Ismail Farajpour

Error and Uncertainty Analysis of Inexact and Imprecise Computer Models

Computer simulations are routinely executed to predict the behavior of complex systems in many fields of engineering and science. These computer-aided predictions involve the theoretical foundation, numerical modeling, and supporting experimental data, all of which come with their associated errors. A natural question then arises concerning the validity of computer model predictions, especially in cases where these models are executed in support of high-consequence decision making. This article lays out a methodology for quantifying the degrading effects of incompleteness and inaccuracy of the theoretical foundation, numerical modeling, and experimental data on the computer model predictions. Through the method discussed in this paper, the validity of model predictions can be judged and communicated between involved parties in a quantitative and objective manner. DOI: 10.1061/(ASCE)CP.1943-5487.0000233.

Optimization-Based Strong Coupling Procedure for Partitioned Analysis

AbstractThe concept of partitioning a complex engineering problem into smaller, manageable components and investigating each individual component autonomously has been in use for many decades. Such partitioning approaches, however, rely on strong and occasional unwarranted assumptions regarding the interactions among different engineering components. Fluid and structure interaction, soil and structure interaction, and human and structure interaction are but a few of the many such partitioned analyses commonly needed in civil engineering applications. Recently, there has been a growing interest in combining the expertise developed separately in traditionally distinct fields to obtain a holistic treatment of engineering problems. Such holistic treatment would ultimately yield not only more realistic and accurate analyses of coupled systems but also improved optimality in engineering designs. This growing interest has resulted in development of mathematical coupling procedures for conjoining multiple, separa...

Partitioned Analysis of Coupled Numerical Models Considering Imprecise Parameters and Inexact Models

The present study develops an integrated coupling and uncertainty quantification framework for strongly coupled models that explicitly considers the propagation of uncertainty and bias inherent in model prediction between constituents during the iterative coupling process. Utilizing optimization techniques, three distinct configurations are formulated that differ in sequence of coupling and uncertainty quantification campaigns. Focusing on a controlled structural dynamics problem, the systematic biases from the constituents are quantified, from which the critical components of the model that require further improvement can be identified to aid in the prioritization of future code development efforts. DOI: 10.1061/(ASCE)CP.1943-5487.0000253.

Constrained optimization of structures with displacement constraints under various loading conditions

Optimization problems often involve constraints and restrictions which must be considered in order to obtain an optimum result and the resultant solution should not deviate from any of the imposed constraints. These constraints and restrictions are imposed either on the design variables or on the algebraic relations between them. Constraints of allowable stress, minimum size and buckling of members in the absence of allowable displacement constraint are the most important factors in optimization of the cross-sectional area of structural elements. When the allowable displacement constraint is included in the problem as a determinant parameter, since the specifications of most of elements affect the displacement rate, the way of imposing and considering this constraint requires special care. In this research the way of simultaneous imposition of multi displacement constraints for optimum design of truss structures in several load cases is described. In this method various constraints for different load cases are divided into active and passive constraints. The mathematical formulation is based on the classical method of Lagrange Multipliers. Overall, this simple method can be employed along with other constraints such as buckling, allowable stress and minimum size of members for imposing the displacement constraint in various load cases.

Adaptively Weighted Support Vector Regression: Prognostic Application to a Historic Masonry Fort

AbstractPrognostic evaluation involves constructing a prediction model based on available measurements to forecast the health state of an engineering system. One particular prognostic technique, support vector regression, has had successful applications because of its ability to compromise between fitting accuracy and model complexity in training prediction models. In civil engineering applications, compromise between fitting accuracy and model complexity depends primarily on the measured response of the system to loads other than those that are of interest for prognostic evaluation, referred to as extraneous noise in this paper. To achieve accurate prognostic evaluation in the presence of such extraneous noise, this paper presents an approach for optimally weighing fitting accuracy and complexity of a support vector regression model in an iterative manner as new measurements become available. The proposed approach is demonstrated in prognostic evaluation of the structural condition of a historic masonry ...

Resource allocation for code development in partitioned models

Purpose – Physical phenomena interact with each other in ways that one cannot be analyzed without considering the other. To account for such interactions between multiple phenomena, partitioning has become a widely implemented computational approach. Partitioned analysis involves the exchange of inputs and outputs from constituent models (partitions) via iterative coupling operations, through which the individually developed constituent models are allowed to affect each other’s inputs and outputs. Partitioning, whether multi-scale or multi-physics in nature, is a powerful technique that can yield coupled models that can predict the behavior of a system more complex than the individual constituents themselves. The paper aims to discuss these issues. Design/methodology/approach – Although partitioned analysis has been a key mechanism in developing more realistic predictive models over the last decade, its iterative coupling operations may lead to the propagation and accumulation of uncertainties and errors ...

Analysis of Numerical Errors in Strongly Coupled Numerical Models

This manuscript focuses on the degrading effects of discretization errors on the simulation results of strongly coupled models. Coupled simulation models, be they multi-scale or multi-physics in nature, in recent years, have gained significant attention for their ability to predict the behavior of complex physical systems by implementing mature, independently developed, constituent models. This investigation evaluates the numerical errors inherent in the predictions of the constituent models and their effects on the predictions of the coupled model. Not only are the discretization errors of each constituent model quantified as they propagate from one constituent to the other during coupling iterations, but their effects on the computational requirements of the coupling procedure are also considered. Furthermore, the sensitivity of the coupled model predictions to each constituent is determined allowing a thorough evaluation of the impact of discretization errors on coupled model predictions. These relationships are demonstrated through a case study of a strongly coupled dynamical system.

Ranking Constituents of Coupled Models for Improved Performance

In partitioned analysis, constituent models representing different scales or physics are routinely coupled to simulate complex physical systems. Such constituent models are invariably imperfect and thus, yield a degree of disagreement with reality, known as model form error. This error propagates through coupling interfaces and degrades the accuracy of the coupled system. To efficiently improve the coupled system, resources must be allocated to systematically improve the constituent models. This study proposes a tool and an associated metric that exploits the availability of experimental data to prioritize constituent models. This metric is useful in tracing the error of coupled systems to their origins and to quantify the contribution of constituent error to the overall error of coupled systems. The proposed metric is used to rank constituents based on (i) the relative model form error of the constituents, (ii) the sensitivity of the model form error of the coupled system to the model form error in the constituents, and (iii) the cost to improve their performance. The applicability of the proposed metric is demonstrated through a proof-of-concept structural example, by coupling individual frame elements to model a portal frame. Coupling and uncertainty inference of the inexact constituent models are achieved using optimization, where both separate-effect and integral-effect experiments are employed to train the model form error of the constituents and coupled system.

A Combined Experimental and Numerical Study: Linking Vibration Response to Load Carrying Capacity of a Masonry Dome

In this manuscript, the authors present a combined experimental and numerical study that empirically links measured vibration response characteristics to the remaining load carrying capacity of a masonry dome as the structure is gradually damaged with discrete and distributed cracks. First, the three-dimensional, nonlinear finite element model of the dome is calibrated using both nondestructive vibration response measurements and destructive load displacement tests. The gradual development of major, discrete cracks is simulated by introducing a mesh discontinuity, while the development of minor, distributed cracks is incorporated by the inherent smeared cracking capability of the finite elements. The calibrated numerical model is used to estimate degradation in both the strength and stiffness of the dome, indicated by a reduction of the load carrying capacity, and by the reduction in natural frequencies, respectively. An empirical function is trained to link the reduction in natural frequencies (a quantity related to stiffness that is feasibly measurable), and the remaining load carrying capacity (a quantity related to strength that is not feasibly measurable) for spherical domes. This empirical relationship is generalized for spherical domes with different span-to-height ratios.

Robust Design Optimization to Account for Uncertainty in the Structural Design Process

Structural systems are subject to inherent uncertainties due to the variability in many hard-to-control ‘noise factors’ including but not limited to external loads, material properties, and construction workmanship. Two design methodologies were developed to quantify the variability associated with the design process: Allowable Stress Design (ASD) and Load and Resistance Factor Design (LRFD). These traditional approaches explicitly recognize the presence of uncertainty, however they do not take robustness against this uncertainty into consideration. Overlooking robustness against uncertainty in the structural design process has two main problems. First, the design may not satisfy the safety requirements if the actual uncertainties in the noise factors are underestimated. Thus, the safety requirements can easily be violated because of the high variation of the system response due to noise factors. Second, to guarantee safety in the presence of this high variability of the system response, the structural designer may be forced to choose an overly conservative, inefficient and thus costly design. When the robustness against uncertainty is not treated as one of the design objectives, this trade-off between the over-design for safety and the under-design for cost-savings is exacerbated. This paper demonstrates that safe and cost-effective designs are achievable by implementing Robust Design concepts originally developed in manufacturing engineering to proactively consider the robustness against uncertainty as one of the design objectives. Robust Design concepts can be used to formulate structural designs which are insensitive to inherent variability in the design process, thus save cost, and exceed the main objectives of user safety and serviceability. This paper presents two methodologies for the application of Robust Design principles to structural design utilizing two optimization schemes: one-at-a-time optimization method and Particle Swarm Optimization (PSO) method.