Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

A Metamodeling Method Based on Support Vector Regression for Robust Optimization

Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensive simulation models. Existing metamodels main focus on polynomial regression（PR）, neural networks（NN） and Kriging models, these metamodels are not well suited for large-scale robust optimization problems with small size training sets and high nonlinearity. To address the problem, a reduced approximation model technique based on support vector regression（SVR） is introduced in order to improve the accuracy of metamodels. A robust optimization method based on SVR is presented for problems that involve high dimension and nonlinear. First appropriate design parameter samples are selected by experimental design theories, then the response samples are obtained from the simulations such as finite element analysis, the SVR metamodel is constructed and treated as the mean and the variance of the objective performance functions. Combining other constraints, the robust optimization model is formed which can be solved by genetic algorithm （GA）. The applicability of the method developed is demonstrated using a case of two-bar structure system study. The performances of SVR were compared with those of PR, Kriging and back-propagation neural networks（BPNN）, the comparison results show that the prediction accuracy of the SVR metamodel was higher than those of other metamodels under uncertainty. The robust optimization solutions are near to the real result, and the proposed method is found to be accurate and efficient for robust optimization. This reaserch provides an efficient method for robust optimization problems with complex structure.

OPTIMIZATION METHOD FOR VIRTUAL PRODUCT DEVELOPMENT BASED ON SIMULATION METAMODEL AND ITS APPLICATION

Virtual product development (VPD) is essentially based on simulation. Due tocomputational inefficiency, traditional engineering simulation software and optimization methods areinadequate to analyze optimization problems in VPD. Optimization method based on simulationmetamodel for virtual product development is proposed to satisfy the needs of complex optimaldesigns driven by VPD. This method extends the current design of experiments (DOE) by variousmetamodeling technologies. Simulation metamodels are built to approximate detailed simulation codes,so as to provide link between optimization and simulation, or serve as a bridge for simulationsoftware integration among different domains. An example of optimal design for composite materialstructure is used to demonstrate the newly introduced method.

Metamodel-based Global Optimization Using Fuzzy Clustering for Design Space Reduction

High fidelity analysis are utilized in modern engineering design optimization problems which involve expensive black-box models.For computation-intensive engineering design problems,efficient global optimization methods must be developed to relieve the computational burden.A new metamodel-based global optimization method using fuzzy clustering for design space reduction(MGO-FCR) is presented.The uniformly distributed initial sample points are generated by Latin hypercube design to construct the radial basis function metamodel,whose accuracy is improved with increasing number of sample points gradually.Fuzzy c-mean method and Gath-Geva clustering method are applied to divide the design space into several small interesting cluster spaces for low and high dimensional problems respectively.Modeling efficiency and accuracy are directly related to the design space,so unconcerned spaces are eliminated by the proposed reduction principle and two pseudo reduction algorithms.The reduction principle is developed to determine whether the current design space should be reduced and which space is eliminated.The first pseudo reduction algorithm improves the speed of clustering,while the second pseudo reduction algorithm ensures the design space to be reduced.Through several numerical benchmark functions,comparative studies with adaptive response surface method,approximated unimodal region elimination method and mode-pursuing sampling are carried out.The optimization results reveal that this method captures the real global optimum for all the numerical benchmark functions.And the number of function evaluations show that the efficiency of this method is favorable especially for high dimensional problems.Based on this global design optimization method,a design optimization of a lifting surface in high speed flow is carried out and this method saves about 10 h compared with genetic algorithms.This method possesses favorable performance on efficiency,robustness and capability of global convergence and gives a new optimization strategy for engineering design optimization problems involving expensive black box models.

Optimization Strategy Using Dynamic Metamodel Based on Trust Region and Biased Sampling Method

Combining a trust region method with a biased sampling method,a novel optimization strategy(TRBSKRG)based on a dynamic metamodel is proposed.Initial sampling points are selected by a maximin Latin hypercube design method,and the metamodel is constructed with Kriging functions.The global optimization algorithm is employed to perform the biased sampling by searching the maximum expectation improvement point or the minimum of surrogate prediction point within the trust region.And the trust region is updated according to the current known information.The iteration continues until the potential global solution of the true optimization problem satisfied the convergence conditions.Compared with the trust region method and the biased sampling method,the proposed optimization strategy can obtain the global optimal solution to the test case,in which improvements in computation efficiency are also shown.When applied to an aerodynamic design optimization problem,the aerodynamic performance of tandem UAV is improved while meeting the constraints,which verifies its engineering application.

An ontological metamodeling framework for semantic simulation model engineering

Recently,the ontological metamodel plays an increasingly important role to specify systems in two forms:ontology and metamodel.Ontology is a descriptive model representing reality by a set of concepts,their interrelations,and constraints.On the other hand,metamodel is a more classical,but more powerful model in which concepts and relationships are represented in a prescriptive way.This study firstly clarifies the difference between the two approaches,then explains their advantages and limitations,and attempts to explore a general ontological metamodeling framework by integrating each characteristic,in order to implement semantic simulation model engineering.As a proof of concept,this paper takes the combat effectiveness simulation systems as a motivating case,uses the proposed framework to define a set of ontological composable modeling frameworks,and presents an underwater targets search scenario for running simulations and analyzing results.Finally,this paper expects that this framework will be generally used in other fields.

A MOP Based Constructive Reflective State Metamodel

Construction, management and extension of state space is crucial for many applications, Combining with frequent change of requirement of state space, these applications are rather complicated. Synthesizing techniques of refection architecture, MOP mechanism and metamodel, this paper advances a MOP(Meta Object Protocol) based constructive state metamodel, which defines construct and rules for building models with extensible structure for state space. Based on this metamodel, modeling with extension of state space that adopts decorator pattern and role object pattern is discussed. An implementation of modeling based on this metamodel is presented. With appropriate extension, models based on this metamodel can dynamically adapt state space change. Key words metamodel - reflection - MOP - state space CLC number TP 311.5 Foundation item: Supported by the National Natural Science Foundation of China (60373086)Biography: Liu Jin (1977-), male, Ph. D candidate, research direction: metamodeling and ontology application.

Robust Design Optimization and Improvement by Metamodel

The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.

Model Transformation Using a Simplified Metamodel

Model Driven Engineering (MDE) is a model-centric software development approach aims at improving the quality and productivity of software development processes. While some progresses in MDE have been made, there are still many challenges in realizing the full benefits of model driven engineering. These challenges include incompleteness in existing modeling notations, inadequate in tools support, and the lack of effective model transformation mechanism. This paper provides a solution to build a template-based model transformation framework using a simplified metamode called Hierarchical Relational Metamodel (HRM). This framework supports MDE while providing the benefits of readability and rigorousness of meta-model definitions and transformation definitions.

A Metamodel-Driven Business Process Modeling Methodology and Its Integrated Environment for Reusing Business Processes

Reusing business process models and best practices can improve the productivity, quality and agility in the early development phases of enterprise software systems. To help developers reuse the business process models and best practices, we propose a methodology and an integrated environment for business process modeling driven by the metamodel. Furthermore, we propose a process-template design method to unify the granularity and separate the commonality and variability of business processes so that business process models can be reused across different enterprise software systems. The proposed methodology enables to create reuse-oriented business process templates before the business process modeling. To support the proposed methodology, we developed an integrated environment for creating, reusing and verifying the business process models. As the key techniques, we describe the methodology and its integrated environment, including a metamodel and notations. We applied the methodology and integrated environment to an actual enterprise software development project, and evaluated that the productivity of business process modeling is improved by at least 46%. As the conclusion, this paper contributes to prove the effectiveness of the meta-model driven business process modeling methodology for the reuse of business process models.

A Metamodel for Agile Requirements Engineering

Value delivery is becoming an important asset for an organization due to increasing competition in industry. Therefore, companies apply Agile Software Development (ASD) to be more competitive and reduce time to market. Using ASD for the development of systems implies that established approaches of Requirements Engineering (RE) undergo some changes in order to be more flexible to changing requirements. To this end, the field of agile RE is emergent and different process models for agile RE have arisen. The aim of this paper is to build an abstract layer about the variety of existing process models by means of a metamodel for agile RE. It has been created in several iterations and relies on the evaluation of related process models. Furthermore, we have derived process models for agile RE in industry by presenting instances of the metamodel in two different cases: one is based on Scrum whereas the other is based on Kanban. This paper contributes to the software development body of knowledge by delivering a metamodel for agile RE that supports researchers and practitioners modeling and improving their own process models. We can conclude that the agile RE metamodel is highly relevant for the industry as well as for the research community, since we have derived it following empirical research in the field of ASD.

Multi-Criterion Optimal Design of Automotive Door Based on Metamodeling Technique and Genetic Algorithm

A method for optimizing automotive doors under multiple criteria involving the side impact, stiffness, natural frequency, and structure weight is presented. Metamodeling technique is employed to construct approximations to replace the high computational simulation models. The approximating functions for stiffness and natural frequency are constructed using Taylor series approximation. Three popular approximation techniques,i.e.polynomial response surface (PRS), stepwise regression (SR), and Kriging are studied on their accuracy in the construction of side impact functions. Uniform design is employed to sample the design space of the door impact analysis. The optimization problem is solved by a multi-objective genetic algorithm. It is found that SR technique is superior to PRS and Kriging techniques in terms of accuracy in this study. The numerical results demonstrate that the method successfully generates a well-spread Pareto optimal set. From this Pareto optimal set, decision makers can select the most suitable design according to the vehicle program and its application.

A metamodel for heritage-based urban recovery

Purpose:The purpose of this paper is to discuss the potential transfer of a metamodel for heritage-based urban development(HBUD)in a postcrisis urban recovery scenario.Design/methodology/approach:After an introduction to the feld of cultural heritage as a resource for urban development,the research question is elaborated,and the current understanding of urban heritage is explored.The use of the metamodel in a postcrisis urban recovery setting is described as a potential solution.The proposed metamodel is introduced along with the grounded theory and design research methodology through which it was developed.The specifc qualities of metamodels and how they can contribute to the proposed use are highlighted.The scenario is then developed further,and specifc ways in which the metamodel could contribute are elaborated.Finally,the metamodel is compared to other methods,such as the historic urban landscape(HUL)approach,and the limitations are discussed.Findings:The metamodel can potentially be used in a postcrisis urban recovery scenario.The metamodel cannot be used directly,owing to the nature of metamodels;however,it can be transferred to a specifc context and help to structure successful heritage-based urban recovery(HBUR)processes.Practical limitations/implications:One limitation is that it can be difcult to understand the diferences between models and metamodels.Only with a comprehensive understanding of the nature of metamodels can this metamodel be applied,for example,to select appropriate models for HBUR.The metamodel can help to ensure that all relevant‘elements’are part of the processes designed for HBUR and emphasise the need for thorough planning,or scoping,of such processes.Originality/value:Metamodelling has not previously been used for HBUD or HBUR.

A point cloud deep neural network metamodel method for aerodynamic prediction

Aiming to reduce the high expense of 3-Dimensional(3D)aerodynamics numerical sim-ulations and overcome the limitations of the traditional parametric learning methods,a point cloud deep learning non-parametric metamodel method is proposed in this paper.The 3D geometric data,corresponding to the object boundaries,are chosen as point clouds and a deep learning neural net-work metamodel fed by the point clouds is further established based on the PointNet architecture.This network can learn an end-to-end mapping between spatial positions of the object surface and CFD numerical quantities.With the proposed aerodynamic metamodel approach,the point clouds are constructed by collecting the coordinates of grid vertices on the object surface in a CFD domain,which can maintain the boundary smoothness and allow the network to detect small changes between geometries.Moreover,the point clouds are easily accessible from 3D sensors.The point cloud deep learning neural network,which employs re-sampling technique,the spatial transformer network and the fully connected layer,is developed to predict the aerodynamic char-acteristics of 3D geometry.The effectiveness of the proposed metamodel method is further verified by aerodynamic prediction and robust shape optimization of the ONERA M6 wing.The results show that the proposed method can achieve more satisfactory agreement with the experimental measurements compared to the parametric-learning-based deep neural network.

Physics-informed machine learning for metamodeling thermal comfort in non-air-conditioned buildings

There is a growing need for accurate and interpretable machine learning models of thermal comfort in buildings.Physics-informed machine learning could address this need by adding physical consistency to such models.This paper presents metamodeling of thermal comfort in non-air-conditioned buildings using physics-informed machine learning.The studied metamodel incorporated knowledge of both quasi-steady-state heat transfer and dynamic simulation results.Adaptive thermal comfort in an office located in cold and hot European climates was studied with the number of overheating hours as index.A one-at-a-time method was used to gain knowledge from dynamic simulation with TRNSYS software.This knowledge was used to filter the training data and to choose probability distributions for metamodel forms alternative to polynomial.The response of the dynamic model was positively skewed;and thus,the symmetric logistic and hyperbolic secant distributions were inappropriate and outperformed by positively skewed distributions.Incorporating physical knowledge into the metamodel was much more effective than doubling the size of the training sample.The highly flexible Kumaraswamy distribution provided the best performance with R2 equal to 0.9994 for the cold climate and 0.9975 for the hot climate.Physics-informed machine learning could combine the strength of both physics and machine learning models,and could therefore support building design with flexible,accurate and interpretable metamodels.

Research on Metamodels Consistency Verification Based on Formalization of Domain-Specific Metamodeling Language

Domain-specific metamodeling language(DSMML) defined by informal method cannot strictly represent its structural semantics,so its properties such as consistency cannot be holistically and systematically verified.In response,the paper proposes a formal representation of the structural semantics of DSMML named extensible markup language(XML) based metamodeling language(XMML) and its metamodels consistency verification method.Firstly,we describe our approach of formalization,based on this,the method of consistency verification of XMML and its metamodels based on first-order logical inference is presented;then,the formalization automatic mapping engine for metamodels is designed to show the feasibility of our formal method.

基于MDR2023的元数据值域语义约束注册标准化模型研究

元数据注册(MetadataRegistry,MDR)是数据治理中元数据精确表达语义的必要前提。通过全面系统地分析国内外的MDR系统,发现国内外MDR更多关注基本数据元素,数据语义约束注册方面的研究缺乏。因此,首先基于ISO/IEC11179:2023(MDR2023)系列标准提出元数据语义约束外延分类模型,明确元数据语义约束范围,并选取其中的值域语义约束详细研究;其次,基于MDR2023标准提出元数据值域语义约束注册元模型,为元数据语义约束注册提供标准化且完整的注册算法流程,从而为元数据值域语义约束注册提供解决方案;最后,以石油领域著名的POSC标准为需求背景,对其中的值域语义约束进行注册,据此实现石油领域元数据值域语义约束的标准化,验证提出的元数据值域语义约束注册元模型的合理性和可行性。提出的元模型对于其他领域数据治理具有普适性。

Robust ensemble of metamodels based on the hybrid error measure

Metamodels have been widely used as an alternative for expensive physical experiments or complex,time-consuming computational simulations to provide a fast but accurate analysis.However,challenge remains in the prior determination of the most suitable metamodel for a particular case because of the lack of information about the actual behavior of a system.In addition,existing studies on metamodels have largely restricted on solving deterministic problems(e.g.,data from finite element models),whereas some real-life engineering problems(e.g.,data from physical experiment)are stochastic problems with noisy data.In this work,a robust ensemble of metamodels(EMs)is proposed by combining three regression stand-alone metamodels in a weighted sum form.The weight factor is adaptively determined according to the hybrid error metric,which combines global and local error measures to improve the accuracy of the EMs.Furthermore,three typical individual metamodels that can filter noise are selected to construct the EMs to extend their application in practical engineering problems.Three well-known benchmark problems with different levels of noise and three engineering problems are used to verify the effectiveness of the proposed EMs.Results show that the proposed EMs have higher accuracy and robustness than the individual metamodels and other typical EMs in major cases.

基于最佳预后元模型的颗粒污垢特性全局敏感性分析

通过敏感性分析可识别出重要变量和无关变量,有效筛选数据降低模型复杂程度,并辅助优化设计。以内置转子传热管内的颗粒污垢为研究对象,采用欧拉-欧拉模型和颗粒污垢模型进行数值实验获取训练数据空间,基于最佳预后元模型开展全局敏感性分析,定量比较了颗粒直径、颗粒浓度、入口流速和入口温度的影响程度。对颗粒污垢四种沉积速率分析表明,入口温度对扩散沉积和热泳沉积的影响最显著,总影响分别为65.4%、58.6%;颗粒直径对湍流泳沉积和重力沉积的影响最明显,总影响分别为53.9%、75.0%。在此基础上,进一步分析了沉积率和污垢热阻的总影响、主影响及交互影响。结果表明:颗粒直径对沉积率和污垢热阻的影响均最大,总影响分别为52.7%、60.2%,各输入变量对沉积率和污垢热阻的交互影响的和分别为59.7%、42.5%,且随着四个输入变量的增加,沉积率和污垢热阻均增大。颗粒直径是影响内置转子传热管颗粒污垢问题的首要因素,在换热器设计中应予以重点考虑,其次是流体温度与流速。