Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM

Marine umbilical is one of the key equipment for subsea oil and gas exploitation,which is usually integrated by a great number of different functional components with multi-layers.The layout of these components directly affects manufacturing,operation and storage performances of the umbilical.For the multi-layer cross-sectional layout design of the umbilical,a quantifiable multi-objective optimization model is established according to the operation and storage requirements.Considering the manufacturing factors,the multi-layering strategy based on contact point identification is introduced for a great number of functional components.Then,the GA-GLM global optimization algorithm is proposed combining the genetic algorithm and the generalized multiplier method,and the selection operator of the genetic algorithm is improved based on the steepest descent method.Genetic algorithm is used to find the optimal solution in the global space,which can converge from any initial layout to the feasible layout solution.The feasible layout solution is taken as the initial value of the generalized multiplier method for fast and accurate solution.Finally,taking umbilicals with a great number of components as examples,the results show that the cross-sectional performance of the umbilical obtained by optimization algorithm is better and the solution efficiency is higher.Meanwhile,the multi-layering strategy is effective and feasible.The design method proposed in this paper can quickly obtain the optimal multi-layer cross-sectional layout,which replaces the manual design,and provides useful reference and guidance for the umbilical industry.

Multi-Objective Optimization Algorithm for Grouping Decision Variables Based on Extreme Point Pareto Frontier

The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

With the increasing demand for electrical services,wind farm layout optimization has been one of the biggest challenges that we have to deal with.Despite the promising performance of the heuristic algorithm on the route network design problem,the expressive capability and search performance of the algorithm on multi-objective problems remain unexplored.In this paper,the wind farm layout optimization problem is defined.Then,a multi-objective algorithm based on Graph Neural Network(GNN)and Variable Neighborhood Search(VNS)algorithm is proposed.GNN provides the basis representations for the following search algorithm so that the expressiveness and search accuracy of the algorithm can be improved.The multi-objective VNS algorithm is put forward by combining it with the multi-objective optimization algorithm to solve the problem with multiple objectives.The proposed algorithm is applied to the 18-node simulation example to evaluate the feasibility and practicality of the developed optimization strategy.The experiment on the simulation example shows that the proposed algorithm yields a reduction of 6.1% in Point of Common Coupling(PCC)over the current state-of-the-art algorithm,which means that the proposed algorithm designs a layout that improves the quality of the power supply by 6.1%at the same cost.The ablation experiments show that the proposed algorithm improves the power quality by more than 8.6% and 7.8% compared to both the original VNS algorithm and the multi-objective VNS algorithm.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

Numerical Analysis of Flow-Induced Vibration and Noise Generation in a Variable Cross-Section Channel

Flow channels with a variable cross-section are important components of piping system and are widely used in variousfields of engineering.Using afinite element method and modal analysis theory,flow-induced noise,mode shapes,and structure-borne noise in such systems are investigated in this study.The results demonstrate that the maximum displacement and equivalent stress are located in the part with variable cross-sectional area.The aver-age excitation force on theflow channel wall increases with theflow velocity.The maximum excitation force occurs in the range of 0–20 Hz,and then it decreases gradually in the range of 20–1000 Hz.Additionally,as theflow velocity rises from 1 to 3 m/s,the overall sound pressure level associated with theflow-induced noise grows from 49.37 to 66.37 dB.Similarly,the overall sound pressure level associated with the structure-borne noise rises from 40.27 to 72.20 dB.When theflow velocity is increased,the increment of the structure-borne noise is higher than that of theflow-induced noise.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

Long-term operation optimization of circulating cooling water systems under fouling conditions

Fouling caused by excess metal ions in hard water can negatively impact the performance of the circulating cooling water system(CCWS)by depositing ions on the heat exchanger's surface.Currently,the operation optimization of CCWS often prioritizes short-term flow velocity optimization for minimizing power consumption,without considering fouling.However,low flow velocity promotes fouling.Therefore,it's crucial to balance fouling and energy/water conservation for optimal CCWS long-term operation.This study proposes a mixed-integer nonlinear programming(MINLP)model to achieve this goal.The model considers fouling in the pipeline,dynamic concentration cycle,and variable frequency drive to optimize the synergy between heat transfer,pressure drop,and fouling.By optimizing the concentration cycle of the CCWS,water conservation and fouling control can be achieved.The model can obtain the optimal operating parameters for different operation intervals,including the number of pumps,frequency,and valve local resistance coefficient.Sensitivity experiments on cycle and environmental temperature reveal that as the cycle increases,the marginal benefits of energy/water conservation decrease.In periods with minimal impact on fouling rate,energy/water conservation can be achieved by increasing the cycle while maintaining a low fouling rate.Overall,the proposed model has significant energy/water saving effects and can comprehensively optimize the CCWS through its incorporation of fouling and cycle optimization.

Multi-Objective Optimization of VBHF in Deep Drawing Based on the Improved QO-Jaya Algorithm

Blank holder force(BHF)is a crucial parameter in deep drawing,having close relation with the forming quality of sheet metal.However,there are different BHFs maintaining the best forming effect in different stages of deep drawing.The variable blank holder force(VBHF)varying with the drawing stage can overcome this problem at an extent.The optimization of VBHF is to determine the optimal BHF in every deep drawing stage.In this paper,a new heuristic optimization algorithm named Jaya is introduced to solve the optimization efficiently.An improved“Quasi-oppositional”strategy is added to Jaya algorithm for improving population diversity.Meanwhile,an innovated stop criterion is added for better convergence.Firstly,the quality evaluation criteria for wrinkling and tearing are built.Secondly,the Kriging models are developed to approximate and quantify the relation between VBHF and forming defects under random sampling.Finally,the optimization models are established and solved by the improved QO-Jaya algorithm.A VBHF optimization example of component with complicated shape and thin wall is studied to prove the effectiveness of the improved Jaya algorithm.The optimization results are compared with that obtained by other algorithms based on the TOPSIS method.

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.

ANALYSIS AND DISCRETIZATION FOR AN OPTIMAL CONTROL PROBLEM OF A VARIABLE-COEFFICIENT RIESZ-FRACTIONAL DIFFUSION EQUATION WITH POINTWISE CONTROL CONSTRAINTS

We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion equation.Due to the impact of the variable diffusivity coefficient,existing regularity results for their constantcoefficient counterparts do not apply,while the bilinear forms of the state(adjoint)equation may lose the coercivity that is critical in error estimates of the finite element method.We reformulate the state equation as an equivalent constant-coefficient fractional diffusion equation with the addition of a variable-coefficient low-order fractional advection term.First order optimality conditions are accordingly derived and the smoothing properties of the solutions are analyzed by,e.g.,interpolation estimates.The weak coercivity of the resulting bilinear forms are proven via the Garding inequality,based on which we prove the optimal-order convergence estimates of the finite element method for the(adjoint)state variable and the control variable.Numerical experiments substantiate the theoretical predictions.

Optimizing Designed Variable Speed Control Moment Gyroscopes with Variable Skew Angle

Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.

Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP

Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered;2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45- and the axial length of mushroom is considered.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Study of the Bearing Capacity at the Variable Cross-Section of A Riser- Surface Casing Composite Pile

Reducing the cost of offshore platform construction is an urgent issue for marginal oilfield development.The offshore oil well structure includes a riser and a surface casing.The riser,surface casing and oil well cement can be considered special variable cross-section piles.Replacing or partially replacing the steel pipe pile foundation with a variable cross-section pile to provide the required bearing capacity for an offshore oil platform can reduce the cost of foundation construction and improve the economic efficiency of production.In this paper,the finite element analysis method is used to investigate the variable cross-section bearing mode of composite piles composed of a riser and a surface casing in saturated clay under a vertical load.The calculation formula of the bearing capacity at the variable section is derived based on the theory of spherical cavity expansion,the influencing factors of the bearing capacity coefficient N_(c) are revealed,and the calculation method of N_(c) is proposed.By comparing the calculation results with the results of the centrifuge test,the accuracy and applicability of the calculation method are verified.The results show that the riser composite pile has a rigid core in the soil under the variable cross-section,which increases the bearing capacity at the variable cross-section.

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.

An XBi-CFAO Method for the Optimization of Multi-Layered Variable Stiffness Composites Using Isogeometric Analysis

This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites.A gradient-based fiber angle optimization method is developed based on isogeometric analysis(IGA).Firstly,the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method(XBi-CFAO).The densities and fiber angles in the base layer are attached to the control points.The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline(NURBS)based IGA.By the benefit of the B-spline space,this method is free from checkerboards,and no additional filtering is needed to smooth the sensitivity numbers.Then the curved fiber paths are generated using the streamline method and the discontinuous fiber paths are smoothed using a partitioned selection process.The proposed method in the paper can alleviate the phenomenon of fiber discontinuity,enhance information retention for the optimized fiber angles of the singular points and save calculating resources effectively.

In-Plane Impact Dynamics Analysis of Re-Entrant Honeycomb with Variable Cross-Section

Due to the unique deformation characteristics of auxetic materials(Poisson’s ratioμ<0),they have better shock resistance and energy absorption properties than traditional materials.Inspired by the concept of variable crosssection design,a new auxetic re-entrant honeycomb structure is designed in this study.The detailed design method of re-entrant honeycomb with variable cross-section(VCRH)is provided,and five VCRH structures with the same relative density and different cross-section change rates are proposed.The in-plane impact resistance and energy absorption abilities of VCRH under constant velocity are investigated by ABAQUS/EXPLICIT.The results show that the introduction of variable cross-section design can effectively improve the impact resistance and energy absorption abilities of auxetic re-entrant honeycombs.The VCRH structure has better Young’s modulus,plateau stress,and specific energy absorption(SEA)than traditional re-entrant honeycomb(RH).The influence of microstructure parameters(such as cross-section change rateα)on the dynamic impact performance of VCRH is also studied.Results show that,with the increase in impact velocity andα,the plateau stress and SEA of VCRH increase.A positive correlation is also found between the energy absorption efficiency,impact load uniformity andαunder both medium and high impact speeds.These results can provide a reference for designing improved auxetic re-entrant honeycomb structures.

Variable Fidelity Surrogate Assisted Optimization Using A Suite of Low Fidelity Solvers

Variable-fidelity optimization (VFO) has emerged as an attractive method of performing, both, high-speed and high-fidelity optimization. VFO uses computationally inexpensive low-fidelity models, complemented by a surrogate to account for the difference between the high-and low-fidelity models, to obtain the optimum of the function efficiently and accurately. To be effective, however, it is of prime importance that the low fidelity model be selected prudently. This paper outlines the requirements for selecting the low fidelity model and shows pitfalls in case the wrong model is chosen. It then presents an efficient VFO framework and demonstrates it by performing transonic airfoil drag optimization at constant lift, subject to thickness constraints, using several low fidelity solvers. The method is found to be efficient and capable of finding the optimum that closely agrees with the results of high-fidelity optimization alone.

Variable Stiffness Identification and Configuration Optimization of Industrial Robots for Machining Tasks

Industrial robots are increasingly being used in machining tasks because of their high flexibility and intelligence.However,the low structural stiffness of a robot significantly affects its positional accuracy and the machining quality of its operation equipment.Studying robot stiffness characteristics and optimization methods is an effective method of improving the stiffness performance of a robot.Accordingly,aiming at the poor accuracy of stiffness modeling caused by approximating the stiffness of each joint as a constant,a variable stiffness identification method is proposed based on space gridding.Subsequently,a task-oriented axial stiffness evaluation index is proposed to quantitatively assess the stiffness performance in the machining direction.In addition,by analyzing the redundant kinematic characteristics of the robot machining system,a configuration optimization method is further developed to maximize the index.For numerous points or trajectory-processing tasks,a configuration smoothing strategy is proposed to rapidly acquire optimized configurations.Finally,experiments on a KR500 robot were conducted to verify the feasibility and validity of the proposed stiffness identification and configuration optimization methods.