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Despite the numerous advances, reinforcement learning remains away from widespread acceptance for autonomous controller design as compared to classical methods due to lack of ability to effectively tackle uncertainty. The reliance on absolute or deterministic reward as a metric for optimization process renders reinforcement learning highly susceptible to changes in problem dynamics. We introduce a novel framework that effectively quantify the uncertainty in the design space and induces robustness in controllers by switching to a reliability-based optimization routine. A model-based approach is used to improve the data efficiency of the method while predicting the system dynamics. We prove the stability of learned neuro-controllers in both static and dynamic environments on classical reinforcement learning tasks such as Cart Pole balancing and Inverted Pendulum.

Most of the existing reliability-based design optimization (RBDO) are not capable of analyzing data from multifidelity sources to improve the confidence of optimal solution while maintaining computational efficiency. In this paper, we propose a novel reliability-based multifidelity optimization (RBMO) framework that adaptively integrates both low- and high-fidelity data for achieving reliable optimal designs. The Gaussian process (GP) modeling technique is first utilized to build a hybrid surrogate model by fusing data sources with different fidelity levels. To reduce the number of low- and high-fidelity data, an adaptive hybrid learning (AHL) algorithm is then developed to efficiently update the hybrid model. The updated hybrid surrogate model is used for reliability and sensitivity analyses in solving an RBDO problem, which provides a pseudo-optimal solution in the RBMO framework. An optimal solution that meets the reliability targets can be achieved by sequentially performing the adaptive hybrid learning at the iterative pseudo-optimal designs and solving RBDO problems. The effectiveness of the proposed framework is demonstrated through three case studies.

To account for the model bias in reliability analysis, various methods have been developed to validate simulation models using precise experimental data. However, it still lacks a strategy to actively seek critical information from both sources for effective uncertainty reduction. This paper presents an active resource allocation approach (ARA) to improve the accuracy of reliability approximations while reducing the computational, and more importantly, experimental costs. In ARA, the Gaussian process (GP) modeling technique is employed to fuse both simulation and experimental data for capturing the model bias, and further predicting actual system responses. To manage the uncertainty due to the lack of data, a two-phase updating strategy is developed to improve the fidelity of GP models by actively collecting the most valuable simulation and experimental data. With the high-fidelity predictive models, sampling-based methods such as Monte Carlo simulation are used to calculate the reliability accurately while the overall costs of conducting simulations and experiments can be significantly reduced. The effectiveness of the proposed approach is demonstrated through four case studies.

Time-variant reliability measures the probability that an engineering system successfully performs intended functions over a certain period of time under various sources of uncertainty. In practice, it is computationally prohibitive to propagate uncertainty in time-variant reliability assessment based on expensive or complex numerical models. This paper presents an equivalent stochastic process transformation approach for cost-effective prediction of reliability deterioration over the life cycle of an engineering system. To reduce the high dimensionality, a time-independent reliability model is developed by translating random processes and time parameters into random parameters in order to equivalently cover all potential failures that may occur during the time interval of interest. With the time-independent reliability model, an instantaneous failure surface is attained by using a Kriging-based surrogate model to identify all potential failure events. To enhance the efficacy of failure surface identification, a maximum confidence enhancement method is utilized to update the Kriging model sequentially. Then, the time-variant reliability is approximated using Monte Carlo simulations of the Kriging model where system failures over a time interval are predicted by the instantaneous failure surface. The results of two case studies demonstrate that the proposed approach is able to accurately predict the time evolution of system reliability while requiring much less computational efforts compared with the existing analytical approach.

To reduce the computational cost, surrogate models have been widely used to replace expensive simulations in design under uncertainty. However, most existing methods may introduce significant errors when the training data is limited. This paper presents a confidence-driven design optimization (CDDO) framework to manage surrogate model uncertainty for probabilistic design optimization. In this study, a confidence-based Gaussian process (GP) modeling technique is developed to handle the surrogate model uncertainty in system performance predictions by taking both the prediction mean and variance into account. With a target confidence level, the confidence-based GP models are used to reduce the probability of underestimating the probability of failure in reliability assessment. In addition, a new sensitivity analysis method is proposed to approximate the sensitivity of the reliability at the target confidence level with respect to design variables, and thus facilitate the CDDO framework. Three case studies are introduced to demonstrate the effectiveness of the proposed approach.

Dynamic reliability measures reliability of an engineered system considering time-variant operation condition and component deterioration. Due to high computational costs, conducting dynamic reliability analysis at an early system design stage remains challenging. This paper presents a confidence-based meta-modeling approach, referred to as double-loop adaptive sampling (DLAS), for efficient sensitivity-free dynamic reliability analysis. The DLAS builds a Gaussian process (GP) model sequentially to approximate extreme system responses over time, so that Monte Carlo simulation (MCS) can be employed directly to estimate dynamic reliability. A generic confidence measure is developed to evaluate the accuracy of dynamic reliability estimation while using the MCS approach based on developed GP models. A double-loop adaptive sampling scheme is developed to efficiently update the GP model in a sequential manner, by considering system input variables and time concurrently in two sampling loops. The model updating process using the developed sampling scheme can be terminated once the user defined confidence target is satisfied. The developed DLAS approach eliminates computationally expensive sensitivity analysis process, thus substantially improves the efficiency of dynamic reliability analysis. Three case studies are used to demonstrate the efficacy of DLAS for dynamic reliability analysis.

Reliability represents safety level in industry practice and may variant due to time-variant operation condition and components deterioration throughout a product life-cycle. Thus, the capability to perform time-variant reliability analysis is of vital importance in practical engineering applications. This paper presents a new approach, referred to as nested extreme response surface (NERS), that can efficiently tackle time dependency issue in time-variant reliability analysis and enable to solve such problem by easily integrating with advanced time-independent tools. The key of the NERS approach is to build a nested response surface of time corresponding to the extreme value of the limit state function by employing Kriging model. To obtain the data for the Kriging model, the efficient global optimization technique is integrated with the NERS to extract the extreme time responses of the limit state function for any given system input. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-variant reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis methods can be used. Three case studies are used to demonstrate the efficiency and accuracy of NERS approach.

With the increasing complexity of engineering systems, ensuring high system reliability and system performance robustness throughout a product life cycle is of vital importance in practical engineering design. Dynamic reliability analysis, which is generally encountered due to time-variant system random inputs, becomes a primary challenge in reliability-based robust design optimization (RBRDO). This article presents a new approach to efficiently carry out dynamic reliability analysis for RBRDO. The key idea of the proposed approach is to convert time-variant probabilistic constraints to time-invariant ones by efficiently constructing a nested extreme response surface (NERS) and then carry out dynamic reliability analysis using NERS in an iterative RBRDO process. The NERS employs an efficient global optimization technique to identify the extreme time responses that correspond to the worst case scenario of system time-variant limit state functions. With these extreme time samples, a kriging-based time predi...

Validating dynamic engineering models is critically important in practical applications by assessing the agreement between simulation results and experimental observations. Though significant progresses have been made, the existing metrics lack the capability of managing uncertainty in both simulations and experiments. In addition, it is challenging to validate a dynamic model aggregately over both the time domain and a model input space with data at multiple validation sites. To overcome these difficulties, this paper presents an area-based metric to systemically handle uncertainty and validate computational models for dynamic systems over an input space by simultaneously integrating the information from multiple validation sites. To manage the complexity associated with a high-dimensional data space, eigenanalysis is performed for the time series data from simulations at each validation site to extract the important features. A truncated Karhunen–Loève (KL) expansion is then constructed to represent the responses of dynamic systems, resulting in a set of uncorrelated random coefficients with unit variance. With the development of a hierarchical data-fusion strategy, probability integral transform (PIT) is then employed to pool all the resulting random coefficients from multiple validation sites across the input space into a single aggregated metric. The dynamic model is thus validated by calculating the cumulative area difference of the cumulative density functions. The proposed model validation metric for dynamic systems is illustrated with a mathematical example, a supported beam problem with stochastic loads, and real data from the vehicle occupant-restraint system.

Validating dynamic engineering models is critically important in practical applications by assessing the agreement between simulation results and experimental observations. Though significant progresses have been made, the existing metrics lack the capability of managing uncertainty in both simulations and experiments, which may stem from computer model instability, imperfection in material fabrication and manufacturing process, and variations in experimental conditions. In addition, it is challenging to validate a dynamic model aggregately over both the time domain and a model input space with data at multiple validation sites. To overcome these difficulties, this paper presents an area-based metric to systemically handle uncertainty and validate computational models for dynamic systems over an input space by simultaneously integrating the information from multiple validation sites. To manage the complexity associated with a high-dimensional data space, Eigen analysis is performed for the time series data from simulations at each validation site to extract the important features. A truncated Karhunen-Loève (KL) expansion is then constructed to represent the responses of dynamic systems, resulting in a set of uncorrelated random coefficients with unit variance. With the development of a hierarchical data fusion strategy, probability integral transform is then employed to pool all the resulting random coefficients from multiple validation sites across the input space into a single aggregated metric. The dynamic model is thus validated by calculating the cumulative area difference of the cumulative density functions. The proposed model validation metric for dynamic systems is illustrated with a mathematical example, a supported beam problem with stochastic loads, and real data from the vehicle occupant restraint system.

Failure of practical engineering systems could be induced by several correlated failure modes, and consequently reliability analysis are conducted with multiple disjointed failure regions in the system random input space. Problems with disjointed failure regions create a great challenge for existing reliability analysis approaches due to the discontinuity of the system performance function between these regions. This paper presents a new enhanced Monte Carlo simulation (EMCS) approach for reliability analysis and design considering disjointed failure regions. The ordinary Kriging method is adopted to construct surrogate model for the performance function so that Monte Carlo simulation (MCS) can be used to estimate the reliability. A maximum failure potential based sampling scheme is developed to iteratively search failure samples and update the Kriging model. Two case studies are used to demonstrate the efficacy of the proposed methodology.Copyright © 2015 by ASME

This paper presents an integrated performance measure approach (iPMA) for system reliability assessment considering multiple dependent failure modes. An integrated performance function is developed to envelope all component level failure events, thereby enables system reliability approximation by considering only one integrated system limit state. The developed integrated performance function possesses two critical properties. First, it represents exact joint failure surface defined by multiple component failure events, thus no error will be induced due to the integrated limit state function in system reliability computation. Second, smoothness of the integrated performance on system failure surface can be guaranteed, therefore advanced response surface techniques can be conveniently employed for response approximation. With the developed integrated performance function, the maximum confidence enhancement based sequential sampling method is adopted as an efficient component reliability analysis tool for system reliability approximation. To furthermore improve the computational efficiency, a new constraint filtering technique is developed to adaptively identify active limit states during the iterative sampling process without inducing any extra computational cost. One case study is used to demonstrate the effectiveness of system reliability assessment using the developed iPMA methodology.

Dynamic reliability is defined as the probability that an engineered system successfully performs the predefined functionality over a certain period of time considering time-variant operation condition and component deterioration. In practice, it is still a major challenge to conduce dynamic reliability analysis due to the prohibitively high computational costs. In this study, a confidence-based meta-modeling approach is proposed for efficient sensitivity-free dynamic reliability analysis, referred to as double-loop adaptive sampling (DLAS). In DLAS a Gaussian process (GP) model is constructed to approximate extreme system responses over time, so that Monte Carlo simulation (MCS) can be employed directly to estimate dynamic reliability. A qualitative confidence measure is proposed to evaluate the accuracy of dynamic reliability estimation while using the MCS approach based on developed GP models. To improve the confidence, a double-loop adaptive sampling scheme is developed to efficiently update the GP model in a sequential manner, by considering system input variables and time concurrently in double sampling loops. The model updating process can be terminated once the user defined confidence target is satisfied. The DLAS approach does not require computationally expensive sensitivity analysis, thus substantially improves the efficiency of dynamic reliability assessment. Two case studies are used to demonstrate the effectiveness of DLAS for dynamic reliability analysis.Copyright © 2014 by ASME

This paper presents a maximum confidence enhancement based sequential sampling approach for simulation-based design under uncertainty. In the proposed approach, the ordinary Kriging method is adopted to construct surrogate models for all constraints and thus Monte Carlo simulation (MCS) is able to be used to estimate reliability and its sensitivity with respect to design variables. A cumulative confidence level is defined to quantify the accuracy of reliability estimation using MCS based on the Kriging models. To improve the efficiency of proposed approach, a maximum confidence enhancement based sequential sampling scheme is developed to update the Kriging models based on the maximum improvement of the defined cumulative confidence level, in which a sample that produces the largest improvement of the cumulative confidence level is selected to update the surrogate models. Moreover, a new design sensitivity estimation approach based upon constructed Kriging models is developed to estimate the reliability sensitivity information with respect to design variables without incurring any extra function evaluations. This enables to compute smooth sensitivity values and thus greatly enhances the efficiency and robustness of the design optimization process. Two case studies are used to demonstrate the proposed methodology.Copyright © 2013 by ASME

Significant technological advances in sensing and communication promote the use of large sensor networks to monitor structural systems, identify damages, and quantify damage levels. Prognostics and health management (PHM) technique has been developed and applied for a variety of safety-critical engineering structures, given the critical needs of the structure health state awareness. The PHM performance highly relies on real-time sensory signals which convey the structural health relevant information. Designing an optimal structural sensor network (SN) with high detectability is thus of great importance to the PHM performance. This paper proposes a generic SN design framework using a detectability measure while accounting for uncertainties in material properties and geometric tolerances. Detectability is defined to quantify the performance of a given SN. Then, detectability analysis will be developed based on structural simulations and health state classification. Finally, the generic SN design framework can be formulated as a mixed integer nonlinear programming (MINLP) using the detectability measure and genetic algorithms (GAs) will be employed to solve the SN design optimization problem. A power transformer study will be used to demonstrate the feasibility of the proposed generic SN design methodology.

This paper presents a new approach, referred to as the nested extreme response surface (NERS), to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The key of the NERS is to convert the time-dependent reliability analysis to time-independent one through constructing a kriging based nested time prediction model. The efficient global optimization technique is integrated with NERS to extract the extreme time responses of limit state functions and an adaptive response prediction and model maturation mechanism is developed for an optimal balancing of the model accuracy and the computational efficiency. With the nested response surface of time, existing advanced reliability analysis and design methods can be used. The NERS approach is integrated with RBDO for the design of engineered systems with time-dependent probabilistic constraints. The case study results demonstrate the accuracy and the effectiveness of the proposed approach.

A primary concern in practical engineering design is ensuring high system reliability throughout a product's lifecycle, which is subject to time-variant operating conditions and component deteriorations. Thus, the capability of dealing with time-dependent probabilistic constraints in reliability-based design optimization (RBDO) is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. This approach employs the kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization (EGO) technique is integrated with the NERS approach to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation (ARPMM) mechanism is developed based on the mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis, and existing advanced reliability analysis and design methods can be used. The NERS approach is compared with existing time-dependent reliability analysis approaches and integrated with RBDO for engineered system design with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deteriorations. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with the NERS to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.Copyright © 2012 by ASME