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Instrumentasi Intelijen
Adhi Harmoko Saputro
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Indirect Sensing
Adhi Harmoko Saputro
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Indirect Sensing
• A situation often arises when some important variables are difficult to be
measured due to unavailability of an appropriate sensor or high noise level.
• The soft sensors are one solution to this problem: uses a model of the process
or plant and the model is simulated in the software to generate the measurand
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Indirect Sensing
• Indirect sensing is another solution to the problem of unavailability of a direct
sensor.
• A soft sensor estimates the model parameters using the secondary measurements
and determines the unknown primary measurand, while indirect sensing estimates
the variable through other measurable variables using one of the following
techniques:
1. Least square parameter estimation
2. Spectral analysis–based parameter estimation
3. Fuzzy logic based
4. ANN based
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Indirect Sensing
• A soft sensor estimates the model parameters using the hard sensor
measurements when it is available while an indirect sensor estimates the model
parameters using some other indirect measurements
• A soft sensor is a temporary solution when the hard sensor is temporarily
unavailable while an indirect sensor is a permanent solution for a measurand when
the hard sensor is not at all available
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Least Square Parameter Estimation

• The method of least squares is about estimating parameters by minimizing the
squared discrepancies between observed data, on the one hand, and their expected
values on the other
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Least Square Parameter Estimation

• The system measurement variable y related to the system parameter vector α and
the corresponding indirect measurement vector Ø given by

y = ∅T α

• The system measurement vector Y and the indirect measurement matrix Ø are
constructed using N measurements

 y (1)   ∅1 (1) ∅ 2 (1)  ∅i (1) 

   
 y ( )
2  ∅ 1( )
2 ∅ 2( )
2  ∅ i( )
2
Y= ∅=
        
   
 y ( N )  ∅1 ( N ) ∅ 2 ( N ) ∅i ( N ) 
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Least Square Parameter Estimation

• The least square estimate of the system parameter vector α is given by

αˆ = {∅ ∅} ∅T Y
T −1
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Example
• In the circuit shown in Figure, the measured variables are the supply voltage Vi, the
circuit current I, and the charge accumulated on the positive plate of the capacitor
q.
• Propose a least square estimation technique to estimate the values of R and C.
• Estimate the frequency of the input voltage from the measured data and the
parameters.
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Example
• The circuit KVL equation can be written as
1
V=
t IR + ∫ Idt
C

∫ Idt = q
1
V=
t IR + q
C
• Writing the above equation in vector form

 1  I 
Vt =  R
 C   q 
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Example
• which is of the form
y =∅T α ⇒ y =Vt ∅T =[ I q]
 1
⇒ α=
 R C 
• Taking N measurements
 Vt (1) 
 I (1) q (1)   
T    V t ( )
2
∅ =    Y=
  
 I ( N ) q ( N )   
Vt ( N ) 
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Example
• Using LS estimation technique, the estimated parameter

−1
αˆ = ∅ ∅  ∅T Y
T
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Example
• the frequency of the input voltage from the measured data and the parameters
i
V=
t IR +
ωC
1
⇒ω = C
(Vt − IR )
• Here, the measured variables are Vi and I.
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Spectral Analysis–Based Parameter Estimation

• Spectral analysis or Spectrum analysis is analysis in terms of a spectrum of
frequencies or related quantities such as energies, eigenvalues, etc
• Spectral estimation, in statistics and signal processing, an algorithm that
estimates the strength of different frequency components (the power spectrum) of
a time-domain signal.
• also be called frequency domain analysis
• The term parameter estimation refers to the process of using sample data (in
reliability engineering, usually times-to-failure or success data) to estimate the
parameters of the selected distribution
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Fuzzy Logic Based

• Least square– or spectral analysis–based parameter estimation techniques
involve complex mathematical computations that need fast real-time processing of
the measurement data
• Fuzzy logic approach is comparativel computationally simpler since it is based on
rules.
• Nonlinear continuous functions are easy to be implemented in fuzzy models.
• The memory requirement is also lower than the look-up table estimation or ANN
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Fuzzy Logic Based

• Fuzzy logic–based system modeling for indirect sensing can be realized by the
following steps
1. Determination of the system model
2. Mapping input–output to fuzzy regions
3. Assigning fuzzy linguistic attributes
4. Fuzzy rule
5. Fuzzy rule–based LUT
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1. Determination of the system model

• The fuzzy model for the system can be developed from two main sources:
1. Static input–output characteristics of the system
2. Dynamic real-time operating effects and interferences
• Once the above two sources are available, the training input–output data can be
used to model the system in a rule-based manner.
• The indirect sensing aims at the measurement of a single output variable
• the fuzzy model will be considered as a single output system while input may
be multidimensional.
• For reducing modelling complexity, the dimension of the input variable should be
as low as possible.
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1. Determination of the system model

• n-input-one-output pairs of measurements

 x1 ( k ) , x2 ( k )  xn ( k ) ; y ( k ) 

• For each pair there are n input data and one output data
• Each point of measurement data presented to the training systems
• n is the number of inputs
• k is the point of data pair
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2. Mapping input–output to fuzzy regions

• It is customary in fuzzy logic to divide the input–output space into several fuzzy
regions
• Nx1, Nx2, …, Nxn and Ny, which are called fuzzy sets
• More number of regions would provide greater accuracy
• memory requirement is also to be considered
• The fuzzy sets for each input–output variable are assigned membership functions
μx1, μx2,…, μxn and μy
• Various types of membership functions can be used in different applications
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2. Mapping input–output to fuzzy regions

• The triangular membership function assigned to the input–output variables
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3. Assigning fuzzy linguistic attributes

• For each membership region, a linguistic attribute is assigned
• This assignment is based on the type of application
• For example, values of variables are grouped in P groups, say P = 3, therefore
• 1: “LOW” for 0 ≤ x(y) < (Max/3)
• 2: “MEDIUM” for (Max/3) ≤ x(y) < (2Max/3)
• 3: “HIGH” for (2Max/3) ≤ x(y) < Max
• Therefore, each membership region will have a unique linguistic attribute, say
LOW1, MEDIUM10, HIGH12, etc
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4. Fuzzy rule
• For each pair of input–output data set, a rule is assigned and each rule has a
degree of confidence
• For example Rule:
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5. Fuzzy rule–based LUT

• From the training data, the corresponding rules are generated and stored in the 2D
table
• The 2D table can accommodate two antecedent linguistic variables and the entries
are the linguistic consequent variables.
• It is not that all linguistic variables have consequents and when there is no
consequent for a rule, entries are marked “×.”
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Example:
A fuzzy model of the dryer for measuring the drying status
• Assign triangular membership functions to the input–output variables
• Dryer inlet temperature (Ti) is divided into two groups: LOW and HIGH
• Tea feed rate (Mi) into three groups: LOW, MEDIUM, and HIGH
• Drier outlet temperature (To) into three groups: LOW, MEDIUM and HIGH
• Drying status into three groups: UNDER, NORMAL, and OVER.
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Example:
A fuzzy model of the dryer for measuring the drying status
• The ranges of the variables and the number of fuzzy membership regions are
• Ti : 85°C−100°C; 16 regions
• Mi : 3 − 15 trays/15 min; 12 regions
• T0 : 60°C − 80°C; 21 regions
• D (dryness): 0%–10%; 21 regions
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Example:
A fuzzy model of the dryer for measuring the drying status
• Regions of membership functions of the input–output variables
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Example:
A fuzzy model of the dryer for measuring the drying status
• Regions of membership functions of the input–output variables
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Example:
A fuzzy model of the dryer for measuring the drying status
• Linguistic Attributes of the Tea Dryer Parameters
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Example:
A fuzzy model of the dryer for measuring the drying status
• Lookup Table of Fuzzy Rule Distribution for Tea Dryer Status Detection
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Example:
A fuzzy model of the dryer for measuring the drying status
• Lookup Table of Fuzzy Rule Distribution for Tea Dryer Status Detection
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Example:
A fuzzy model of the dryer for measuring the drying status
• For example data Nos. 3 and 4 of pattern 5 form the following two rules,
respectively:
• Rule 1: IF Ti is H9, Mi is L3 and T0 is L1 THEN D is 01
• Rule 2: IF Ti is H9, Mi is L3 and T0 is L1 THEN D is 02
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Example:
A fuzzy model of the dryer for measuring the drying status
• the rule with the highest membership function will be used. For example:
• When Ti: 92°C, Mi: 3 trays/15 min and T0: 65°C, then the degree of the membership
functions for the two rules are
• Rule 1: μH9(Ti) = 1.0, μL3(μi) = 1.0, μL1(T0) = 1.0, and μ01(D) = 0.8
• Rule 2: μH9(Ti) = 1.0, μL3(μi) = 1.0, μL1(T0) = 1.0, and μ01(D) = 1.0
• The degree of the two rules are
• Rule 1: 1.0 × 1.0 × 1.0 × 0.8 = 0.8
• Rule 2: 1.0 × 1.0 × 1.0 × 1.0 = 1.0
• Therefore, rule 2, with stronger degree, is used as rule base and stored in the LUT in
column H9 and row L1 as 02.
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Terima Kasih
Adhi Harmoko Saputro