CTAN for Risk Assessments Using Multilevel Stochastic Networks

Measuring projects’ cost and schedule risks in an integrated framework using simulation has several modeling challenges that have yet to be addressed by researchers. This paper presents a multilevel network modeling approach that aims to integrate a combination of different networks in one framework, and presents a computer simulation implementation to the cost and time risk assessment network (CTAN). The CTAN is an integrated network that includes uncertainties in the realization of the schedule logic, in activities durations, in project scope, and in cost. The simulation model is a decision support simulation system (DSSS) that currently consists of three modules: the CTAN, the stochastic decision trees, and the stochastic shortest/longest rout network. The CTAN-DSSS may be used in cost and schedule risk assessment. It completely integrates with other DSSS networks and deals with risks associated with cost, time, and scope at equal importance. The DSSS was verified by conducting several tests and validated by its extensive use for both undergraduate and graduate courses in Civil Engineering at the University of Calgary over the last three years.     

Stochastic Flow Analysis for Predicting River Scour of Cohesive Soils

Damage to bridge crossings during flood events endangers the lives of the traveling public and causes costly disruptions to traffic flow. The most common causes of bridge collapse are scouring of the streambed and banks and erosion of highway embankments. This study couples a synthetic river flow simulation technique with a scour model for cohesive soils and determines the expected scour depth for a given lifetime of the bridge. A fractionally differenced autoregressive integrated moving average model generates synthetic streamflow sequences of the same length as the expected lifetime of the bridge. The scour model predicts the progression of scour depth through time in a multilayered soil. The model is used to determine the scour depth associated with different replicates of the synthetic flow sequences of the same length as the lifetime of the bridge. The probability distribution of scour depth is estimated by repeating this simulation procedure over a number of independent realizations of streamflow series for a given life of the bridge. This approach provides a framework for the probabilistic design and risk analysis of bridge foundations subjected to scour.     

Stochastic Response and Stability of a Nonintegrable System

For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method.     

Stochastic Finite-Element Analysis of Seismic Soil–Structure Interaction

A procedure is presented for the probabilistic analysis of the seismic soil-structure interaction problem. The procedure accounts for uncertainty in both the free-field input motion as well as in local site conditions, and structural parameters. Uncertain parameters are modeled using a probabilistic framework as stochastic processes. The site amplification effects are accounted for via a randomized relationship between the soil shear modulus and damping on the one hand, and the shear strain of the subgrade on the other hand, as well as by modeling the shear modulus at low strain level as randomly fluctuating with depth. The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented by their coordinates with respect to the polynomial chaos basis. These coordinates are then evaluated by a combination of weighted residuals and stratified sampling schemes. The expansion can be used to carry out very efficiently, extensive Monte Carlo simulations. The procedure is applied to the seismic analysis of a nuclear reactor facility.     

Stochastic Modeling of Deterioration Processes through Dynamic Bayesian Networks

A generic framework for stochastic modeling of deterioration processes is proposed, based on dynamic Bayesian networks. The framework facilitates computationally efficient and robust reliability analysis and, in particular, Bayesian updating of the model with measurements, monitoring, and inspection results. These properties make it ideally suited for near-real time applications in asset integrity management and deterioration control. The framework is demonstrated and investigated through two applications to probabilistic modeling of fatigue crack growth.     

Safety Hazard Identification on Construction Projects

Hazard identification is fundamental to construction safety management; unidentified hazards present the most unmanageable risks. This paper presents an investigation indicating the current levels of hazard identification on three U.K. construction projects. A maximum of only 6.7% of the method statements analyzed on these projects managed to identify all of the hazards that should have been identified, based upon current knowledge. Maximum hazard identification levels were found to be 0.899 (89.9%) for a construction project within the nuclear industry, 0.728 (72.8%) for a project within the railway industry, and 0.665 (66.5%) for a project within both the railway and general construction industry sector. The results indicate that hazard identification levels are far from ideal. A discussion on the reasons for low hazard identification levels indicates key barriers. This leads to the presentation of an Information Technology (IT) tool for construction project safety management (Total-Safety) and, in particular, a module within Total-Safety designed to help construction personnel develop method statements with improved levels of hazard identification.     

Case-Based Reasoning Approach to Construction Safety Hazard Identification: Adaptation and Utilization

Risk assessment, consisting of hazard identification and risk analysis, is an important process that can prevent costly incidents. However, due to operational pressures and lack of construction experience, risk assessments are frequently poorly conducted. In order to improve the quality of risk assessments in the construction industry, it is important to explore the use of artificial intelligence methods to ensure that the process is efficient and at the same time thorough. This paper describes the adaptation process of a case-based reasoning (CBR) approach for construction safety hazard identification. The CBR approach aims to utilize past knowledge in the form of past hazard identification and incident cases to improve the efficiency and quality of new hazard identification. The overall approach and retrieval mechanism are described in earlier papers. This paper is focused on the adaptation process for hazard identification. Using the proposed CBR approach, for a new work scenario (the input case), a most relevant hazard identification tree and a set of incident cases will be retrieved to facilitate hazard identification. However, not all information contained in these cases are relevant. Thus, less relevant information has to be pruned off and all the retrieved information has to be integrated into a hazard identification tree. The proposed adaptation is conducted in three steps: (1) pruning of the retrieved hazard identification tree; (2) pruning of the incident cases; and (3) insertion of incident cases into the hazard identification tree. The adaptation process is based on the calculation of similarity scores of indexes. A case study based on actual hazard identifications and incident cases is used to validate the feasibility of the proposed adaptation techniques.     

Cost of Risk Transfer: Pricing Agreements in Residential Supply Chains

Theoretical and computational studies of supply chains are confined mainly to buyer-supplier dyads. Evaluation of more tiers in the construction sector specifically is also rare, perhaps in part because short-term partnerships are typical. However, supplier selection in residential construction is often conducted in support of multiple subdivision tracts over a comparatively long time-horizon. This paper describes the lumber supply chain for residential construction, extending from the homebuyer to the lumber company. A particular case for a real builder is examined in which a builder adopted a pricing strategy to control their lumber cost risk. The strategy included minimum time periods of fixed pricing, insulating the builder from price fluctuations during those periods. Consideration of supply-chain lead times allows financial risk modeling for the builder-framer/lumber yard–lumber company portion of the supply chain in order to evaluate the cost-effectiveness of this strategy. Historical records of lumber prices were used to conduct Monte Carlo simulations of three tiers of the supply chain. The pricing strategy is shown to result in a risk premium generally in excess of the true commodity price risk.     

Stochastic Response of an Inclined Shallow Cable with Linear Viscous Dampers under Stochastic Excitation

Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force at the dampers location and the first sine term as shape functions, a reduced four-degree-of-freedom system of nonlinear stochastic ordinary differential equations are derived to describe dynamic response of the cable. Since only polynomial-type terms are contained, the fourth-order cumulant-neglect closure together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level and viscous coefficient of the damper are fixed. Moreover, the peak frequency and half-band width of the spectra of both the in-plane and the out-of-plane displacements are increasing with excitation level when the damper size is constant. It is also observed that, even though the actual optimal damper size is slightly greater than the one obtained by the complex modal theory, the difference of statistical moment of the cable caused by these two damper size is negligible, so the vibration reduction effect provided by the theoretical optimal viscous coefficient is satisfactory.     

Polynomial Chaos Decomposition for the Simulation of Non-Gaussian Nonstationary Stochastic Processes

A method is developed for representing and synthesizing random processes that have been specified by their two-point correlation function and their nonstationary marginal probability density functions. The target process is represented as a polynomial transformation of an appropriate Gaussian process. The target correlation structure is decomposed according to the Karhunen–Loève expansion of the underlying Gaussian process. A sequence of polynomial transformations in this process is then used to match the one-point marginal probability density functions. The method results in a representation of a stochastic process that is particularly well suited for implementation with the spectral stochastic finite element method as well as for general purpose simulation of realizations of these processes.     

Stochastic Time–Cost Optimization Model Incorporating Fuzzy Sets Theory and Nonreplaceable Front

In a real construction project, the duration and cost of each activity could change dynamically as a result of many uncertain variables, such as weather, resource availability, productivity, etc. Managers/planners must take these uncertainties into account and provide an optimal balance of time and cost based on their own experience and knowledge. In this paper, fuzzy sets theory is applied to model the managers’ behavior in predicting time and cost pertinent to a specific option within an activity. Genetic algorithms are used as a searching mechanism to establish the optimal time–cost profiles under different risk levels. In addition, the nonreplaceable front concept is proposed to assist managers in recognizing promising solutions from numerous candidates on the Pareto front. Economic analysis skills, such as the utility theory and opportunity cost, are integrated into the new model to mimic the decision making process of human experts. A simple case study is used for testing the new model developed. In comparison with the previous models, the new model provides managers with greater flexibility to analyze their decisions in a more realistic manner. The results also indicate that greater robustness may be achieved by taking some risks. This research is relevant to both industry practitioners and researchers. By incorporating the concept of fuzzy sets, managers can represent the range of possible time–cost values as well as their associated degree of belief. The model presented in this paper can, therefore, support decision makers in analyzing their time–cost optimization decision in a more flexible and realistic manner. Many novel ideas have also been incorporated in this paper to benefit the research community. Examples of these include the use of fuzzy sets theory, nonreplaceable front concept, utility theory, opportunity cost, etc. With suitable modifications, these concepts can be applied to model to other similar optimization problems in construction.     

Stochastic Modeling for Pavement Warranty Cost Estimation

This paper presents a cost estimation model for long-term pavement warranties with multiple distress indicators. One application area for such warranties involves performance-based specifications (PBSs). In contrast to traditional approaches, PBS gives contractors the flexibility to select construction methods, materials, and even design. However, the contractors then must warrant the performance of their work for a specified period of time. Therefore, an accurate estimation of the risks associated with the warranty is a significant cost issue for any contractor to cover potential risks while still being competitive in bidding. Quantitative evaluation of the cost of risk incurred by the warranty has several difficulties. The deterioration of a highway project is a complex process, which is affected by pavement structure, material, traffic load, and weather conditions. Based on a probabilistic risk analysis of failures of performance indicators, the resulting model can estimate the warranty cost at a detailed level. The application of the model has been demonstrated via a numerical case study using long-term pavement performance data.     

Linear Stochastic Dynamical System under Uncertain Load: Inverse Reliability Analysis

The reliability of a linear dynamical system driven by a partially known Gaussian load process, specified only through its total average energy, is studied. A simple dynamic parallel and series system reliability network is investigated for the failure analysis using the crossing theory of stochastic processes. The critical input power spectral density of the load process which maximizes the mean crossing rate of a parallel or series system network emerges to be fairly narrow banded and hence fails to represent the erratic nature of the random input realistically. Consequently, a tradeoff curve between the maximum mean crossing rate of the reliability network and the disorder in the input, quantitatively measured through its entropy rate, is generated. Mathematically, the generation of the tradeoff curve of nondominated solutions, known as the Pareto optimal set, leads to a nonlinear, nonconvex, and multicriteria optimization problem with conflicting objectives. A recently developed Pareto optimization technique, implemented through genetic algorithm, has been successfully exploited to solve the optimization problem. A suitable exploitation of stochastic process theory circumvents the task of handling an apparent robust optimization problem (i.e., optimization under uncertainty) and at the same time, reduces the dimensionality of the multiobjective optimization scheme in view of both the multiobjectivity and constraints in the aforementioned methodology. The optimally disordered inputs which simulate the worst performance of the system of a spring-supported coupled rod assembly, has been studied as a numerical illustration of the mathematical formulation.     

Evaluation of Karhunen–Loève, Spectral, and Sampling Representations for Stochastic Processes

The Karhunen–Loève, spectral, and sampling representations, referred to as the KL, SP, and SA representations, are defined and some features/limitations of KL-, SP-, and SA-based approximations commonly used in applications are stated. Three test applications are used to evaluate these approximate representations. The test applications include (1) models for non-Gaussian processes; (2) Monte Carlo algorithms for generating samples of Gaussian and non-Gaussian processes; and (3) approximate solutions for random vibration problems with deterministic and uncertain system parameters. Conditions are established for the convergence of the solutions of some random vibration problems corresponding to KL, SP, and SA approximate representations of the input to these problems. It is also shown that the KL and SP representations coincide for weakly stationary processes.     

Simulation of Nonstationary Stochastic Processes by Spectral Representation

This paper presents a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly’s evolutionary spectral representation theory. Applying this formula, sample functions can be generated with great computational efficiency. The simulated stochastic process is asymptotically Gaussian as the number of terms tends to infinity. This paper shows that (1) these sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number of terms in the cosine series is large, i.e., the ensemble averaged evolutionary power spectral density function (PSDF) or autocorrelation function approaches the corresponding target function as the sample size increases, and (2) the simulation formula, under certain conditions, can be reduced to that for nonstationary white noise process or Shinozuka’s spectral representation of stationary process. In addition to derivation of simulation formula, three methods are developed in this paper to estimate the evolutionary PSDF of a given time-history data by means of the short-time Fourier transform (STFT), the wavelet transform (WT), and the Hilbert-Huang transform (HHT). A comparison of the PSDF of the well-known El Centro earthquake record estimated by these methods shows that the STFT and the WT give similar results, whereas the HHT gives more concentrated energy at certain frequencies. Effectiveness of the proposed simulation formula for nonstationary sample functions is demonstrated by simulating time histories from the estimated evolutionary PSDFs. Mean acceleration spectrum obtained by averaging the spectra of generated time histories are then presented and compared with the target spectrum to demonstrate the usefulness of this method.     

Risk and Price in the Bidding Process of Contractors

Formal and analytical risk models prescribe how risk should be incorporated into construction bids. However, the actual process of how contractors and their clients negotiate and agree to price is complex and not clearly articulated in the literature. With participant observation, the entire tender process was shadowed in two leading U.K. construction firms. This was compared with propositions in analytical models, and significant differences were found. A total of 670?h of work observed in both firms revealed three stages of the bidding process. Bidding activities were categorized and their extent estimated as deskwork (32%), calculations (19%), meetings (14%), documents (13%), off-days (11%), conversations (7%), correspondence (3%), and travel (1%). Risk allowances of 1–2% were priced in some bids, and three tiers of risk apportionment in bids were identified. However, priced risks may be excluded from the final bid to enhance competitiveness. Although risk apportionment affects a contractor’s pricing strategy, other complex microeconomic factors also affect price. Instead of including pricing contingencies, risk was priced primarily through contractual rather than price mechanisms to reflect commercial imperatives. These findings explain why some assumptions underpinning analytical models may not be sustainable in practice and why what actually happens in practice is important for those who seek to model the pricing of construction bids.     

Stochastic Time-Cost-Resource Utilization Optimization Using Nondominated Sorting Genetic Algorithm and Discrete Fuzzy Sets

In a construction project, the cost and duration of activities could change due to different uncertain variables such as weather, resource availability, etc. Resource leveling and allocation strategies also influence total time and costs of projects. In this paper, two concepts of time-cost trade-off and resource leveling and allocation have been embedded in a stochastic multiobjective optimization model which minimizes the total project time, cost, and resource moments. In the proposed time-cost-resource utilization optimization (TCRO) model, time and cost variables are considered to be fuzzy, to increase the flexibility for decision makers when using the model outputs. Application of fuzzy set theory in this study helps managers/planners to take these uncertainties into account and provide an optimal balance of time, cost, and resource utilization during the project execution. The fuzzy variables are discretized to represent different options for each activity. Nondominated sorting genetic algorithm (NSGA-II) has been used to solve the optimization problem. Results of the TCRO model for two different case studies of construction projects are presented in the paper. Total time and costs of the two case studies in the Pareto front solutions of the TCRO model cover more than 85% of the ranges of total time and costs of solutions of the biobjective time-cost optimization (TCO) model. The results show that adding the resource leveling capability to the previously developed TCO models provides more practical solutions in terms of resource allocation and utilization, which makes this research relevant to both industry practitioners and researchers.     

Fast and Accurate Risk Evaluation for Scheduling Large-Scale Construction Projects

This paper presents the development of a novel probabilistic scheduling model that enables fast and accurate risk evaluation for large-scale construction projects. The model is designed to overcome the limitations of existing probabilistic scheduling methods, including the inaccuracy of the program evaluation and review technique (PERT) and the long computational time of the Monte Carlo simulation method. The model consists of three main modules: PERT model; fast and accurate multivariate normal integral method; and a newly developed approximation method. The new approximation method is designed to focus the risk analysis on the most significant paths in the project network by identifying and removing insignificant paths that are either highly correlated or have high probability of completion time. The performance of the new model is analyzed using an application example. The results of this analysis illustrate that the new model was able to reduce the computational time for a large-scale construction project by more than 94% while keeping the error of its probability estimates to less than 3%, compared with Monte Carlo Simulation methods.