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Summary Predicting Food Quality (FQD-31306)
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Summary of the lectures, lecture notes, and the knowledge clips of the course "Predicting Food Quality" (FQD-31306).
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Module 0: Introduction to Food QualityWhy would we want to predict food quality?
- Fast changing consumer demands
o Safe, healthy, atraccte, sustainable, funcconal
- Concnuous product detelopment
o Raw materials change
- Increasing demands on food quality
o Consumer wishes, food laws
- Efcient product and process design
o Sating of cme, money, and resources
Quality means sacsfying the expectacons of the consumer. It is a difcult concept, broad, tague, and
elusite. It is not just a property of the food, but of the food and the consumer. Therefore there is
decomposicon of the broad concept into food quality atributes, into something measurable.
Q=f(Qint, Qext). Roughly, quality can be defned as: sacsfying the expectacons of the consumer.
The intrinsic quality is changed by the taste, fatour, shape, colour, texture, nutriconal talue,
contenience, shelf-life, and food safety. These atributes can be measured.
In terms of food science there are seteral aspects: chemical aspects (Maillard reaccon and
oxidacon), biochemical aspects (e.g. enzyymacc browning, proteolysis, lipolysis, hydrolysis), physical
aspects (e.g. rheology, fracture mechanics, coalescence, coagulacon, diiusion, phase changes), and
microbiological aspects (growth of micro-organisms, inacctacon).
Food technology is about the applicacon of thermodynamics (what changes are possible) and
kineccs (how fast do changes occur). The possible changes, but especially their rates aiect food
quality.
With QACCP (quality analysis criccal control points) criccal control points can be made, just as with
HACCP. These criccal control points are factors aieccng processes. QACCP is broader than HACCP:
HACCP is about pretencng hazyards, whereas QACCP is about promocng quality. Pretencng hazyards
is about food safety and therefore also about food quality.
We can get a grip on the quality changes by:
- Chain analysis of what actors are doing
- Idencfying the processes that aiect quality (chemical, biochemical, physical, microbiological)
- Idencfying the factors that infuence the processes (e.g. temperature, pH, relacte humidity)
- Idencfy what is happening in the food
- Turn the analysis results into a model
,Module 1: Models, errors and uncertainties
Structure of mathematical models
A mathemaccal model should refect quanctactely a dependence between tariables. The input is
the independent tariable (the x-talue), and the output is the dependent/response tariable (the y-
talue). The independent tariable is something we can control (e.g. cme, pH, and temperature), and
the dependent tariable (or response tariable) is something related to x that we can obserte or
measure (e.g. concentracon, enzyyme acctity, and texture). a and b (e.g. in y=a+bx) are the
parameters. Parameters form the core of a model and summarise the informacon in the data, giten
a certain model.
The models mostly hate to be based on experimental obsertacons. There can also be a theory that
may predict a certain model. Models are in the form of algebraic equacons (e.g. Stokes’ law about
creaming and the Growth model for micro-organisms), diierencal equacons (e.g. frst-order model),
and parcal diierencal equacons.
Deterministi models protide an outcome that seems to be without uncertainty, but parameters in
models are escmated from experiments that contain unexplainable tariacon. Hence, parameter
escmates are uncertain. Models are only approximacons to reality, and hence contain uncertainty.
Consequently, model prediccons will be uncertain. The quescon is how well or how bad a model
approximates reality.
Deterministic and stochastic models: uncertainty and errors
The uncertainty is described by the error term
(an epsilon in formulas). Experiments can and
must be done to get an impression of the
uncertainty. Stoihasti or probaabailisti
models: the same input does not always gite
the same output but shows tariacon. There are two sources contribucng to total uncertainty:
- Variabaility (biological tariacon): inherent tariacon in the system under study (e.g. biological
tariability in raw materials for foods); cannot be reduced for a giten system
- Uniertainty (experimental tariacon): refects our state of knowledge about the system
under study; can be reduced by beter and more measurements
Separacon of the two sources is of importance so that appropriate measures can be taken. Both
tariacons can be characterised by descripcte stacsccs.
There is a “new” way of expressing uncertainty tia “resampling”, which is data generacon tia
computer methods based upon an experimental data set (e.g. Bootstrapping and Monte Carlo).
There is no need for assumpcon of hypotheccal models such as a normal distribucon. The only
assumpcon is that the experimental data represents the parent populacon.
“Errors” due to uncertainty and tariability can be expressed as standard error of the mean, for
instance. It is not a real error in the sense of a mistake. Errors that accumulate due to small mistakes
and fuctuacons in equipment performance are experimental errors. Atencon for errors is needed
for characterisacon of experimental errors, characterisacon of uncertainty in model parameters,
model discriminacon, and as a quanctacte measure of uncertainty in prediccons.
Frequently, a prediccon is based upon the
combinacon of seteral tariables. The errors or
standard detiacons in each of the tariables will
, accumulate (propagate) in the fnal result. There are formulas for standard detiacons of derited
talues.
There are two fundamental problems with measurements: the experimental errors:
- Systemati errors: how close is the measured talue to the true talue
o Indicated by the term accuracy
o Cannot the characterised or corrected by
stacsccs
o Responsibility of researcher (so should be
atoided): calibracon needed
- Random errors: measurements neter gite exactly
the same results
o Indicated by precision
o Must be characterised by mean ± standard detiacon, or coefcient of tariacon (CC),
or confdence intertals
Residuals and regression
The regression is a procedure to obtain a “best-
ft” of the data in a model. Well-known is least-
squares regression: minimisacon of the sums of
squares. This refects the experimental errors if
the model is correct, otherwise the residuals
refect experimental errors and model errors.
Experimental errors are model independent and
can be obtained from repeated experiments.
Knowledge of error structure of data is
important. It facilitates subsequent escmated of
parameters and model etaluacon. If you want to
do meaningful prediccons, spend considerable eiort to know the error structure of your data.
A look at residuals immediately shows how a model is performing. Residuals should be distributed
randomly, there should be no trend. If residuals are randomly distributed this means that all useful
informacon has been extracted from the data; the scater lef is only random (homoscedascc errors).
A plot of the data and the models and the residuals should be made.
In the case of heteroscedascc errors (errors increase/decrease with x): determine the tariance for
each measurement, either by repeccons, or by independent measurements. The weights w i for
measurements at xi from tariance should be calculated (w i=1/si2). Regression is not allowed to be
applied, but weighted regression can correct heteroscedascc errors, where each data-point y is
weighted by its own tariance (assuming that that is known).
Linear and nonlinear regression
Linear regression is easy and exact and should be used for linear models. Nonlinear regression is an
approximacon and should be used for nonlinear models (Solter in Excel). Howeter, somecmes
nonlinear models can be changed into linear models by a mathemaccal transformacon. The problem
with transformacon is that not only the funccon but also the error structure of data becomes
1
transformed. There is a correccon for transformacon: w= 2 . Linear models can produce a
σ ¿¿
curted line, for instance a polynomial of the form y=a+bx+cx 2. The word linear refers to the
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