A method of steepest ascent for multiresponse surface optimization using a desirability function method

Lee, Dong‐Hee; Kim, So‐Hee; Byun, Jai-Hyun

doi:10.1002/qre.2666

Cited by 13 publications

(14 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the single surrogate model for multiple limit states is usually complex, since all the states must be considered simultaneously in the sequential enrichment process of DOE. Some ideas of multiresponse optimization 46 can be used for reference to solve this problem.…”

Section: Discussionmentioning

confidence: 99%

An active learning Bayesian ensemble surrogate model for structural reliability analysis

Xiao

Park

Ouyang

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

Surrogate models have been proven to be powerful tools to alleviate the computational burden of structural reliability analysis. An appropriate surrogate model can guarantee prediction accuracy with limited samples. However, the traditional single modeling technique ignores the model‐form uncertainty due to insufficient knowledge of the physical system, leading to unreliable prediction results or time‐consuming computation. To overcome the aforementioned deficiencies, an active learning ensemble surrogate model under the framework of Bayesian inference is proposed for structural reliability analysis. Based on the derived Bayesian posterior distribution of the predicted response, a learning function integrating the modified U function and the distance information between design points is developed to sequentially select the next point. Besides, in order to further enhance the computational efficiency, we propose an adaptive method to identify the sampling region according to the prediction uncertainty of the estimated limit state surface. Five benchmark examples are employed to verify the effectiveness and efficiency of the proposed algorithm. Comparison results show that the proposed active learning reliability analysis method based on the Bayesian ensemble surrogate model can greatly reduce the computational expense with a competitive prediction accuracy. Taking the 10‐bar truss problem as an example, compared with AK‐MCS+U, ALR‐Bpce, and ALR‐SVR, the improved rate of the proposed method in efficiency is 51.58%, 12.78%, and 25.96%, respectively. Meanwhile, its prediction accuracy is high and much better than ALR‐ELSM. In addition, the superior performance is robust in a wide range of application cases.

show abstract

Section: Discussionmentioning

confidence: 99%

An active learning Bayesian ensemble surrogate model for structural reliability analysis

Xiao

Park

Ouyang

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…They are typical examples of multiple response problems in the welding process field. Multiple response surface optimization (MRSO) is a research field for solving the multiple response problem based on the RSM framework [6]. In MRSO, multiple responses are often in conflict.…”

Section: Fig 1 Examples Of Tzm Beadsmentioning

confidence: 99%

“…A common approach to multi-response optimization is to construct empirical models for multiple responses under the RSM framework and analyze the empirical models to obtain the optimal settings for the input variables. This approach is referred to as MRSO [6]. The multi-response problem can be formally expressed as follows:…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing the Mean and Variance of Bead Geometry in the Wire + Arc Additive Manufacturing Using a Desirability Function Method

Lee

Seo

Kim

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Wire + arc additive manufacturing (WAAM) is an arc welding process that uses non-consumable tungsten electrodes to produce the weld. The material used in this study is a titanium, carbon, zirconium, and molybdenum (TZM) alloy that is physically and chemically stable and has good performance for use as a welding and high-temperature heating element. However, the price is higher than that of other materials. Because welding cannot be modified after manufacturing, economic losses are high in the case of a defective product. Therefore, it is important to find the best welding settings for the target bead geometry during welding. In this study, welding experiments are designed based on a central composite design, and single-layer WAAM is performed using a TZM material. Consequently, we obtain 17 beads and measure the height, width, as well as left and right toe angles, which represent the geometry of the beads. Based on the measured geometry, we obtain the optimal settings for the WAAM parameters whereat the mean of each geometry is close to its target value and its variance is minimized by using a desirability function method. Furthermore, we conduct additional experiments to validate the optimal settings that we obtain. We compare the predicted and actual geometry values and find that they are quite close. This result indicates that valid optimal settings for the process parameters can be obtained via the proposed method.

show abstract

“…[3] developed the method of game theory; but this technique ends up masking the details of the experimental process. [17] used a posterior preference approach to perform robust multi-response optimization; but, this method is yet only efficient when the decision maker's preference information is available, and fails otherwise [29,30,20].…”

Section: Introductionmentioning

confidence: 99%

Multivariate-Based Technique for Solving Multi-Response Surface Optimization (MRSO) Problems: The Case of a Maximization Problem

Usen

Akpan

Ugbe

et al. 2021

AJPAS

View full text Add to dashboard Cite

Multi-response surface optimization (MRSO) is a problem that is peculiar to an industrial setting, where the aim of a process engineer is to set his process at operating conditions that simultaneously optimize a set of process responses. In Statistics, several methods have been proffered for tackling problems of this nature. Some of such methods are that of: overlapping contour plots, constrained optimization problem, loss function approach, process capability approach, distance function approach, game theory approach, and the desirability function approach. These, methods are however, not without teething flaws as they are either too problem specific, or require very complex and inflexible routines; little wonder, the method of desirability function has gained popularity especially because it overcomes the latter limitation. In this article, we have proposed and implemented a multivariate-based technique for solving MRSO problems. The technique fused the ideas of response surface methodology (RSM), multivariate multiple regression and Pareto optimality. In our technique, RSM was implemented on an all-maximization problem as a case-study process; in which case, first-order models (FOMs) for the responses were fitted using 2k factorial designs until the FOMs proved to be inadequate, while uniform precision rotatable central composite design was used to obtain second-order models (SOMs) for the respective responses in the event of model inadequacy of the FOMs. With the implementation of the proposed technique to the case study, optimal operating conditions were obtained, with observations stemming thereof summarized as axioms. The first, second and third axioms respectively stated that: (1) the mid-point of all optimal operating conditions obtained via the proposed technique is Pareto optimal, (2) the mid-point of all optimal responses at the Pareto optimal operating condition is Pareto optimal, and (3) the region bounded by each of the optimal operating conditions from each second-order model (SOM) is a Pareto front.

show abstract

A method of steepest ascent for multiresponse surface optimization using a desirability function method

Cited by 13 publications

References 18 publications

An active learning Bayesian ensemble surrogate model for structural reliability analysis

An active learning Bayesian ensemble surrogate model for structural reliability analysis

Optimizing the Mean and Variance of Bead Geometry in the Wire + Arc Additive Manufacturing Using a Desirability Function Method

Multivariate-Based Technique for Solving Multi-Response Surface Optimization (MRSO) Problems: The Case of a Maximization Problem

Contact Info

Product

Resources

About