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## Water Resources Systems Modeling Techniques

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**Water Resources Systems Modeling Techniques**Prof. V. Jothiprakash Assistant Professor Department of Civil Engineering Indian Institute of Technology Bombay Powai, Mumbai 400 076 vprakash@civil.iitb.ac.in**Introduction**• Water • Crucial element for human survival • Key element in the socio-economic development of a country • Demand • Increasing • Extensive and intensive agriculture • Power production • Municipal and industrial use (urbanization and industrialization)**Contd…**• Availability • Constant over a period of time • Spatial and temporal variations • To over come this variations and to meet the demands • Judicial use is needed • Effective and efficient utilization is also needed • Large, medium and small reservoirs • Need to be operated to optimal condition • The best possible manner • Requires systematic study**SWOT analysis of Water Resources**• Strength • India is gifted with large number of rivers • 400 x 1010 m3 of water available • Weakness • Spatial and temporal distribution • Rainfall 11,500 mm at Cherrapunji 215 mm at Jaisalamer • 69 x1010m3 is utilizable form • Storage insufficient to meet the demand • Monsoon failure or excess rainfall in one monsoon**Contd…**• Reservoirs • Improper operation • No single algorithm available to solve WR problem • Topography does not allow construction of very large dams • Improper understanding of the hydrological phenomena • Complex interaction between human and nature**Contd…**• Opportunities • To store them in small reservoirs • To operate the reservoirs optimally • To allocate water to various users • To maximize the economic return • Augment the sources • On form developmental works • Reuse and recycling • Desalinization**Contd…**• Threats • Large spatial and temporal variations • Demand is ever increasing • Sociological problems • Implementation of best polices But in INDIA many reservoirs need optimal operating polices • Systematic study is needed**Solving the problems-really we solve it?**• Real life problems are solved • By developing theoretical equations • My models • Some time based on experience • Most of the time SHM – Some How Managed • In Engineering – Four Generations-in solutions • Empirical methods/Experiments • Analytical Equations • Numerical schemes Systems approach • Data Driven methods Soft computing techniques**Empirical methods/ Model Experiments**• Based on the observed data and their statistical correlations – conventional models • Conducting experimental works and relating it to the real world problems • Started long back, now again gaining importance by introduction of new ANN models**Engineering problem solving Generations**• Numerical Schemes • Finite Difference Scheme • Finite Element Scheme • These are possible only when equations are possible to develop and solve (high order differential equations solved using computers) • Data driven methods New yet to be widely accepted**MODELS**Characteristic representation of the prototype • Iconic models • Physical models • Analogue models • Mathematical models • Optimization (prescriptive models) • Best solution • Simulation (descriptive models) • Answers “what if” conditions**Why we need model studies?????**USES of MODEL STUDIES • To study the behaviour of the prototype • To study the impact of the prototype • To study the effect of the variation in the parameters • To solve the real world problems • Prototype are costlier and time consuming-once constructed they cannot be changed? • Thus before going in for prototype a model study will be carried out • It is very important in Water Resources • Dam design and analysis, flow condition over a spill way, dam break analysis, operation of reservoirs, planning of canal management etc….**Introduction**• Definition • Prototype - Model**Physical model study on Jump formation downstream of a**spillway**Model study to study the effect of discharge from a spillway****Sample Satellite imageries of Tsunami- large scale data base**management studies**SYSTEM**Input Output Systems approach • System • A system is composed of a large number of components each of which may or may not serve a different purpose but all of which contribute to a common purpose or goal Systematic study System design System analysis System synthesis**Why we need systems approach?**• System is large and complex • System should involve / necessitate knowledge from many disciplines • The objective need to be quantified in mathematical terms (or logical terms) • One or more variables involve uncertainty • The problem has many alternative solutions**Steps in systems analysis**• Definition of system and objectives • Identification of system components and boundaries • Identification of decision makers • Clear definition and quantification of objectives • Generation and evaluation of alternatives • Construction of a mathematical model • Define variables, relationship between variables, optimization model • Solution to the model • Implementation of the best solutions • Performance of the solutions • Feedback to step 1.**Optimizations**• Objective functions • Cost minimization • Benefit Maximization • Technical objectives • Increase power. Minimize loss, maximize release etc… • Constraints • Physical • Economical • Sociological • Technical Conventional Optimization Model • Linear programming • Integer programming • Goal programming • Non-linear programming • Dynamic programming Soft Computing Techniques**Conventional Models**• Linear Programming models • Most popular optimization technique • Readily available solution methodology • Easy availabilities of software packages • Suitable for large scale water resources systems • Applied when the objective function and constraints are linear • Non Linear Programming models • Applied when the objective function and constraints are non-linear • Dynamic programming models • Suited for sequential decision problems • Stage coach / sales man problem • Reservoir operation rules**Simulation**• Used for the evaluation of the performance of water resources systems • Can answer “what if condition” • Now a days mostly used along with optimizations**What are Soft computing techniques**• Soft Computing tools • Neural Networks • Fuzzy logic • Genetic Algorithms • Genetic Programming • Cellular Automata • Ant colony algorithms • Hybrid system • Probabilistic reasoning • GIS**Artificial Neural Networks**• Definition • Works on the principles of human brain • Requires training • Supervised or unsupervised mode • Requires validation • To test the ability of understanding • Used for prediction of future values • Success depends up on the • type of activation • Number of training data points • One of the most successful Soft Computing tool in Civil Engineering**Application in Civil Engineering**• Water Resources • Time series Prediction • Rainfall-runoff prediction • Rainfall forecasting • Stream-flow prediction • Reservoir inflow prediction • Reservoir operation • Hydrology, irrigation engineering • Evaporation prediction • Evapotranspiration prediction • Irrigation return-flow prediction**Application in Civil Engineering**• Structural Engineering • Automated conceptual design of structural systems • Structural dynamics involving Earthquake • Non-linear analysis of plates • Detection of damages • Vibration analysis • Transportation Engineering • Traffic flow simulation • Automatic signals • Priority of highway maintenance**Application in Civil Engineering**• Geotechnical Engineering • Hydraulic conductivity • Soil thermal resistivity • Strain-rate dependent behaviour of soils • Prediction of settlements during tunneling • Predict settlement of shallow foundation • Assessment of damage of pre-stressed piles • Capacity of piles in cohesionless soils**Advantages and Disadvantages of ANN**• Advantages • Nonlinearity • Input-output mapping • Adaptivity • Trained to operate in a specific environment and can e run with minor changes to environment • Disadvantages • Lack of physical concept and relations between input and output • It just mimic the hydrologic process • Cannot be used for extrapolation • No standardized way of selecting the network architecture**Fuzzy Programming**Real world problem is very complex • Deterministic approaches • Stochastic approaches • Implicit and explicit approaches • Handle statistical uncertainty • Cannot handle non statistical uncertainty • Vagueness or impreciseness Fuzzy theory introduced by Zadeh (1965) • Can handle the impreciseness • Fuzzy logic • Fuzzy set theory • Fuzzy optimization**Genetic Algorithms**• Genetic algorithms are computerized search and optimization algorithms based on the mechanics of natural genetics and natural selection • Derived by biologists • The offspring have certain desirable characteristics • Steps in GA modeling • Coding • Fitness function evaluation • Selection • Crossover, and • Mutation**Contd…**• Coding • Each chromosome coded in binary bits of 0 to 1 represents a potential solution consisting of the components of the decision variables (genes), that either form can be used to evaluate the objective function. • Each variable is coded to a specified length 1 0 1 0 1 • Length may vary from variable to variable • All substrings are then concatenated together to form a single string 1 0 1 0 1 0 1 1 0 1 • Fitness function evaluation • To evaluate the string • The sub-strings are decoded and fitted into the objective function**Contd…**• Selection • string is selected for mating to form the next generation • with a probability, proportional to its fitness value • weak solutions are eliminated and strong solutions survive to form the next generation “the survival of the fittest” fitness function evaluation + selection processes = reproduction • Crossover • the selected individuals are exchanged between two selected chromosomes to create new chromosomes that preserve the best material from two parent strings • Single point • Two point • Uniform crossover**Single point crossover**Parents Offspring 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 01 1 0 0 1 1 1 0 1 • Two point cross over 1 0 1 0 1 0 1 0 1 1 1 00 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 11 0 1 • Uniform cross over 1 0 1 0 1 0 1 0 1 1 11 0 1 1 1 00 1 1 0 0 1 1 0 0 0 1 0 0 01 00 0 1**Contd…**• Mutation • Gives a new genetic character to the string • Uniform • Non uniform • Modified mutation • Fitness function and convergence • Average fitness of the population approach the best individual values • Higher population quicker in convergence • Lower population misses some values • Relation between population size and length of string**Application of GA in water resources**• Pipe network • Design of networks, and analysis • Ground water management problems • Quantity and quality management models • Reservoir operation • Single purpose single reservoir • Multi-purpose single reservoir • Multi-reservoir systems • Multi-purpose multi-reservoir systems**Advantages of GA model**• The GA typically uses a coding of the decision variable set, not the decision variable itself • The GA searches from a population of decision variable sets, not a single decision variable set • The GA uses the objective function itself not the derivative information • The GA algorithm uses probabilistic (not deterministic) search rules • GA takes care of stochasticity also • GA does not requires discretization of state variables • GA does not requires transition probabilities • GA does not have curse of dimensionality problems • GA models results in optimal or near optimal solutions**Disadvantages of GA model**• Cannot handle large number of constraints like LP models • Computationally difficult to provide very long string length with binary coding • - To some extent overcome by hexagonal coding • Every iteration need objective function evaluation • Difficult to handle mutation Still GA model provide better solutions than the conventional optimization techniques in developing reservoir operating rules**Application case study – 1Artificial Neural Network model**to predict inflow into a reservoir**Inflow into a reservoir**• Most important input variable in water resources planning and management • Considered as • Deterministic variable • Probabilistic variable • Stochastic variable • Fuzzy variable • Historical data or Generated data**Conventional Models of Synthetic Streamflow generation**• AR • AR(1) • AR(2) • ARMA • ARIMA • Thomas-Fierring model • All the models uses the statistical properties of the inflow • Can be used for monthly, seasonal and annual inflow prediction**Neural Network Model for Synthetic Streamflow generation**• Using the ANN technique • Using the daily inflow data • Training of the network • Validating the network • Predicting the inflow**Backpropagation Network (BPN)**• BPN is a fully interconnected, layered, and feed forward network. • No connection bypasses one layer to go directly to a later layer. • A versatile Network, useful in handling problems that require recognition of complex patterns and in performing nontrivial mapping functions.**Application of BPN (Inflow Prediction)**• The pattern matching ability of ANN is utilised in the present study, to match the daily inflow values • The network was trained with a data set for twenty years. • The output from the network is validated for five years**Input Layer**Hidden Layer Output Layer Inflow volume during Time t-1 It-1 Inflow volume during Time t-2 It-2 Inflow volume during time t It time period t-1 time period t time period t-2 ANN model developed for predicting the daily inflow into the reservoir