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Surrogate models are extensively used to substitute real models which are expensive to evaluate in the time-dependent reliability analysis. Normally, different surrogate models have different scopes of application. However, information is often insufficient for analysts to select the most appropriate surrogate model for a specific application. Thus, the result precited by individual surrogate model tends to be suboptimal or even inaccurate. Ensemble model can effectively deal with the above concern. This work aims to study the application of ensemble model for reliability analysis of time-independent problems.

In this work, a method of reliability analysis for time-dependent problems based on ensemble learning of surrogate models is developed. The ensemble of surrogate models includes Kriging, radial basis function, and support vector machine. The prediction is approximated by the weighted average model. The ensemble learning of surrogate models is updated by finding and adding the sample points with large prediction errors throughout the entire procedure.

The effectiveness of the proposed method is verified by several examples. The results show that the ensemble of surrogate models can effectively propagate the uncertainty of time-varying problems, and evaluate the reliability with high prediction accuracy and computational efficiency.

This work proposes an adaptive learning framework for the uncertainty propagation of time-dependent problems based on the ensemble of surrogate models. Compared with individual surrogate models, the ensemble model not only saves the effort of selecting an appropriate surrogate model especially when the knowledge of unknown problem is lacking, but also improves the prediction accuracy and computational efficiency.

In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy.

Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution.

The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method.

This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.

The conventional design method relies on a priori knowledge, which limits the rapid and efficient development of electronic packaging structures. The purpose of this study is to propose a hybrid method of data-driven inverse design, which couples adaptive surrogate model technology with optimization algorithm to to enable an efficient and accurate inverse design of electronic packaging structures.

The multisurrogate accumulative local error-based ensemble forward prediction model is proposed to predict the performance properties of the packaging structure. As the forward prediction model is adaptive, it can identify respond to sensitive regions of design space and sample more design points in those regions, getting the trade-off between accuracy and computation resources. In addition, the forward prediction model uses the average ensemble method to mitigate the accuracy degradation caused by poor individual surrogate performance. The Particle Swarm Optimization algorithm is then coupled with the forward prediction model for the inverse design of the electronic packaging structure.

Benchmark testing demonstrated the superior approximate performance of the proposed ensemble model. Two engineering cases have shown that using the proposed method for inverse design has significant computational savings while ensuring design accuracy. In addition, the proposed method is capable of outputting multiple structure parameters according to the expected performance and can design the packaging structure based on its extreme performance.

Because of its data-driven nature, the inverse design method proposed also has potential applications in other scientific fields related to optimization and inverse design.

Surrogate-assisted evolutionary algorithms (SAEAs) are the most popular algorithms used to solve design optimization problems of expensive and complex engineering systems. However, it is difficult for fixed surrogate models to maintain their accuracy and efficiency in the face of different issues. Therefore, the selection of an appropriate surrogate model remains a significant challenge. This paper aims to propose a dynamic adaptive hybrid surrogate-assisted particle swarm optimization algorithm (AHSM-PSO) to address this issue.

A dynamic adaptive hybrid selection method (AHSM) is proposed. This method can identify multiple ensemble models formed by integrating different numbers of excellent individual surrogate models. Then, according to the minimum root-mean-square error, the best suitable surrogate model is dynamically selected in each generation and is used to assist PSO.

Experimental studies on commonly used benchmark problems, and two real-world design optimization problems demonstrate that, compared with existing algorithms, the proposed algorithm achieves better performance.

The main contribution of this work is the proposal of a dynamic adaptive hybrid selection method (AHSM). This method uses the advantages of different surrogate models and eliminates the shortcomings of experience selection. Furthermore, the empirical results of the comparison of the proposed algorithm (AHSM-PSO) with existing algorithms on commonly used benchmark problems, and two real-world design optimization problems demonstrate its competitiveness.

Extreme support vector regression (ESVR) has been widely used in the design, analysis and optimization of engineering systems of its fast training speed and good computational ability. However, the ESVR model is only able to utilize one-fidelity information of engineering system. To solve this issue, this paper extends extreme support vector regression (ESVR) to a multi-fidelity surrogate (MFS) model which can make use of a few expensive but higher-fidelity (HF) samples and a lot of inaccurate but cheap low-fidelity (LF) samples, named ESVR-MFS.

In the ESVR-MFS model, a kernel matrix is designed to evaluate the relationship between the HF and LF samples. The root mean square error of HF samples is used as the training error metric, and the optimal hyper-parameters of the kernel matrix are obtained through a heuristic algorithm.

A number of numerical problems and three engineering problems are used to compare the ESVR-MFS model with the single-fidelity ESVR model and two benchmark MFS models. The results show that the ESVR-MFS model exhibits competitive performance in both numerical cases and practical cases tested in this work.

The proposed approach exhibits great capability for practical multi-fidelity engineering design problems.

A MFS model is proposed based on ESVR, which can make full use of the advantages of both HF data and LF data to achieve optimal results at same or lower cost.

Assessing the failure probability of engineering structures is still a challenging task in the presence of various uncertainties due to the involvement of expensive-to-evaluate computational models. The traditional simulation-based approaches require tremendous computational effort, especially when the failure probability is small. Thus, the use of more efficient surrogate modeling techniques to emulate the true performance function has gained increasingly more attention and application in recent years. In this paper, an active learning method based on a Kriging model is proposed to estimate the failure probability with high efficiency and accuracy.

To effectively identify informative samples for the enrichment of the design of experiments, a set of new learning functions is proposed. These learning functions are successfully incorporated into a sampling scheme, where the candidate samples for the enrichment are uniformly distributed in the n-dimensional hypersphere with an iteratively updated radius. To further improve the computational efficiency, a parallelization strategy that enables the proposed algorithm to select multiple sample points in each iteration is presented by introducing the K-means clustering algorithm. Hence, the proposed method is referred to as the adaptive Kriging method based on K-means clustering and sampling in n-Ball (AK-KBⁿ).

The performance of AK-KBⁿ is evaluated through several numerical examples. According to the generated results, all the proposed learning functions are capable of guiding the search toward sample points close to the LSS in the critical region and result in a converged Kriging model that perfectly matches the true one in the regions of interest. The AK-KBⁿ method is demonstrated to be well suited for structural reliability analysis and a very good performance is observed in the investigated examples.

In this study, the statistical information of Kriging prediction, the relative contribution of the sample points to the failure probability and the distances between the candidate samples and the existing ones are all integrated into the proposed learning functions, which enables effective selection of informative samples for updating the Kriging model. Moreover, the number of required iterations is reduced by introducing the parallel computing strategy, which can dramatically alleviate the computation cost when time demanding numerical models are involved in the analysis.

This paper aims to study the sampling methods (or design of experiments) which have a large influence on the performance of the surrogate model. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study.

The high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. First, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set uniformly distributed. Third, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated.

The SCSM has better performance in efficiency, accuracy and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence.

The SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimisation problems.

Earned value management (EVM)–based models for estimating project actual duration (AD) and cost at completion using various methods are continuously developed to improve the accuracy and actualization of predicted values. This study primarily aimed to examine natural gradient boosting (NGBoost-2020) with the classification and regression trees (CART) base model (base learner). To the best of the authors' knowledge, this concept has never been applied to EVM AD forecasting problem. Consequently, the authors compared this method to the single K-nearest neighbor (KNN) method, the ensemble method of extreme gradient boosting (XGBoost-2016) with the CART base model and the optimal equation of EVM, the earned schedule (ES) equation with the performance factor equal to 1 (ES1). The paper also sought to determine the extent to which the World Bank's two legal factors affect countries and how the two legal causes of delay (related to institutional flaws) influence AD prediction models.

In this paper, data from 30 construction projects of various building types in Iran, Pakistan, India, Turkey, Malaysia and Nigeria (due to the high number of delayed projects and the detrimental effects of these delays in these countries) were used to develop three models. The target variable of the models was a dimensionless output, the ratio of estimated duration to completion (ETC(t)) to planned duration (PD). Furthermore, 426 tracking periods were used to build the three models, with 353 samples and 23 projects in the training set, 73 patterns (17% of the total) and six projects (21% of the total) in the testing set. Furthermore, 17 dimensionless input variables were used, including ten variables based on the main variables and performance indices of EVM and several other variables detailed in the study. The three models were subsequently created using Python and several GitHub-hosted codes.

For the testing set of the optimal model (NGBoost), the better percentage mean (better%) of the prediction error (based on projects with a lower error percentage) of the NGBoost compared to two KNN and ES1 single models, as well as the total mean absolute percentage error (MAPE) and mean lags (MeLa) (indicating model stability) were 100, 83.33, 5.62 and 3.17%, respectively. Notably, the total MAPE and MeLa for the NGBoost model testing set, which had ten EVM-based input variables, were 6.74 and 5.20%, respectively. The ensemble artificial intelligence (AI) models exhibited a much lower MAPE than ES1. Additionally, ES1 was less stable in prediction than NGBoost. The possibility of excessive and unusual MAPE and MeLa values occurred only in the two single models. However, on some data sets, ES1 outperformed AI models. NGBoost also outperformed other models, especially single models for most developing countries, and was more accurate than previously presented optimized models. In addition, sensitivity analysis was conducted on the NGBoost predicted outputs of 30 projects using the SHapley Additive exPlanations (SHAP) method. All variables demonstrated an effect on ETC(t)/PD. The results revealed that the most influential input variables in order of importance were actual time (AT) to PD, regulatory quality (RQ), earned duration (ED) to PD, schedule cost index (SCI), planned complete percentage, rule of law (RL), actual complete percentage (ACP) and ETC(t) of the ES optimal equation to PD. The probabilistic hybrid model was selected based on the outputs predicted by the NGBoost and XGBoost models and the MAPE values from three AI models. The 95% prediction interval of the NGBoost–XGBoost model revealed that 96.10 and 98.60% of the actual output values of the testing and training sets are within this interval, respectively.

Due to the use of projects performed in different countries, it was not possible to distribute the questionnaire to the managers and stakeholders of 30 projects in six developing countries. Due to the low number of EVM-based projects in various references, it was unfeasible to utilize other types of projects. Future prospects include evaluating the accuracy and stability of NGBoost for timely and non-fluctuating projects (mostly in developed countries), considering a greater number of legal/institutional variables as input, using legal/institutional/internal/inflation inputs for complex projects with extremely high uncertainty (such as bridge and road construction) and integrating these inputs and NGBoost with new technologies (such as blockchain, radio frequency identification (RFID) systems, building information modeling (BIM) and Internet of things (IoT)).

The legal/intuitive recommendations made to governments are strict control of prices, adequate supervision, removal of additional rules, removal of unfair regulations, clarification of the future trend of a law change, strict monitoring of property rights, simplification of the processes for obtaining permits and elimination of unnecessary changes particularly in developing countries and at the onset of irregular projects with limited information and numerous uncertainties. Furthermore, the managers and stakeholders of this group of projects were informed of the significance of seven construction variables (institutional/legal external risks, internal factors and inflation) at an early stage, using time series (dynamic) models to predict AD, accurate calculation of progress percentage variables, the effectiveness of building type in non-residential projects, regular updating inflation during implementation, effectiveness of employer type in the early stage of public projects in addition to the late stage of private projects, and allocating reserve duration (buffer) in order to respond to institutional/legal risks.

Ensemble methods were optimized in 70% of references. To the authors' knowledge, NGBoost from the set of ensemble methods was not used to estimate construction project duration and delays. NGBoost is an effective method for considering uncertainties in irregular projects and is often implemented in developing countries. Furthermore, AD estimation models do fail to incorporate RQ and RL from the World Bank's worldwide governance indicators (WGI) as risk-based inputs. In addition, the various WGI, EVM and inflation variables are not combined with substantial degrees of delay institutional risks as inputs. Consequently, due to the existence of critical and complex risks in different countries, it is vital to consider legal and institutional factors. This is especially recommended if an in-depth, accurate and reality-based method like SHAP is used for analysis.

The purpose of this paper is to improve the efficiency of particle optimization method by using direct and indirect surrogate modeling in inverse design problems.

The new algorithm emphasizes the use of a direct and an indirect design prediction based on local surrogate models in particle swarm optimization (PSO) algorithm. Local response surface approximations are constructed by using radial basis neural networks. The principal role of surrogate models is to answer the question of which individuals should be placed into the next swarm. Therefore, the main purpose of surrogate models is to predict new design points instead of estimating the objective function values. To demonstrate its merits, the new approach and six comparative algorithms were applied to two different test cases including surface fitting of a geographical terrain and an inverse design of a wing, the averaged best-individual fitness values of the algorithms were recorded for a fair comparison.

The new algorithm provides more than 60 per cent reduction in the required generations as compared with comparative algorithms.

The comparative study was carried out only for two different test cases. It is possible to extend test cases for different problems.

The proposed algorithm can be applied to different inverse design problems.

The study presents extra ordinary application of double surrogate modeling usage in PSO for inverse design problems.

This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.

The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency.

To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations.

The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.