Adaptive Control of Flood Diversion in an Open Channel and Channel Network - PowerPoint PPT Presentation

Loading...

PPT – Adaptive Control of Flood Diversion in an Open Channel and Channel Network PowerPoint presentation | free to download - id: 5f9fc6-MGNjM



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Adaptive Control of Flood Diversion in an Open Channel and Channel Network

Description:

National Center for Computational Hydroscience and Engineering The University of Mississippi Adaptive Control of Flood Diversion in an Open Channel and Channel Network – PowerPoint PPT presentation

Number of Views:92
Avg rating:3.0/5.0
Slides: 65
Provided by: ncc84
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Adaptive Control of Flood Diversion in an Open Channel and Channel Network


1
Adaptive Control of Flood Diversion in an Open
Channel and Channel Network
National Center for Computational Hydroscience
and Engineering The University of Mississippi
Presented by
  • Yan Ding

National Center for Computational Hydroscience
and Engineering The University of
Mississippi April 29, 2005
2
Outline
  • Introduction
  • Nonlinear Models for Forecasting Flood Events
  • Adjoint Sensitivity Analysis and Boundary
    Conditions for Adjoint Equations
  • Optimization Procedures
  • Applications to a Variety of Flood Diversion
    Control Scenarios
  • Conclusions and Future Research Topics

3
Flood Damage
Flooded Street, Mississippi River Flood of 1927
From L.S.U. Library at the URL
http//www.lib.lsu.edu/mmarti3/smith/pages/mainst
reet.htm
4
An Example of Flood Diversion The Bonnet
Carre Spillway
Floodways and flow distribution during major
floods in the Lower Mississippi River Valley
The spillway (highlighted in green) stretches
from the Mississippi River,at right, northward to
Lake Ponchartrain, on the left of the photo.
From http//www.mvn.usace.army.mil/pao/bcarre/bca
rre.htm
5
Scheduled Water Delivery and Pollutant Disposal
  • Optimal Water Delivery

To give an optimal water delivery through
irrigation canals to irrigation areas
  • Optimal Pollutant Discharge

To find a optimal discharge to meet regulation
for water quality protection, e.g., a tolerable
amount of pollutant into water body
  • Flow-Optimized Discharges
  • (Scheduled Disposal)

Discharging pollutants to waters only during high
river flows may mimic the pattern of natural
diffuse pollutant loads in waters (such as
nutrients or suspended solids exports from the
catchment). Scheduled disposal
6
Applicability of Flow Control Problems
  • Prevent levee of river from breaching or
    overflowing during flood season by using the most
    secure or efficient approach, e.g., operating dam
    discharge, diverting flood, etc.
  • ? Optimal Flood Control ?
    Adaptive Control
  • Perform an optimally-scheduled water delivery for
    irrigation to meet the demand of water resource
    in irrigation canal
  • ? Optimal Water Resource
    Management
  • To give the best pollutant disposal by
    controlling pollutant discharge to obey the
    policy of water quality protection
  • ? Best Environmental
    Management

Goal Real Time Adaptive Control of Open Channel
Flow
7
Difficulties in Control of Open Channel Flow
  • Temporally/spatially non-uniform open channel
    flow
  • Requires that a forecasting model can
    predict accurately complex water flows in space
    and time in single channel and channel network
  • Nonlinearity of flow control
  • Nonlinear process control, Nonlinear
    optimization
  • Difficulties to establish the relationship
    between control actions and responses of the
    hydrodynamic variables
  • Requirement of fast flow solver and optimization
  • In case of fast propagation of flood wave, a
    very short time is available for predicting the
    flood flow at downstream. Due to the limited time
    for making decision of flood mitigation, it is
    crucial for decision makers to have a very
    efficient forecasting model and a control model.

8
Objectives
  • Theoretically,
  • Through adjoint sensitivity analysis, make
    nonlinear optimization capable of flow control in
    complex channel shape and channel network in
    watershed
  • ? Real-Time Nonlinear Adaptive
    Control Applicable to unsteady river flows
  • Establish a general numerical model for
    controlling hazardous floods so as to make it
    applicable to a variety of control scenarios
  • ? Flexible Control System and a
    general tool for real-time flow control
  • For Engineering Applications,
  • Integrate the control model with the CCHE1D flow
    model,
  • Apply to practical problems

9
General Analysis Frameworks of Optimal Theories
10
Integrated Watershed Channel Network Modeling
with CCHE1D
11
de Saint Venant Equations - Dynamic Wave
where Q discharge Zwater stage
ACross-sectional Area qLateral
outflow ?correction factor
Rhydraulic radius n Mannings roughness
12
Initial Conditions and Boundary Conditions
I.C. (Base Flow)
B.C.s
Upstream
(Hydrograph)
Downstream
or
(Stage-discharge rating curve)
or open downstream boundary
13
Control Actions - Available Control Variables in
Open Channel Flow
  • Control lateral flow at a certain location x0
    Real-time flow diversion rate q(x0, t) at a
    spillway
  • Control lateral flow at the optimal location x
    Real-time levee breaching rate q(x, t) at the
    optimal location
  • Control upstream discharge Q(0, t) real-time
    reservoir release
  • Control downstream stage Z(L, t) real-time gate
    operation
  • Control downstream discharge Q(L, t) real-time
    pump rate control
  • Control bed friction (roughness n)

14
An Objective Function for Flood Control
  • To evaluate the discrepancy between predicted and
    maximum allowable stages, a weighted form is
    defined as

where Tcontrol duration L channel length
ttime xdistance along channel Zpredicted
water stage Zobj(x) maximum allowable water
stage in river bank (levee) (or objective water
stage) x0 target location where the water stage
is protective ? Dirac delta function
15
Mathematical Framework for Optimal Control
  • The optimazition is to find the control variable
    q satisfying a dynamic system such that
  • where Q and Z are satisfied with the
    continuity equation and momentum equation,
    respectively (i.e., de Saint Venant Equations)
  • Local minimum theory
  • Necessary Condition If n is the true value,
    then ?J(n)0
  • Sufficient Condition If the Hessian matrix ?
    2J(n) is positive definite, then n is a strict
    local minimizer of f

16
Sensitivity Analysis - Establishing A
Relationship between Control Actions and System
Variables
  • Compute the gradient of objective function,
    q(X, q), i.e., sensitivity of control variable
    through
  • 1. Influence Coefficient Method (Yeh, 1986)
  • Parameter perturbation trial-and-error
    lower accuracy
  • 2. Sensitivity Equation Method (Ding, Jia,
    Wang, 2004)
  • Directly compute the sensitivity ?X/?q by
    solving the sensitivity equations
  • Drawback different control variables have
    different forms in the equations, no general
    measures for system perturbations The number of
    sensitivity equations the number of control
    variables.
  • Merit Forward computation, no worry about
    the storage of codes
  • 3. Adjoint Sensitivity Method (Ding and Wang,
    2003)
  • Solve the governing equations and their
    associated adjoint equations sequentially.
  • Merit general measures for sensitivity,
    limited number of the adjoint equations (number
    of the governing equations) regardless of the
    number of control variables.
  • Drawback Backward computation, has to save
    the time histories of physical variables before
    the computation of the adjoint equations.

17
Variational Analysis - To Obtain Adjoint Equations
Extended Objective Function
where ?A and ?Q are the Lagrangian multipliers
Necessary Condition
on the conditions that
Fig. Solution domain
18
Variation of Extended Objective Function
where
Top width of channel
19
Variations of J with Respect to Control Variables
Formulations of Sensitivities
Lateral Outflow
Upstream Discharge
Downstream Section Area or Stage
Bed Friction
Remarks Control actions for open channel flows
may rely on one control variable or a rational
combination of these variables. Therefore, a
variety of control scenarios principally can be
integrated into a general control model of open
channel flow.
20
General Formulations of Adjoint Equations for
the Full Nonlinear Saint Venant Equations
According to the extremum condition, all terms
multiplied by ?A and ?Q can be set to zero,
respectively, so as to obtain the equations of
the two Lagrangian multipliers, i.e, adjoint
equations (Ding Wang 2003)
21
Transversality Conditions and Boundary Conditions
Considering the contour integral in ?J, This
term ?I needs to be zero.
Transversality (Final) Conditions
Backward Computation
Upstream B.C.
Downstream B.C.
Fig. Solution domain
22
Internal Boundary Conditions for Channel
Network
I.B.C.s of Flow Model
I.B.C.s of Adjoint Equations
Fig. Confluence
23
Numerical Techniques
1-D Time-Space Discretization (Preissmann, 1961)
where ? and ? are two weighting parameters in
time and space, respectively ?ttime increment
?xspatial length
Solver of the resulting linear algebraic
equations (Pentadiagonal Matrix)
Double Sweep Algorithm based on the Gauss
Elimination
24
Minimization Procedures for Nonlinear Optimization
  • CG Method (Fletcher-Reeves method) (Fletcher
    1987)
  • The convergence direction of minimization is
    considered as the gradient of objective function.
  • Trust Region Method (e.g Sakawa-Shindo method)
  • considering the first order derivative of
    performance function only, stable in most of
    practical problems (Ding et al 2004)
  • Limited-Memory Quasi-Newton Method (LMQN)
  • Newton-like method, applicable for large-scale
    computation, considering the second order
    derivative of objective function (the approximate
    Hessian matrix) (Ding Wang 2005)
  • Others

25
Minimization Procedures
  • Limited-Memory Quasi-Newton Method (LMQN)
  • Newton-like method, applicable for large-scale
    computation (with a large number of control
    parameters), considering the second order
    derivative of objective function (the approximate
    Hessian matrix)
  • Algorithms
  • BFGS (named after its inventors,
    Broyden, Fletcher, Goldfarb, and Shanno)
  • L-BFGS (unconstrained optimization)
  • L-BFGS-B (bound constrained
    optimization)

26
Limited-Memory Quasi-Newton Method (LMQN) (Basic
Concept 1)
  • Given the iteration of a line search method for
    parameter q
  • qk1 qk ?kdk
  • ?k the step length of line search
  • sufficient decrease and curvature
    conditions
  • dk the search direction (descent direction)
  • Bk n?n symmetric positive definite matrix
  • For the Steepest Descent Method Bk I
  • Newtons Method Bk? 2J(nk)
  • Quasi-Newton Method
  • Bk an approximation of the Hessian ?
    2J(nk)

27
L-BFGS (One of LMQN method) (1)
  • Difficulties of Newtons method in large-scale
    optimization problem obtain the inverse Hessian
    matrix, because
  • the Hessian is fully dense, or,
  • the Hessian cannot be computed.
  • BFGS (Broyden, Fletcher, Goldfarb, and Shanno,
    1970)
  • Constructs the inverse Hessian
    approximation ,

However, all of the vector pairs (sk, yk) have to
be stored.
28
L-BFGS (2)
  • Updating process of the Hessian by using the
    information from the last m Q-N iterations

Where m is the number of Q-N updates supplied by
the user, Generally (Nocedal Wright, 1999),
3 ? m ? 7 and
Only m vector pairs (si, yi),i1, m, need to be
stored
29
Flow chart of Finding optimal control variable
by using LMQN procedure
  • Three Major Modules
  • Flow Solver
  • Sensitivity Solver
  • Minimization Process

30
L-BFGS-B
  • The purpose of the L-BFGS-B method is to
    minimize the objective function J(q) , i.e.,
  • min J(q),
  • subject to the following simple bound constraint,
  • qmin ? q ? qmax,
  • where the vectors qmin and qmax mean lower and
    upper bounds on the control variables.
  • L-BFGS-B is an extension of the limited memory
    algorithm (L-BFGS) (Liu Nocedal, 1989) for
    bound constrained optimization (Byrd et al, 1995)
    .

31
Flooding and Flood Control
Levee Failure, 1993 flood. Missouri.
Flood Gate, West Atchafalaya Basin, Charenton
Floodgate, Louisiana
32
Control of Flood Diversion in A Single Channel
A Simplified Problem
Objective Function
33
Optimal Control of Flood Diversion Rate ( Case
1) - A Hypothetic Single Channel
Lateral Outflow
Z03.5m
Cross-section
A Triangular Hydrograph
This value is used for solving adjoint equations
34
Optimal Lateral Outflow and Objective Function
(Case 1)
Optimal Outflow q
Objective function and Norm of gradient of the
function
Iterations of optimal lateral outflow
35
Comparison of Water Stages in Space and Time
(Case 1)
Allowable Stage Z03.5
No Control
Optimal Control of Lateral Outflow
36
Comparison of Discharge in Time and Space (Case 1)
No Control
Optimal Control of Lateral Outflow
37
Sensitivity ?J/?q(x,t)
Fast searching
Sensitivity of q in time and space at the 1st
iteration
Iterative history of sensitivity at the control
point
38
Optimal Control of Lateral Outflow (Case 2)
Under the limitation of the maximum lateral
outflow rate
Application of the quasi-Newton method with bound
constraints (L-BFGS-B)
Suppose that the maximum lateral outflow rate is
specified due to the limited capacity of flood
gate or pump station, e.g. q ? 50.0 m3/s
Bound Constraints
39
Optimal Lateral Outflow with Constraint
Comparison of optimal lateral outflow rates
between Case 1 and Case 2
Iterations of optimal lateral outflow
40
Controlled Stage and Discharge in the Channel
(Case 2)
Allowable stage Z03.5m
Stage in time and space
Discharge in time and space
41
Optimal Control of Lateral Outflows Multiple
Lateral Outflows (Case 3)
Condition of control
Suppose that there are three flood gates (or
spillways) in upstream, middle reach, and
downstream.
42
Optimal Lateral Outflow Rates in Three Diversions
(Case 3)
Optimal lateral outflow rates of three floodgates
(Case 4)
Optimal lateral outflow of only one gate (q1)
(Case 1)
43
Controlled Stage and Discharge by Three
Diversions (Case 3)
Allowable stage Z03.5m
Stage in time and space
Discharge in time and space
44
Comparisons of Diversion Percentages and
Objective Functions
Case qmax Number of floodgate
1 N/A 1
2 50.0m3/s 1
3 N/A 3
Case Diversion Volume (m3) Percentage of Diversion ()
1 3,952,231 41.3
2 3,743,379 39.1
3 3,180,661 33.2
45
Optimal Control of Lateral Outflow (Case 4)
Allowable stage changing along with the channel
Condition of Allowable Stage
Suppose that the tolerable stage is changing
along with the channel as a function of channel
length, e.g, Z0(x) 5.5-0.2x, x(km).
Mississippi river levee, from http//images.usace.
army.mil/main.html
46
Optimal Lateral Outflow and Stage in the Channel
(Case 4)
Allowable stage Z0(x)5.5-0.0002x
Stage in time and space
Iterations of Lateral Outflow Rate
47
Control of Flood Diversion in A Channel Network
48
Optimal Control of One Lateral Outflow in a
Channel Network (Case 5)
Z03.5m
q(t)?
Compound Channel Section
Confluence
49
Optimal Lateral Outflow and Objective Function
(Case 5 Channel Network)
50
Comparisons of Stages (Case 5)
51
Comparisons of Discharges (Case 5)
Discharge increased !!
Discharge increased !!
52
Optimal Control of Multiple Lateral Outflows in a
Channel Network (Case 6)
1
3
q1(t)?
m
0
0
0
,
4

1
L
q2(t)?
Z03.5m
L

3
1
3
,
0
0
0
m
2
.
o
l
N
e
n
n
h
a
C
m
q3(t)?
0
5
0
4
,

L
2
Compound Channel Section
53
Optimal Lateral Outflow Rates and Objective
Function (Case 6)
One Diversion
Three Diversions
Optimal lateral outflow rates at three diversions
Comparison of objective function
54
Comparisons of Stages (Case 6)
55
Comparisons of Discharges (Case 6)
56
Flood Diversion Control in River Flow (Real
Storms)
57
Allowable Elevations along the River and Rating
Curve at Outlet
Zobj (x)
Z-Q
58
Optimal Control of One Flood Gate in River Flow
Comparison of Stages
Optimal diversion hydrograph
Storm Hydrograph
59
Comparisons of Water Stages
60
Comparisons of Discharges
61
Iterations of Objective Functions
62
Optimal Control of Two Floodgates in River Flow
63
Comparisons of Water Stages (Two Floodgates)
64
Comparisons of Discharges (Two Floodgates)
65
Comparison of Objective Functions
66
Data Flows for Optimal Control Based on the
CCHE1D Flow Model
67
Conclusions
  • The Adjoint Sensitivity Analysis provides the
    nonlinear flow control with comprehensive and
    accurate measures of sensitivities on control
    actions.
  • The control model is capable of solving a
    large-scale flow control problem efficiently.
  • The integrated flow model (the CCHE1D) and the
    adjoint equations are suitable for computing
    channel network with complex geometries By
    taking the advantages of the flow model in
    dealing with channel network, this control model
    can be applied readily to realistic flow control
    problems in natural streams and channel network.
  • The adaptive control framework is general and
    available for practicing a variety of flow
    control actions in open channel, e.g., flood
    diversion, damgate operation, and water delivery.
  • The control model also can assist engineers to
    plan the best locations and capacities of
    floodgates from hydrodynamic point of view.

68
Research Topics In the Future
  • Find a real case to apply the model to flood
    control problem or water delivery problem
  • Flood control with water security management
  • Develop further modules for other process
    controls, e.g. water disposal control, water
    quality control, sediment transport and
    morphological process control
  • Flow controls with uncertainties under natural
    conditions
  • Others

69
Acknowledgements
  • This work was a result of research sponsored by
    the USDA Agriculture Research Service under
    Specific Research Agreement No. 58-6408-2-0062
    (monitored by the USDA-ARS National Sedimentation
    Laboratory) and The University of Mississippi.
  • Special appreciation is expressed to Dr. Sam S.
    Y. Wang, Dr. Mustafa Altinakar, Dr. Weiming Wu,
    and Dr. Dalmo Vieira for their comments and
    cooperation.

70
Optimal Water Delivery
  • Objective To deliver a desired water to a target
    area quickly without any large water stage
    fluctuations Scheduled Water Delivery
  • Objective Function To evaluate the discrepancy
    between predicted and objective water stages, a
    objective function is defined as

where Tcontrol duration L channel length
ttime xdistance along channel Zpredicted
water stage Zobj(x) objective water stage in
cross-section ?Ztolerable difference of
objective water stage.
71
Optimal Control of Upstream Discharge
Z0-3.5m, ?Z0.1m
Q(0,t)?
Sensitivity of Q(0,t)
Constraint of Q Q(0,t) 100.0m3/s
72
Optimal Water Release at Upstream
Initial Estimation
Optimal Discharge
73
Controlled Stages and Discharges
Objective stage 3.5m, Tolerable difference
0.1m
Stage in time and space
Discharge in time and space
74
Objective Function J
  • A general form of objective function for optimal
    control is introduced as follows

where X physical variables, e.g.
stage, discharge, and/or velocity in open
channel q control variables (or
control forces), e.g., discharge at upstream or
downstream, lateral outflow, or
location of control structure t0 the
starting time of control, tf the
final time of control x1, x2 target
area for control r used-defined
measured function, e.g., discrepancy of stage
between predicted and target values
75
Mathematical Framework for Optimal Control
  • The optimazition is to find the control variable
    q satisfying a dynamic system such that
  • where Q and Z are satisfied with the
    continuity equation and momentum equation,
    respectively (i.e., de Saint Venant Equations)
  • Local minimum theory
  • Necessary Condition If n is the true value,
    then ?J(n)0
  • Sufficient Condition If the Hessian matrix ?
    2J(n) is positive definite, then n is a strict
    local minimizer of f

76
Optimal Control of Open Channel Flow A
Brief Review
Note CGM Conjugate Gradient Method
ASM Adjoint Sensitivity Method LBFGS
Limited memory Broyden, Fletcher, Goldfarb, and
Shanno Algorithm
77
CCHE1D Sediment Transport Model
  • Non-uniform Total-Load Transport
  • Non-equilibrium Transport Model
  • Coupled Sediment Transport Equations Solution
    (Direct Solution Technique)
  • Bank Erosion and Mass Failure
  • Several Methods for Determination of
    Sediment-Related Parameters
About PowerShow.com