Chapter 1 Introduction § 1.1 Problem and Analysis § 1.2 Data Engineering § 1.3 Scope § 1.4 Limitations of Course R. J. Chang Department of Mechanical Engineering NCKU

§ 1.1 Problem and Analysis(1) 1.Problem Cognition (1) Human and Physical interactions Interactions model Q: How does the human being interacted with physical world through data?

§ 1.1 Problem and Analysis(2) Human cognition model

§ 1.1 Problem and Analysis(3) (2)Engineering problem Inverse problem ： Engineering analysis Forward problem ： Engineering design

§ 1.1 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 Problem and Analysis(5) To trade off between cost and performance

§ 1.1 Problem and Analysis(6) 2.Information Extraction (1)Physical aspect ： Interaction model

§ 1.1 Problem and Analysis(7) (2)Mathematical aspect ： Transformation model

§ 1.1 Problem and Analysis(8) (3)Engineering aspect ： Causality model

§ 1.2 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 Data Engineering(2) (b)Stochastic signal and information Amplitude: Probability density function Time: Autocorrelation function Frequency (Temporal, Spatial): Power spectrum density function

§ 1.2 Data Engineering(3) 2.Data Analysis (a)General procedure

§ 1.2 Data Engineering(4) Algorithm:

§ 1.2 Data Engineering(5) (b)Mathematical Model

§ 1.2 Data Engineering(6) (c)Engineering Model Error can be additive or multiplicative.

§ 1.3 Scope(1) 1. Phases of Data Analysis

§ 1.3 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.

§ 1.3 Scope(3) Ex. A Simple estimation (1) Signal information Mean value: (2) Data set: (3) Data constraint: N (4) Noise Error : || ||, “ || ||’’ : Norm

§ 1.3 Scope(4) 3.Main Information (1) Single state: Mean value: Mean square variance: Probability density function: Autocorrelation function: Power spectral density function:

§ 1.3 Scope(5) (2) Multiple states (2-D for example) Correlation coefficient: Cross correlation: Cross spectrum: Coherence function: Joint probability density:

§ 1.3 Scope(6) 4. System Applications

§ 1.4 Limitations of Course(1) Data engineering approach Classical nonparametric analysis Concern on stationary one-dimensional process 1. Content Limitation

§ 1.4 Limitations of Course(2) 2. Knowledge Limitation