Electronic measurement and Instrumentation

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Prof. Rong-yong Zhao

(zhaorongyong@tongji.edu.cn)

Second Semester,2013-2014

Bachelor Program

Electronic Measurement and Instrumentation

• Book information:

• Author: K.B.KLAASSEN,

• IBM Almaden Research Center, San Jose

• Translation from Dutch: S.M. Gee

• CAMBRIDGE UNIVERSITY PRESS

Almaden has a rich history of achievement including a legacy of disk drive innovation, the creation of an industry 2

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Sections of this book

• Section 1 =Chapter 1, a general section;

• Section 2=Chapter 2, physical quantities measuring;

• Section 3 =Chapter 3+Chapter 4, electrical and electronic measurements.

note: Transducer , to convert the non-electrical quantity into a measurable electrical quantity.

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Chapter 1 Basic principles of measurement

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Chapter structure

• 1.1 definition of measurement

• 1.2 why measuring?

• 1.3 measurement theory

• 1.4 measurement of non-physical quantities

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Measurement

Tachometer

(Engine Rotating meter)

odometer

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1.1 Definition of measurement

• Intuitional definition: measurement is the acquisition of information;

• A most essential aspect: information gathering;

• Measurand: the object of measurement;

Measurement aspects

descriptive

selective

objective 7 2014/4/27

Aspect 1-Descriptive

• A measurement must be descriptive about status or phenomenon;

• Necessary but Not sufficient,

• Example , Reading book =gathering information≠ measurement

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Aspect 2 -Selective

• Only select the measurand information

Aspect 3 -Objective

• Measurement : independent of arbitrary observer. To get the same information and same conclusion.

Cold Hand

Normal Water

Warm hand Subjective

Objective

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Measurement definition

• The acquisition of information in the form of measurement results, concerning characteristics, states, or phenomena of the world that surrounds us, observed with the aid of measurement systems.

descriptiveness selectivity objectivity

guarantee

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Information types

• Structural information: state, structure, nature of a certain characteristic;

• Acquisition : qualitative measurement; (first)

• Metric information: magnitude, intensity of a certain characteristic;

• Acquisition: quantitative measurement;(second)

Water

(Structural, qualitative)

Temperature;

(Metric, quantitative)

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1.2 why measuring

• One reason(learning): to increase knowledge of the world-----pure science, p.s.;

• Second reason(changing): to regulate ,control or alter the world-------applied science, a.s.;

• Fig.1.1 the purpose to measure

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Fig.1.1 Measurement as the link between the real world (left) and its concept in the pure sciences and applied sciences(right)

p.s.: abbreviation of pure science

a.s.: abbreviation of applied science

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1.3 Measure theory

• Measurement :representation of the actual empirical quantity;

• Measurement: mapping of source set(empirical domain space) to image set( abstract range space);

• Mapping=transformation function

• Fig.1.2 measurement constitution

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Fig. 1.2measurement constitutes according to measurement theory the mapping between an empirical domain and a

range or image space

Quantity

Real number set

Electrical current

Certain number Magnitude

Abstract symbols with a

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Further measurement definition

• (Measurement theory)Measurement is the mapping of elements from an empirical source set onto elements of an abstract image set according to a particular transformation function.

Assignment algorithms

Rules Procedures

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Measurement is descriptive

• According to set theory, element relations in source set must be maintained under the transfromation in the image set:

• “Larger than”

• “Equal to”

• “Smaller than”

• Measurement only represents that which is measured if the two systems are identical

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Formal expression

},...,,{ 21 nsssS Source set jRWith empirical relations

},...,,{ 21 miiiI Image set jNWith relations

k

l

kl If Then measurement output suggest more information than measurand

mn If The mapping resolution is inadequate

lkmn ,If A unique mapping function f

jnjn NsfsfsfRsss )(),...,(),(,...,, 2121

The relational systems are isomorphic, avoid information lossing

Single-valued, monotonic

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Isomorphism

• To solve the representation problem of the measurement theory;

• To preserve the source set relation structure; • Allowed transformations, a group of

representations; • To contemplate a more detailed assignment of

values, two limitations: ① Theoretical limitation: mapping actually exists in

empirical domain S; ② Practical limitation: mapping available system

can accomplish;

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Note:Isomorphism

• Isomorphisms are studied in mathematics in order to extend insights from one phenomenon to others: if two objects are isomorphic, then any property which is preserved by an isomorphism and which is true of one of the objects, is also true of the other.

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Measurement category(5)

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Measurement result Uniqueness

• To solve the Problem of uniqueness, warrant a cardinal measurement:

• A measurement is unique if and only if the cardinal measurement can only be transferred in one way: by the identity transformation g(i)=i;

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Nominal measurement Note

• Nominal measurement: the absolute significance of equality and in equality, one-to-one ,or one-to-one inverse function;

• To indicate: whether event occurs or not, or which occurs;

• Results are exclusive mutually, Binary output; • Most primitive type of measurement, detection

system; • Cost: simple and cheap; • Examples: burglar alarms, smoke detectors

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Ordinal measurement Note

• Quantitative measurement;

• Based on the two quantities comparison(absolute significance);

• Equal to, larger than, smaller than;

• Only present the relative order or magnitude;

• Without any significant information;

IQ(Intelligence quotient) 140 ≠2× IQ 70

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Interval measurement Note

• Not only whether one quality is larger , equal to , or smaller than another, but also whether this is true for the interval(difference);

• Linear , increasing function: can add or multiply with both sides;

the term linear function is sometimes used to mean a first-degree polynomial function of one variable

f(x) = mx + b

(called slope-intercept form)

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Ratio measurement Note

• g(i)=mi,m>0;

• Ratio: m, positive real number;

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Cardinal measurement Note

• Highest type of measurement;

• Need a reference , but without the reference symbol;

• g(i)=i;

• 10kg:10 times of 1 kg,10 means 10 kg;

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Uncertainty and Axiom

• Uncertainty (vague):thermal noise, low resolution and repeatability, cause that

s1=s2 simultaneously , s1 ≠s2;

• Correctness axiom:

• The case(s1=s2 )and case(s1 ≠s2) are mutually exclusive;

• The case(s1 ≥ s2) and s2>s1 are mutually exclusive;

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Axioms

• Ratio existence axiom: • If s1<s2 then a finite real number n exists, so that ns1 ≥s2; • Transitiveness axiom: • If s1 ≥s2 and s2 ≥s3, then s1≥s3; • Usage note: • When s1 ,s2 are very close ,we can use Correctness axiom; • In interval measurement, correctness and transitiveness

axiom; • Based on error propagation techniques, the three axioms

can be employed;

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1.4 Measurement of non-physical quantities

• Measurands: friendliness, intelligence,religiosity,tiredness;

• Non-physical quantities are difficult to measure because: • 1) the object is complex system, organization, society;

rarely using cardinal measurement; • 2)measurand depends on other quantities, impossible to

correct the errors, not selcetive; • 3)impossible measurement repetition, not objective; • 4) impossible to modify variables, example: increasing the

food scarcity to measure spending behaviour; • 5) subject is conscious

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Example : conscious rat

To meet with ethical objections, laboratory rat.

To stimulate the “pleasure centre” in the phypothalamus

To measure the response the heart rate to electrical and mechanical stimulation of the brain.

This process is intended to be used as a “reward” in learning process.

The measurement validity for learning behaviour of a rat in normal conditions must be doubted!

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Factors causing non-physical quantities measurement difficult

• Complexity of the system including object; • Complexity of object; • Dependence between object and environment; • Impossible isolation experiment; • No free variable modification ; • Non-repetition; • Restriction of experimental choice(ethical,

political or economic); • Consciousness of subject; • Irreversible damage of experiment;

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