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Tutorial on Data-Driven Modeling in Water Resourceand Environmental Engineering Using Matlab
Feb 2014
Waqar S. Qureshi
Teaching AssociateAsian Institute of Technology
February 11, 2014
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based models
IntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 2 / 33
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based models
IntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 3 / 33
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Todays major challenges forwater engineers include:
Securing water resources for people
Protecting vital echosystems
Dealing with variability and uncertainty of water in space and time
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based models
IntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 5 / 33
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based models
IntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 5 / 33
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System modeling for water engineeringWhat is modeling
The term model refers to tools, softwares, and programs used to
represent real-world systems.
Modeling of a system is used to predict the system behavior and responseto the changing factors.
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based models
IntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 6 / 33
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System modeling for water engineeringTypes of modeling
Physical model is rescaled copy of the actual system, example, DAM
models.
Mathematical model is baed on mathematical logic, knowledge, andequations.
Figure: classification of models
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System modeling for water engineeringApplications and complexity
As water and environmental engineers, system modeling can be applied inmany applications such as:
Simulation of natural phenomenon
Synthetic data generation
Forecasting and warning of extreme events
Developing decision making rules
Modeling a system in the field of water engineering is difficult:
Physicalcomplexity of natural phenomenon.Time consumingprocess of analyzing different components of thesystem.
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 8 / 33
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System modeling for water engineeringData-driven models
Models that can simulate a system by the experimental data of thatsystem is known as data-driven models.
Data-driven models enable us to mapcausal factorsandconsequentoutcomesfrom the observed patterns (experimental data), without deepunderstanding of the complex physical process.
The purpose of data-driven modeling in water engineering can include thefollowing:
Data classification and clustering.
Extreme value predition with ephasis on floods and droughts.
Water quality simulation and prediction.Extending the length of hydroclimatological data from the historicalones.
Modeling water balance concerning different components of ahydrological system.
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System modeling for water engineeringdata-driven models
For a complex system, data-driven models are inexpensive, accurate,precise, andflexiblein contrast to their counter physical models oranalytical models.
Data-driven models can be used for problems where we have lessinformation about the intrinsic complexityof the phenomenon, in contrastto analytical modeling.
Two groups of Data-driven models are:
Statistical modelingSoft computing (Artificial intelligence)
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 10 / 33
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System modeling for water engineeringStatistical model
A statistical model is comprised of random and deterministic variables.Deterministic variables are defined by mathematical model and use a set ofequations to generate data, while random variable is represented by aprobabilistic models for example a probability density function to generatedata.
The probabilistic models can be parametric and non parametric.
Parametric model can be described by its mean, variance, etc.
Non-parametric models can be described by loosely confined assumptionssuch as nearest neighbor.
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 11 / 33
S d li f i i
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System modeling for water engineeringSoft computing model
In soft computing the system is modeled using fuzzy logic,neuro-computing, and genetic algorithms.
It is tolerant of imprecision, uncertainty, partial truth, and approximation.
The role model of soft computing is human mind.
Example: A suitable temperature of a room to make people feelcomfortable!
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O li
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 12 / 33
S d li f i i
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System modeling for water engineeringSpatio-temporal complexity
The model complexity can also be classified in spacial and temporalmanner.
The spacial and temporal characteristics of a model is essential to study
the effects due to the dynamic change of natural phenomenon on thesystem.
The spacial complexity of a model can be characterized as lumped,semi-distributed, and distributed models.
Let us take an example of rainoff modeling to understand spacialcomplexity of models.
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System modeling for water engineeringLumped models
Lumped modeling methods were used due to complex data collection
methods and software limitations.Lumped models are still useful for producing flood guidance. They requireless data input and less computational power than more modern methods.
Figure: Spacial complexity for runoff model
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S t d li f t i i
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System modeling for water engineeringSemi-distributed models
Semi-distributed modeling is a variation of the lumped method and is
sometimes referred to as a pseudo-distributed approach. Using thisapproach, a basin is broken down into smaller sub-basins. Runoff amountsfrom methods such as unit hydrograph are used to estimate stream flowfrom each of these sub-basins
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System modeling for water engineering
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System modeling for water engineeringSemi-distributed models
A trulydistributed modelingis one that represents processes in a gridded
manner.
Each cell has its parameters allowing for its own stream flow estimates.
If these data in each cell are not available, they must somehow beestimated, introducing an uncertainty factor.
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System modeling for water engineering
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System modeling for water engineeringTemporal complexity
Data-driven models can be static or dynamic.
A rainoff isdynamicif its parameters changes as it receives newinformation, and is consideredstaticif the model relies only on the
historical data.In summary, thepurposeof modeling is an essential criteria to select amodel and determines itscomplexity,developing time,runtime, itsaccuracy, andprecision.
Modeling also depends upon the type of data that is available, and thetime required to acquire it.
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Outline
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 17 / 33
System modeling for water engineering
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System modeling for water engineeringType of data
Figure: Types of Data, (a) discrete data, (b) continuous data, (c) spacial data,(d) temporal data
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Outline
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroductionRegression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 18 / 33
System modeling for water engineering
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System modeling for water engineeringGeneral approach to develop a data-driven model
Figure: General approach to develop a data-driven model
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Outline
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 20 / 33
Outline
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 20 / 33
Regression-based models
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Regression based modelsIntroduction
Theregression-basedmodels are data-driven models that are easy to use
and popular.
They ranges from linear to nonlinear and parametric to nonparametricmodels.
Following are the application areas of regression based models
Prediction, forecasting, and estimation of missing data.
Interpolation and extrapolation of data.
They are segregated as
Multiple linear regression model.Conventional non linear regression method.
KNN non parametric model.
logistic regression model.
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Outline
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Outline
1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4
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Regression-based models
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gRegression model application
Figure: A summary on the application of regression models in water resources andenvironmental engineering
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Outline
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1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4
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Regression-based models
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gLinear regression
Linear regression is used to model the linear relationship between the
continuous dependent variable (y) and an independent variable (x).The regression model aim to identify what variables are associated with y,to predict the future observations of y.
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Regression-based models
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gLinear regression
Let x and y two variables, then a plot between x and y shows if y is
positive, negative linear or non-linear function.
Figure: Different type of correlation between Y and X
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Linear regression
The strength of linear relationship between two variables is measured by
simplecorrelation coefficient.The Correlation coefficient between n observations f X and Y is calculatedas
Figure: Correlation coefficient
Figure: sample script for corrcoef(x)
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Linear regression
A simplest regression function is refined as
y=o+1.x, where o and 1 are parameters of the model
Figure: Samples of errors in linear regression fitting
The linear regression modeling tends to fit a line onto the observed datasuch that the sum of absolute errors of fitting for n-observations isminimized.
S2 =n
i=1
2i =n
i=1
(yi o+1.xi)2
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Regression-based models
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Linear regression
In case of multiple independent variables xi ... xn the model becomes
multiple linear regression and is represented by the equation.
y=o+1.x1+ 2.x2+ 3.x3+ 3.x3+ 4.x4
The dependent variable y can be a deterministic or a probabilistic. In case
it becomes a probabilistic, then the stochastic equation of the form isgiven as
y=o+1.x+e
, where e is the estimation error.The output at any instant of x can be represented by a distributionfunction. The expected value of the estimation is in fact the average valueof this distribution which is given by y=o+1.x.
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Regression-based models
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Linear regression
Figure: PDF of dependent variable in a linear regression model
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Outline
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1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 28 / 33
Regression-based models
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Linear regression-example
Interpolation of water quality values.
Water quality of a river as a function of distane from the upstream of riveris tabulated. Use a linear regression model to interpolate total dissolvedsolution (TDS) at different locations of the river.
Figure: Data presented for Example
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1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 29 / 33
Regression-based modelsLi i l
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Linear regression-example
Solve the above Example in a probabilistic manner and calculate theprobable range of TDS at the distance of 125km from the upstream.
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Outline
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1 Major challenges for water engineers2 System modeling for water engineering
What is modelingTypes of modelingData-driven modelsStatistical modelsSoft computing model
Spatio-temporal complexityType of dataGeneral approach to develop a data-driven model
3 Regression-based modelsIntroduction
Regression model applicationLinear regressionLinear-regression-example-1Linear-regression-example-2
4 Matlab TutorialWaqar Qureshi (AIT) Modeling for WREE February 11, 2014 31 / 33
Matlab Tutorial
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