MATHEMATICAL MODEL

e.g. compare the drag of different bodytypes and determine if engine can fit underthe hood


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Team Exercise

4. Application (identify the pertinentinformation) e.g. What force is requiredto allow the car to go 60 mph knowingthe car has a 30ft2 projected area and a0.35 drag coefficient based on wind

tunnel data?


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Team Exercise 5. Comprehension (use the data and

explicit theory to solve the problem)

F = 1/2 Cd V A V2

F=force

Cd=drag coef. V=air density A=protected

frontal area V=speed


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Difficulties in Problem Solving

Most common difficulty: failure to use known

information.

To avoid this problem:

Write the problem in primitive form and

sketch an accurate picture of the setup (whereapplicable).

Transform the primitive statements to simplerlanguage.

Translate verbal problems to more abstract

mathematical statement(s) and figures,

diagrams, charts, etc.


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General Problem SolvingMethod

Define and understand problem

1. Sketch the problem2. Gather information

3. Generate and evaluate potentialsolutions

Use applicable theories and assumptions

4. Refine and implement solution

5. Verify and test solution


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Define and Understand

Understand what is being asked

Describe input/output (I/O) what are you given

knowns

what are you trying to find

unknowns

Sketch the problem


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Gather Information

Collect necessary data

List relevant equations/theories State all assumptions


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Generate Solution Methods Apply theories and assumptions.

Typically, there is more than one approach

to solving a problem Work problem by hand using the potential

solution methods

Break problem into parts; scale it down; etc. e.g., if the problem was to calculate the average

of 1000 numbers, work the problem by hand

using, say, 10 numbers, in order to establish a

meth

od


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Refine and Implement

Evaluate solution methods.

accuracy

ease of implementation

etc.

Implement best solution.


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Verify and Test

Compare solution to the problem statement

Is this what you were looking for?

Does your answer make sense?

Clearly identify the solution

Sketch if appropriate


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CHECK YOURWORK!!

Dont stop at getting an answer!!

Think about whether the answer makesphysical sense.

you are the instructor and you have to turn in

final grades. In yourhaste, you calculate the

average of Susies grades (100, 70, 90) to be

78 and give Susie a C...


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Getting It Right

The problem solving process may be aniterative process.

If at first you dont succeed (i.e., thealgorithm test fails), try again

The more thorough you are at each

step of the problem solving process, themore likely you are to get it right thefirst time!!


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Team Exercise

Given: A student is in a stationary hot-

air balloon that is momentarily fixed at1325 ft above a piece of land. This pilot

looks down 60o (from horizontal) and

turns laterally 360o.

Note: 1 acre = 43,560 ft2


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Team Exercise; cont

Required:

a) Sketch the problem b) How many acres of land are

contained by the cone created by herline of site?

c) How high would the balloon be if,using the same procedure, an areafour times greater is encompassed?


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Creative Problem Solving

The nine dots shown

are arranged in equally

spaced rows andcolumns. Connect all

nine points with four

straight lines without

lifting the pencil from

the paper and without

retracing any line.

y y yy y y

y y yIndividual Exercise (3 minutes)


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Creative Problem Solving

y y yy y y

y y y


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Creative Problem Solving If you enjoy solving puzzles, you will enjoy

engineering

Crick and Watson figured DNA when theywere young

Engineers create from nature what did notexist before

In this creative process, the engineermarshals skills in mathematics, materials, andother engineering discipline and from theseresources create a new solution for a human

need


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Creative Problem Solving Engineering is not dull or stifling; send

people to moon, communication from

battlefield, etc Creative artists spent many years

perfecting their skills

Engineers need patience, practice, andgaining problem-solving techniques bytraining


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Self-Questions for Problem Solving

How important is the answer to a givenproblem?

Would a rough, preliminary estimate besatisfactory or high degree accuracydemanded?

How much time do you have and whatresources are at your disposal?

Data available or should be collected,equipments and personnel, etc


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Self-Questions for Problem Solving

What about the theory you intend to use?Can you use it now or must learn to use it?

Is it state of the art? Can you make assumptions that simplify

without sacrificing needed accuracy?

Are other assumptions valid and applicable?

Optimize time and resources vs reliability


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Engineering Method1. Recognize and understand the

problem (most difficult part)

2. Accumulate data and verify accuracy3. Select the appropriate theory or

principles

4. Make necessary assumptions5. Solve the problem

6. Verify and check results


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Engineering Method Perfect solutions to real problems do

not exist. Simplify the problem to solve

it; steady state, rigid body, adiabatic,isentropic, static etc

To solve a problem, use mathematical

model; direct methods, trial-and-error,graphic methods, etc.


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Problem Presentation Problem statement

Diagram

Theory

Assumptions

Solution steps Identify results and verify accuracy


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Standards of Problem Presentation

Engineers should have ability to presentinformation with great clarity in a neat,

careful manner

Poor engineering documents can belegal problems in courts

Follow standard forms such as shown inthe textbooks


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Algorithms Algorithm: a step-by-step procedure

for solving a problem or accomplishing

an end (Webster)

Algorithms can be described by

Pseudocode

Flowcharts


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Pseudocode English-like description of each step of

algorithm

Not computer code

Example - take out trash barrelswhile there are more barrels

take barrel to street

return to garage

end


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Flowcharts Graphical description of algorithm

Standard symbols used for specificoperations

Input/Output

Start/Stop

Branch Test

Process Step

Process Flow


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Flowchart ExampleDefine the

problem

Read

input

Solve the

problem

Can I

solve this?

Output

results

What do I need

to know?

Ask for

more input

Begin

Can I

solve this?

End

yes

no

yes

no


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Top Down Design State problem clearly

Sketch problem

Describe input/output(I/O)

Work problem by hand

Algorithm: pseudocode or flowchart Decomposition - break problem into steps

Stepwise refinement - solve each step

Test the algorithm/check your work!!


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Example (Team exercise, 15

min) State problem clearly:

Given ax2 + bx + c = 0, find x.

Describe I/O:

Input: a, b, c

Output: x


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Example (cont.) Hand example:

a=1, b=4, c=4

equation? (See Chapter 6, MathematicsSupplement)

x=?


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Example (cont.) Algorithm development

write an algorithm in pseudocode to take

any set of coefficients (i.e., a, b, c) andgive the value of x for each set

Test your algorithm a,b,c = 1,4,4

a,b,c = 1,1,-6

a,b,c = 1,0,1

other good test cases?

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