Mechanical and Structural Engineering

Abstract

Advances in sensor deployment and computational modeling have allowed significant strides to be recently made in the field of Structural Health Monitoring (SHM). One widely used SHM strategy is to perform a vibration analysis where a model of the structure’s pristine (undamaged) condition is compared with vibration response data collected from the physical structure. Discrepancies between model predictions and monitoring data can be interpreted as structural damage. Unfortunately, multiple sources of uncertainty must also be considered in the analysis, including environmental variability, unknown model functional forms, and unknown values of model parameters. Not accounting for these sources of uncertainty can lead to false-positives or false-negatives in the structural condition assessment. To manage the uncertainty, we propose a robust SHM methodology that combines three technologies. A time series algorithm is trained using “baseline” data to predict the vibration response, compare predictions to actual measurements collected on a potentially damaged structure, and calculate a user-defined damage indicator. The second technology handles the uncertainty present in the problem. An analysis of robustness is performed to propagate this uncertainty through the time series algorithm and obtain the corresponding bounds of variation of the damage indicator. The uncertainty description and robustness analysis are both inspired by the theory of info-gap decision-making. Lastly, an appropriate “size” of the uncertainty space is determined through physical experiments performed in laboratory conditions. Our hypothesis is that examining how the uncertainty space changes throughout time might lead to superior diagnostics of structural damage as compared to only monitoring the damage indicator. This methodology is applied to a portal frame structure to assess if the strategy holds promise for robust SHM.

Keywords

Structural health monitoring, Time series modeling, Uncertainty quantification

Abstract

This work proposes a method for statistical effect screening to identify design parameters of a numerical simulation that are influential to performance while simultaneously being robust to epistemic uncertainty introduced by calibration variables. Design parameters are controlled by the analyst, but the optimal design is often uncertain, while calibration variables are introduced by modeling choices.We argue that uncertainty introduced by design parameters and calibration variables should be treated differently, despite potential interactions between the two sets. Herein, a robustness criterion is embedded in our effect screening to guarantee the influence of design parameters, irrespective of values used for calibration variables. The Morris screening method is utilized to explore the design space, while robustness to uncertainty is quantified in the context of info-gap decision theory. The proposed method is applied to the National Aeronautics and Space Administration Multidisciplinary Uncertainty Quantification Challenge Problem, which is a blackbox code for aeronautic flight guidance that requires 35 input parameters. The application demonstrates that a large number of variables can be handled without formulating simplifying assumptions about the potential coupling between calibration variables and design parameters. Because of the computational efficiency of the Morris screening method, we conclude that the analysis can be applied to even larger-dimensional problems.

keywords

sensitivity analysis; effect screening; robust design; uncertainty quantification; optimization

Abstract

Applications in engineering analysis and design have benefited from the use of numerical models to supplement or replace the costly design-build-test paradigm. Previous work has acknowledged that design optimization should not only consider the performance of the model, but also be as insensitive as possible, or robust, to sources of uncertainty that are used to define the simulation. Clearly, evaluating robustness to sources of uncertainty can be computationally expensive, due to the number of iterations required at every step of the optimization. Multifidelity techniques have been introduced to mitigate this computational expense by taking advantage of fast-running lower-fidelity models or emulators. Herein, to achieve robust design, we argue that it is more effective to reduce the total range of variation in model performance rather than to reduce the standard deviation of model performances due to uncertainty in calibration variables of the model. We utilize a multifidelity approach to apply this paradigm to a sub-problem of the NASA Uncertainty Quantification Challenge problem, which is a high-dimensional and nonlinear MATLAB-based code used to simulate dynamics of remotely operated aircraft developed at NASA Langley. This method demonstrates an alternative and computationally efficient approach to robust design. ֲ© The Society for Experimental Mechanics, Inc. 2015.

Author keywords

Info-gap; Metamodels; Multi-fidelity optimization; Robust design; Uncertainty

Abstract

This paper discusses evaluation techniques of the robustness function of trusses, which is regarded as one of measures of structural robustness, under the uncertainties of member stiffnesses and external forces. By using quadratic embedding of the uncertainty and the S-procedure, we formulate a quasiconvex optimization problem which provides lower bounds of the robustness functions. A bisection method is proposed, where we solve a finite number of semidefinite programming problems in order to obtain a global optimal solution to the proposed quasiconvex optimization problem. The lower bounds of the robustness functions are computed for various trusses under several uncertainty circumstances.

Keywords:

Robustness; Structural safety; Semidefinite program; Quasiconvex optimization; Data uncertainty.

Abstract

A wide variety of model-based modal test design methodologies have been developed over the past two decades using a non-validated baseline model of the structure of interest. Due to the presence of lack of knowledge, this process can lead to less than optimal distributions of sensors and exciters due to the discrepancy between the model and the prototype behaviors. More recent strategies take into account statistical variability in model parameters but the results depend strongly on the hypothesized distributions. This paper provides a decision making tool using a robust satisficing approach that provides a better understanding of the trade-off between the performance of the test design and its robustness to model form errors and associated imprecisions. The latter will be represented as an info-gap model and the proposed methodology seeks a sensor and exciter distribution that will satisfy a given design performance while tolerating a specified degree of modeling error. The evolution of this performance for increasing horizons of uncertainty is an important information for the test planner in choosing the total number of sensors. The methodology will be illustrated on an academic but practically useful example under severe uncertainty.

Author keywords

Info-gap; Lack of knowledge; Robustness; Sensor placement; Uncertainty.

Abstract

Advances in sensor deployment and computational modeling have allowed significant strides to be made recently in the field of Structural Health Monitoring (SHM). One widely used SHM technique is to perform a vibration analysis where a model of the structure’s pristine (undamaged) condition is compared with vibration response data collected from the physical structure. Discrepancies between model predictions and monitoring data can be interpreted as structural damage. Unfortunately, multiple sources of uncertainty must also be considered in the analysis, including environmental variability and unknown values for model parameters. Not accounting for uncertainty in the analysis can lead to false-positives or false-negatives in the assessment of the structural condition. To manage the aforementioned uncertainty, we propose a robust- SHM methodology that combines three technologies. A time series algorithm is trained using “baseline” data to predict the vibration response, compare predictions to actual measurements collected on a potentially damaged structure, and calculate a user-defined damage indicator. The second technology handles the uncertainty present in the problem. An analysis of robustness is performed to propagate this uncertainty through the time series algorithm and obtain the corresponding bounds of variation of the damage indicator. The uncertainty description and robustness analysis are both inspired by the theory of info-gap decision-making. Lastly, an appropriate “size” of the uncertainty space is determined through physical experiments performed in laboratory conditions. Our hypothesis is that examining how the uncertainty space changes in time might lead to superior diagnostics of structural damage as compared to only monitoring the damage indicator. This methodology is applied to a portal frame structure to assess if the strategy holds promise for robust SHM.

Author keywords

Robustness; Structural health monitoring; Time series modeling; Uncertainty.

Abstract

Advances in computational sciences in the past three decades, such as those embodied by the finite element method, have made it possible to perform design and analysis using numerical simulations. While they offer undeniable benefits for rapid prototyping and can shorten the design-test-optimize cycle, numerical simulations also introduce assumptions and various sources of uncertainty. Examples are modeling assumptions proposed to represent a nonlinear material behavior, energy dissipation mechanisms and environmental conditions, in addition to numerical effects such as truncation error, mesh adaptation and artificial dissipation. Given these sources of uncertainty, what is the best way to support a design decision using simulations? We propose that an effective simulation-based design hinges on the ability to establish the robustness of its performance to assumptions and sources of uncertainty. Robustness means that exploring the uncertainty space that characterizes the simulation should not violate the performance requirement. The theory of information-gap (“info-gap”) for decision-making under severe uncertainty is applied to assess the robustness of two competing designs. The application is the dynamic stress performance of a mechanical latch for a consumer electronics product. The results are that the variant design only yields 10% improvement in robustness to uncertainty while requiring 44% more material for manufacturing. The analysis provides a rigorous rationale to decide that the variant design is not viable.

Author keywords

Finite element analysis; Mechanical latch; Robust design; Uncertainty quantification.

Abstract

The double impulse has extensively been used to evaluate the critical response of an elastoplastic structure against a pulse-type input, including near-fault earthquake ground motions. In this paper, we propose a robustness assessment method for elastoplastic single-degree-of-freedom structures subjected to the double impulse input. Uncertainties in the initial velocity of the input, as well as the natural frequency and the strength of the structure, are considered. As fundamental properties of the structural robustness, we show monotonicity of the robustness measure with respect to the natural frequency. In contrast, we show that robustness is not necessarily improved even if the structural strength is increased. Moreover, the robustness preference between two structures with different values of structural strength can possibly reverse when the performance requirement is changed.

Author keywords

Impulse, Elastoplastic response, Info-gap model, Near-fault ground motion, Robustness, Uncertainty

Abstract

Seismic design for buildings is usually subject to various uncertainties, often severe, which have the potential to undermine engineering decisions. It is crucial that these uncertainties be accounted for in seismic design. We formulated a performance-based seismic design model that takes into account uncertainty in the seismic design spectrum of the αmax and Tg. We used info-gap theory for satisfying the critical performance requirements, while at the same time maximized the robustness to uncertainty through nested optimization. The design implications of this robust-satisfying approach were demonstrated with a three-span six-floor steel frame design example. It is shown that design preferences depend upon the performance requirements considering the trade-off between robustness to uncertainty. Also, the result reveals that the proposed method provides a novel tool for the performance-based seismic reliability design under the lack of knowledge.

Keywords

Info-Gap theory; Robust; Seismic design; Uncertainty

Abstract

The words of ‘unexpected issue’ and ‘earthquake resilience’ are frequently used after the 2011 off the Pacific coast of Tohoku earthquake which occurred March 11, 2011. Although the unexpected issues are hard to include in the structural design stage of civil structures, those certainly decrease the earthquake resilience of those civil structures. Once these unexpected issues are taken into account in the structural design, those issues become expected issues. However these repetitions of cycles, i.e. experiences of unexpected issues during earthquakes and incorporation into design codes, never resolve the essential problems in structural earthquake engineering. In this paper, a historical review is made on the development of critical excitation methods as worst-scenario analysis and some possibilities of application of this concept to upgrading of building earthquake resilience are discussed.

Keywords

Earthquake resilience; Critical excitation method; Uncertainty analysis; Robustness; Redundancy; Earthquake engineering

Abstract

When we encounter a devastating earthquake disaster, we have upgraded the earthquake resistant design codes in the long history of earthquake structural engineering. However the repetition of this action does never resolve the essential problem. This is because building structures and input ground motions have various complex uncertainties and unexpected phenomena often occur. The 2011 off the Pacific coast of Tohoku earthquake also provided some unexpected phenomena. This review paper discusses how to narrow unexpected issues in future earthquakes by referring to several concepts. Critical excitation methods, info-gap theories for uncertainty representation and interval analysis methods are the principal concepts.

Keywords

critical excitation method; earthquake resilience; earthquake resistant design; info-gap uncertainty model; interval analysis; worst case analysis

Abstract

Aiming at the inability to obtain enough information to describe the random distribution of uncertain variables accurately, the Information-Gap theory which is abbreviated as Info-Gap theory is adopted. Firstly, a robust reliability model for uncertainty analysis of stability about karst roof under foundation pile is established based on the research about the method to measure the uncertainty degree of uncertain variables and to determine the allowable change range of these uncertain variables on the condition that the structural performance can satisfy the intended function. Secondly, according to the existing limit equilibrium analysis method on safety factor of karst roof under foundation pile under different failure modes, a response output model to the stabilization and security function of karst roof is set up; then the calculation method of the robust reliability index is brought forward by interval combination algorithm; so an uncertainty analysis method for the stability of karst roof under foundation pile based on Info-Gap theory is put forward. It not only has lower requirement for the message amount of engineering data but also can not know the random distribution shape of uncertain variables; and it is a supplement and improvement for the existing relative research. What’s more, because these uncertain variables are divided into design variables and design parameters in this method to achieve the dynamic analysis of allowable uncertain degree of design parameters under different design variables; thus, the method proposed has the function of not only passive reply but also active disposal. Finally, the rationality and feasibility of the method are verified by analysis of practical engineering example.

Keywords

Foundation pile; Info-Gap theory; Karst; Pile foundations; Robust reliability index; Stability of karst roof; Uncertainty analysis

Abstract

This paper addresses the plastic limit analysis of a truss with some deficient structural components. Given the upper bound for the number of deficient members, we consider uncertainty in the locations of deficient members, i.e., the set of deficient members is not specified in advance. Then we attempt to find the worst scenario of deficiency, in which the limit load factor attains the minimum value. We formulate this combinatorial optimization problem as a mixed integer linear programming problem and solve it by using an algorithm with guaranteed global convergence. The deficient structural components in the worst scenario are regarded as key elements which cause the largest degradation of structural performance. Numerical examples illustrate that the set of key elements, as well as the collapse mode in the worst scenario, depends on the number of deficient structural components.

Keywords:

Robustness, Uncertainty, Structural degradation, Structural integrity, Plastic limit analysis, Integer optimization

Abstract

The Function Impact Method (FIM) is a semi-quantitative eco-design methodology that is targeted specifically towards the early stages of the design process. The FIM allows a designer to predict the environmental impacts associated with a new functional embodiment by extrapolating knowledge from Life cycle assessment (LCA) of similar existing designs. LCA however, is associated with substantial sources of uncertainty. Furthermore, the FIM uses a subjective weighting scheme for representing function-structure affinities. In the authors’ previous work, a Monte-Carlo variation analysis was used to estimate sensitivity of the input data and select the preferred redesign strategy. This paper proposes a method to formalize the input uncertainties in the FIM by modeling the uncertainties present in the results of the LCA’s and the involved function-structure affinities using Info-gap decision theory. The desirability of redesigning a particular function based on the magnitude of its function-connectivity and eco-impact is estimated, and a decision making methodology based on robust satisficing is discussed. This method is applied for making robust redesign decisions with regards to re-designing a pneumatic impact wrench for sustainability.

Keywords

Decision making; Eco-design; Function Impact Method; Info-gap decision theory; Life Cycle Analysis

Abstract

A novel Info-Gap robust design concept to structural robust optimization under severe uncertainties is presented in this paper. This Info-Gap model is a non-probabilistic method for the problem considering severe uncertainties using the Info-Gap Decision Theory (IGDT). IGDT models the clustering of uncertain events in families of nested sets instead of assuming a probability structure, which only require the nominal estimate of uncertain parameters to be known before analysis or use in optimization. The heuristic algorithm is applied to the nested optimizations in IGDT and simulation results show that the proposed approach can solve complex problems effectively.

Abstract

The paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case, and the best limit in the other case of rigid perfectly-plastic structures subjected to uncertain-but-bounded applied loads using an Info-Gap model. The methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem, and vice versa for the best collapse load limit. The formulation for capturing the worst collapse load limit (robust worst case solution) takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm, whilst that for the best collapse load limit is a standard linear programming problem. The efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples.

Keywords

Linear programming; Load limits; Mathematical programming; Uncertainty analysis; Collapse resistance; Complementarity; Info-gap model; Limit analysis; Linear programming problem; Mathematical program with equilibrium constraints; Uncertain kinematics; Uncertainty; Rigid structures

Abstract

The notching profile defines the loading conditions for satellite subsystem shake tests. Its model-based design is a critical issue in the space field and must be defined early in order to initiate as soon as possible discussions between launch authorities and subcontractors. This discussion revolves around the following dilemma: how conservative can the loading be and still be safe for the subsystem interfaces? Indeed, the significant lack of knowledge present in the non-validated model can result in overloading conditions. This paper will propose a global strategy for the model-based design of notching profiles which accounts for epistemic modeling uncertainties using an info-gap approach. The latter provides a generic framework for evaluating and comparing the performances of competing profile designs as well as addressing issues of lack of knowledge in both deterministic and probabilistic model parameters. The proposed methodologies will be illustrated on an academic test case.

Keywords

Notching, robustness, info-gap, uncertainty, lack of knowledge

Abstract

Spacecraft mechanical tests aim at qualifying structures with respect to a launcher flight environment and investigating the finite element model (FEM) ability to correctly represent experimental measurements. An input spectrum is specified by the launcher authority to encompass flight events, but in order to avoid over testing in frequency bands with highly excited modes due to the presence of huge lack of knowledge in the non-validated model, it must be locally decreased. This model-based design is a critical issue in the space field and must be defined early in order to initiate as soon as possible discussions between launcher authorities and subcontractors. This discussion revolves around the following dilemma: how conservative can the loading be and still be safe for the subsystem interfaces? This paper will propose a global strategy for the model-based design of notching profiles which accounts for epistemic modeling uncertainties using an info-gap approach. The latter provides a generic framework for evaluating the performances of profile designs as well as addressing issues of lack of knowledge in this approach. The proposed methodologies will be illustrated on an academic test case, modeling the first and second longitudinal modes for a medium-size scientific satellite. Solutions will then be discussed in order to turn this methodology applicable on real industrial satellite structures.

Abstract

A wide variety of model-based modal test design methodologies have been developed over the past two decades using a non-validated baseline model of the structure of interest. Due to the presence of lack of knowledge, this process can lead to less than optimal distributions of sensors and exciters due to the discrepancy between the model and the prototype behaviors. More recent strategies take into account statistical variability in model parameters but the results depend strongly on the hypothesized distributions. This paper provides a decision making tool using a robust satisficing approach that provides a better understanding of the trade-off between the performance of the test design and its robustness to model form errors and associated imprecisions. The latter will be represented as an info-gap model and the proposed methodology seeks a sensor distribution that will satisfy a given design performance while tolerating a specified degree of modeling error. The evolution of this performance for increasing horizons of uncertainty is an important information for the test planner in choosing the total number of sensors. © The Society for Experimental Mechanics, Inc. 2015.

Author keywords

Info-gap; Lack of knowledge; Robustness; Sensor placement; Uncertainty

Abstract

In this article, Information-Gap Decision Theory (IGDT), an approach to robust decision making under severe uncertainty, is applied to decisions about a remanufacturing process. IGDT is useful when only a nominal estimate is available for an uncertain quantity; the amount that estimate differs from the quantity’s actual value is not known. The decision strategy in IGDT involves maximizing robustness to uncertainty of unknown size, while still guaranteeing no worse than some “good enough” critical level of performance, rather than optimal performance. The design scenario presented involves selecting the types of technologies and number of stations to be used in a remanufacturing process. The profitability of the process is affected by severe uncertainty in the demand for remanufactured parts. Because nothing is know about demand except an estimate based on a different product from a previous year, info-gap theory will be used to determine an appropriate tradeoff between performance and robustness to severe uncertainty. Which design is most preferred is seen to switch depending on choice of critical performance level. Implications of findings, as well as future research directions, are discussed.

Abstract

This paper presents a method for computing an info-gap robustness function of structures, which is regarded as one measure of structural robustness, under uncertainties associated with the limit load factor. We assume that the external load in the plastic limit analysis is uncertain around its nominal value. Various uncertainties are considered for the live, dead, and reference disturbance loads based on the nonstochastic info-gap uncertainty model. Although the robustness function is originally defined by using the optimization problem with infinitely many constraints, we show that the robustness function is obtained as an optimal value of a linear programming (LP) problem. Hence, we can easily compute the info-gap robustness function associated with the limit load factor by solving an LP problem. As the second contribution, we show that the robust structural optimization problems of trusses and frames can also be reduced to LP problems. In numerical examples, the robustness functions, as well as the robust optimal designs, are computed for trusses and framed structures by solving LP problems.

Abstract

This paper develops a new structural design concept which incorporates uncertainties in both the load and the structural model parameters. Info-gap models of uncertainty are used to represent uncertainty in the power spectral density of the load and in parameters of the vibration model of the structure. It is demonstrated that any design which optimizes functional performance will also minimize the robustness to uncertainty. Since uncertainties are prevalent in many applications, this paper argues that it is necessary to satisfy critical performance requirements (rather than to optimize performance), and to maximize the robustness to uncertainty. The design implications of this robust-satisficing approach are demonstrated with several heuristic structural design examples. It is shown that design preferences depend upon performance requirements: preferences between designs can be reversed when performance requirements change. Also, we show that the info-gap robustness function provides an attractive tool for adjudicating between conflicting objectives in multi-criteria design.

Keywords

Earthquake excitation, building design, information-gap decision theory, uncertainty, robustness.