Chapter 1 IntroductionChapter 1 Introduction

§ 1.1 Problem and Analysis

§ 1.2 Data Engineering

§ 1.3 Scope

§ 1.4 Limitations of Course

R. J. ChangDepartment of Mechanical Engineering

NCKU

§ § 1.1 1.1 Problem and Analysis(1)Problem and Analysis(1)

1.Problem Cognition (1) Human and Physical interactions

Human BeingPhysical World

Cognition problem

Communication

Control

Interactions model

Q: How does the human being interacted with physical

world through data?

§ § 1.1 1.1 Problem and Analysis(2)Problem and Analysis(2)

 Human cognition model

TheoreticalLinguistics

ExperimentalPsychology

ComputerScience

§ § 1.1 1.1 Problem and Analysis(3)Problem and Analysis(3)

(2)Engineering problem

Inverse problem： Engineering analysisForward problem： Engineering design

ProductsInformation

Forward

Inverse

Human Society

§ § 1.1 1.1 Problem and Analysis(4)Problem and Analysis(4)

Design problem:

(a)Objective (b)Design parameters (c)Design constraints

Engineering decision making:

Cost： Expense for data collection and processing Performance： Information extraction and service

§ § 1.1 1.1 Problem and Analysis(5)Problem and Analysis(5)

To trade off between cost and performance

PerformanceCost

§§ 1.1 1.1 Problem and Analysis(6)Problem and Analysis(6)

2.Information Extraction (1)Physical aspect： Interaction model 

InformationField

PhysicalField

Interaction issue

Instrumentation

§§ 1.1 1.1 Problem and Analysis(7)Problem and Analysis(7)

(2)Mathematical aspect： Transformation model 

PhysicalWorld

InformationSpace

MathematicalSpace

Transformation(Topological

Space)

AnalyticalSpace

Modeling issue

§§ 1.1 1.1 Problem and Analysis(8)Problem and Analysis(8)

(3)Engineering aspect： Causality model

Uncertainty issue

AlgorithmInformation

DisplayPhysical

Data

§§ 1.2 1.2 Data Engineering(1)Data Engineering(1)1.Design Activity (a)Design problem 1. Object: Max(signal/noise) 2. Controlled parameter: (1)Hardware for data processing (2)Software by algorithm (math + numerical) 3. Constraints: (1)Hardware (2)Software (3)Data constraint: finite data length finite sampling rate finite bandwidth

§§ 1.2 1.2 Data Engineering(2)Data Engineering(2)

(b)Stochastic signal and information

Amplitude: Probability density function

Time: Autocorrelation function

Frequency (Temporal, Spatial): Power spectrum density function

§§ 1.2 1.2 Data Engineering(3)Data Engineering(3)

2.Data Analysis (a)General procedure

SignalSource

Algorithm

Data Information

Analysis andDecision making

Display

§§ 1.2 1.2 Data Engineering(4)Data Engineering(4)

Algorithm:

DataPreparation

DataQualification

DataAnalysis

* Data collection* Data conversion* Data preprocessing

* Qualitative classification* Stationarity* Periodicity* Nonstationarity

* Amplitude-domain distribution* Time-domain distribution* Spatial-domain distribution (2-D and above)* Frequency-domain distribution

§§ 1.2 1.2 Data Engineering(5)Data Engineering(5)

(b)Mathematical Model

UncertainPhysicalWorld

MathRepresentation

StatisticalExperiment

ProbabilitySpace

Randomizationdesign and test

Probabilityaxioms

Statisticalmodeling

Probabilitymodeling

Modeling and mapping

§§ 1.2 1.2 Data Engineering(6)Data Engineering(6)

(c)Engineering Model

Algorithm+

Hardware

OutputInformation

+

Error

Input DataArray

Additive error

Error can be additive or

multiplicative.

§§ 1.3 1.3 Scope(1)Scope(1)

1. Phases of Data Analysis

SignalSource

PropagationPath

Data Acquisition

Pre-processingData Reduction

*Reduced Signature Analysis* Features

Classification

Noise

Parameters

Go/No Go Specific Problem

Noise(N)

S/N Max. (optimal)

DataBase

GenerationMechanism

Signal(S)

§§ 1.3 1.3 Scope(2)Scope(2)

2.Information Estimator (1) Hypothesis： The existence and uniqueness of true information in data set. (2) Objective：Maximize S/N under the constraints of data, algorithm, and hardware.

Data Algorithm

Hardware

S/N

§§ 1.3 1.3 Scope(3)Scope(3)

Ex. A Simple estimation

(1) Signal information

Mean value:

(2) Data set:

(3) Data constraint: N

(4) Noise

Error : || || , “ || ||’’ : Norm

1

1 N

x ii

xN

ix

μ -μx x

§§ 1.3 1.3 Scope(4)Scope(4)

3.Main Information

(1) Single state:

Mean value:

Mean square variance:

Probability density function:

Autocorrelation function:

Power spectral density function:

2 2( )x xRMS

x

( )p x

( )xxR

( )xxS

§§ 1.3 1.3 Scope(5)Scope(5)

(2) Multiple states (2-D for example)

Correlation coefficient:

Cross correlation:

Cross spectrum:

Coherence function:

Joint probability density:

( , )X Y

( )xyR Z

( )xyS j

2 ( )( )

( ) ( )

xy

xx yy

xyS j

rS S

xyp

§§ 1.3 1.3 Scope(6)Scope(6)

4. System Applications

Engineeringsystem

Realization

Performance testing

Operation

Analysis

Test

Non-parametric approach

Parametric approach

Source identificationPath identification

System health

Quality control

Transmission properties

§§ 1.4 1.4 Limitations of Course(1)Limitations of Course(1)

Data engineering approach

Classical nonparametric analysis Concern on stationary one-dimensional process

1. Content Limitation

§§ 1.4 1.4 Limitations of Course(2)Limitations of Course(2)

2. Knowledge Limitation

DecisionIntelligence

Engineering Knowledge

Signal Information

Random Data