§ 4.1 Instrumentation and Measurement Systems § 4.2 Dynamic Measurement and Calibration § 4.3 Data Preparation and Analysis § 4.4 Practical Considerations Chapter 4 Data Acquisition and Preprocessing R. J. Chang Department of Mechanical Engineering NCKU

1. Introduction (1) Signal and Noise § 4.1 Instrumentation and Measurement Systems(1) * ： convolution

(3) Measurement quality ─ S/N ratio § 4.1 Instrumentation and Measurement Systems(2) (2) Ideal measurement system

2. System structure (1) Fundamental structure § 4.1 Instrumentation and Measurement Systems(3)

(2) Three stages structure § 4.1 Instrumentation and Measurement Systems(4)

(3) Sensor/Transducer (a) Passive (b) Active Open loop type: Servo type: § 4.1 Instrumentation and Measurement Systems(5)

Ex : Accelerometer for vibration data Stress and strain gauges for deflection data Microphone for acoustical data Seismometers for seismic data STM probe for atom distribution § 4.1 Instrumentation and Measurement Systems(6)

3. Signal and Standard units (1) Signal space O ─ Optics E ─ Electricity M ─ Mechanics C ─ Chemistry § 4.1 Instrumentation and Measurement Systems(7)

(2) International system of unit (SI) (a) Base units Length ─ meter(m) Mass ─ Kilogram(kg) Time ─ second(s) Current ─ ampere(A) Temperature ─ kelvin(K) Amount of sunstance ─ mole(mol) Luminous intensity ─ candela(cd) (b) Supplement units Plane angle ─ radian(rad) Solid angle ─ steradian(sr) § 4.1 Instrumentation and Measurement Systems(8)

1. Instrument characteristics § 4.2 Dynamic Measurement and Calibration(1)

2. Uncertainties and Error (1) Causes Variations of system parameters External disturbance Uncertain operational state (2) Classification Absolute and relative System and random Static and dynamic Human and instrument § 4.2 Dynamic Measurement and Calibration(2)

(3) System and Random error Definition ： Error sources ： System ─ calibration, operation, loading Random─ noise, bits operation § 4.2 Dynamic Measurement and Calibration(3) Systematic error = ||True value – Estimated value|| Random error = Distribution deviation of estimated value

(4) Accuracy and Precision Physical meaning: Data interpretation ： Accuracy error ─ systematic error Precision error─ random error Note: Errors of sample mean and variance need to be further analyzed statistically. § 4.2 Dynamic Measurement and Calibration(4) High Precision High Accuracy High Accuracy and Precision

3. Static and Dynamic characteristics § 4.2 Dynamic Measurement and Calibration(5) (1) Static

Frequency range § 4.2 Dynamic Measurement and Calibration(6) (2) Dynamic Time domain delay

4. Calibration and Measurement (1) Characteristics calibration § 4.2 Dynamic Measurement and Calibration(7) S y :Sample standard deviation

(2) Measurement applications § 4.2 Dynamic Measurement and Calibration(8)

1. Digitization (1) Signal transmission § 4.3 Data Preparation and Analysis(1)

(2)Signal classification Discrete, D t Continuous, C t Discrete, D a D a -D t D a -C t Continuous, C a C a -D t C a -C t Time Amplitude (1) Analog (C a -C t )(2) Sample (D a -C t ) (3) Discrete (C a -D t )(4) Digital (D a -D t ) § 4.3 Data Preparation and Analysis(2)

2. Interface card and Operation EX ： A Capacitance S/H device (1) Sample and Hold Ideal sampler with zero-order hold(ZOH), h<< ∆t § 4.3 Data Preparation and Analysis(3)

Mathematical analysis § 4.3 Data Preparation and Analysis(4)

(2) A/D and D/A converter EX ： 4 bits D/A converter § 4.3 Data Preparation and Analysis(5)

If V i =10V for rating value For 5V analog input EX ： Successive approximation 4 bits A/D converter § 4.3 Data Preparation and Analysis(6)

§ 4.3 Data Preparation and Analysis(7) (3)Computer sampling

A/D conversion procedure § 4.3 Data Preparation and Analysis(8)

§ 4.3 Data Preparation and Analysis(9) 2. Filtering (1) Types of filter

§ 4.3 Data Preparation and Analysis(10) (a)Analog filter Pass band – High pass, Low pass, Band pass, Band stop, … Power supply – Active filter, Passive filter (b) Digital filter Pass band Algorithm – Batch type, Recursive type Realization – Software filter, Hardware filter Adaptive / Non-adaptive

(b) Practical filter EX : Butterworth low–pass filter (2) Analog filter (a) Ideal filter § 4.3 Data Preparation and Analysis(11) Low PassBand PassHigh Pass

(3) Digital filter (a) Nonrecursive filter § 4.3 Data Preparation and Analysis(12) Req’d : Stable operation BIBO stability iff IIR filter Infinite impulse response FIR filter Finite impulse response

(b) Recursive filter § 4.3 Data Preparation and Analysis(13) Fourier transform

EX : 2 nd – order recursive filter (a) Low pass (b) Band pass (c)High pass § 4.3 Data Preparation and Analysis(14)

§ 4.3 Data Preparation and Analysis(15) (4) Filter design Filter specs → Analog filter → Digital filter → Realization Filter specs → Digital filter → Realization (5) Filter realization a. Software digital filter b. Hardware digital filter EX : DSP realization- Use key operations Convolution Correlation Filtering Discrete transformation c. Error – Finite bits operation, Round off error Discretization

§ 4.3 Data Preparation and Analysis(16) Continuous and Discrete transformations.. Continuous systemsDiscrete systems

3. Trend removing x(t) = r(t) + z(t) r(t) ： deterministic trend Effects of trend ： (a) Distortion in correlation and spectral estimations (b) Nullify the estimation of low frequency spectral content (c) Finite bits computation problem (d) Possible extraction of deterministic time function for obtaining stationary data § 4.3 Data Preparation and Analysis(17)

Linear least square estimation § 4.3 Data Preparation and Analysis(18) (1) Linear trend t t t

§ 4.3 Data Preparation and Analysis(19) (2) Polynomial trend Use nonlinear curve fitting for trend removing. t t t

§ 4.3 Data Preparation and Analysis(20) (3) Periodic trend Use low-pass filter for trend removing. t t t

1. Finite sampling frequency Sampling frequency ω s is finite. (1) Aliasing issue (a) Line spectrum § 4.4 Practical Considerations(1)

(b) Continuous spectrum § 4.4 Practical Considerations(2)

(2) Solution (a) Nyquist sampling rule Nyquist frequency : § 4.4 Practical Considerations(3) (b) Practical solution Cascaded Anti-aliasing filter

2. Finite record length § 4.4 Practical Considerations(4) w ( t ): Window function

(1) Leakage problem § 4.4 Practical Considerations(5) (a) Ideal record length (b) Non-ideal record length A

(2) Solution Use zero taping Data mirror extension Use improved window functions § 4.4 Practical Considerations(6)

3. Finite bits representation § 4.4 Practical Considerations(7) (1)Issues Finite resolution Fixed point Floating point (2) Solution Higher bits representation Proper coding scheme Least Significant Bit (LSB) Most Significant Bit (MSB)

§ 4.4 Practical Considerations(8) 4. Wild point Causes: Data transmission loss Digital bit error (1)Issues (a) Raising overall noise level in estimated spectrum (b) Produce spurious frequencies in estimated power spectrum

(2) Solution § 4.4 Practical Considerations(9) Note: Other issues include signal clipping, temporary dropouts, etc. Use predictor-corrector algorithm for replacing wild data