Αισθητήρες και Συστήµατα Οργάνων · E.g. the previous diaphragm might...

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Αισθητήρες και Συστήµατα Οργάνων

•  Εισαγωγή

•  Βασική Θεωρία Μετρήσεων

•  Αρχές των Βασικών Αισθητήρων

•  Αισθητήρες ΜΕΜΣ

•  Σήµατα και Θόρυβο

•  Ενισχυτές Σηµάτων

•  Σύνδεση και Προστασία Σηµάτων

•  Συλλογή δεδοµένων και Μετατροπείς Δεδοµένων

•  Ηλεκτρική Ασφάλεια σε Ιατρικά Συστήµατα

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Στόχοι

•  Να ξέρετε τις βασικές κατηγορίες µετρήσεων •  Να γνωρίζετε τους όρους: Ακρίβεια (Precision) , απόλυτη ακρίβεια (Accuracy) , ανάλυση (Resolution), αξιοπιστία (Reliability) και εγκυρότητα (Validity) µετρήσεων

•  Να καταλάβετε και να αξιολογήσετε τον ρόλο και την φύση του σφάλµατος στις µετρήσεις

•  Να γνωρίζετε πως να µειώσετε το σφάλµα στις µετρήσεις.

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Κατηγορίες Μετρήσεων Categories of Measurement

•  Direct Measurements (Άµεσες Μετρήσεις) -Measure height using a measuring stick - Put the thermometer directly into the appropriate space

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•  Indirect Measurements (Έµµεσες µετρήσεις) -  Measure the temperature of the

walls of a furnace"-  Measure blood pressure by

sphygmomanometry"

"

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•  Null Measurements (Μετρήσεις Μηδενισµού διαφοράς) Null measurements are made by comparing a calibrated source to an

unknown measurand and then adjusting either one until the difference between them is zero.

In this measurement the variable voltage reference is adjusted till no current

flows through the galvanometer. At that point the value of the voltage reference is the output of the measurement process. The advantage of the null measurement in this case is that the galvanometer cannot load the system a the null point since it is not passing any current

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Ορολογίες σε Μετρήσεις Measurement terminology

•  Σφάλµα (Error) •  Refers to normal random variation and not mistakes! •  Assume a true value of X0 •  If multiple measurements are taken there will be a deviation ΔX

which is the error term •  As ΔX→0, Xi →X0

X0 Xi

ΔX

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•  Εγκυρότητα (Validity) •  The validity of a measurement is a statement of how well the

instrument actually measures what it is supposed to measure. E.g. an electronic blood pressure sensor may actually be

measuring the deflection of a thin metallic diaphragm of know area, which is in turn measured by the strain applied to a strain gauge element cemented to the diaphragm. What determines the validity of a sensor measurement is the extent to which the measurement of the deflection of the diaphragm relates to the applied pressure and over what range and what conditions.

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•  Αξιοπιστία και Ικανότητα Επανάληψης (Reliability and Repeatability) The reliability of the measurement is a statement of it’s

consistency (σταθερότητα) when discerning the measurand on different trials. E.g. the previous diaphragm might fatigue and give different results for the same pressure.

Repeatability refers to the ability of the instrument to return to

the same value when repeated to the exact same stimulant

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•  Απόλυτη ακρίβεια και Ακρίβεια (Accuracy and Precision) The accuracy of a measurement refers to the freedom from

error, or the degree or conformity between the measurand and the standard. In an accurate measurement the mean value of the normal distribution curve is close to the true value.

The precision refers to the exactness of successive

measurements. A precise measurement has a small standard deviation under repeated trials.

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•  Ανάλυση (Resolution) Resolution refers to the degree to which the measurand can

be broken into identifiable adjacent parts. In digital instrument the number of bits of resolution representing a

value determine how fine the measurand can be broken down

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Σφάλµατα σε Μετρήσεις Measurement Errors

•  Errors are inherent in measurements

•  Errors can be expressed in absolute terms X ± x cm

•  Errors can be expressed in relative terms X cm ± 1%

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Κατηγορίες Σφάλµατος Categories of Error

Theoretical Errors •  Each measurement is based on a measurement

theory (model) that predicts how a value will behave when a certain procedure is applied.

•  Models used are usually linearised versions of a more complex nonlinear model and thus constrain the validity of the model to a small region.

E.g. Mean arterial pressure (MAP) model

3DiastolicSystolicDiastolicP −

+= ∫=2

1

)(1 t

t

dttPT

Por

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Static Errors Static errors consist of a number of subclasses that are

related as these errors are not functions of time or frequency. •  Reading Static Errors- parallax error, interpolation error, last digit

bobble error •  Environmental Static errors – caused by temperature, pressure,

electromagnetic fields, radiation..etc. •  Characteristic Static Errors – originates from the instrument itself

e.g. zero offset error, processing error, gain error, linearity error, hysteresis error, repeatability and resolution errors

•  Quantisation error – originates from rounding up or down a signal to the nearest digital value

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Dynamic Errors Dynamic errors arise when the measurand is changing or

in motion during the measurement process. e.g. momentum of needle of analogue meter or when there

is a frequency, phase or slew rate limitation.

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Instrument Insertion Errors “THE MEASUREMENT PROCESS SHOULD

NOT SIGNIFICANTLY ALTER THE PHENOMENON BEING MEASURED”

Examples: - Pressure sensors add volume so the pressure

being measured might be lower - A voltmeter might draw current -  A thermometer might change the temperature if

the object is very small. -  A flow meter might add turbulence, or modify

the flow path properties.

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Χειρισµοί για Μείωση των Σφαλµάτων Reducing Measurement Errors

-Choose the appropriate instrument for the job… i.e. that least disturbs the measurand. (Know I/O characteristics)

-Measure by using several different instruments and average out the result.

-Beware of ground loop voltage drops

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Ανάλυση Σφαλµάτων Error Contribution Analysis

•  Error Analysis is performed to identify and quantify all contributing sources of error

•  Worst Case Analysis assumes that all component errors are biased in a single direction and are maximised (for each positive and negative direction)

•  Analyse consequences of the worst case scenario •  Error Budget can be used to design systems and

allocate an allowable error to individual components

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For errors that are: •  Independent of each other •  Are random rather than biased in one direction •  Are of the same order or magnitude One can use the root of the sum of the squares (rss)

value of the errors and use it as a composite error term in planning a measurement system

∑= 2irss εε

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A collection of repetitive measurements of a phenomenon can be considered a sampled population and treated as such.

The mean arithmetic average is given by: Which alone does not address the issue of error. Thus we

need to add a correction factor to the mean representing the error.

∑=

=n

iiXn

X1

1

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The extra term can be the standard error of the mean given by:

Where σm is the standard deviation of the original

distribution and n is the sample size thus giving which allows us to estimate the error

nm

mσ

σ =

mXX σ±=

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Ορισµός Διαδικασιών σε Μετρήσεις Operational Definitions in Measurement

•  An Operational definition of a measurement process is a standardised procedure that must be followed, and it specifies as many factors as necessary to control the measurement, so changes can be properly attributed to the unknown variable.

•  These can help to minimise ambiguity and provide more consistent results.

•  Widely accepted operational definitions or that are adopted by a recognised authority are called standards.

E.g. A manufacturer could state “Calibrated according to The National Institute for Standards and Technology procedure (NIST2007.145)”

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Ορισµός Διαδικασιών σε Μετρήσεις Operational Definitions in Measurement

Example: Procedure to test conductivity of dialysate mix used in kidney dialysis:

1.  Immerse two 1cm diameter circular nickel electrodes,

space 5cm apart facing each other to a depth of 3cm into a 500mL beaker of test solution

2.  Bring the solution to 4°C 3.  Measure the electrical resistance (R) between the

electrodes using the Snotz model 1120 digital ohmmeter

4.  Find the conductance (G) by taking the reciprocal of resistance (G=1/R)

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FURTHER READING

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How to measure blood pressure using a sphygmomanometer

The non-invasive ausculatory method is one of the most common ways of monitoring a patient's blood pressure. The subject sits down and rests their arm on a table so the brachial artery is level with the heart. This is important when monitoring blood pressure, as pressure is proportional to height ( Δp = ρgΔh ). For example, if one measures the blood pressure at head height, the systolic/diastolic pressure readings will be approximately 35mmHg less compared to readings taken at heart level, whereas at ground height the pressure readings will be 100mmHg greater. A sphygmomanometer cuff is wrapped around the subject's upper arm, just above the elbow and a stethoscope is placed on the hollow of the elbow, over the brachial artery as shown below.

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FURTHER READING

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The cuff is 'pumped- up' to a pressure of 180mmHg, compressing the brachial artery hence causing the artery to collapse once the systolic pressure (the maximum pressure exerted by the blood against the wall of the brachial artery when the heart beats) has been exceeded. At the point where the pressure of the cuff is greater then the systolic pressure, the artery has collapsed thus, there is no flow of blood through the brachial artery. The valve on the pump is loosened slowly to allow the pressure of the sphygmomanometer cuff to decrease. Once the systolic pressure is reached (approximately 120mmHg in the 'normal' case), the brachial artery opens causing volatile blood flow, which cause vibrations against the artery walls. These noises are called Korotkoff sounds (named after their discoverer) and can be heard through a stethoscope as the pressure exerted onto the brachial artery falls. The blood flow through the brachial artery increases steadily, until the pressure of the sphygmomanometer cuff falls below the diastolic pressure (the pressure between successive heart beats, the low pressure), approximately 80mmHg. This is the point where the blood flow through the artery is laminar.

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