A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty

In this paper, the effects of uncertainty and expected costs of failure on optimum structural design are investigated, by comparing three distinct formulations of structural optimization problems. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation grossly neglects parameter uncertainty and its effects on structural safety. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probabilities used as constraints in the analysis. Risk optimization (RO) increases the scope of the problem by addressing the compromising goals of economy and safety. This is accomplished by quantifying the monetary consequences of failure, as well as the costs associated with construction, operation and maintenance. RO yields the optimum topology and the optimum point of balance between economy and safety. Results are compared for some example problems. The broader RO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when optimum safety coefficients are used as constraints in DDO, the formulation leads to configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs (including expected costs of failure). When (optimum) system failure probability is used as a constraint in RBDO, this solution also reduces manufacturing costs but by increasing total expected costs. This happens when the costs associated with different failure modes are distinct. Hence, a general equivalence between the formulations cannot be established. Optimum structural design considering expected costs of failure cannot be controlled solely by safety factors nor by failure probability constraints, but will depend on actual structural configuration. (c) 2011 Elsevier Ltd. All rights reserved.

New Optimization Algorithms for Structural Reliability Analysis

Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.

Reliability-based design optimization strategies based on FORM: a review

In deterministic optimization, the uncertainties of the structural system (i.e. dimension, model, material, loads, etc) are not explicitly taken into account. Hence, resulting optimal solutions may lead to reduced reliability levels. The objective of reliability based design optimization (RBDO) is to optimize structures guaranteeing that a minimum level of reliability, chosen a priori by the designer, is maintained. Since reliability analysis using the First Order Reliability Method (FORM) is an optimization procedure itself, RBDO (in its classical version) is a double-loop strategy: the reliability analysis (inner loop) and the structural optimization (outer loop). The coupling of these two loops leads to very high computational costs. To reduce the computational burden of RBDO based on FORM, several authors propose decoupling the structural optimization and the reliability analysis. These procedures may be divided in two groups: (i) serial single loop methods and (ii) unilevel methods. The basic idea of serial single loop methods is to decouple the two loops and solve them sequentially, until some convergence criterion is achieved. On the other hand, uni-level methods employ different strategies to obtain a single loop of optimization to solve the RBDO problem. This paper presents a review of such RBDO strategies. A comparison of the performance (computational cost) of the main strategies is presented for several variants of two benchmark problems from the literature and for a structure modeled using the finite element method.

Improved ground motion intensity measures for reliability-based demand analysis of structures

In Performance-Based Earthquake Engineering (PBEE), evaluating the seismic performance (or seismic risk) of a structure at a designed site has gained major attention, especially in the past decade. One of the objectives in PBEE is to quantify the seismic reliability of a structure (due to the future random earthquakes) at a site. For that purpose, Probabilistic Seismic Demand Analysis (PSDA) is utilized as a tool to estimate the Mean Annual Frequency (MAF) of exceeding a specified value of a structural Engineering Demand Parameter (EDP). This dissertation focuses mainly on applying an average of a certain number of spectral acceleration ordinates in a certain interval of periods, Sa,avg (T1,…,Tn), as scalar ground motion Intensity Measure (IM) when assessing the seismic performance of inelastic structures. Since the interval of periods where computing Sa,avg is related to the more or less influence of higher vibration modes on the inelastic response, it is appropriate to speak about improved IMs. The results using these improved IMs are compared with a conventional elastic-based scalar IMs (e.g., pseudo spectral acceleration, Sa ( T(¹)), or peak ground acceleration, PGA) and the advanced inelastic-based scalar IM (i.e., inelastic spectral displacement, Sdi). The advantages of applying improved IMs are: (i ) "computability" of the seismic hazard according to traditional Probabilistic Seismic Hazard Analysis (PSHA), because ground motion prediction models are already available for Sa (Ti), and hence it is possibile to employ existing models to assess hazard in terms of Sa,avg, and (ii ) "efficiency" or smaller variability of structural response, which was minimized to assess the optimal range to compute Sa,avg. More work is needed to assess also "sufficiency" and "scaling robustness" desirable properties, which are disregarded in this dissertation. However, for ordinary records (i.e., with no pulse like effects), using the improved IMs is found to be more accurate than using the elastic- and inelastic-based IMs. For structural demands that are dominated by the first mode of vibration, using Sa,avg can be negligible relative to the conventionally-used Sa (T(¹)) and the advanced Sdi. For structural demands with sign.cant higher-mode contribution, an improved scalar IM that incorporates higher modes needs to be utilized. In order to fully understand the influence of the IM on the seismis risk, a simplified closed-form expression for the probability of exceeding a limit state capacity was chosen as a reliability measure under seismic excitations and implemented for Reinforced Concrete (RC) frame structures. This closed-form expression is partuclarly useful for seismic assessment and design of structures, taking into account the uncertainty in the generic variables, structural "demand" and "capacity" as well as the uncertainty in seismic excitations. The assumed framework employs nonlinear Incremental Dynamic Analysis (IDA) procedures in order to estimate variability in the response of the structure (demand) to seismic excitations, conditioned to IM. The estimation of the seismic risk using the simplified closed-form expression is affected by IM, because the final seismic risk is not constant, but with the same order of magnitude. Possible reasons concern the non-linear model assumed, or the insufficiency of the selected IM. Since it is impossibile to state what is the "real" probability of exceeding a limit state looking the total risk, the only way is represented by the optimization of the desirable properties of an IM.

A probabilistic approach to classify the levee reliability

This work aims to evaluate the reliability of these levee systems, calculating the probability of “failure” of determined levee stretches under different loads, using probabilistic methods that take into account the fragility curves obtained through the Monte Carlo Method. For this study overtopping and piping are considered as failure mechanisms (since these are the most frequent) and the major levee system of the Po River with a primary focus on the section between Piacenza and Cremona, in the lower-middle area of the Padana Plain, is analysed. The novelty of this approach is to check the reliability of individual embankment stretches, not just a single section, while taking into account the variability of the levee system geometry from one stretch to another. This work takes also into consideration, for each levee stretch analysed, a probability distribution of the load variables involved in the definition of the fragility curves, where it is influenced by the differences in the topography and morphology of the riverbed along the sectional depth analysed as it pertains to the levee system in its entirety. A type of classification is proposed, for both failure mechanisms, to give an indication of the reliability of the levee system based of the information obtained by the fragility curve analysis. To accomplish this work, an hydraulic model has been developed where a 500-year flood is modelled to determinate the residual hazard value of failure for each stretch of levee near the corresponding water depth, then comparing the results with the obtained classifications. This work has the additional the aim of acting as an interface between the world of Applied Geology and Environmental Hydraulic Engineering where a strong collaboration is needed between the two professions to resolve and improve the estimation of hydraulic risk.

Development of the Heat and Energy Concept Inventory: Preliminary Results on the Prevalence and Persistence of Engineering Students' Misconceptions

BACKGROUND Students frequently hold a number of misconceptions related to temperature, heat and energy. There is not currently a concept inventory with sufficiently high internal reliability to assess these concept areas for research purposes. Consequently, there is little data on the prevalence of these misconceptions amongst undergraduate engineering students. PURPOSE (HYPOTHESIS) This work presents the Heat and Energy Concept Inventory (HECI) to assess prevalent misconceptions related to: (1) Temperature vs. Energy, (2) Temperature vs. Perceptions of Hot and Cold, (3) Factors that affect the Rate vs. Amount of Heat Transfer and (4) Thermal Radiation. The HECI is also used to document the prevalence of misconceptions amongst undergraduate engineering students. DESIGN/METHOD Item analysis, guided by classical test theory, was used to refine individual questions on the HECI. The HECI was used in a one group, pre-test-post-test design to assess the prevalence and persistence of targeted misconceptions amongst a population of undergraduate engineering students at diverse institutions. RESULTS Internal consistency reliability was assessed using Kuder-Richardson Formula 20; values were 0.85 for the entire instrument and ranged from 0.59 to 0.76 for the four subcategories of the HECI. Student performance on the HECI went from 49.2% to 54.5% after instruction. Gains on each of the individual subscales of the HECI, while generally statistically significant, were similarly modest. CONCLUSIONS The HECI provides sufficiently high estimates of internal consistency reliability to be used as a research tool to assess students' understanding of the targeted concepts. Use of the instrument demonstrates that student misconceptions are both prevalent and resistant to change through standard instruction.

Multi-node TOA-DOA cooperative LOS-NLOS localization : enabling high accuracy and reliability

This dissertation investigates high performance cooperative localization in wireless environments based on multi-node time-of-arrival (TOA) and direction-of-arrival (DOA) estimations in line-of-sight (LOS) and non-LOS (NLOS) scenarios. Here, two categories of nodes are assumed: base nodes (BNs) and target nodes (TNs). BNs are equipped with antenna arrays and capable of estimating TOA (range) and DOA (angle). TNs are equipped with Omni-directional antennas and communicate with BNs to allow BNs to localize TNs; thus, the proposed localization is maintained by BNs and TNs cooperation. First, a LOS localization method is proposed, which is based on semi-distributed multi-node TOA-DOA fusion. The proposed technique is applicable to mobile ad-hoc networks (MANETs). We assume LOS is available between BNs and TNs. One BN is selected as the reference BN, and other nodes are localized in the coordinates of the reference BN. Each BN can localize TNs located in its coverage area independently. In addition, a TN might be localized by multiple BNs. High performance localization is attainable via multi-node TOA-DOA fusion. The complexity of the semi-distributed multi-node TOA-DOA fusion is low because the total computational load is distributed across all BNs. To evaluate the localization accuracy of the proposed method, we compare the proposed method with global positioning system (GPS) aided TOA (DOA) fusion, which are applicable to MANETs. The comparison criterion is the localization circular error probability (CEP). The results confirm that the proposed method is suitable for moderate scale MANETs, while GPS-aided TOA fusion is suitable for large scale MANETs. Usually, TOA and DOA of TNs are periodically estimated by BNs. Thus, Kalman filter (KF) is integrated with multi-node TOA-DOA fusion to further improve its performance. The integration of KF and multi-node TOA-DOA fusion is compared with extended-KF (EKF) when it is applied to multiple TOA-DOA estimations made by multiple BNs. The comparison depicts that it is stable (no divergence takes place) and its accuracy is slightly lower than that of the EKF, if the EKF converges. However, the EKF may diverge while the integration of KF and multi-node TOA-DOA fusion does not; thus, the reliability of the proposed method is higher. In addition, the computational complexity of the integration of KF and multi-node TOA-DOA fusion is much lower than that of EKF. In wireless environments, LOS might be obstructed. This degrades the localization reliability. Antenna arrays installed at each BN is incorporated to allow each BN to identify NLOS scenarios independently. Here, a single BN measures the phase difference across two antenna elements using a synchronized bi-receiver system, and maps it into wireless channel’s K-factor. The larger K is, the more likely the channel would be a LOS one. Next, the K-factor is incorporated to identify NLOS scenarios. The performance of this system is characterized in terms of probability of LOS and NLOS identification. The latency of the method is small. Finally, a multi-node NLOS identification and localization method is proposed to improve localization reliability. In this case, multiple BNs engage in the process of NLOS identification, shared reflectors determination and localization, and NLOS TN localization. In NLOS scenarios, when there are three or more shared reflectors, those reflectors are localized via DOA fusion, and then a TN is localized via TOA fusion based on the localization of shared reflectors.

Improvement of Mechanical Properties and Life Extension of High Reliability Structural Components by Laser Shock Processing

Profiting by the increasing availability of laser sources delivering intensities above 109 W/cm2 with pulse energies in the range of several Joules and pulse widths in the range of nanoseconds, laser shock processing (LSP) is being consolidating as an effective technology for the improvement of surface mechanical and corrosion resistance properties of metals and is being developed as a practical process amenable to production engineering. The main acknowledged advantage of the laser shock processing technique consists on its capability of inducing a relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly, the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Following a short description of the theoretical/computational and experimental methods developed by the authors for the predictive assessment and experimental implementation of LSP treatments, experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (specifically Al and Ti alloys) under different LSP irradiation conditions are presented. In particular, the analysis of the residual stress profiles obtained under different irradiation parameters and the evaluation of the corresponding induced surface properties as roughness and wear resistance are presented.

Reliability of tunnel liners

The possibility of application of structural reliability theory to the computation of the safety margins of excavated tunnels is presented. After a brief description of the existing procedures the limitations of the safety coefficients such as they usually defined, the proposed limit states are precised as well as the random variables and the applied methodology. Also presented are simple examples, some of them based in actual cases, and to end, some conclusions are established the most important one being the probability of using the method to solve the inverse problem of identification.

Level II reliability methods for tunnels

In tunnel construction, as in every engineering work, it is usual the decision making, with incomplete data. Nevertheless, consciously or not, the builder weighs the risks (even if this is done subjectively) so that he can offer a cost. The objective of this paper is to recall the existence of a methodology to treat the uncertainties in the data so that it is possible to see their effect on the output of the computational model used and then to estimate the failure probability or the safety margin of a structure. In this scheme it is possible to include the subjective knowledge on the statistical properties of the random variables and, using a numerical model consistent with the degree of complexity appropiate to the problem at hand, to make rationally based decisions. As will be shown with the method it is possible to quantify the relative importance of the random variables and, in addition, it can be used, under certain conditions, to solve the inverse problem. It is then a method very well suited both to the project and to the control phases of tunnel construction.

Level 2 reliability of simplified pushover methods

Pushover methods are being used as an everyday tool in engineering practice and some of them have been included in Regulatory Codes. Recently several efforts have been done trying to look at them from a probabilistic viewpoint. In this paper the authors shall present a Level 2 approach based on a probabilistic definition of the characteristic points defining the response spectra as well as a probabilistic definition of the elasto-plastic pushover curve representing the structural behavior. Comparisons with Montecarlo simulations will help to precise the accuracy of the proposed approach.

Induction of engineered residual stresses fields and enhancement of fatigue life of high reliability metallic components by laser shock processing

Laser shock processing (LSP) is being increasingly applied as an effective technology for the improvement of metallic materials mechanical and surface properties in different types of components as a means of enhancement of their corrosion and fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, follow-on experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (especially Al and Ti alloys characteristic of high reliability components in the aerospace, nuclear and biomedical sectors) under different LSP irradiation conditions are presented along with a practical correlated analysis on the protective character of the residual stress profiles obtained under different irradiation strategies. Additional remarks on the improved character of the LSP technique over the traditional “shot peening” technique in what concerns depth of induced compressive residual stresses fields are also made through the paper

Application of Bayesian approach in geotechnical engineering

En esta Tesis Doctoral se emplean y desarrollan Métodos Bayesianos para su aplicación en análisis geotécnicos habituales, con un énfasis particular en (i) la valoración y selección de modelos geotécnicos basados en correlaciones empíricas; en (ii) el desarrollo de predicciones acerca de los resultados esperados en modelos geotécnicos complejos. Se llevan a cabo diferentes aplicaciones a problemas geotécnicos, como es el caso de: (1) En el caso de rocas intactas, se presenta un método Bayesiano para la evaluación de modelos que permiten estimar el módulo de Young a partir de la resistencia a compresión simple (UCS). La metodología desarrollada suministra estimaciones de las incertidumbres de los parámetros y predicciones y es capaz de diferenciar entre las diferentes fuentes de error. Se desarrollan modelos "específicos de roca" para los tipos de roca más comunes y se muestra cómo se pueden "actualizar" esos modelos "iniciales" para incorporar, cuando se encuentra disponible, la nueva información específica del proyecto, reduciendo las incertidumbres del modelo y mejorando sus capacidades predictivas. (2) Para macizos rocosos, se presenta una metodología, fundamentada en un criterio de selección de modelos, que permite determinar el modelo más apropiado, entre un conjunto de candidatos, para estimar el módulo de deformación de un macizo rocoso a partir de un conjunto de datos observados. Una vez que se ha seleccionado el modelo más apropiado, se emplea un método Bayesiano para obtener distribuciones predictivas de los módulos de deformación de macizos rocosos y para actualizarlos con la nueva información específica del proyecto. Este método Bayesiano de actualización puede reducir significativamente la incertidumbre asociada a la predicción, y por lo tanto, afectar las estimaciones que se hagan de la probabilidad de fallo, lo cual es de un interés significativo para los diseños de mecánica de rocas basados en fiabilidad. (3) En las primeras etapas de los diseños de mecánica de rocas, la información acerca de los parámetros geomecánicos y geométricos, las tensiones in-situ o los parámetros de sostenimiento, es, a menudo, escasa o incompleta. Esto plantea dificultades para aplicar las correlaciones empíricas tradicionales que no pueden trabajar con información incompleta para realizar predicciones. Por lo tanto, se propone la utilización de una Red Bayesiana para trabajar con información incompleta y, en particular, se desarrolla un clasificador Naïve Bayes para predecir la probabilidad de ocurrencia de grandes deformaciones (squeezing) en un túnel a partir de cinco parámetros de entrada habitualmente disponibles, al menos parcialmente, en la etapa de diseño. This dissertation employs and develops Bayesian methods to be used in typical geotechnical analyses, with a particular emphasis on (i) the assessment and selection of geotechnical models based on empirical correlations; on (ii) the development of probabilistic predictions of outcomes expected for complex geotechnical models. Examples of application to geotechnical problems are developed, as follows: (1) For intact rocks, we present a Bayesian framework for model assessment to estimate the Young’s moduli based on their UCS. Our approach provides uncertainty estimates of parameters and predictions, and can differentiate among the sources of error. We develop ‘rock-specific’ models for common rock types, and illustrate that such ‘initial’ models can be ‘updated’ to incorporate new project-specific information as it becomes available, reducing model uncertainties and improving their predictive capabilities. (2) For rock masses, we present an approach, based on model selection criteria to select the most appropriate model, among a set of candidate models, to estimate the deformation modulus of a rock mass, given a set of observed data. Once the most appropriate model is selected, a Bayesian framework is employed to develop predictive distributions of the deformation moduli of rock masses, and to update them with new project-specific data. Such Bayesian updating approach can significantly reduce the associated predictive uncertainty, and therefore, affect our computed estimates of probability of failure, which is of significant interest to reliability-based rock engineering design. (3) In the preliminary design stage of rock engineering, the information about geomechanical and geometrical parameters, in situ stress or support parameters is often scarce or incomplete. This poses difficulties in applying traditional empirical correlations that cannot deal with incomplete data to make predictions. Therefore, we propose the use of Bayesian Networks to deal with incomplete data and, in particular, a Naïve Bayes classifier is developed to predict the probability of occurrence of tunnel squeezing based on five input parameters that are commonly available, at least partially, at design stages.