Optimization of surface acoustic wave sensor arrays and application to high performance liquid chrom

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Optimization of surface acoustic wave sensor
arrays and application to high performance liquid
chromatography
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Introduction

• Sensor arrays are used for many applications,
  like process control, environmental monitoring,
  or quality control.
• The great flexibility that sensor arrays provide
  becomes a problem when it is desirable to
  optimize a sensor array for a certain application.

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• There are a number of statistical criteria that
  can be used to perform sensor array
  optimizations.
• The most popular optimization criteria are
  Lorbers figures of merit and nonlinear
  generalizations.
• The SAW devices coated with polymers have been
  become a feasible tool for the qualification as
  well as the quantification of solvents and
  mixtures.

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TheoreticalNotation and assumptions

• The sensor system is constructed in such a way
  that single sensors can be removed or added.
• The array to be optimized can be hold M sensors
  that are to be chosen out of Mo possible ones and
  that the application requires the quantification
  of K substances.

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• The relation between the K-dimensional
  concentrations vector x and the M-dimensional
  sensor signal vector y is described by the linear
  additive model.
  
  
• Or by a general nonlinear model

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Lorbers figures of merit

• The purpose of any sensor system is to enable an
  accurate estimation of analyte concentrations x
  from sensor signals y.
• Lorber has shown how the variance of such an
  estimation can be minimized.

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Nonlinear generalization

• An estimator of the M-dimension sensor response
  function f is needed.
• A local spectrum at any location x in analyte
  space is

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Implementation issues

• It is usually not necessary to find the exact
  optimum. In most of the cases, a value close to
  the optimum is sufficient. Therefore, a genetic
  algorithm is used to perform the search.
• An array is represented as an individual with a
  certain set of genes corresponding to the
  combination of sensors.
• A population competes with each other to pass on
  their genes.

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• The biological term fitness corresponds to the
  criteria to evaluate an array.
• As in evolution theory, two concepts are
  implemented survival of the fittest and
  mutation.
• After a number of repeated applications of these
  principles, only the best genomes have survived
  and are accepted as a solution of the
  optimization problem.

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Application

• The on-line control of process high performance
  liquid chromatography (PHPLC) is correlated to
  the analysis of volatile organic compounds (VOC).
• The sensor array of a gas sensor microsystem
  (SAGAS PC) nine polymer-coated SAW-resonators
  (fo 433 MHz)

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• Reversed phase (RP)-PHPLC examples are used for
  quantitative determination of methanol/water
  mixtures.
• Normal phase(NP)-PHPLC examples are used for the
  sensor reduction application (hexane/ethyl
  acetate).
• The data is split into a calibration set and a
  test set.

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Sensor selection

• For RP-HPLC application, 16 different sensor
  coatings are tested. In order to choose the best
  eight sensors out of the 16 possible ones, the
  computer program uses a genetic algorithm to
  check the 12870 possible combinations.
• The data complies to the linear additive model.
  The optimization criterion is relative
  selectivity.

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• 1,2,6,7,10,12,15,16 chosen by the computer
  program
• 2,5,8,9,11,12,13,15 chosen with experimenters
  intuition

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Sensor reduction

• It is interesting to check whether the number of
  sensors in the array can be reduced for simple
  measurement tasks.
• If only four or less sensitive coatings are
  necessary to solve the analytical problems than
  it is possible to include a spare sensor of all
  sensors in the array effectively doubling the
  lifetime of the system.
• The data proves to be highly nonlinear. The
  optimization criterion is relative selectivity.
  The nonlinear smoother is applied for estimating
  the sensor response function f.

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