Reliability-Based Economic Design Optimization of Spread Foundations

This technical note develops a design approach that integrates economic design optimization with reliability-based methodologies to rationally account for geotechnical-related uncertainties. The geotechnical related uncertainties are addressed using a reliability-based approach in the assessment of ultimate limit state (ULS) and serviceability limit state (SLS) requirements. This design approach is illustrated using an example of spread foundation under drained uplift loading. Comparison of the economically optimized design with conventional designs shows that cost of the economically optimized design is lower than that of other feasible designs, and increasing foundation depth is a relatively effective way to increase uplift capacity. Impacts of geotechnical property uncertainties on foundation construction costs are quantified, and the results form a basis of a quantitative cost-benefit analysis of reducing geotechnical property uncertainties. Operative horizontal stress coefficient (K) is shown to be the key parameter that significantly affects the design of a spread foundation under drained uplift, and therefore, deserves attention in site investigation. For a typical allowable uplift displacement ya = 25?mm, the spread foundation design is dictated by the ULS requirement, and the effect of ya, or SLS requirement, is negligible.     

Characterization of Model Uncertainty in the Static Pile Design Formula

Level 1 reliability methods have been internationally accepted as the basis for development of the new generation of geotechnical design codes. A key requirement of this design approach is the identification and quantification of uncertainties associated with the geotechnical design under consideration. This paper presents four load test databases from South Africa for driven piles in noncohesive soils (29 tests), bored piles in noncohesive soils (33 tests), driven piles in cohesive soils (59 tests), and bored piles in cohesive soils (53 tests). The capacity model factor is defined as the ratio of the interpreted capacity (Chin-Davisson approach) and the predicted capacity (static pile design formula). The uncertainty in the capacity model factor is modeled as a lognormal random variable. The model factor statistics reported in this study are required for reliability-based ultimate limit state design. The uncertainty in the load-settlement behavior is characterized by fitting measured load-settlement data to a hyperbolic equation and then normalizing the hyperbolic curve with the interpreted capacity. The resulting exercise reduces uncertainties in a set of nonlinear continuous curves to uncertainties in two hyperbolic curve-fitting parameters. This approach is practical and grounded realistically on the load test database with minimal assumptions. The hyperbolic parameter statistics reported in this study are required for reliability-based serviceability limit state design.     

Financial Viability Analysis and Capital Structure Optimization in Privatized Public Infrastructure Projects

Numerous public infrastructure projects have been privatized worldwide, where responsibilities, risks, and rewards are substantially reallocated between pubic and private sectors. The financial evaluation of a privatized infrastructure project is complex and challenging because of the risks and uncertainties due to the large size, long contract duration, nonrecourse financing, multiple project participants with different motives and interest, and the complexity of the contractual arrangements. Improved financial engineering techniques are required to overcome the limitations of traditional financial analysis techniques in addressing risks and uncertainties. This paper develops a methodology for capital structure optimization and financial viability analysis that reflects the characteristics of project financing, incorporates simulation and financial engineering techniques, and aims for win–win results for both public and private sectors. This quantitative methodology defines the capital structure of a privatized project in four dimensions, examines different project participants’ perspectives of the capital structure, optimizes the capital structure, and evaluates the project’s financial viability when it is under construction risk, bankruptcy risk and various economic risks (that are dealt with as stochastic variables), and is subject to other constraints imposed by different project participants. This methodology also evaluates the impact of governmental guarantees and supports, and addresses the issue of the equity holders’ commitment to project success by initiating the concepts of equity at project risks, value of governmental loan guarantee, and project bankrupt probability during construction. A framework and a solution algorithm are provided for this proposed methodology. These research outputs will significantly facilitate both public and private sector in evaluating a privatized project’s financial viability and collectively determining an optimal capital structure that safeguards their respective interests.     

Reliability-Based Optimal Design of Truss Structures Using Particle Swarm Optimization

In this work, the particle swarm optimization method is employed for the reliability-based optimal design of statically determinate truss structures. Particle swarm optimization is inspired by the social behavior of flocks (swarms) of birds and insects (particles). Every particle’s position represents a specific design. The algorithm searches the design space by adjusting the trajectories of the particles that comprise the swarm. These particles are attracted toward the positions of both their personal best solution and the best solution of the swarm in a stochastic manner. In typical structural optimization problems, safety is dealt with in a yes/no manner fulfilling the set of requirements imposed by codes of practice. Considering uncertainty for the problem parameters offers a measure to quantify safety. This measure provides a rational basis for the estimation of the reliability of the components and of the entire system. Incorporating the reliability into the structural optimization framework one can seek a reliability-based optimal design. For the problems examined herein, the reliability indexes of the structural elements are obtained from analytical expressions. The structure is subsequently analyzed as a series system of correlated elements and the Ditlevsen bounds are used for the calculation of its reliability index. The uncertain-random parameters considered in this work are the load, the yield-critical stress; and the cross sections of the elements. The considered design variables of the optimization problem are the cross-sectional areas of the groups, which control the size of the truss, and the heights and lengths that control the shape of the truss. The results of the optimization are presented for a 25-bar truss and a 30-bar arch and the robustness of the optimization scheme is discussed.     

Building Orientation and Wind Effects Estimation

The methodology for estimating wind effects presented in this paper is based on the database-assisted design approach. It accounts for the effects of wind directionality, for the effects of the uncertainties in the parameters that determine wind effects, and for the effects of building orientation. The methodology yields estimates of wind effects that are far more realistic than those based on the conventional building code approach, which disregards uncertainties in those parameters, as well as the effects of wind directionality and building orientation, or accounts for these effects through the use of a blanket reduction factor. The pilot software on which the calculations presented in this paper are based is a first step toward modern computer-intensive electronic standards wherein wind loads can be calculated by using database-assisted reliability-based calculations of wind effects. We believe such standards will go a long way toward achieving significantly safer and more economical buildings in regions affected by strong winds.     

Aircraft Icing Detection, Identification, and Reconfigurable Control Based on Kalman Filtering and Neural Networks

Flight in all weather conditions has necessitated correctly detecting icing and taking reasonable measures against it. This work aims at the detection and identification of airframe icing based on statistical properties of aircraft dynamics and reconfigurable control protecting aircraft from hazardous icing conditions. A Kalman filter is used for the data collection for the detection of icing, which aerodynamically deteriorates flight performance. A neural network process is applied for the identification of icing model of the aircraft, which is represented by five parameters based on past experiments for iced wing airfoils. Icing is detected by a Kalman filtering innovation sequence approach. A neural network structure is embodied such that its inputs are the aircraft estimated measurements and its outputs are the parameters affected by ice, which corresponds to the aircraft inverse dynamic model. The necessary training and validation set for the neural network model of the iced aircraft are obtained from the simulations of nominal model, which are performed for various icing conditions. In order to decrease noise effects on the states and to increase training performance of the neural network, the estimated states by the Kalman filter are used. A suitable neural network model of aircraft inverse dynamics is obtained by using system identification methods and learning algorithms. This trained model is used as an application for the control of the aircraft that has lost its controllability due to icing. The method is applied to F16 military and A340 commercial aircraft models and the results seem to be good enough.     

New Experimental Method to Find Equilibrium Scour at Bridge Piers

A new methodology for the experimental analysis of the equilibrium scour depth at bridge piers is introduced and validated for clear-water conditions. The proposed experimental methodology determines the flow conditions for a given equilibrium scour instead of determining the equilibrium scour for given flow conditions, which is the usual practice. The basic hypothesis is that the shape of the scour hole is essentially related to the scour depth and sediment properties, but not to flow conditions. This hypothesis is checked experimentally. The proposed methodology may drastically reduce the time period required for experiments (from weeks to hours), and avoids the uncertainties due to the equilibrium scour being usually achieved asymptotically. Some preliminary results of the equilibrium scour obtained with the proposed methodology are compared to the expressions given in the literature, showing fair agreement.     

Calibration of Water Distribution Hydraulic Models Using a Bayesian-Type Procedure

Estimating model parameters is a difficult, yet critical step in the use of water distribution system models. Most of the optimization-based approaches developed so far concentrate primarily on efficient and effective ways of obtaining optimal calibration parameter values. At the same time, very little effort has been made to determine the uncertainties (i.e., errors) associated with those values (and related model predictions). So far, this has typically been done using the first-order second moment (FOSM) method. Even though reasonably computationally efficient, the FOSM approach relies on several restrictive assumptions and requires computationally demanding calculation of derivatives. To overcome these limitations, the recently developed shuffled complex evolution metropolis (SCEM-UA) global optimization algorithm is linked to the Epanet2 hydraulic model and used to solve a least-squares-type calibration problem. The methodology is tested and verified on the Anytown literature case study. The main advantage of the SCEM-UA algorithm over existing approaches is that both calibration parameter values and associated uncertainties can be determined in a single optimization model run. In addition, no model linearity or parameter normality assumptions have to be made nor any derivatives calculated. The main drawback of the SCEM-UA methodology is that it could, potentially, be computationally demanding, although this is not envisaged as a major problem with current computers.     

Expanded Reliability-Based Design Approach for Drilled Shafts

This paper develops a more general reliability-based design approach for drilled shafts that formulates the design process as an expanded reliability problem in which Monte Carlo simulations (MCS) are used in the design. Basic design parameters, such as the shaft diameter (B) and depth (D), are formulated as discrete uniform random variables. Then the design process becomes one in which failure probabilities are developed for various combinations of B and D [i.e., conditional probability p(Failure∣B,D)] and are compared with a target probability of failure pT. Equations are derived for this expanded reliability-based design (RBDE) approach, and criteria are established for the minimum number of MCS samples to ensure a desired level of accuracy. Its usefulness is illustrated using a drilled shaft design example. This RBDE approach has the following advantages: (1) it gives results that agree well with current RBD designs, but it improves the resolutions of the designs; (2) it offers design engineers insight into how the expected design performance level changes as B and D change; (3) it gives design engineers the ability to adjust pT, without additional calculation effort, to accommodate specific needs of a particular project; and (4) it is transparent and “visible” to design engineers who are given the flexibility to include uncertainties deemed appropriate. Finally, the effects of uncertainties in the at-rest horizontal soil stress coefficient (K0) and allowable displacement (ya) are illustrated using this approach.     

Analysis of Spatial Scenarios Aiding Decision Making for Regional Irrigation Water-Demand Planning

Regional irrigation water-demand planning is utilized to establish appropriate cropping patterns and estimate irrigation water demand. Although optimization methods have been extensively adopted, uncertainties of meteorological conditions and the complexity of spatial contexts make developing explicit and structured decision making extremely difficult. Rather than generating a single optimal solution, decision makers prefer to generate several possible scenarios and compare results. This study proposes a novel spatial scenario-based planning framework, with a database, model base, and scenario-setting modules, to generate flexible spatial planning scenarios for improving irrigation water-demand planning. Possible demand planning scenarios for irrigation managers are discussed. A prototype of the proposed scenario-based framework is implemented on a geographic information system platform to assist in spatial decision making. Demand planning during a drought period for the Chia-Nan irrigation command area, the largest one in Taiwan, is adopted as a case study to demonstrate the proposed framework for spatial scenario analysis.     

Evaluating and Comparing Bidding Optimization Effectiveness

Competitive bidding is the means by which pricing of numerous services takes place. Optimization models have been developed to support bidding, but no consistent and structured methodology has been followed in evaluating those models. This paper provides such a methodology and demonstrates it in the comparison of three bidding optimization approaches aimed at profit maximization. The methodology represents a modification and refinement of previously used evaluation approaches. In addition, the methodology incorporates the determination of an upper bound on effectiveness in order to provide an indicator of how much improvement in effectiveness remains. Real construction bidding data are used to demonstrate the comparison of the optimization procedures.     

Bayesian Modal Updating using Complete Input and Incomplete Response Noisy Measurements

The problem of identification of the modal parameters of a structural model using complete input and incomplete response time histories is addressed. It is assumed that there exist both input error (due to input measurement noise) and output error (due to output measurement noise and modeling error). These errors are modeled by independent white noise processes, and contribute towards uncertainty in the identification of the modal parameters of the model. To explicitly treat these uncertainties, a Bayesian framework is adopted and a Bayesian time-domain methodology for modal updating based on an approximate conditional probability expansion is presented. The methodology allows one to obtain not only the optimal (most probable) values of the updated modal parameters but also their uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite-element model based on these modal estimates. The proposed approach requires only one set of excitation and corresponding response data. It is found that the updated probability density function (PDF) can be well approximated by a Gaussian distribution centered at the optimal parameters at which the posterior PDF is maximized. Numerical examples using noisy simulated data are presented to illustrate the proposed method.     

Construction Project Risk Assessment Using Existing Database and Project-Specific Information

This paper develops a risk assessment methodology for construction projects by combining existing large quantities of data and project-specific information through updating approaches. Earlier studies have indicated that risk assessment is still difficult for practicing engineers to use due to the requirement of data on too many input variables. However, the availability of existing large quantities of data and project-specific information makes it possible to simplify the risk assessment procedure. Two main ideas are pursued in this paper to facilitate practical implementation: identify and evaluate the critical risk events, and develop a systematic updating methodology. Both epistemic and aleatory types of uncertainties in the data are considered, and corresponding updating procedures are developed. The proposed methodology is illustrated for the construction risk assessment of a cable-stayed bridge.     

Optimum Design of Cantilever Retaining Walls Using Target Reliability Approach

In this paper, an approach for reliability-based design optimization of reinforced concrete cantilever retaining wall is described. A parametric study is conducted to assess the effect of uncertainties in design parameters on the probability of failure of cantilever retaining walls. In total, ten modes of failure are considered, viz. overturning of the wall about its toe, sliding of the wall on its base, eccentricity, bearing capacity failure below the base slab, and shear and moment failure in the toe slab, heel slab, and stem. The analysis is performed by treating backfill and foundation soil properties, geometric properties of wall, and reinforcement and concrete properties as random variables. These results are used to develop a set of reliability-based design charts for different coefficients of variation of friction angle of backfill soil (5 and 10%) and targeting reliability index (βt) in the range of 3–3.2 for all failure modes. A comparative study is also presented, which shows that optimized sections have less areas of cross section compared to those obtained from specifications on dimensioning of retaining walls available in literature.     

A prospectively planned cumulative meta-analysis applied to a series of concurrent clinical trials

Sequential designs are now a familiar part of clinical trial methodology. In particular, the triangular test has been used in several individual studies. Methods of combining studies are also well-known from the literature on meta-analysis. However, the combination of the two approaches is new. Consider the situation where a series of studies is to be conducted, following broadly similar protocols comparing a new treatment with a control treatment. In order to obtain an answer as quickly as possible to an efficacy or safety question it may be desirable to perform a cumulative meta-analysis on one particular variable. This could, for example, be the primary efficacy variable, an expensive assessment conducted in only a subgroup of patients, or a serious side-effect. To allow for the size of the treatment difference varying from study to study we might wish to provide a global estimate. Hence a random effects combined analysis, within a sequential framework, would appear to be appropriate. A methodology which utilizes efficient score statistics and Fisher's information is presented. Simulations show that the proposed methodology will achieve the specified error probabilities with reasonable accuracy provided that any random effect is relatively small. Ignoring random effects when they are present can lead to inaccuracies. A simulated example illustrates a number of practical issues.     

Assessment of Variable Uncertainties for Reliability-Based Design of Foundations

LRFD shows promise as a viable alternative to the present working stress design (WSD) approach to shallow foundation design. The key improvements of LRFD over the traditional WSD are the ability to provide a more consistent level of reliability and the possibility of accounting for load and resistance uncertainties separately. For LRFD to gain acceptance in geotechnical engineering, a framework for the objective assessment of resistance factors is needed. Such a framework, based on reliability analysis, is proposed in this paper. Probability density functions (PDFs), representing design variable uncertainties, are required for analysis. A systematic approach to the selection of PDFs is presented. A procedure such as that proposed provides a rational probabilistic basis for the development of LRFD methods in geotechnical engineering.     

Multiple Resistance Factor Design for Shallow Transmission Line Structure Foundations

This paper presents the development of simplified reliability-based design (RBD) equations that are suitable for spread foundations subjected to uplift. Emphasis is placed on the loading and foundation characteristics relevant to the electric utility industry. A general reliability calibration procedure is used to derive robust resistance/deformation factors for load and resistance factor design (LRFD) and multiple resistance factor design (MRFD) formats. Two target reliability indices of 3.2 and 2.6 are proposed based on an extensive study of existing designs for ultimate and serviceability limit state, respectively. The main advantage of using these RBD factors is that a known level of reliability can be consistently achieved over a wide range of design conditions. Simple design calculations using the MRFD format are shown to demonstrate their ability to account for parametric uncertainties in a rational manner.     

Numerical Approximations of Design Points in Reliability Analysis under Parametric Changes

Traditional approaches for repeatedly updating reliability estimates, as needed in reliability-based optimal designs or real-time system control, require the iterative application of a reliability method. This paper explores a new strategy for repeatedly estimating reliability under frequent parameter variations. The central idea is to update the design point in the parameter domain, rather than in the traditional random variable domain, by evaluating several parametric sensitivity measures which are systems of nonlinear first-order ordinary differential equations relating the design point to parameter changes. Four numerical algorithms for evaluating the sensitivity measures are developed using the Euler and the improved Euler algorithms. Two solution procedures are applied. One procedure solves for the updated design point directly, while the other solves for both the unit normal vector at the design point and the reliability index separately, and evaluates the product of these to determine the updated design point. The numerical techniques are thoroughly compared with the classical Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm in five numerical examples regarding efficiency and accuracy. It is found that they are efficient and robust under given conditions.     

A Methodology For Design And Operation Of Heap Leaching Systems

Leaching is a hydrometallurgical activity widely used in mineral processing, both for metallic and non-metallic ores, and in soil remediation. The dissolution of valuable species by heap leaching is strongly dependent on the design and operating variables, so the study of the influence of these variables on recovery and their optimization for the best performance are attractive tasks for the development of the mining industry. In this work, a methodology is developed that enables the planning and design of leaching systems. This methodology uses a proposed superstructure and a mathematical model to analyze the system behavior and determine the optimal design and operating conditions. The model was generated with a Mixed Integer Nonlinear Programming (MINLP) approach and solved by different solvers under GAMS® software (General Algebraic Modelling System). The Spatial Branch-and-Bound (SBB) solver obtained the global optimum in the shortest times. Based on a case of study for copper leaching, it is demonstrated that the procedure allows achieving optimal design and operational conditions.     

Modelling risk from a disease in time and space

This paper combines existing models for longitudinal and spatial data in a hierarchical Bayesian framework, with particular emphasis on the role of time- and space-varying covariate effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by a tentative re-analysis of Ohio lung cancer data 1968-1988. Two approaches that adjust for unmeasured spatial covariates, particularly tobacco consumption, are described. The first includes random effects in the model to account for unobserved heterogeneity; the second adds a simple urbanization measure as a surrogate for smoking behaviour. The Ohio data set has been of particular interest because of the suggestion that a nuclear facility in the southwest of the state may have caused increased levels of lung cancer there. However, we contend here that the data are inadequate for a proper investigation of this issue.