Optimal Control of Open-Channel Flow Using Adjoint Sensitivity Analysis

An optimal flow control methodology based on adjoint sensitivity analysis for controlling nonlinear open channel flows with complex geometries is presented. The adjoint equations, derived from the nonlinear Saint-Venant equations, are generally capable of evaluating the time-dependent sensitivities with respect to a variety of control variables under complex flow conditions and cross-section shapes. The internal boundary conditions of the adjoint equations at a confluence (junction) derived by the variational approach make the flow control model applicable to solve optimal flow control problems in a channel network over a watershed. As a result, an optimal flow control software package has been developed, in which two basic modules, i.e., a hydrodynamic module and a bound constrained optimization module using the limited-memory quasi-Newton algorithm, are integrated. The effectiveness and applicability of this integrated optimal control tool are demonstrated thoroughly by implementing flood diversion controls in rivers, from one reach with a single or multiple floodgates (with or without constraints), to a channel network with multiple floodgates. This new optimal flow control model can be generally applied to make optimal decisions in real-time flood control and water resource management in a watershed.     

Parameter Estimation for Flow in Open-Channel Networks

Two mathematical models for parameter estimation in closed-loop, open-channel flow networks are presented. The parameter estimation models seek to determine the parameter values that would reproduce an observed flow profile in the channel network. The governing equations for gradually varied flow in channel networks are the optimization models’ constraints. The projected augmented Lagrangian method is used to solve the optimization models. Performance of these two optimization models is evaluated for a given closed-loop network configuration. Results establish the potential of the developed models for use in real-life flow scenarios.     

Parameter Sensitivity and Importance Measures in Nonlinear Finite Element Reliability Analysis

Finite element reliability methods allow the analyst to define material, load, and geometry parameters as random variables to represent uncertainties in these model parameters. Approximate probabilistic analysis methods produce estimates of the response variance/covariances, probabilities of exceeding specified structural performance thresholds, and parameter importance measures. A necessary ingredient for such analysis is consistent, efficient, and accurate algorithms for computing finite element response sensitivities. In this paper, unified response sensitivity equations with respect to material, load, and geometry parameters are developed for the time- and space-discretized finite element model. The sensitivities with respect to nodal coordinates and global shape parameters in the presence of material and geometric nonlinearities represent an extension of previous work. Practical computer implementation issues are emphasized. The equations are implemented in the comprehensive, open-source, object-oriented finite element software OpenSees. Importance measures from reliability analysis, employing the sensitivity results, are presented to enable the investigation of the relative importance of uncertainty in the parameters of a finite element model. Two example applications demonstrate that the variability in nodal coordinates of a structure can be a significant source of uncertainty along with that in key material and load parameters.     

Parameter Sensitivity and Predictive Uncertainty in a New Water Quality Model, Q2

A new dynamic model of water quality, Q2, has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q2 for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q2 model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.     

Software Framework for Parameter Updating and Finite-Element Response Sensitivity Analysis

The finite-element software framework OpenSees is extended with parameter updating and response sensitivity capabilities to support client applications such as reliability, optimization, and system identification. Using software design patterns, member properties, applied loadings, and nodal coordinates can be identified and repeatedly updated in order to create customized finite-element model updating applications. Parameters are identified using a Chain of Responsibility software pattern, where objects in the finite-element model forward a parameterization request to component objects until the request is handled. All messages to identify and update parameters are passed through a Facade that decouples client applications from the finite-element domain of OpenSees. To support response sensitivity analysis, the Strategy design pattern facilitates multiple approaches to evaluate gradients of the structural response, whereas the Visitor pattern ensures that objects in the finite-element domain make the proper contributions to the equations that govern the response sensitivity. Examples demonstrate the software design and the steps taken by representative finite-element model updating and response sensitivity applications.     

Parameter Optimization and Sensitivity Analysis for Disturbed State Constitutive Model

Constitutive models for geologic materials and interfaces involve a number of parameters that need to be determined from appropriate laboratory tests. Because the test behavior is influenced by a number of factors such as material variability in test specimens, initial density, mean pressure, and stress paths, the parameters determined from such tests need to be averaged or optimized. The averaging procedure is often used. However, in view of the importance of the parameters in analysis and design, it is desirable and necessary to use advanced procedures such as optimization methods so as to find their improved and realistic values. This paper presents an optimization procedure for the determination of parameters in the unified disturbed state concept constitutive models. A series of multiaxial laboratory tests on a sand under different initial mean pressures, density, and stress paths are used to evaluate the optimized parameters. The stress-strain and volume change behavior is then back-predicted using the parameters from the conventional averaging procedure and the proposed optimization procedure. The results show that the optimized parameters provide improved predictions of the test data. The optimized parameters are used in a finite element procedure to predict cyclic behavior in a boundary value problem involving a shake table test. The proposed procedure can provide a useful methodology for the optimization of parameters for a wide range of available (plasticity, creep, damage, etc.) constitutive models. It can lead to improved analysis and design of geotechnical problems, particularly while using computer (finite element) procedures.     

Method for Assessing Impacts of Parameter Uncertainty in Sediment Transport Modeling Applications

The predictions from a numerical sediment transport model inevitably include uncertainty because of assumptions in the model’s mathematical structure, the values of parameters, and various other sources. In this paper, the writers aim to develop a method that quantifies the degree to which parameter values are constrained by calibration data and the impacts of the remaining parameter uncertainty on model forecasts. The method uses a new multiobjective version of generalized likelihood uncertainty estimation. The likelihoods of parameter values are assessed using a function that weights different output variables on the basis of their first-order global sensitivities, which are obtained from the Fourier amplitude sensitivity test. The method is applied to Sedimentation and River Hydraulics—One Dimension (SRH-1D) models of two flume experiments: an erosional case and a depositional case. Overall, the results suggest that the sensitivities of the model outputs to the parameters can be rather different for erosional and depositional cases and that the outputs in the depositional case can be sensitive to more parameters. The results also suggest that the form of the likelihood function can have a significant impact on the assessment of parameter uncertainty and its implications for the uncertainty of model forecasts.     

Aquifer Parameter Estimation for a Constant-Flux Test Performed in a Radial Two-Zone Aquifer

A patchy aquifer or an aquifer with a finite thickness skin can be considered as a radial two-zone aquifer system, which can be characterized by five parameters, i.e., the thickness of the first zone and four aquifer parameters including the transmissivity and storage coefficient for each of the first and second zones. This paper proposes an approach based on an analytical solution of a constant-flux pumping in a confined two-zone aquifer and the simulated annealing algorithm to determine the five parameters simultaneously. The estimated results for the five parameters are fairly good even assuming the aquifer as a single-zone system at the beginning of the data analysis. The estimated results indicate that the first-zone parameters are much more difficult to accurately identify than the second-zone parameters due to insufficient early-time data and high correlation of the sensitivities among the first-zone parameters. However, the problem of inaccurate results obtained at the first-zone can be significantly improved if more densely temporal drawdown measurements are used.     

Closed-Form Fragility Estimates, Parameter Sensitivity, and Bayesian Updating for RC Columns

Reinforced concrete (RC) columns are the most critical components in bridges under seismic excitation. In this paper, a simple closed-form formulation to estimate the fragility of RC columns is developed. The formulation is used to estimate the conditional probability of failure of an example column for given shear and deformation demands. The estimated fragilities are as accurate as more sophisticated estimates (i.e., predictive fragilities) and do not require any reliability software. A sensitivity analysis is carried out to identify to which parameter(s) the reliability of the example column is most sensitive. The closed-form formulation uses probabilistic capacity models. A Bayesian procedure is presented to update existing probabilistic models with new data. The model updating process can incorporate different types of information, including laboratory test data, field observations, and subjective engineering judgment, as they become available.     

Probability and Sensitivity Analysis in Flotation Circuit of Bama Lead and Zinc Processing Plant Using Monte Carlo Simulation Method

The feed to mineral processing plants has fluctuations in assay, particle size, etc. These fluctuations have a strong influence on the efficiency of purifying lead and zinc processes. In simple circuits of mineral processing units, sensitivity analysis is applicable using analytical solutions, but this method is very difficult, time consuming and inaccurate for simulation of complex circuits. Nevertheless, Monte Carlo simulation method is an accepted tool for probability calculation and sensitivity analysis of complex circuits. In this paper, input data are collected from line 1 of flotation circuit of Bama lead and zinc processing plant (Isfahan, Iran) during 3 months of three 8-hour shifts per day. Distribution and probability density function of input data are determined using @Risk software in Excel. Then, the probability density function of output data (flow rates of lead concentrate, zinc concentrate, tailings, recovery of lead and zinc) are calculated using Monte Carlo simulation (with 100,000 iterations). Finally, the sensitivity of output parameters to input parameters is determined.     

Acid-Gas Storage in a Deep Saline Aquifer: Numerical Sensitivity Study to Evaluate Parameter and Model Uncertainty

A modeling study is conducted to evaluate the sensitivity of acid gas evolution in a deep saline aquifer to expected variations of multiple geologic and engineering variables. Relative permeability hysteresis, aquifer heterogeneity variance, formation water salinity, permeability of caprock and leakage wells, injection rate, regional hydraulic gradient, and formation depth are evaluated as uncertain input parameters to a three-dimensional synthetic aquifer model with fully heterogeneous permeability. To understand the effect of conceptual model uncertainty on predicting gas flow and storage, permeability of the heterogeneous model is upscaled to equivalent permeability for three increasingly homogenized stratigraphic models: an eight-unit facies model, a three-unit depositional model, and a one-unit formation model. Two upscaling methods are used: a flow-based numerical method and an analytical averaging method. Over 120?years (20?years of injection and 100?years of monitoring), multiphase compositional simulation is conducted to model gas migration and trapping in the aquifer and its dissolution in the formation brine. Results suggest that among the variables evaluated, gas-relative permeability hysteresis, heterogeneity variance, and injection rate have the most significant impact predicting the total mobile gas in the storage system, whereas caprock permeability is the most important factor influencing the prediction of total gas leakage and thus the storage security. Over the simulation time scale, for the fixed amount of gas injected, regional hydraulic gradient, salinity, and formation depth have lesser impact on gas flow and storage predictions. Further, leakage through abandoned wells can occur when permeability of the wellbore is as low as 1?mdarcy (md), while caprock permeability becomes critical to storage security when it is more than 1×10-4??md, in which case significant leakage occurs during the monitoring phase. Compared to the predictions of the heterogeneous model, the greater the number of stratigraphic units in the upscaled models, the better its accuracy in predicting gas storage and plume sweep. However, the accuracy of the stratigraphic models depends on aquifer variance, upscaling method, and type of prediction outcome that is being evaluated.     

Parallel Computing Techniques for Sensitivity Analysis in Optimum Structural Design

Among different activities of the optimum structural design using the gradient-based optimization approaches, design sensitivity analysis is the most time-consuming computational process. By introducing parallel computing techniques for sensitivity computation, significant speedup has been obtained in optimum structural design. Computation of design sensitivities is characteristically uncoupled, thus opening the door to parallelization. In this paper, two types of approaches viz. single-level and multilevel parallelisms are pursued for design sensitivities. The design sensitivities are computed using analytical and finite-difference methods. Numerical studies show that the performance of the parallel algorithms for design sensitivities on message passing systems is very good. Good speedups have been achieved in parallel multilevel sensitivity calculation. The parallel algorithms for design sensitivity analysis have been implemented on message passing parallel systems within the software platform of Parallel Computer Adaptive Language.     

Methods and Object-Oriented Software for FE Reliability and Sensitivity Analysis with Application to a Bridge Structure

This paper addresses the growing demand for finite-element software with capabilities to incorporate uncertainty in the input parameters. Reliability and response sensitivity algorithms are implemented in the general-purpose finite-element software OpenSees, which employs an object-oriented programming approach to achieve a sustainable software with focus on maintainability and extensibility. The product is a comprehensive and freely available library of software tools for finite-element reliability and response sensitivity analysis. A numerical example involving a detailed model of a highway bridge with inelastic material behavior and 320 random variables is presented to demonstrate features of the methodology and the software. Importance vectors are employed to rank the input parameters according to their relative influence on the structural reliability. The required response sensitivities are obtained by an extensive implementation of the direct differentiation method.