This paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.
Design/methodology/approach
The cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.
Findings
The new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.
Originality/value
1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.
本文旨在构建适用于任意多面体网格的三维对流扩散方程的保正有限体积方案。扩散通量采用经典的非线性两点通量近似法离散化。为确保完全离散方案具有正保全特性，提出了一种改进的对流通量离散方法。此外，还从对流通量离散化的线性重构中推导出了一种新的保正顶点插值方法。此外，Picard 迭代法在求解非线性系统时可能收敛较慢。因此，采用了 Picard 迭代法的 Anderson 加速法来求解非线性系统。新方案适用于任意多面体网格，并具有二阶精度。数值实验结果也证实了离散化方案的保正性。本文针对三维对流扩散方程提出了一种新的保正有限体积方案。2.构建了新的对流通量离散化方案。3.给出了一种新的二阶插值算法，以消除通量表达式中的辅助未知量。4.采用改进的安德森加速法加速 Picard 迭代的收敛。5.该方案能以二阶精度求解扭曲网格上的对流扩散方程。
{"title":"The cell-centered positivity-preserving finite volume scheme for 3D convection–diffusion equation on distorted meshes","authors":"Gang Peng","doi":"10.1108/ec-10-2023-0668","DOIUrl":"https://doi.org/10.1108/ec-10-2023-0668","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>This paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>The cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141773226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<h3>Purpose</h3> <p>This study focuses on the CFD numerical simulation and analysis of the vortex stacking problem at the top of the impeller of a high-speed fuel pump, mainly using LCS and entropy production theory to visualize the vortex at the top of the impeller as well as quantitatively analyzing the energy loss caused by the vortex at the top of the impeller. By combining the two methods, the two are well verified with each other that the stacking problem of the vortex at the top of the impeller and the location of the energy loss caused by the vortex are consistent with the vortex location. Such a method can reveal the problem of vortex buildup at the top of the lobe well, and provide a novel guidance idea for improving the performance of high-speed fuel pumps.</p><!--/ Abstract__block --> <h3>Design/methodology/approach</h3> <p>Based on CFD numerical simulation and analysis, this study mainly uses LCS and entropy production theory to visualize the top vortex of the impeller. Through the combination of the two methods, the accumulation problem of the top vortex of the impeller and the location of the energy loss caused by the vortex can be well revealed.</p><!--/ Abstract__block --> <h3>Findings</h3> <p>(1) The CFD numerical simulation analysis of the high-speed fuel pump is carried out, and the test is conducted to verify the numerical simulation results. The inlet and outlet pressure difference? P is used as the validation index, and the error analysis shows that the error between numerical simulation and test results is within 10%, which meets our requirements. Therefore, we carry out the next analysis with the help of CFD numerical simulation. By analyzing the full working condition simulation, its inlet and outlet differential pressure? P and efficiency? Are evaluated. It is found that its differential pressure decreases with the flow rate and its efficiency reaches its maximum at Qv = 9.87 L/s with a maximum efficiency of 78.32%. (2) We used the LCS in the analysis of vortices at the top of the impeller blades of a high-speed fuel pump. One of the metrics used to describe the LCS in fluid dynamics is the FTLE. The high FTLE region represents the region with the highest and fastest particle trajectory stretching velocity in the fluid flow. We performed a cross-sectional analysis of the FTLE field on the different height surfaces of the impeller on 25% Plane, 50% Plane, and 75% Plane, respectively. And a quarter turn of the rotor rotation was analyzed as a cycle divided into 8 moments. It is found that on 25% Plane, the vortex at the top of the lobe is not obvious, but there are high FTLE values on the shroud surface. On 50% Plane, the lobe top vortex is relatively obvious and the number of vortices is three. The vortex pattern remains stable with the rotating motion of the rotor. At 75% Plane, the lobe top vortex is more visible and its number of vortices increases to about 5 and the vortex morphology is relatively stable. The FTLE ri
{"title":"Lagrangian coherent structure combined with entropy production theory for the analysis of vortex build-up on the impeller top in a high-speed fuel pump","authors":"Jiahao Lu, Ran Tao, Di Zhu, Ruofu Xiao","doi":"10.1108/ec-01-2024-0001","DOIUrl":"https://doi.org/10.1108/ec-01-2024-0001","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>This study focuses on the CFD numerical simulation and analysis of the vortex stacking problem at the top of the impeller of a high-speed fuel pump, mainly using LCS and entropy production theory to visualize the vortex at the top of the impeller as well as quantitatively analyzing the energy loss caused by the vortex at the top of the impeller. By combining the two methods, the two are well verified with each other that the stacking problem of the vortex at the top of the impeller and the location of the energy loss caused by the vortex are consistent with the vortex location. Such a method can reveal the problem of vortex buildup at the top of the lobe well, and provide a novel guidance idea for improving the performance of high-speed fuel pumps.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>Based on CFD numerical simulation and analysis, this study mainly uses LCS and entropy production theory to visualize the top vortex of the impeller. Through the combination of the two methods, the accumulation problem of the top vortex of the impeller and the location of the energy loss caused by the vortex can be well revealed.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>(1) The CFD numerical simulation analysis of the high-speed fuel pump is carried out, and the test is conducted to verify the numerical simulation results. The inlet and outlet pressure difference? P is used as the validation index, and the error analysis shows that the error between numerical simulation and test results is within 10%, which meets our requirements. Therefore, we carry out the next analysis with the help of CFD numerical simulation. By analyzing the full working condition simulation, its inlet and outlet differential pressure? P and efficiency? Are evaluated. It is found that its differential pressure decreases with the flow rate and its efficiency reaches its maximum at Qv = 9.87 L/s with a maximum efficiency of 78.32%. (2) We used the LCS in the analysis of vortices at the top of the impeller blades of a high-speed fuel pump. One of the metrics used to describe the LCS in fluid dynamics is the FTLE. The high FTLE region represents the region with the highest and fastest particle trajectory stretching velocity in the fluid flow. We performed a cross-sectional analysis of the FTLE field on the different height surfaces of the impeller on 25% Plane, 50% Plane, and 75% Plane, respectively. And a quarter turn of the rotor rotation was analyzed as a cycle divided into 8 moments. It is found that on 25% Plane, the vortex at the top of the lobe is not obvious, but there are high FTLE values on the shroud surface. On 50% Plane, the lobe top vortex is relatively obvious and the number of vortices is three. The vortex pattern remains stable with the rotating motion of the rotor. At 75% Plane, the lobe top vortex is more visible and its number of vortices increases to about 5 and the vortex morphology is relatively stable. The FTLE ri","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141773228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the development of fracturing technology, the research of multi-well hydrofracturing becomes the key issue. Frac-hits in multi-well hydrofracturing has an important effect on fracture propagation and final production of fractured well; in the process of hydrofracturing, there are many implement parameters that can affect frac-hits, and previous studies in this area have not systematically targeted the influence of a single parameter on multi-well hydrofracturing. Therefore, it is of great significance to study the occurrence rule and influence of frac-hits for optimizing the design of fracturing wells.
Design/methodology/approach
Based on the proposed numerical models, the effects of different fracturing implement parameters (perforation cluster spacing, well spacing and injection rate) on frac-hits are compared in numerical cases. Through the analysis of fracture network, stress field and microseismic, the effects of different fracturing implement parameters on frac-hits and connections are compared.
Findings
The simulation results show that the effect of perforation cluster spacing and well spacing on frac-hits is greater than that of injection rate. Smaller well spacing makes it easier for fractures between adjacent wells to interact with each other, which increases the risk of frac-hits and reduces the risk of fracture connections. Smaller perforation cluster spacing results in larger individual fracture lengths and greater deflection angles, which makes the possibility of frac-hits and connections greater. The lower the injection rate, the lower the probability of frac-hits.
Originality/value
In this study, the influence of different fracturing implement parameters on frac-hits and connections in multi-well hydrofracturing is studied, and the mechanism of frac-hits and connections is analyzed through fracture network, stress field and microseismic analysis. Different simulation results are compared to optimize fracturing well parameter design and provide reference for engineering application.
{"title":"Frac-hits and connections of multi-well hydrofracturing fracture network involving the variable factors: well spacing, perforation cluster spacing and injection rate","authors":"Yongliang Wang, Liangchun Li, Nana Liu","doi":"10.1108/ec-01-2024-0077","DOIUrl":"https://doi.org/10.1108/ec-01-2024-0077","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>With the development of fracturing technology, the research of multi-well hydrofracturing becomes the key issue. Frac-hits in multi-well hydrofracturing has an important effect on fracture propagation and final production of fractured well; in the process of hydrofracturing, there are many implement parameters that can affect frac-hits, and previous studies in this area have not systematically targeted the influence of a single parameter on multi-well hydrofracturing. Therefore, it is of great significance to study the occurrence rule and influence of frac-hits for optimizing the design of fracturing wells.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>Based on the proposed numerical models, the effects of different fracturing implement parameters (perforation cluster spacing, well spacing and injection rate) on frac-hits are compared in numerical cases. Through the analysis of fracture network, stress field and microseismic, the effects of different fracturing implement parameters on frac-hits and connections are compared.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The simulation results show that the effect of perforation cluster spacing and well spacing on frac-hits is greater than that of injection rate. Smaller well spacing makes it easier for fractures between adjacent wells to interact with each other, which increases the risk of frac-hits and reduces the risk of fracture connections. Smaller perforation cluster spacing results in larger individual fracture lengths and greater deflection angles, which makes the possibility of frac-hits and connections greater. The lower the injection rate, the lower the probability of frac-hits.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>In this study, the influence of different fracturing implement parameters on frac-hits and connections in multi-well hydrofracturing is studied, and the mechanism of frac-hits and connections is analyzed through fracture network, stress field and microseismic analysis. Different simulation results are compared to optimize fracturing well parameter design and provide reference for engineering application.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ningjun Xu, Miaomiao Sun, Zhangsong Shi, Jin Zhang
<h3>Purpose</h3> <p>Firepower conflicts usually decay the firepower plan's enforceability, thus incurring high survival risks. Previous studies have shown little attention to avoiding firepower conflicts during the weapon target assignment process. This research proposes a new constrained optimization model named Firepower Conflict Free WTA (FCFWTA) and designs a Survival Evolution (SE) strategy for Artificial Fish Swarm Algorithm (AFSA) to solve the complex constrained WTA problem. In this way, commanders can get more reliable firepower assignment decision support.</p><!--/ Abstract__block --> <h3>Design/methodology/approach</h3> <p>A new constrained optimization model named Firepower Conflict Free WTA (FCFWTA) is constructed. FCFWTA unifies firepower decision variables for different kinds of weapons and takes the firing time point as a clue for firepower conflict checking. The objective function of FCFWTA is the weighted sum of the minimum threat value rest rate (RRTV), maximum hit efficiency (HE) and minimum latest interception time percentage (PLT). Since previous algorithms do not check and resolve intermediate results during optimization, an adapted strategy named Survival Evolution is designed. It enables making full use of the limited firepower without adjusting the coordination scenario in execution.</p><!--/ Abstract__block --> <h3>Findings</h3> <p>The proposed method offers significant advantages in two aspects. Firstly, it effectively enhances the optimization results of WTA in the absence of firepower conflicts. Evidence from Figure. 6 confirms that without the proposed method, there is a high likelihood of generating invalid outcomes. After implementing firepower conflict check and resolution, there is a substantial degradation in the objective function value. Secondly, the method excels at equitably distributing firepower among multiple targets while also enhancing the overall interception probability, irrespective of the varying complexities presented by different scenarios. This ability to maintain balance and efficiency is crucial for tackling defense-related issues.</p><!--/ Abstract__block --> <h3>Research limitations/implications</h3> <p>Specifically, SE is tailored for MWMT problem under time and space constraints. This approach diverges significantly from conventional MWMT research, which typically focuses solely on ammunition quantity or firing range. Consequently, the primary objective was to verify the efficacy of this method. Test results indicated that SE does not exhibit uniform performance across different algorithms; while it significantly enhances the efficacy with PSO and AFSA, its influence is considerably diminished when applied to GA. It might be attributed to the inherent randomness associated with crossover and mutation, which can increase the likelihood of firepower conflicts, coupled with SE's reorganization of the chromosome.</p><!--/ Abstract__block --> <h3>Originality/value</h3> <p>The work described was
目的火力冲突通常会降低火力计划的可执行性，从而带来很高的生存风险。以往的研究很少关注在武器目标分配过程中避免火力冲突。本研究提出了一种名为 "火力无冲突 WTA（FCFWTA）"的新约束优化模型，并设计了人工鱼群算法（AFSA）的生存进化（SE）策略来解决复杂的约束 WTA 问题。设计/方法/途径构建了一个名为 "火力无冲突 WTA（FCFWTA）"的新约束优化模型。FCFWTA 统一了不同种类武器的火力决策变量，并以发射时间点为线索进行火力冲突检查。FCFWTA 的目标函数是最小威胁值休息率（RRTV）、最大命中效率（HE）和最小最新拦截时间百分比（PLT）的加权和。由于之前的算法在优化过程中无法检查和解决中间结果，因此设计了一种名为 "生存进化 "的调整策略。研究结果所提出的方法在两个方面具有显著优势。首先，它能在没有火力冲突的情况下有效提高 WTA 的优化结果。图 6 证明了这一点。图 6 证实，如果不采用所提出的方法，就很有可能产生无效结果。在实施火力冲突检查和解决后，目标函数值会大幅下降。其次，该方法擅长在多个目标之间公平分配火力，同时还能提高总体拦截概率，而不受不同场景所带来的不同复杂性的影响。这种保持平衡和效率的能力对于解决国防相关问题至关重要。研究局限/意义具体而言，SE 是针对时间和空间限制下的 MWMT 问题量身定制的。这种方法与传统的 MWMT 研究大相径庭，后者通常只关注弹药数量或射击范围。因此，首要目标是验证这种方法的有效性。测试结果表明，SE 在不同算法中的表现并不一致；虽然它显著提高了 PSO 和 AFSA 的效率，但在应用于 GA 时，其影响却大大减弱。这可能是由于交叉和变异具有固有的随机性，会增加火力冲突的可能性，再加上 SE 对染色体的重组。
{"title":"A new optimal weapon target assignment method using an artificial fish swarm algorithm with survival evolution","authors":"Ningjun Xu, Miaomiao Sun, Zhangsong Shi, Jin Zhang","doi":"10.1108/ec-11-2023-0844","DOIUrl":"https://doi.org/10.1108/ec-11-2023-0844","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>Firepower conflicts usually decay the firepower plan's enforceability, thus incurring high survival risks. Previous studies have shown little attention to avoiding firepower conflicts during the weapon target assignment process. This research proposes a new constrained optimization model named Firepower Conflict Free WTA (FCFWTA) and designs a Survival Evolution (SE) strategy for Artificial Fish Swarm Algorithm (AFSA) to solve the complex constrained WTA problem. In this way, commanders can get more reliable firepower assignment decision support.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>A new constrained optimization model named Firepower Conflict Free WTA (FCFWTA) is constructed. FCFWTA unifies firepower decision variables for different kinds of weapons and takes the firing time point as a clue for firepower conflict checking. The objective function of FCFWTA is the weighted sum of the minimum threat value rest rate (RRTV), maximum hit efficiency (HE) and minimum latest interception time percentage (PLT). Since previous algorithms do not check and resolve intermediate results during optimization, an adapted strategy named Survival Evolution is designed. It enables making full use of the limited firepower without adjusting the coordination scenario in execution.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The proposed method offers significant advantages in two aspects. Firstly, it effectively enhances the optimization results of WTA in the absence of firepower conflicts. Evidence from Figure. 6 confirms that without the proposed method, there is a high likelihood of generating invalid outcomes. After implementing firepower conflict check and resolution, there is a substantial degradation in the objective function value. Secondly, the method excels at equitably distributing firepower among multiple targets while also enhancing the overall interception probability, irrespective of the varying complexities presented by different scenarios. This ability to maintain balance and efficiency is crucial for tackling defense-related issues.</p><!--/ Abstract__block -->\u0000<h3>Research limitations/implications</h3>\u0000<p>Specifically, SE is tailored for MWMT problem under time and space constraints. This approach diverges significantly from conventional MWMT research, which typically focuses solely on ammunition quantity or firing range. Consequently, the primary objective was to verify the efficacy of this method. Test results indicated that SE does not exhibit uniform performance across different algorithms; while it significantly enhances the efficacy with PSO and AFSA, its influence is considerably diminished when applied to GA. It might be attributed to the inherent randomness associated with crossover and mutation, which can increase the likelihood of firepower conflicts, coupled with SE's reorganization of the chromosome.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The work described was","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Parameter estimation in complex engineering structures typically necessitates repeated calculations using simulation models, leading to significant computational costs. This paper aims to introduce an adaptive multi-output Gaussian process (MOGP) surrogate model for parameter estimation in time-consuming models.
Design/methodology/approach
The MOGP surrogate model is established to replace the computationally expensive finite element method (FEM) analysis during the estimation process. We propose a novel adaptive sampling method for MOGP inspired by the traditional expected improvement (EI) method, aiming to reduce the number of required sample points for building the surrogate model. Two mathematical examples and an application in the back analysis of a concrete arch dam are tested to demonstrate the effectiveness of the proposed method.
Findings
The numerical results show that the proposed method requires a relatively small number of sample points to achieve accurate estimates. The proposed adaptive sampling method combined with the MOGP surrogate model shows an obvious advantage in parameter estimation problems involving expensive-to-evaluate models, particularly those with high-dimensional output.
Originality/value
A novel adaptive sampling method for establishing the MOGP surrogate model is proposed to accelerate the procedure of solving large-scale parameter estimation problems. This modified adaptive sampling method, based on the traditional EI method, is better suited for multi-output problems, making it highly valuable for numerous practical engineering applications.
目的复杂工程结构中的参数估计通常需要使用仿真模型进行重复计算，从而导致大量计算成本。本文旨在介绍一种自适应多输出高斯过程（MOGP）代理模型，用于耗时模型的参数估计。设计/方法/途径建立 MOGP 代理模型是为了在估算过程中取代计算成本高昂的有限元法（FEM）分析。受传统预期改进（EI）方法的启发，我们提出了一种新颖的 MOGP 自适应采样方法，旨在减少建立代用模型所需的采样点数量。通过两个数学实例和一个混凝土拱坝的回溯分析应用测试，证明了所提方法的有效性。提出的自适应采样方法与 MOGP 代理模型相结合，在涉及评估成本高昂的模型的参数估计问题中，尤其是那些具有高维输出的参数估计问题中，显示出明显的优势。这种基于传统 EI 方法的改进型自适应采样方法更适合多输出问题，因此在众多实际工程应用中具有很高的价值。
{"title":"An adaptive multi-output Gaussian process surrogate model for large-scale parameter estimation problems","authors":"Xiaolong Lyu, Dan Huang, Liwei Wu, Ding Chen","doi":"10.1108/ec-10-2023-0719","DOIUrl":"https://doi.org/10.1108/ec-10-2023-0719","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>Parameter estimation in complex engineering structures typically necessitates repeated calculations using simulation models, leading to significant computational costs. This paper aims to introduce an adaptive multi-output Gaussian process (MOGP) surrogate model for parameter estimation in time-consuming models.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>The MOGP surrogate model is established to replace the computationally expensive finite element method (FEM) analysis during the estimation process. We propose a novel adaptive sampling method for MOGP inspired by the traditional expected improvement (EI) method, aiming to reduce the number of required sample points for building the surrogate model. Two mathematical examples and an application in the back analysis of a concrete arch dam are tested to demonstrate the effectiveness of the proposed method.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The numerical results show that the proposed method requires a relatively small number of sample points to achieve accurate estimates. The proposed adaptive sampling method combined with the MOGP surrogate model shows an obvious advantage in parameter estimation problems involving expensive-to-evaluate models, particularly those with high-dimensional output.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>A novel adaptive sampling method for establishing the MOGP surrogate model is proposed to accelerate the procedure of solving large-scale parameter estimation problems. This modified adaptive sampling method, based on the traditional EI method, is better suited for multi-output problems, making it highly valuable for numerous practical engineering applications.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"154 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141608599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<h3>Purpose</h3> <p>In the present study, the application of a recent damage plasticity model is presented for nonlinear dynamic analysis of the Koyna gravity dam. This is a single surface isotropic damage plasticity concrete model, which is based on the decomposition of stresses and was proposed in a previous study. The theoretical aspects of the model are initially reviewed, and a few preliminary verification examples are illustrated. Thereafter, the HHT-α (i.e. Hilber–Hughes–Taylor) algorithm is presented for nonlinear dynamic analysis of concrete gravity dams.</p><!--/ Abstract__block --> <h3>Design/methodology/approach</h3> <p>Based on the prepared tools, nonlinear behavior of the Koyna Dam is studied by applying the invoked damage plasticity model. For this purpose, three cases are considered for the present study. Case A, which is based on the linear model, is mainly used for comparative purposes. The other two cases (B and C) correspond to the nonlinear (i.e. damage plasticity) model. The basic data for these two cases are similar. However, the employed damping algorithms are different and correspond to constant and variable damping algorithms, respectively. This means that the damping matrix is either kept constant or updated for all iterations of different time increments through the course of analysis.</p><!--/ Abstract__block --> <h3>Findings</h3> <p>The time histories of horizontal displacement at the dam crest were initially compared for the three cases: the linear Case A, and two nonlinear Cases B and C. It was observed that nonlinear cases’ responses begin to deviate from the corresponding linear case after the time of about 4.3 s. However, the amount of change for Case C (i.e. variable damping) was much greater than for Case B (i.e. constant damping). This was manifested initially in the peaks of response. It was also noticed that the period of response changed slightly for Case B in comparison with the linear Case A, while this change was significant for Case C. The obtained tensile and compressive damages were subsequently compared for the two nonlinear cases. For constant damping Case B, it was noticed that tensile damage occurred in the D/S face kink and on the U/S face slightly at a lower elevation. Moreover, it had a scattered nature. However, in variable damping Case C, it was noticed that tensile damage was much more localized and acted similar to a discrete crack. Of course, both cases also show tensile damages at the dam’s heel. In regard to compressive damages, it is observed that low values are occurring for both nonlinear cases as expected.</p><!--/ Abstract__block --> <h3>Originality/value</h3> <p>The application of a recent single surface isotropic damage plasticity concrete model is presented for nonlinear dynamic analysis of the Koyna gravity dam. The nonlinear response of the dam is investigated for two different damping algorithms. Moreover, the influence of variable characteristic length is also investigated i
目的 在本研究中，介绍了一种最新的损伤塑性模型在 Koyna 重力坝非线性动态分析中的应用。这是一个基于应力分解的单面各向同性损伤塑性混凝土模型，是在之前的研究中提出的。首先回顾了该模型的理论方面，并举例说明了几个初步验证实例。随后，介绍了用于混凝土重力坝非线性动态分析的 HHT-α（即 Hilber-Hughes-Taylor）算法。为此，本研究考虑了三种情况。情况 A 基于线性模型，主要用于比较。另外两种情况（B 和 C）与非线性（即损伤塑性）模型相对应。这两种情况的基本数据相似。但是，采用的阻尼算法不同，分别对应恒定阻尼算法和可变阻尼算法。这意味着在分析过程中，阻尼矩阵要么保持不变，要么在不同时间增量的所有迭代中进行更新。研究结果初步比较了三种情况下坝顶水平位移的时间历程：线性情况 A 以及两种非线性情况 B 和 C。据观察，非线性情况的响应在约 4.3 秒后开始偏离相应的线性情况。然而，情况 C（即可变阻尼）的变化量远大于情况 B（即恒定阻尼）。这首先表现在响应峰值上。我们还注意到，与线性情况 A 相比，情况 B 的响应周期略有变化，而情况 C 的变化则很大。对于恒定阻尼情况 B，可以发现拉伸破坏发生在 D/S 面的扭结处，U/S 面的高度稍低。此外，它还具有分散性。然而，在可变阻尼情况 C 中，人们注意到拉伸损伤更加局部化，其作用类似于离散裂缝。当然，这两种情况在大坝跟部也都出现了拉伸破坏。在压缩破坏方面，两种非线性情况下的破坏值都很低，符合预期。研究了两种不同阻尼算法下大坝的非线性响应。此外，本研究的后半部分还研究了可变特征长度的影响。
{"title":"Application of single surface isotropic damage plasticity model in nonlinear dynamic analysis of the Koyna Dam","authors":"Vahid Lotfi, Ali Akbar Jahanitabar","doi":"10.1108/ec-02-2024-0108","DOIUrl":"https://doi.org/10.1108/ec-02-2024-0108","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>In the present study, the application of a recent damage plasticity model is presented for nonlinear dynamic analysis of the Koyna gravity dam. This is a single surface isotropic damage plasticity concrete model, which is based on the decomposition of stresses and was proposed in a previous study. The theoretical aspects of the model are initially reviewed, and a few preliminary verification examples are illustrated. Thereafter, the HHT-α (i.e. Hilber–Hughes–Taylor) algorithm is presented for nonlinear dynamic analysis of concrete gravity dams.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>Based on the prepared tools, nonlinear behavior of the Koyna Dam is studied by applying the invoked damage plasticity model. For this purpose, three cases are considered for the present study. Case A, which is based on the linear model, is mainly used for comparative purposes. The other two cases (B and C) correspond to the nonlinear (i.e. damage plasticity) model. The basic data for these two cases are similar. However, the employed damping algorithms are different and correspond to constant and variable damping algorithms, respectively. This means that the damping matrix is either kept constant or updated for all iterations of different time increments through the course of analysis.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The time histories of horizontal displacement at the dam crest were initially compared for the three cases: the linear Case A, and two nonlinear Cases B and C. It was observed that nonlinear cases’ responses begin to deviate from the corresponding linear case after the time of about 4.3 s. However, the amount of change for Case C (i.e. variable damping) was much greater than for Case B (i.e. constant damping). This was manifested initially in the peaks of response. It was also noticed that the period of response changed slightly for Case B in comparison with the linear Case A, while this change was significant for Case C. The obtained tensile and compressive damages were subsequently compared for the two nonlinear cases. For constant damping Case B, it was noticed that tensile damage occurred in the D/S face kink and on the U/S face slightly at a lower elevation. Moreover, it had a scattered nature. However, in variable damping Case C, it was noticed that tensile damage was much more localized and acted similar to a discrete crack. Of course, both cases also show tensile damages at the dam’s heel. In regard to compressive damages, it is observed that low values are occurring for both nonlinear cases as expected.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The application of a recent single surface isotropic damage plasticity concrete model is presented for nonlinear dynamic analysis of the Koyna gravity dam. The nonlinear response of the dam is investigated for two different damping algorithms. Moreover, the influence of variable characteristic length is also investigated i","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"27 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ying Wang, Chaojie Wang, Zhenhua Hu, Yonghui Chen, Bo Min
Purpose
The soft stabilized slab and pile-supported (SSPS) embankment is an improvement technique to increase the efficiency of resources in road construction. To capture the effects of stabilized slabs on the stress transfer mechanism, the differential settlements and the lateral displacement of the embankment completely. A theoretical model of SSPS is proposed by considering the effect of soil arching and the interaction between the embankment fill, stabilized soil, pile, foundation soil and bearing stratum.
Design/methodology/approach
In the theoretical model, the stress and strain coordination relationship of the system was analyzed in view of the minimum potential energy theory and equal settlement plane theory. Subsequently, the theoretical method was applied to field tests for comparison. Finally, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and foundation settlement were examined.
Findings
In addition to the experimental findings, the method has been revealed to be reasonable and feasible, considering its ability to effectively exploit the stabilized slab effect and improve the bearing capacity of soil and piles. An economical and reasonable arrangement scheme for the thickness and strength of stabilized slabs was obtained. The results reveal that the optimum elastic modulus was chosen as 28 MPa–60 MPa, and the optimum thickness of the stabilized slab was selected as 1.5 m–2.1 m using the parameters of field tests, which can provide guidance to engineering design.
Originality/value
An optimization calculation method is established to analyze the load transfer mechanics of the SSPS embankment based on a double-equal settlement plane. The model’s rationality was analyzed by comparing the settlement and stress concentration ratios in the field tests. Subsequently, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and settlement were examined. An economical and reasonable arrangement scheme for the thickness and elastic modulus of stabilized slabs was obtained, which can provide a novel approach for engineering design.
{"title":"Settlement and stress analysis in stabilized slab- and pile-supported embankment based on double-equal settlement plane","authors":"Ying Wang, Chaojie Wang, Zhenhua Hu, Yonghui Chen, Bo Min","doi":"10.1108/ec-09-2023-0582","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0582","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>The soft stabilized slab and pile-supported (SSPS) embankment is an improvement technique to increase the efficiency of resources in road construction. To capture the effects of stabilized slabs on the stress transfer mechanism, the differential settlements and the lateral displacement of the embankment completely. A theoretical model of SSPS is proposed by considering the effect of soil arching and the interaction between the embankment fill, stabilized soil, pile, foundation soil and bearing stratum.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>In the theoretical model, the stress and strain coordination relationship of the system was analyzed in view of the minimum potential energy theory and equal settlement plane theory. Subsequently, the theoretical method was applied to field tests for comparison. Finally, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and foundation settlement were examined.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>In addition to the experimental findings, the method has been revealed to be reasonable and feasible, considering its ability to effectively exploit the stabilized slab effect and improve the bearing capacity of soil and piles. An economical and reasonable arrangement scheme for the thickness and strength of stabilized slabs was obtained. The results reveal that the optimum elastic modulus was chosen as 28 MPa–60 MPa, and the optimum thickness of the stabilized slab was selected as 1.5 m–2.1 m using the parameters of field tests, which can provide guidance to engineering design.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>An optimization calculation method is established to analyze the load transfer mechanics of the SSPS embankment based on a double-equal settlement plane. The model’s rationality was analyzed by comparing the settlement and stress concentration ratios in the field tests. Subsequently, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and settlement were examined. An economical and reasonable arrangement scheme for the thickness and elastic modulus of stabilized slabs was obtained, which can provide a novel approach for engineering design.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"40 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maximilian Kannapinn, Michael Schäfer, Oliver Weeger
Purpose
Simulation-based digital twins represent an effort to provide high-accuracy real-time insights into operational physical processes. However, the computation time of many multi-physical simulation models is far from real-time. It might even exceed sensible time frames to produce sufficient data for training data-driven reduced-order models. This study presents TwinLab, a framework for data-efficient, yet accurate training of neural-ODE type reduced-order models with only two data sets.
Design/methodology/approach
Correlations between test errors of reduced-order models and distinct features of corresponding training data are investigated. Having found the single best data sets for training, a second data set is sought with the help of similarity and error measures to enrich the training process effectively.
Findings
Adding a suitable second training data set in the training process reduces the test error by up to 49% compared to the best base reduced-order model trained only with one data set. Such a second training data set should at least yield a good reduced-order model on its own and exhibit higher levels of dissimilarity to the base training data set regarding the respective excitation signal. Moreover, the base reduced-order model should have elevated test errors on the second data set. The relative error of the time series ranges from 0.18% to 0.49%. Prediction speed-ups of up to a factor of 36,000 are observed.
Originality/value
The proposed computational framework facilitates the automated, data-efficient extraction of non-intrusive reduced-order models for digital twins from existing simulation models, independent of the simulation software.
{"title":"TwinLab: a framework for data-efficient training of non-intrusive reduced-order models for digital twins","authors":"Maximilian Kannapinn, Michael Schäfer, Oliver Weeger","doi":"10.1108/ec-11-2023-0855","DOIUrl":"https://doi.org/10.1108/ec-11-2023-0855","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>Simulation-based digital twins represent an effort to provide high-accuracy real-time insights into operational physical processes. However, the computation time of many multi-physical simulation models is far from real-time. It might even exceed sensible time frames to produce sufficient data for training data-driven reduced-order models. This study presents TwinLab, a framework for data-efficient, yet accurate training of neural-ODE type reduced-order models with only two data sets.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>Correlations between test errors of reduced-order models and distinct features of corresponding training data are investigated. Having found the single best data sets for training, a second data set is sought with the help of similarity and error measures to enrich the training process effectively.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>Adding a suitable second training data set in the training process reduces the test error by up to 49% compared to the best base reduced-order model trained only with one data set. Such a second training data set should at least yield a good reduced-order model on its own and exhibit higher levels of dissimilarity to the base training data set regarding the respective excitation signal. Moreover, the base reduced-order model should have elevated test errors on the second data set. The relative error of the time series ranges from 0.18% to 0.49%. Prediction speed-ups of up to a factor of 36,000 are observed.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The proposed computational framework facilitates the automated, data-efficient extraction of non-intrusive reduced-order models for digital twins from existing simulation models, independent of the simulation software.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"29 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study examines two distinct bearing stiffness calculation methods, both of which are based on the displacement-load function. Previous research typically incorporated one type of bearing stiffness into their system mechanics or vibration analysis. However, these two methods of calculating stiffness lead to different vibration models. This implies that the choice for vibration investigation is not merely about selecting one of the two types of stiffness, but also about how to appropriately implement that chosen stiffness within a model. The primary objective of this work is to compare these two methods of bearing calculation and to discuss the suitable applications of each method in both static and dynamic analyses.
Design/methodology/approach
This study compares two distinct methods for calculating bearing stiffness. It explores the relationships between varying bearing stiffnesses, their internal structures, and contact features. Furthermore, it examines the impact of external loads on the static properties and dynamic characteristics of different bearing stiffnesses. Finally, based on the outcomes observed under various operating conditions, the study discusses the suitability of each method for static and dynamic analysis.
Findings
Mean stiffness is more suitable for calculating load transmissibility in a static state or capturing the delivery performance at instantaneous equilibrium positions in a dynamic state. Since the variation of the equilibrium positions is ignored, the alternating stiffness model is better suited for capturing the fluctuating properties of the vibration behaviors, especially under variable external load conditions.
Originality/value
We compare the two bearing calculation methods and discuss the appropriate applications of each method for static and dynamic analysis.
{"title":"A comparison of rolling element bearing stiffness calculation methods","authors":"Zi Wang","doi":"10.1108/ec-09-2023-0550","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0550","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>This study examines two distinct bearing stiffness calculation methods, both of which are based on the displacement-load function. Previous research typically incorporated one type of bearing stiffness into their system mechanics or vibration analysis. However, these two methods of calculating stiffness lead to different vibration models. This implies that the choice for vibration investigation is not merely about selecting one of the two types of stiffness, but also about how to appropriately implement that chosen stiffness within a model. The primary objective of this work is to compare these two methods of bearing calculation and to discuss the suitable applications of each method in both static and dynamic analyses.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>This study compares two distinct methods for calculating bearing stiffness. It explores the relationships between varying bearing stiffnesses, their internal structures, and contact features. Furthermore, it examines the impact of external loads on the static properties and dynamic characteristics of different bearing stiffnesses. Finally, based on the outcomes observed under various operating conditions, the study discusses the suitability of each method for static and dynamic analysis.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>Mean stiffness is more suitable for calculating load transmissibility in a static state or capturing the delivery performance at instantaneous equilibrium positions in a dynamic state. Since the variation of the equilibrium positions is ignored, the alternating stiffness model is better suited for capturing the fluctuating properties of the vibration behaviors, especially under variable external load conditions.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>We compare the two bearing calculation methods and discuss the appropriate applications of each method for static and dynamic analysis.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A stochastic technique for solving interval non-linear problems using generalized Hukuhara (GH)-difference is proposed. The non-linear programming problem in interval form is transformed into an equivalent non-linear programming problem with real coefficients by associating a Gaussian random variable to the interval and the six-sigma rule. The conceptualized idea eliminates the decision maker’s instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. To demonstrate a coherent understanding, numerical examples have been used.
Design/methodology/approach
A stochastic approach has been used to develop a solution technique for solving interval nonlinear programming problems which arise in the modeling of scientific and engineering problems under uncertain environments.
Findings
The proposed idea eliminates the decision maker’s instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. This method provides specific results rather than in the interval form, which are more practical and implementable by the decision maker.
Originality/value
This is to certify, that the research paper submitted is an outcome of original work. I have duly acknowledged all the sources from which the ideas and extracts have been taken. This article has not been submitted elsewhere for publication.
{"title":"A stochastic technique to solve interval non-linear programming problems using GH-difference","authors":"Shaveta Kumari, Saurabh Srivastava","doi":"10.1108/ec-09-2023-0624","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0624","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>A stochastic technique for solving interval non-linear problems using generalized Hukuhara (GH)-difference is proposed. The non-linear programming problem in interval form is transformed into an equivalent non-linear programming problem with real coefficients by associating a Gaussian random variable to the interval and the six-sigma rule. The conceptualized idea eliminates the decision maker’s instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. To demonstrate a coherent understanding, numerical examples have been used.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>A stochastic approach has been used to develop a solution technique for solving interval nonlinear programming problems which arise in the modeling of scientific and engineering problems under uncertain environments.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The proposed idea eliminates the decision maker’s instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. This method provides specific results rather than in the interval form, which are more practical and implementable by the decision maker.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>This is to certify, that the research paper submitted is an outcome of original work. I have duly acknowledged all the sources from which the ideas and extracts have been taken. This article has not been submitted elsewhere for publication.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"3 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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