138755986 problem-solving-methods-ppt

Chapter 3Problem Solving

Methods

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 the problem.

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

Many things must pull together to solve a problem.

Problem Solving Problem solving is a combination

of experience, knowledge, process, and art

Design process is a series of logical steps that when followed produce an optimal solution given time and resources as two constraints

Problem Solving; cont’

A problem is a situation, quantitative or otherwise, that confronts an individual or group of individuals, that requires resolution, and for which the individual sees no apparent path to the solution.

Problem Solving; cont’

Problem solving is a process, an activity whereby a best value is determined for an unknown, subject to a specific set of conditions. It is a means by which an individual uses previously acquired knowledge, skills and understanding to satisfy the demands of an unfamiliar situation.

What skills must be used when solving a problem?

KnowledgeMotivation Experience Communication Skills Learning Skills Group Skills

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,

common sense, and know-how; to know when and how rigorously science should be applied and whether the resulting answer reasonably satisfies the original problem is an art

Techniques for Error Free Problem Solving

Always draw a picture of the physical situation,if possible. State any assumptions made. Indicate all given properties on the diagram with their units. Convert units to a given unit system. Label unknown quantities with a question mark.

Techniques for Error Free 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.

Techniques for Error Free 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.

Techniques for Error Free Problem Solving

Insure that all units cancel. Check one last time for sign error. Compute the answer. Clearly mark the final answer. Indicate units! Insure that the final answer makes physical sense! Insure that all questions have been answered.

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

Skills used in Implementing Problem Solving Strategies

SynthesisUse creativity to: Develop ideas via brainstorming Evaluate the ideas by analysis when

enough ideas have been generated

Skills used in Implementing Problem Solving Strategies

Decision MakingUse 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 decision making

3.1 Types of Problems

Research Problems Knowledge Problems Troubleshooting Problems Mathematics Problems Resource Problems Social Problems Design Problems

Types of Problems; cont’

Research Problems A hypothesis be proven or disproved Example; CFC may destroy the earth’s

ozone layer is a hypothesis. Design an experiment that either proves or disproves the hypothesis

Types of Problems; cont’ Knowledge Problems

When a person encounters a situation that he doesn’t understand

Example; A chemical engineer noticed that the

chemical plant produces more product when it rains

Further study showed that heat exchanger cooled by rain increasing product

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 frequency of the beam

Types of Problems; cont’ Troubleshooting Problems; cont’ e.g. an electronic amplifier has a

loud “hum” when it is in a room with fluorescent lights.

Types of Problems; cont’ Mathematics Problems

Describe physical phenomena with mathematical models

Engineers can unleash the extraordinary power of mathematics, with the rigorously proven theorems and algorithms

Example; Isaac Newton’s sine square law can be applied to hypersonic flow

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

Types of Problems; cont’

Resource Problems There is never enough time, money, or

equipment to accomplish the task Engineers who can get the job done in

spite of resource limitations are highly prized and awarded e.g. how will we get the money to build our new factory?

Types of Problems; cont’

Social Problems For example, if a factory is relocated to

where there is shortage of skilled worker, engineers should set up training program for employees

e.g. how can we improve education?

Types of Problems; cont’

Design Problems Require creativity, teamwork, and broad

knowledge Example; design a new car Economy car? SUV? Design goal and parameters

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 team’s preference

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 pollution

standards 5. Appeals to aesthetic tastes

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 a whole) e.g. we can combine an aerodynamic body with a fuel efficient engine to make a new car with very high fuel efficiency

Team Exercise3. Analysis

identify relationships, distinguish fact from opinion, detect logic information, make conclusions from evidence, select relevant information, TRANSLATE REAL-WORLD PROBLEM INTO

MATHEMATICAL MODEL e.g. compare the drag of different body

types and determine if engine can fit under the hood

Team Exercise

4. Application (identify the pertinent information) e.g. What force is required to allow the car to go 60 mph knowing the car has a 30ft2 projected area and a 0.35 drag coefficient based on wind tunnel data?

Team Exercise 5. Comprehension (use the data

and explicit theory to solve the problem) F = 1/2 Cd A V2

F=force Cd=drag coef. =air density

A=protected frontal area V=speed

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 (where applicable).

Transform the primitive statements to simpler language.

Translate verbal problems to more abstract mathematical statement(s) and figures, diagrams, charts, etc.

General Problem Solving Method

Define and understand problem1. Sketch the problem2. Gather information3. Generate and evaluate potential

solutions Use applicable theories and

assumptions4. Refine and implement solution5. Verify and test solution

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

Gather Information

Collect necessary data List relevant equations/theories State all assumptions

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 method

Refine and Implement

Evaluate solution methods. accuracy ease of implementation etc.

Implement “best” solution.

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

CHECK YOUR WORK!!

Don’t stop at getting an answer!! Think about whether the answer makes

physical sense. you are the instructor and you have to turn in

final grades. In your haste, you calculate the average of Susie’s grades (100, 70, 90) to be 78 and give Susie a C...

Getting It Right The problem solving process may

be an iterative process. If at first you don’t succeed (i.e., the

algorithm test fails), try again… The more thorough you are at

each step of the problem solving process, the more likely you are to get it right the first time!!

Team Exercise

Given: A student is in a stationary hot-air balloon that is momentarily fixed at 1325 ft above a piece of land. This pilot looks down 60o (from horizontal) and turns laterally 360o.

Note: 1 acre = 43,560 ft2

Team Exercise; cont’

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

contained by the cone created by her line of site?

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

Creative Problem Solving

The nine dots shown are arranged in equally spaced rows and columns. Connect all nine points with four straight lines without lifting the pencil from the paper and without retracing any line.

Individual Exercise (3 minutes)

Creative Problem Solving

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

engineering Crick and Watson figured DNA when they

were young Engineers create from nature what did not

exist before In this creative process, the engineer

marshals skills in mathematics, materials, and other engineering discipline and from these resources create a new solution for a human need

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, and gaining problem-solving techniques by training

Self-Questions for Problem Solving How important is the answer to a given

problem? Would a rough, preliminary estimate be

satisfactory or high degree accuracy demanded?

How much time do you have and what resources are at your disposal? Data available or should be collected,

equipments and personnel, etc

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

Engineering Method1. Recognize and understand the

problem (most difficult part)2. Accumulate data and verify accuracy3. Select the appropriate theory or

principles4. Make necessary assumptions5. Solve the problem6. Verify and check results

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.

Problem Presentation Problem statement Diagram Theory Assumptions Solution steps Identify results and verify accuracy

Standards of Problem Presentation Engineers should have ability to

present information with great clarity in a neat, careful manner

Poor engineering documents can be legal problems in courts

Follow standard forms such as shown in the textbooks

Team Assignment Page 141 Problem 3.20

Algorithms Algorithm: “a step-by-step

procedure for solving a problem or accomplishing an end” (Webster)

Algorithms can be described by Pseudocode Flowcharts

Pseudocode English-like description of each step

of algorithm Not computer code Example - take out trash barrels

while there are more barrelstake barrel to streetreturn to garage

end

Flowcharts Graphical description of algorithm Standard symbols used for specific

operations

Input/Output

Start/Stop

Branch Test

Process Step

Process Flow

Flowchart ExampleDefine theproblem

Readinput

Solve theproblem

Can Isolve this?

Outputresults

What do I needto know?

Ask formore input

Begin

Can Isolve this?

End

yes

no

yes

no

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!!

Example (Team exercise, 15 min) State problem clearly:

Given ax2 + bx + c = 0, find x. Describe I/O:

Input: a, b, c Output: x

Example (cont.) Hand example:

a=1, b=4, c=4 equation? (See Chapter 6,

Mathematics Supplement) x=?

Example (cont.) Algorithm development

write an algorithm in pseudocode to take any set of coefficients (i.e., a, b, c) and give 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?