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Optimizing personnel allocation: An integer linear programming problem for enhanced workplace efficiency 优化人员配置:一个提高工作效率的整数线性规划问题
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-03 DOI: 10.1016/j.cie.2025.111724
Giuseppe Olivieri, Agostino Marcello Mangini, Maria Pia Fanti
In large organizations, the allocation of personnel within office spaces presents significant challenges, particularly with the adoption of modern working methodologies such as smart working, co-working, and agile working. This paper addresses the optimization of workspace assignments to balance occupancy levels while ensuring cohesion within organizational units and compliance with individual work schedules. The proposed approach incorporates constraints to prevent overcrowding, maintain consistent desk assignments, and enforce separation between specific personnel groups. A multi-objective Integer Linear Programming formulation is developed and validated through a real case study. Results demonstrate that the methodology effectively reduces peak occupancy imbalances and strengthens team cohesion, providing human resources departments with a practical decision-support tool that requires minimal technical expertise. The solution features an intuitive web interface that facilitates efficient space management in dynamic working environments.
在大型组织中,办公空间内的人员分配面临着重大挑战,尤其是在采用智能工作、联合工作和敏捷工作等现代工作方法的情况下。本文解决了工作空间分配的优化,以平衡占用水平,同时确保组织单位内的凝聚力和个人工作时间表的遵从性。拟议的办法包括限制措施,以防止过度拥挤,保持一致的办公桌分配,并在特定人员群体之间实行隔离。提出了一个多目标整数线性规划公式,并通过实例进行了验证。结果表明,该方法有效地减少了高峰占用不平衡,增强了团队凝聚力,为人力资源部门提供了一个实用的决策支持工具,需要最少的技术专长。该解决方案具有直观的web界面,有助于在动态工作环境中进行有效的空间管理。
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引用次数: 0
Deep learning approaches for weld defect detection: A comprehensive review of models, applications, and future directions 焊接缺陷检测的深度学习方法:模型、应用和未来方向的全面回顾
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-03 DOI: 10.1016/j.cie.2025.111725
Berkay Eren
This review provides a structured analysis of AI-based techniques for weld defect detection, covering model architectures, industrial deployment, and future directions. Conventional machine learning approaches are first outlined, followed by a detailed comparison of modern deep learning models. Convolutional neural networks (CNNs) remain widely applied, achieving over 95% accuracy in classification and mean IoU around 85–91% in segmentation, though their performance is often dataset-dependent. Detection-oriented architectures, especially YOLO derivatives, stand out by combining high accuracy (mAP above 95%) with real-time inference, making them the most practical for industrial use. Attention-augmented and transformer hybrids further improve small-defect recognition and multimodal learning, reaching up to 99% precision, but their computational demand limits deployment. Meta-analytical synthesis highlights that CNN classifiers are robust but sensitive to data bias, segmentation networks are effective yet variable, YOLO-based detectors consistently provide the best accuracy–speed balance, and Transformer hybrids achieve the highest precision at greater cost. Lightweight models such as MobileNet, YOLOv7-tiny, and EfficientNet-lite, often enhanced by quantization or pruning, enable deployment on resource-constrained hardware like Jetson Nano and Raspberry Pi. The adoption of Explainable AI (XAI) tools is also growing, particularly in safety–critical contexts requiring interpretability. Remaining challenges include the lack of standardized evaluation protocols, limited use of multimodal fusion and self-supervised learning, and uncertain benefits of GAN-based synthetic data. Overall, this review emphasizes that the most suitable approach depends on balancing accuracy, robustness, efficiency, and deployment feasibility, offering guidance toward reliable industrial solutions.
本文对基于人工智能的焊接缺陷检测技术进行了结构化分析,涵盖了模型架构、工业部署和未来发展方向。首先概述了传统的机器学习方法,然后详细比较了现代深度学习模型。卷积神经网络(cnn)仍然被广泛应用,在分类方面的准确率超过95%,在分割方面的平均IoU约为85-91%,尽管它们的性能通常依赖于数据集。面向检测的架构,特别是YOLO衍生产品,通过将高精度(mAP高于95%)与实时推理相结合而脱颖而出,使其在工业应用中最实用。注意增强和变压器混合技术进一步提高了小缺陷识别和多模态学习,达到99%的精度,但它们的计算需求限制了部署。元分析综合强调,CNN分类器鲁棒但对数据偏差敏感,分割网络有效但易变,基于yolo的检测器始终提供最佳的精度-速度平衡,变压器混合方法以更高的成本实现最高的精度。轻量级模型,如MobileNet、YOLOv7-tiny和EfficientNet-lite,通常通过量化或修剪来增强,可以部署在资源受限的硬件上,如Jetson Nano和Raspberry Pi。可解释AI (XAI)工具的采用也在增长,特别是在需要可解释性的安全关键环境中。剩下的挑战包括缺乏标准化的评估协议,多模态融合和自监督学习的使用有限,以及基于gan的合成数据的不确定收益。总之,本文强调最合适的方法取决于平衡精度、鲁棒性、效率和部署可行性,为可靠的工业解决方案提供指导。
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引用次数: 0
Fast initial response-based r-EWMA single control chart for joint monitoring of location and scale parameters with nonlinear multiple quality characteristics 基于快速初始响应的r-EWMA单控制图对具有非线性多重质量特征的位置和尺度参数联合监测
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-02 DOI: 10.1016/j.cie.2025.111719
Cang Wu , Min Luo , Dong Wang , Wenpo Huang , Lijun Shang , Shubin Si
Monitoring shifts in location and scale (L&S) parameters during production processes is crucial, and control charts serve as indispensable tools for this purpose. They can be categorized into single chart and two-chart, with the former being more advantageous due to their simplicity and effectiveness in identifying changes. The problem at issue is that existing methods for monitoring unknown process distributions inadequately address simultaneous shifts in both L&S parameters. This paper presents the rank-based Exponentially Weighted Moving Average (r-EWMA) control chart, designed to monitor multiple processes without relying on the conventional premise of a multivariate normal distribution. This method combines rank-based statistics with local statistics derived from the k-nearest neighbors method and employs an EWMA control scheme. To assess the effectiveness of the proposed scheme, a Monte Carlo simulation has been executed and real-world case studies have been examined. The results of the simulation demonstrate that r-EWMA outperforms comparative control charts regarding the Median Run Length (MRL), when detecting out-of-control (OC) signals across various changes in non-normally distributed and nonlinear mixed distributions. Two case studies further validate the superiority of r-EWMA in handling shifts in L&S parameters under unknown process distributions, particularly when considering nonlinear correlations in multiple quality characteristics.
在生产过程中监测位置和规模(L&;S)参数的变化是至关重要的,控制图是实现这一目的不可或缺的工具。它们可以分为单图和双图,前者更有优势,因为它们在识别变化方面简单有效。问题是现有的监测未知过程分布的方法不能充分地处理两个L&;S参数的同时变化。本文提出了基于秩的指数加权移动平均(r-EWMA)控制图,该控制图旨在监测多个过程,而不依赖于多元正态分布的传统前提。该方法将基于秩的统计量与基于k近邻的局部统计量相结合,采用EWMA控制方案。为了评估所提出方案的有效性,进行了蒙特卡洛模拟,并对实际案例进行了研究。仿真结果表明,在检测非正态分布和非线性混合分布中各种变化的失控(OC)信号时,r-EWMA在中位数运行长度(MRL)方面优于比较控制图。两个案例研究进一步验证了r-EWMA在处理未知过程分布下L&;S参数变化方面的优势,特别是在考虑多个质量特性的非线性相关性时。
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引用次数: 0
Dynamic Location–Allocation–Routing scheduling for long-range maritime rescue operations using shipboard helicopters: A Q-learning-based hyper-heuristic approach 舰载直升机远程海上救援行动的动态定位-分配-路由调度:基于q学习的超启发式方法
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-01 DOI: 10.1016/j.cie.2025.111722
Xu Luo, Yong Liu, Jiawei Wu
The increasing frequency and complexity of maritime activities demand more efficient and responsive rescue operations. To address this need in long-range scenarios, this study develops a dynamic “Location-Allocation-Routing” model that coordinates multiple accident points and rescue centers using shipboard helicopters. A distinguishing feature of this model is its incorporation of several dynamic factors: the ongoing drift of accident locations, the psychological panic of personnel, and the emergence of unexpected tasks during operations. The model is structured around two primary objectives: to minimize the maximum time required for any single rescue and to reduce the overall psychological panic costs involved. This bi-objective approach serves to highlight and prioritize the most critical rescue tasks. To solve the model, a Q-learning-based hyper-heuristic algorithm framework is proposed. This algorithm is designed to effectively integrate global exploration with adaptive learning, enabling a robust response to evolving rescue scenarios. Furthermore, a dynamic path segmentation mechanism is embedded within the algorithm to enhance its flexibility. The model’s adaptability and the algorithm’s effectiveness are confirmed through extensive numerical experiments and case studies, providing a solid foundation of both theoretical and practical support for advanced oceanic emergency rescue systems.
海上活动日益频繁和复杂,需要更有效和反应迅速的救援行动。为了解决远程场景中的这一需求,本研究开发了一个动态的“定位-分配-路由”模型,该模型使用舰载直升机协调多个事故点和救援中心。该模型的一个显著特点是它结合了几个动态因素:事故地点的持续漂移,人员的心理恐慌,以及行动中意外任务的出现。该模型围绕两个主要目标构建:最小化任何单一救援所需的最大时间,并减少所涉及的总体心理恐慌成本。这种双目标方法有助于突出和优先处理最关键的救援任务。为了求解该模型,提出了一种基于q学习的超启发式算法框架。该算法旨在有效地将全局探索与自适应学习相结合,从而对不断变化的救援场景做出稳健的响应。此外,该算法还嵌入了动态路径分割机制,提高了算法的灵活性。通过大量的数值实验和实例研究,验证了模型的适应性和算法的有效性,为先进的海洋应急救援系统提供了坚实的理论和实践支持基础。
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引用次数: 0
Optimizing design refresh decisions for long life systems production 为长寿命系统生产优化设计更新决策
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-01 DOI: 10.1016/j.cie.2025.111723
Chad Uhles , Hugh Medal , Michael Sherwin , Jessica Bean , Dallas Rosson , Kristi-Anna Stageberg , Seth Shuchat
Diminishing manufacturing sources and material shortages is a growing problem for industries that rely on systems with a long life expectancy. Technological developments and economic factors often cause parts within the system to become obsolete, the effects of which must be mitigated. An under-utilized resolution approach is the proactive design refresh, which replaces system designs that use soon-to-be obsolete parts with designs that do not use soon-to-be obsolete parts. In this work, we propose a mixed-integer programming optimization model that minimizes the present value of costs of an obsolescence management plan for a system subject to part obsolescence, leveraging proactive design refreshes and balancing part inventories. We experimentally test the computational scalability of our model and compare the policies to existing models in the literature and a reactive approach used in practice. The computational scalability experiment shows that our model scales well to the size of the bill of materials. Likewise, the comparison of policies experiment shows that our model produces solutions that are more cost-effective than other methodologies while being more flexible to different system production schedules. The main benefit of this work is our model’s ability to identify opportunities for significant obsolescence management cost avoidance due to the detailed resolution schedules that are generated and the utilization of part inventories to inform resolution schedules. Furthermore, this work validates the notion that a properly leveraged proactive design refresh is indeed an effective way to resolve events of part obsolescence.
对于依赖长寿命系统的行业来说,制造来源减少和材料短缺是一个日益严重的问题。技术发展和经济因素经常导致系统内的部件过时,必须减轻其影响。一种未充分利用的解决方法是主动设计刷新,它用不使用即将过时部件的设计替换使用即将过时部件的系统设计。在这项工作中,我们提出了一个混合整数规划优化模型,该模型利用主动设计更新和平衡零件库存,使一个受零件报废影响的系统的报废管理计划的成本现值最小化。我们通过实验测试了模型的计算可扩展性,并将策略与文献中的现有模型和实践中使用的反应性方法进行了比较。计算可扩展性实验表明,我们的模型可以很好地扩展到物料清单的尺寸。同样,策略实验的比较表明,我们的模型产生的解决方案比其他方法更具成本效益,同时对不同的系统生产计划更灵活。这项工作的主要好处是,我们的模型能够识别由于生成的详细解决方案计划和利用零件清单来通知解决方案计划而导致的重大报废管理成本避免的机会。此外,这项工作验证了这样一个概念,即适当地利用主动设计更新确实是解决部件过时事件的有效方法。
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引用次数: 0
Dynamic cloud manufacturing service composition based on runtime QoS prediction: A predictive process monitoring-based method 基于运行时QoS预测的动态云制造服务组合:一种基于预测过程监控的方法
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-01 DOI: 10.1016/j.cie.2025.111701
Reza Aalikhani , Mohammad Fathian , Mohammad Reza Rasouli , Rik Eshuis
In the context of Cloud Manufacturing (CMfg), Service Composition (SC) approaches are used to improve the delivery of flexible and personalized services. Dynamic SC necessitates adapting to changes in Quality of Service (QoS) in real-time. Current SC methods lack the ability to dynamically predict QoS through monitoring of providers’ capabilities and resources. This paper proposes a novel method for dynamic SC that addresses real-time QoS predictions for the CMfg services by monitoring the related resources. For this purpose, a predictive process monitoring model is first proposed to predict the next sub-task of a CMfg process. Then, an adaptive service selection model is developed to predict the run-time QoS of relevant services that can fulfill the next sub-task. At runtime, the method dynamically selects the resource with the shortest predicted completion time for the SC. The proposed method was evaluated through a case study involving networked medical laboratories in Iran. Results demonstrate the method’s ability to accurately predict both subsequent process sub-tasks and overall process completion time during SC. Specifically, it achieved a next sub-task prediction precision exceeding 0.82 and produced feasible CMfg processes with over 72% feasibility. Furthermore, by accurately predicting the completion time of candidate resources, with a MAE below 7.5 minutes, the method proposed SCs that were over 94% similar to the best historical compositions. The core contribution of this research is the proposal of a dynamic SC method, incorporating adaptive service monitoring models to predict process completion times by considering real-time resource workloads within CMfg processes.
在云制造(CMfg)的背景下,服务组合(SC)方法被用于改进灵活和个性化服务的交付。动态SC需要实时适应服务质量(QoS)的变化。当前的SC方法缺乏通过监控提供者的能力和资源来动态预测QoS的能力。本文提出了一种新的动态SC方法,通过监控相关资源来解决CMfg服务的实时QoS预测问题。为此,首先提出了一个预测过程监控模型来预测CMfg过程的下一个子任务。然后,建立了一个自适应服务选择模型来预测能够完成下一个子任务的相关服务的运行时QoS。在运行时,该方法动态选择具有最短预测完成时间的SC资源。该方法通过涉及伊朗网络化医学实验室的案例研究进行了评估。结果表明,该方法能够准确预测SC过程中后续工艺子任务和整体工艺完成时间。具体而言,该方法的下一个子任务预测精度超过0.82,产生可行的CMfg工艺的可行性超过72%。此外,通过准确预测候选资源的完成时间,在MAE低于7.5分钟的情况下,该方法提出的SCs与最佳历史作文的相似度超过94%。本研究的核心贡献是提出了一种动态SC方法,结合自适应服务监控模型,通过考虑CMfg过程中的实时资源负载来预测过程完成时间。
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引用次数: 0
Impurity-based borderline SMOTE with affinity propagation for imbalanced data classification 不平衡数据分类中基于杂质的边界SMOTE与关联传播
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-30 DOI: 10.1016/j.cie.2025.111720
R.J. Kuo , Kai-Wen Zheng , Ferani E. Zulvia , Timothy Kuo
The problem of imbalanced data classification is prevalent in many real-world applications, where certain classes contain significantly more instances than others. This imbalance negatively impacts classification performance, often leading to the misclassification of minority class instances. Data resampling techniques, such as oversampling and undersampling, offer a promising solution. However, conventional resampling approaches rely on local neighbor information to generate new instances in a linear manner, which can result in inaccurate and redundant samples.
Therefore, this study proposes a novel automatic clustering oversampling method to address imbalanced data classification problem. First, an advanced clustering technique is used to improve Affinity Propagation (AP) algorithm’s clustering quality and identifies clusters for oversampling using the Gini impurity index. This technique can automatically construct clusters and define the number of clusters. Second, an improved Borderline Synthetic Minority Over-sampling Technique (iB-SMOTE) differentiates between safe and risky minority samples, generating new data in both areas to reinforce class boundaries. By using different formulas to generate synthetic minority data, this algorithm strengthens the border between minority and majority classes while expanding the area of minority data without encroaching on the majority area.
Experimental results on 27 imbalanced datasets using six classifiers show that the proposed AP-iB-SMOTE algorithm significantly outperforms conventional methods in terms of F1-score and AUC metrics. Furthermore, statistical tests confirm the superiority of AP-iB-SMOTE algorithm in effectively handling imbalanced data.
不平衡数据分类的问题在许多实际应用程序中很普遍,其中某些类比其他类包含更多的实例。这种不平衡对分类性能产生负面影响,经常导致少数类实例的错误分类。数据重采样技术,如过采样和欠采样,提供了一个有前途的解决方案。然而,传统的重采样方法依赖于局部邻居信息以线性方式生成新实例,这可能导致样本不准确和冗余。因此,本研究提出了一种新的自动聚类过采样方法来解决不平衡数据分类问题。首先,采用一种先进的聚类技术来提高亲和性传播(Affinity Propagation, AP)算法的聚类质量,并利用基尼杂质指数来识别过采样的聚类。该技术可以自动构建集群并定义集群的数量。其次,改进的边界合成少数样本过度采样技术(iB-SMOTE)区分了安全和有风险的少数样本,在两个区域生成新数据以加强类别边界。该算法通过使用不同的公式生成合成的少数类数据,加强了少数类和多数类之间的边界,同时在不侵犯多数类的情况下扩大了少数类数据的区域。在27个不平衡数据集上使用6个分类器的实验结果表明,本文提出的AP-iB-SMOTE算法在f1得分和AUC指标方面明显优于传统方法。此外,统计检验证实了AP-iB-SMOTE算法在有效处理不平衡数据方面的优越性。
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引用次数: 0
Optimizing sustainable production scheduling and routing in supply chains 优化供应链中的可持续生产调度和路线
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-29 DOI: 10.1016/j.cie.2025.111712
Tanzila Azad , Humyun Fuad Rahman , Daryl Essam , Ripon K. Chakrabortty
This research addresses an integrated production scheduling and vehicle routing problem in a flexible job-shop-based manufacturing supply chain, with a focus on achieving both economic and environmental sustainability. A bi-objective mathematical model is developed to minimize total tardiness from delivery delays and CO2 emissions from production and distribution operations. To solve this complex problem, we propose a hybrid, non-dominated sorting genetic algorithm (HNSGA-II). The proposed approach is benchmarked against classical optimization methods using CPLEX, non-hybridized versions of NSGA-II and NSGA-III, and Yağmur & Kesen (2023)s’ algorithm as a state-of-the-art approach. Performance comparisons on realistic problem instances reveal that HNSGA-II consistently provides higher-quality Pareto solutions, achieving better trade-offs between objectives within comparable runtimes. These findings demonstrate the proposed algorithm’s efficiency and applicability to integrated production and distribution optimization in sustainable supply chains.
本研究解决了基于柔性作业车间的制造供应链中的集成生产调度和车辆路线问题,重点是实现经济和环境的可持续性。开发了一个双目标数学模型,以最大限度地减少交货延迟和生产和分销操作中的二氧化碳排放。为了解决这个复杂的问题,我们提出了一种混合的非支配排序遗传算法(HNSGA-II)。所提出的方法与经典优化方法进行基准测试,使用CPLEX, NSGA-II和NSGA-III的非杂交版本,以及Yağmur &; Kesen(2023)的算法作为最先进的方法。对实际问题实例的性能比较表明,HNSGA-II始终提供更高质量的Pareto解决方案,在可比较的运行时间内实现目标之间的更好权衡。这些结果证明了该算法在可持续供应链中生产与分配一体化优化中的有效性和适用性。
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引用次数: 0
Reactive-proactive rescheduling in blood supply chain management 血液供应链管理中的反应-主动重新调度
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-29 DOI: 10.1016/j.cie.2025.111692
Maria Meneses, Daniel Santos, Ana Barbosa-Póvoa
The timely and efficient availability of blood products is essential in the Blood Supply Chain. Yet, the unpredictable nature of blood donations and demand, combined with various disturbances to scheduled activities, poses a significant challenge for the effective management of this network at the operational level. To address these issues, this research proposes a reactive-proactive rescheduling model for Blood Supply Chain management, referred to as Blood-OPE. This model considered real-time data and anticipated disturbances to adjust the existing master plan. The main goal is to sustain the service level provided to demand nodes and safety stock targets, while lowering deviations from planned activities (nervousness) and reducing waste. To demonstrate the model’s applicability, Blood-OPE is applied to the Portuguese Blood Supply Chain network, quantifying the trade-offs between various rescheduling flexibilities. The main findings indicate that having rescheduling flexibility helps meet demand and safety stock targets while reducing waste compared to relying solely on reactive measures. The sensitivity analysis emphasizes the importance of tailored strategies for different blood types and safety stock targets.
及时和有效地提供血液制品对血液供应链至关重要。然而,献血和需求的不可预测性,加上对预定活动的各种干扰,对在业务一级有效管理这一网络构成了重大挑战。为了解决这些问题,本研究提出了一种用于血液供应链管理的反应-主动重新调度模型,称为Blood- ope。该模型考虑了实时数据和预期干扰来调整现有的总体规划。主要目标是维持提供给需求节点和安全库存目标的服务水平,同时降低与计划活动的偏差(紧张)并减少浪费。为了证明该模型的适用性,Blood- ope应用于葡萄牙血液供应链网络,量化了各种重新调度灵活性之间的权衡。主要研究结果表明,与仅仅依靠被动措施相比,重新调度的灵活性有助于满足需求和安全库存目标,同时减少浪费。敏感性分析强调了针对不同血型和安全库存目标量身定制策略的重要性。
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引用次数: 0
Exploring multi-fidelity networks and adapting their architecture: A paradigm for enhanced learning and efficiency 探索多保真度网络并调整其架构:提高学习和效率的范例
IF 6.5 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-29 DOI: 10.1016/j.cie.2025.111721
Bayan Hamdan , Pingfeng Wang
Multi-Fidelity Networks (MFNets) are a promising approach for surrogate modeling, particularly in scenarios with limited data and heterogeneous models. They establish relationships between models using parameters rather than relying solely on inputs or outputs. The covariance matrix, which captures the interconnections between the parameters, typically follows a peer structure assumption. When low-fidelity models exhibit dependencies, alternative architectures can better capture these relationships. This paper proposes a modified MFNets model that incorporates a hierarchical structure and presents a generalized formulation applicable to diverse applications. Two benchmark numerical problems are implemented to demonstrate the advantages of considering different underlying model architectures. The results showcase improved predictive capabilities of MFNets when estimating high-fidelity functions and leveraging available low-fidelity data and their relationships with each other.
多保真度网络(MFNets)是一种很有前途的代理建模方法,特别是在数据有限和异构模型的情况下。它们使用参数来建立模型之间的关系,而不是仅仅依赖于输入或输出。协方差矩阵捕获参数之间的相互联系,通常遵循对等结构假设。当低保真度模型显示依赖关系时,替代架构可以更好地捕获这些关系。本文提出了一个改进的MFNets模型,该模型采用了层次结构,并给出了一个适用于各种应用的通用公式。实现了两个基准数值问题,以证明考虑不同底层模型体系结构的优点。结果表明MFNets在估计高保真函数和利用可用的低保真数据及其相互关系时提高了预测能力。
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