A Mixed-Variable Experimental Design Method

Mixed-variable problems are inevitable in engineering. However, few researches pay attention to discrete variables. This paper proposed a mixed-variable experimental design method (ODCD): first, the design variables were divided into discrete variables and continuous variables;then, the DVD method was employed for handling discrete variables, the LHD method was applied for continuous variables, and finally, a Columnwise-Pairwise Algorithm was used for the overall optimization of the design matrix. Experimental results demonstrated that the ODCD method outperforms in terms of the sample space coverage performance.

Structural Optimization of Concrete Slab Frame Bridges Considering Investment Cost

The present study investigates computer-antomated design and structural optimization of concrete slab frame bridges considering investment cost based on a complete 3D model. Thus, a computer code with several modules has been developed to produce parametric models of slab frame bridges. Design loads and load combinations are based on the Eurocode design standard and the Swedish design standard for bridges. The necessary reinforcement diagrams to satisfy the ultimate and serviceability limit states, including fatigue checks for the whole bridge, are calculated according to the aforementioned standards. Optimization techniques based on the genetic algorithm and the pattern search method are applied. A case study is presented to highlight the efficiency of the applied optimization algorithms. This methodology has been applied in the design process for the time-effective, material-efficient, and optimal design of concrete slab frame bridges.

Failure mechanism of directional roof cutting and design method optimization

Directional roof cutting(DRC)is one of the key techniques in non-pillar coal mining with self-formed entries(NCMSE)mining method.Due to the inability to accurately measure the expansion coefficient of the goaf rock mass,the implementation of this technology often encounters design challenges,leading to suboptimal results and increased costs.This paper establishes a structural analysis model of the goaf working face roof,revealing the failure mechanism of DRC,and clarifies the positive role of DRC in improving the stress of the roadway surrounding rock and reducing the subsidence of the roof through numerical simulation experiments.On this basis,the paper further analyses the roadway pressure and roof settlement under different DRC design heights,and ultimately proposes an optimized design method for the DRC height.The results indicate that the implementation of DRC can significantly optimize the stress environment of the working face roadway surrounding rock.At the same time,during the application of DRC,three scenarios may arise:insufficient,reasonable,and excessive DRC height.Insufficient height will significantly reduce the effectiveness of the technology,while excessive height has little impact on the implementation effect but will greatly increase construction costs and difficulty.Engineering verification shows that the optimized DRC design method proposed in this paper reduces the peak stress of the protective coal pillar in the roadway by 27.2%and the central subsidence of the roof by 41.8%,demonstrating excellent application results.This method provides technical support for the further promotion of NCMSE mining method.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Numerical and Experimental Analysis of A Ducted Propeller Designed by A Fully Automated Optimization Process Under Open Water Condition

A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.

Optimum Design for Offshore Platform Structural Reliability

In this paper, the main problems concerning reliability design of offshore platform structure are described and the general steps for the use of Safety Coefficient Method are presented.

OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS

The optimum design method based on the reliability is presented to the stochastic structure systems （i. e., the sectional area, length, elastic module and strength of the structural member are random variables ） under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique（PNET） method were obtained. After derivation calculus ,the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Finding Symbolic and All Numerical Solutions for Design Optimization Based on Monotonicity Analysis and Solving Polynomial Systems

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

Study on optimal design to improve auto-body structural crashworthiness

In this paper the optimal model of the main energy absorbed structure in an auto-body “front rail”, based on structural crashworthiness is built. For an optimal design on structure crashworthiness, the new method is based on a response surface model and Pareto GA, which improves the efficiency and flexibility of an optimal design, that is brought forward. The traditional optimal method can not be applied in the design of an impact structure due to the high nonlinearity and large time cost of crashworthiness FE analysis. So the method of an optimal design based on crashworthiness is brought forward. After constructing the response surface model of auto-body crashworthiness, the Pareto GA can be applied to find the multi-objective globally. The optimal solution set can then be used to provide many scheme combinations for choice structural parameters.To acquire the optimized structure parameters on front rail crashworthiness, this simplified model of an original design is built. After studying various ways of reinforcing the cross-section to control the structural failure mode, a better method has been found. On the precondition of not increasing the mass of the structure, an optimal design of the front rail is performed further. Finally, the optimized scheme is implemented in the full-car impact analysis and crashworthiness is studied. With proper measures to control deformation of the front rail structure the crashworthiness can be improved with minor structural modifications.

An Overview of Recently Developed Coupled Simulation Optimization Approaches for Reliability Based Minimum Cost Design of Water Retaining Structures

This paper reviews several recently-developed techniques for the minimum-cost optimal design of water-retaining structures (WRSs), which integrate the effects of seepage. These include the incorporation of uncertainty in heterogeneous soil parameter estimates and quantification of reliability. This review is limited to methods based on coupled simulation-optimization (S-O) models. In this context, the design of WRSs is mainly affected by hydraulic design variables such as seepage quantities, which are difficult to determine from closed-form solutions or approximation theories. An S-O model is built by integrating numerical seepage modeling responses to an optimization algorithm based on efficient surrogate models. The surrogate models (meta-models) are trained on simulated data obtained from finite element numerical code solutions. The proposed methodology is applied using several machine learning techniques and optimization solvers to optimize the design of WRS by incorporating different design variables and boundary conditions. Additionally, the effects of several scenarios of flow domain hydraulic conductivity are integrated into the S-O model. Also, reliability based optimum design concepts are incorporated in the S-O model to quantify uncertainty in seepage quantities due to uncertainty in hydraulic conductivity estimates. We can conclude that the S-O model can efficiently optimize WRS designs. The ANN, SVM, and GPR machine learning technique-based surrogate models are efficiently and expeditiously incorporated into the S-O models to imitate the numerical responses of simulations of various problems.

Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.

Structural Topology Optimization by Combining BESO with Reinforcement Learning

In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.

Optimal Building Frame Column Design Based on the Genetic Algorithm

Building structure is like the skeleton of the building,it bears the effects of various forces and forms a supporting system,which is the material basis on which the building depends.Hence building structure design is a vital part in architecture design,architects often explore novel applications of their technologies for building structure innovation.However,such searches relied on experiences,expertise or gut feeling.In this paper,a new design method for the optimal building frame column design based on the genetic algorithm is proposed.First of all,in order to construct the optimal model of the building frame column,building units are divided into three categories in general:building bottom,main building and building roof.Secondly,the genetic algorithm is introduced to optimize the building frame column.In the meantime,a PGA-Skeleton based concurrent genetic algorithm design plan is proposed to improve the optimization efficiency of the genetic algorithm.Finally,effectiveness of the mentioned algorithm is verified through the simulation experiment.

Design parameter optimization method for a prestressed steel structure driven by multi-factor coupling

To achieve efficient structural design,it is crucial to reduce the cost of materials while ensuring structural safety.This study proposes an optimization method for design parameters(DPs)in a prestressed steel structure driven by multi-factor coupling.To accomplish this,a numerical proxy model of prestressed steel structures is established with integration of DPs and mechanical parameters(MPs).A data association-parameter analysis-optimization selection system is established.A correlation between DPs and MPs is established using a back propagation(BP)neural network.This correlation provides samples for parameter analysis and optimization selection.MPs are used to characterize the safety of the structure.Based on the safety grade analysis,the key DPs that affect the mechanical properties of the structure are obtained.A mapping function is created to match the MPs and the key DPs.The optimal structural DPs are obtained by setting structural materials as the optimization objective and safety energy as the constraint condition.The theoretical model is applied to an 80-m-span gymnasium and verified with a scale test physical model.The MPs obtained using the proposed method are in good agreement with the experimental results.Compared with the traditional design method,the design cycle can be shortened by more than 90%.Driven by the optimal selection method,a saving of more than 20% can be achieved through reduction of structural material quantities.Moreover,the cross-sectional dimensions of radial cables have a substantial influence on vertical displacement.The initial tension and cross-sectional size of the upper radial cable exhibit the most pronounced impact on the stress distribution in that cable.The initial tension and cross-sectional size of the lower radial cable hold the greatest sway over the stress distribution in that cable.

Dynamic analysis and optimization of car's body-in-white based on superelement approach

An approach based on the superelement theory is proposed, and it is applied to model the car's body-in-white as well as to dynamic simulation and optimization. This approach can improve the calculation speed and do the dynamic optimization among substructures respectively in the car's body design. To meet the car's design of harshness, a dynamic optimal design model, based on the mean square of vertical displacement response at two points of the car floor, is proposed. Satisfactory results are achieved.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

Shape optimization of plate with static and dynamic constraints via virtual laminated element

The virtual laminated element method (VLEM) can resolve structural shap e optimization problems with a new method. According to the characteristics of V LEM , only some characterized layer thickness values need be defined as design v ariables instead of boundary node coordinates or some other parameters determini ng the system boundary. One of the important features of this method is that it is not necessary to regenerate the FE(finite element) grid during the optimizati on process so as to avoid optimization failures resulting from some distortion grid elements. Th e thickness distribution in thin plate optimization problems in other studies be fore is of stepped shape. However, in this paper, a continuous thickness distrib ution can be obtained after optimization using VLEM, and is more reasonable. Fur thermore, an approximate reanalysis method named ″behavior model technique″ ca n be used to reduce the amount of structural reanalysis. Some typical examples are offered to prove the effectiveness and practicality of the proposed method.

Structural mass prediction in conceptual design of blended-wing-body aircraft

The Blended-Wing-Body(BWB) is an unconventional configuration of aircraft and considered as a potential configuration for future commercial aircraft. One of the difficulties in conceptual design of a BWB aircraft is structural mass prediction due to its unique structural feature. This paper presents a structural mass prediction method for conceptual design of BWB aircraft using a structure analysis and optimization method combined with empirical calibrations. The total BWB structural mass is divided into the ideal load-carrying structural mass, non-ideal mass, and secondary structural mass. Structural finite element analysis and optimization are used to predict the ideal primary structural mass, while the non-ideal mass and secondary structural mass are estimated by empirical methods. A BWB commercial aircraft is used to demonstrate the procedure of the BWB structural mass prediction method. The predicted mass of structural components of the BWB aircraft is presented, and the ratios of the structural component mass to the Maximum TakeOff Mass(MTOM) are discussed. It is found that the ratio of the fuselage mass to the MTOM for the BWB aircraft is much higher than that for a conventional commercial aircraft, and the ratio of the wing mass to the MTOM for the BWB aircraft is slightly lower than that for a conventional aircraft.

旋风分离器内置导流叶片结构参数优化研究

为研究旋风分离器内置导流叶片各个结构参数之间的相互作用,基于CFD数值模拟方法和BBD试验设计,采用二阶多项式基函数建立了Stairmand旋风分离器的叶片轴向位置、叶片长度及叶片偏转角度与分离效率及压降间的数学模型。拟合结果表明:响应目标的决定系数均在0.99以上,表明相关性和回归模型效果较好。使用Design Expert软件处理数据后选择了最佳推荐点,对分离器结构进行了优化。优化后的模型与原结构对比结果如下:优化模型的压降略有上升;颗粒直径在1~20μm范围内时,优化前后分离器的分离效率变化明显,尤其在1~15μm范围内时,优化前分离效率为6.8%~31.0%,优化后则达到了17.0%~54.0%,提升约20个百分点;而当粒径在15~40μm区间时,优化前后的分离效率变化不明显,尤其是在粒径20~40μm时,优化前的分离效率为71.0%~98.0%,而优化后的分离效率只有77%~99%,提升约10个百分点;优化后的模型性能符合“高效低阻”的设计目标。所得结论可为旋风分离器内置叶片的改进提供设计指导。

基于正交试验的硅基MEMS齿形后坐保险机构参数敏感性

为了对硅基MEMS后坐保险机构进行优化设计和性能研究,基于正交试验与有限元仿真软件相结合的方法,选择齿高、齿宽、弹簧线宽、闭锁梁宽、锁钩间距、初始距离这6个设计参数,对后坐保险机构在正常发射和勤务跌落载荷下的位移和应力的影响进行参数敏感性分析。通过极差分析与方差分析,定量地给出了后坐保险机构各参数对结构在不同冲击载荷下的影响。结果表明,齿高的影响最显著,是影响后坐保险机构位移与应力响应的最主要因素;初始距离、弹簧线宽、齿宽是影响勤务跌落最大位移的次要因素;其他因素均对正常发射与勤务跌落载荷下位移和应力不显示显著性。在相对少的试验次数中定量得出不同设计参数对硅基后坐保险机构的影响大小,对多参数双目标的硅基后坐保险机构优化提供了一定的参考。