Latin Hypercube Design Method Research Articles

Inaccurate search based sequential approximate constrained optimization method for Solid Rocket Motor design

Surrogate based constrained optimization methods are widely utilized in practical solid rocket motor (SRM) design problems. To improve the design performance, this paper proposes an inaccurate search based sequential approximate constrained optimization (ISSACO) method consisting of an efficient recursive evolution Latin hypercube design (RELHD) method and a three-stage constrained sampling method. The RELHD method divides large-sample experiment design problem into several small-sample design problems to ensure the computational efficiency and the design uniformity at the same time. The three-stage constrained sampling method employs the elite archives mechanism to balance the feasibility and the optimality in optimization. Results of the numerical cases indicate that the proposed ISSACO algorithm is competitive with other state-of-art constrained optimization method in efficiency and effectiveness. The finocyl grain design and the impulse mass ratio optimization are also conducted to make further verifications, and the ISSACO method can efficiently obtain feasible optimum and proves to be a potential method for computationally intensive solid rocket motor design problems.

Multi-Objective Optimization Design of Dynamic Performance of Hydrofoil with Gurney Flap

The horizontal axis tidal turbine, as a crucial device for capturing tidal energy, has gained significant attention because it has better energy efficiency performance. Enhancing the performance of foils, a vital part of tidal turbine blades, can significantly improve tidal turbine performance. Among numerous methods to enhance the foil performance, the Gurney flap has gained significant attention due to its avoidance of complex structural design. Currently, there is limited research on optimizing the design of Gurney flaps while considering the dynamic performance of foils. In this study, the S809 foil with a blade cross-section was selected as the research subject, a multi-objective optimization design platform was created by integrating a multi-objective optimization algorithm with Computational Fluid Dy-namics (CFD) numerical simulation techniques. The objective of this platform is to enhance the dynamic performance of the hydrofoil by optimizing the geometric structure of the Gurney flap. The improvement of dynamic lift and the size of the dynamic stall hysteresis loop are used as objective variables in this study to evaluate the hydrofoil’s dynamic performance. The optimal Latin hypercube design method is used in the optimization process to choose sample locations, and the Kriging approximation model is used to determine the relationship between the design variables and the objective variables. Meanwhile, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is used to create a multi-objective optimization platform for solving the optimization problem, and the optimized results are validated using CFD. Comparative validation results show that quantifying the dynamic performance during hydrofoil pitching oscillation and using the optimal Latin hypercube design method and Kriging approximation model for optimizing the Gurney flap structure is rational and accurate. This study explores the mechanism of the Gurney flap through in-depth CFD numerical simulations and finds that the Gurney flap affects the flow characteristics at the hydrofoil’s trailing edge, thereby influencing the performance. It increases the pressure difference between the pressure and suction surfaces, thus enhancing the hydrofoil’s lift. Finally, this article provides three recommended parameters to improve the dynamic performance of the hydrofoil. This research can serve as a reference for the application of Gurney flaps in tidal turbine blade design.

Research on the lightweight design and multilevel optimization method of B‐pillar of hybrid material based on side‐impact safety and multicriteria decision‐making

AbstractThis paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

Crashworthiness analysis and structural optimization of shrink tube under interference condition

This paper aims to study the crashworthiness of shrink tubes for rail vehicles under axial impact loading. A theoretical model of shrink tube for platform force prediction under interference fit conditions was proposed. The trolley crash test was used to experimentally study the structural energy absorption and characteristics during collision, and a corresponding finite element model was constructed and validated. The finite element model validated the accuracy of the theoretical model. The influence of structural parameters on the crashworthiness of shrink tube under interference conditions was then studied. Structural design variables, including the magnitude of interference (int_pre), thickness (T), long right-angle edge (tri_x) and short right-angle edge (tri_z) were sampled using a full factorial and a Latin hypercube design method. Based on the above samples, the moving least squares method (MLSM) was used to construct an approximate model of peak force (Fmax), specific energy absorption (SEA), and platform force (Fplt). The main effects analysis illustrated that the tri_z had the most significant effects on the peak force, specific energy absorption and platform force. To minimize Fmax and maximize SEA, the global response surface method (GRSM) was employed for parameter optimization. Finally, the optimized configurations were obtained with int_pre=0.067mm, T=10.003mm, tri_x=21.485mm, and tri_z=6.101mm. Compared to the initial design, the SEA value was increased by 16.41 %, while the Fmax value was decreased by 2.21%. The error of platform force derived from the optimal solution and theoretical prediction was 3.62%, which verified that the theoretical prediction model was credible within an acceptable range.

Assessment of an Optimal Design Method for a High-Energy Ultrasonic Igniter Based on Multi-Objective Robustness Optimization

The current deterministic optimization design method ignores uncertainties in the material properties and potential machining error which could lead to unreliable or unstable designs. To improve the design efficiency and anti-jamming ability of a high-energy ultrasonic igniter, a Six Sigma multi-objective robustness optimization design method based on the response surface model and the design of the experiment has been proposed. In this paper, the initial structural dimensions of a high-energy ultrasonic igniter have been obtained by employing one-dimensional longitudinal vibration theory. The finite element simulation method of COMSOL Multiphysics software has been verified by the finite element simulation results of ANSYS Workbench software. The optimal igniter design has been achieved by using the proposed method, which is based on the finite element method, the Optimal Latin Hypercube Design method, Grey Relational Analysis, the response surface model, the non-dominated sorting genetic algorithm, and the mean value method. Considering the influence of manufacturing errors on the igniter’s performance, the Six Sigma method was used to optimize the robustness of the igniter. The Eigenfrequency analysis and the vibration velocity ratio calculation were conducted to verify the design’s effectiveness. The results reveal that the longitudinal resonant frequency of the deterministic optimization scheme and the robustness optimization scheme are closer to the design’s target frequency. The relative error is less than 0.1%. Compared with the deterministic optimization scheme, the vibration velocity ratio of the robustness optimization scheme is 2.8, which is about 15.7% higher than that of the deterministic optimization scheme, and the quality level of the design targets is raised to above Six Sigma. The proposed method can provide an efficient and accurate optimal design for developing a new special piezoelectric transducer.

Shape adjustment for uncertain mesh reflectors using machine learning

Mesh reflectors are uncertain structures due to manufacturing and assembly errors. Shape adjustment must be made to meet the surface precision requirement of space missions by changing the lengths of adjustable cables. It is desirable to find the optimum adjustment amount based on the current state of the actual prototype. However, it is hard to build an accuracy simulation model reflecting mechanical behavior of the actual prototype because only part information about the actual prototype can be measured. Therefore, it is necessary to deal with the parameter uncertainty of the actual prototype in order to provide a reliable structure state to guide the shape adjustment. This field has not been well studied because it involves an uncertainty analysis of parameters and the nonlinearity of high coupling of node displacements. To improve the efficiency of shape adjustment of uncertain mesh reflectors, this paper combines finite element model, actual prototype, and machine learning algorithm to develop a prediction model for precision analysis of the mesh reflector under multi-uncertainties using a machine learning algorithm (extreme gradient boosting), with the reflector surface node position as the input and the cable length adjustment amount required to displace it to a high precision surface as the output. First, based on the nominal design model, the sample data is collected by the Latin hypercube design method; the nonlinearity of the structure was taken into account by iterative solution during the data sampling, and the uncertain models containing different random errors are fused from the perspective of data sampling. The Bayesian optimization algorithm is used to obtain the optimal hyperparameters that enables strong generalization of the prediction model. Next, learning from the idea of K-nearest neighbor algorithm, the prediction model is updated based on the actual prototype data, which further improves the prediction ability of the current prototype to be adjusted. The incremental learning algorithm is used to reduce the time-consuming of the prediction model updating. Finally, numerical examples and experiments show that the proposed method has higher adjustment efficiency and precision with less workload.

Shape Optimization of the Streamlined Train Head for Reducing Aerodynamic Resistance and Noise

Aiming to improve the comprehensive aerodynamic performance of a high-speed train, a multi-objective shape optimization method for a streamlined train head is proposed in this work. The shape of the streamlined train head is parameterized with some spline curves. The optimization design variables are uniformly sampled using the optimal Latin hypercube design method. The aerodynamic resistance and dipole noise sources are chosen as the optimization objectives, which can be obtained through the computational fluid dynamics (CFD) method. An approximate calculation model is established by the radial basis function neural network so as to effectively predict the values of optimization objectives. The error between the predicted values and actual values of the aerodynamic resistance is less than 1%, and that of the dipole noise source is less than 3 dB, which demonstrate the validity of the approximate calculation model. In the optimization process, the algorithm NSGA-II is adopted to update the values of the optimization design variables, and the approximate calculation model is used to calculate the optimization objectives, which greatly reduces the optimization computation time of the streamlined head shape. Through iterative computation of the optimization algorithm in the design space, each optimized design variable shows a trend of convergence, and the aerodynamic resistance and dipole noise source generally show a decreasing trend. The Pareto front is corrected by the CFD method after optimization. The aerodynamic resistance can be reduced by up to 4.5%, and the dipole noise source can be reduced by up to 3.9 dB.

Solution to the problem of bridge structure damage identification by a response surface method and an imperialist competitive algorithm

To increase the efficiency of structural damage identification (SDI) methods and timeously and accurately detect initial structural damage, this research develops an SDI method based on a response surface method (RSM) and an imperialist competitive algorithm (ICA). At first, a Latin hypercube design method is used for experimental design and selection of sample points based on RSM. Then, a high-order response surface surrogate model for the target frequency response and stiffness reduction factor is established. Finally, analysis of variance is performed to assess the overall goodness-of-fit and prediction accuracy of the established model. Then the results obtained are combined with structural dynamic response data to construct objective functions; furthermore, the optimal solution of parameter vector in the objective function is solved based on the ICA. Then damage positioning and quantification can be achieved according to location and degree of change in each parameter; finally, the RSM-ICA-based SDI method proposed is applied to damage identification of high-dimensional damaged simply-supported beam models. To verify the effectiveness of the proposed method, the damage identification results are compared with the results obtained from traditional optimization algorithms. The results indicate that: average errors in the structural stiffness parameters and natural frequency that are identified by the proposed method are 6.104% and 0.134% respectively. The RSM-ICA-based SDI method can more accurately identify the location and degree of damages with more significantly increased identification efficiency and better precision compared to traditional algorithms. This approach provides a novel means of solving SDI problems.

CFD-based multi-objective optimization of the duct for a rim-driven thruster

Rim-driven thruster (RDT) is a new integrated thruster that has attracted much attention recently. The RDT provides the benefits of reducing vibration and noise and increasing useable volume by mounting the propulsion motor stator into the duct and fusing the motor rotor with the propeller blades. The calculation method of RDT considering the motor gap was discussed and validated. A simulation-based design optimization framework was proposed for the particularity of RDT ducts. The parametric reconstruction of the duct was executed based on the Bézier curve. The optimal Latin hypercube design method was used to generate samples, and the approximate model was developed based on the radial basis function (RBF) neural network. The fitting R2 of efficiency, minimum pressure, blade thrust, and total thrust of the approximate model reached 0.998, 0.955, 0.998, and 0.990, respectively. On this basis, the NSGA-II was employed to optimize the duct with minimum pressure and efficiency as the optimization objectives. Sensitivity analyses indicate that the optimization objectives are significantly affected by the nozzle size, followed by the internal nozzle profile. The typical Pareto solutions were verified by CFD calculation, and the duct optimization can improve efficiency by 3.3% or minimum pressure by 5.3%.

Aerodynamic Shape Optimization Design of the Air Rectification Cover for Super High-Speed Elevator

To reduce the aerodynamic load of super high-speed elevators, in this paper, the coefficient of drag [Formula: see text] and the coefficient of yawing moment [Formula: see text] of the elevator are selected as optimization objectives for the optimization of the air rectification cover (ARC) shape. The elliptic curve method was used to build the parametric model of the ARCs, six design variables were selected, and the design space of the ARC was determined. With the optimal Latin hypercube design method, the training points were selected, and the computational fluid dynamics numerical simulation was conducted to calculate the corresponding responses. Then, the relationship between the design variables and the responses was analyzed. The radial basis function (RBF) surrogate model of the relationship between the design variables and responses was constructed. Finally, the non-dominated sorting genetic algorithm-II (NSGA-II) was employed to optimize the shape of the ARC. The results show that the [Formula: see text] and [Formula: see text] decrease by 16.51% and 60.92%, respectively, compared with the unoptimized ARC, indicating that the ARC designed in this paper is optimized and can effectively reduce the aerodynamic load. Furthermore, among all the design variables, the bluntness of the ARC in the [Formula: see text]-direction has the most significant effect on the aerodynamic load, and the height of the ARC ([Formula: see text] and [Formula: see text]) has the second most significant effect on the aerodynamic load of elevators.

Energy absorption characteristics and multi-objective optimization of a novel reentrant hierarchical honeycomb bumper system

This paper aims to introduce the hierarchy design into sandwich beams and bumper systems to improve their mechanical performance. Two kinds of reentrant hierarchical sandwich beams are proposed and their energy absorption characteristics have been systematically investigated. Based on its excellent energy absorption ability, the reentrant hierarchical honeycombs with equilateral triangle substructures (RHT) core are introduced to the design of the bumper system, and the hierarchical bumper system exhibits better mechanical properties than the traditional bumper and the aluminum foam-filled bumper under different loading conditions. Then, the multi-objective optimization model of the hierarchical bumper system is established by combining the optimal Latin hypercube design method (OLHD) and the response surface model (RSM). The non-dominated sorting genetic algorithm-II (NSGA-II) algorithm is adopted to optimize the design parameters. The optimization results show that the objectives are optimized efficiently, and it performs remarkable performances in bumper system design.

Crashworthiness optimization method for sandwich plate structure under impact loading

Energy absorbing structures like sandwich plate structure (SPS) are lightweight, fuel economical and environmentally friendly for lightweight ship design. Aimed to improve passive safety protection, a composite SPS is designed for better crashworthiness of ship in this paper. Compared with the replaced stiffened plate, the energy absorption performance of designed SPS is significantly improved. A fast and efficient three-stage combinatorial optimization method, synthesized by optimal Latin-hypercube design (OLHD) method, radial basis function (RBF) surrogate model and multi-objective particle swarm optimization (MOPSO) evolutionary algorithm, is proposed to reduce the number of collision FE simulations required and improve the efficiency of crashworthiness optimization of SPS. Based on sample points obtained from OLHD, the approximation relationships between the crashworthiness indexes, the energy absorbption (EA) and the peak crushing force (PCF), and the structure design variables is formulated using RBF surrogate models. The MOPSO algorithm is applied to multi-objective optimization process to obtain the maximum EA and minimum PCF. Finally the Pareto optimal front of SPS is obtained. The results allow us to determine the structure with the best crashworthiness. SPS and optimization methods proposed are expected to provide inspiration for improving the safety of protective structures and lightweight composite ships.

Multi-objective surrogate model-based optimization of a small aircraft engine air-intake duct

Aviation industry is constantly striving for more efficient design processes in respect to optimal time, human and computational resources utilization. This implies a need for application of an approximation techniques enabling for fast responses generation with maintained level of results quality. This study focuses on an advancement of aerodynamic shape optimization process of a small aircraft engine intake system by introduction of a surrogate modelling step into the design loop. The multi-objective metamodel assisted optimization is carried out in order to reduce pressure losses along the engine intake duct and increase flow homogeneity at the engine compressor intake plane. Latin Hypercube Design method is utilized in order to sample the design space. A set of initial objective function evaluations is generated with application of Reynolds-averaged Navier–Stokes solver. The ensemble of samples is further used to train a Kriging-based surrogate model. The Efficient Global Optimization algorithm basing on the Expected Improvement function is employed to gradually increase the metamodel prediction quality by usage of sequential sampling technique. Finally, the optimal point predicted by the Kriging surrogate is validated against the high-fidelity model with usage of the Computational Fluid Dynamics code. The paper presents an application of the abovementioned methodology to the design process of the I-31T aircraft turboprop engine intake system. Proposed Kriging-based optimization workflow is utilized in order to reduce pressure losses and improve flow homogeneity in the engine air-intake duct.

Surrogate-adjoint refine based global optimization method combining with multi-stage fuzzy clustering space reduction strategy for expensive problems

In engineering optimization, surrogate model (SM) is widely used to replace the involved time expensive model, due to the expensive model is complex and high precise requirement caused a long calculation cycle. In traditional process of engineering optimization, the separation of the surrogate model static construction stage and dynamic optimization stage depresses the optimization accuracy and efficiency. Moreover, in order to ensure the accuracy of the surrogate model, expensive model had to be intensively invoked to get enough representative samples in the design space for the SM training. In this paper, a surrogate model adjoint refine based global optimization method combining with the multi-stage fuzzy clustering space reduction strategy (MFCPR-SGO) is proposed to improve the optimization accuracy and efficiency. Firstly, the optimal Latin hypercube design method (OLHD) is used to sample in design space to assure the initial sample set with strong space filling property. Then, the design space is subdivided into three tiered subspaces by using the space reduction strategy of multi-stage fuzzy clustering, which has the ability of space focusing, space reduction and jumping out of local optimum. On this basis, the hierarchical optimization method with ADAM gradient descent is proposed to quickly and accurately search the local minimum value of the objective function in each subspaces. At the same time, combined with the extremum sampling and the gaussian process sampling, a dynamic sampling algorithm is given to realize the synchronization of optimization and surrogate model update. Finally, the benchmark test problems in 12 different dimensions are used to verify the proposed method. The results show that the optimization accuracy can be improved by 21.3% and expensive model invoking times are reduced by 31.5% compared with other three heuristic optimization methods and the three recent surrogate-based optimization (SGO) algorithms. It indicated that the optimization precision and efficiency can be greatly improved by synchronizing the dynamic updating of the surrogate model with the engineering optimization search.

In-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve

In order to efficiently evaluate and design honeycomb structures with excellent energy-absorbing ability, in-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve are performed in this work. By establishing the in-plane impact finite element model, the deformation modes and in-plane dynamic responses of the sinusoidal NPR honeycomb structures under different impact velocities are detailed studied. And the geometric parameters (e.g., the amplitude and period) of the sinusoidal curve that affect the energy absorption performance of the structure are analyzed. Combining the optimal latin hypercube design method with the double-points infilling criterion, the high-precision adaptive Kriging models of the peak crush force (PCF) and the specific energy absorption (SEA) with respect to the amplitude and period are constructed. And then, a multi-objective crashworthiness optimization is carried out by non-dominated sorting genetic algorithm (NSGA-II). The Pareto optimal solution set is gained and the final compromise solution is then obtained based on the fitness function. The optimized results show the PCF of the sinusoidal NPR honeycomb structure decreases by 30.53%, while the SEA increases by 38.55%. It indicates that the optimized sinusoidal honeycomb structure has better energy absorption performance than the conventional concave hexagonal honeycomb. The results can provide some important design guidance for other honeycomb energy-absorbing structures.

Sequential approximate optimization on projectile disturbances of the moving tank based on BP neural network

For the firing accuracy problem of the moving tank with different speed and different road level, the modelling and optimization method of the projectile disturbances of the moving tank under the general driving conditions were studied. A high-dimensional multi-objective optimization method for the projectile disturbances of the moving tank considering the different driving conditions was proposed based on the sequential approximate optimization method. Therein, a projectile disturbance multi-disciplinary simulation model of the moving tank considering multiple nonlinear factors was built and the sliced Latin hypercube design method was introduced to apply the experimental design. On the basis, the BP neural network surrogate model of the projectile disturbances at muzzle-exit of the moving tank under the general driving conditions was established. With the genetic algorithm and the potential optimal criterion, the sample points were updated to improve the accuracy of the surrogate model during the optimization. The optimization results show that the projectile disturbances at muzzle-exit of the moving tank under the general driving conditions were reduced effectively, and the comprehensive firing accuracy of the moving tank was improved. The research can provide a reference for realizing the reasonable match between firing accuracy and mobility of the tank.

Energy saving potential of a model-predicted frost prevention method for energy recovery ventilators

This study evaluates the energy-saving potential of a prediction model-based pre-heat coil operation method for frost prevention in energy recovery ventilators, compared to existing approaches. Energy recovery ventilator (ERV) requires pre-heating of the incoming outdoor air to prevent undesirable condensation and frost formation in the enthalpy exchanger during winter. Conventionally, the introduced outdoor air is pre-heated to a certain constant temperature using a pre-heat coil, resulting in unnecessary energy consumption. Maintaining a constant pre-heat temperature during the operation of the ERV is not ideal as the frost threshold temperature varies with the outdoor air temperature and humidity. Therefore, to reduce pre-heating energy consumption, a prediction model-based pre-heat coil operation method is proposed herein. A numerical model predicting the frost threshold temperature based on the outdoor air and exhaust air conditions was developed, and validated using the optimal Latin hypercube design method. Subsequently, a series of energy simulations was performed considering an identical residential model, located in 8 cities with different climatic conditions, to evaluate the energy-saving potential of the proposed pre-heat coil operation method compared to conventional methods. The proposed method consumed 7%–72% less energy in the ERV operation and required a 1%–21% smaller pre-heat coil capacity than the conventional method. Thus, the proposed operation method is superior to the conventional method as it prevents frost formation and consumes a minimal amount of energy.

Multi-objective optimization of CFRP engine hood considering dynamic performance based on surrogate model

This paper uses a steel engine hood as a prototype to design a carbon fiber reinforced plastic (CFRP) engine hood, analyzes the dynamic performance of the engine hood and optimizes the dynamic stiffness index while considering lightweight of the structure. Taking the layer thickness of each ply orientation of the CFRP engine hood as the design variable, the optimal Latin hypercube design (Opt-LHD) method is applied for uniform sampling. Moreover, the Kriging model method and response surface model (RSM) method are used to construct the surrogate model of the total mass, equivalent dynamic stiffness of critical points, and the first-order modal frequency. Then the Non-dominated Sorting Genetic Algorithm NSGA-II is used for multi-objective optimization with the equivalent dynamic stiffness and mass of the CFRP engine hood as the optimization objective. Finally, the optimized CFRP engine hood was trial-produced and compared with the original steel engine hood. The results indicate that the optimized CFRP engine hood has better dynamic stiffness performance; furthermore, the lightweight effect reaches 24.4 %.

Knowledge Mining of Low Specific Speed Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition Method

To clarify the complex relation between the pump blade shape and its corresponding hydraulic performance, the knowledge mining method of centrifugal pump impeller based on proper orthogonal decomposition (POD) was proposed. The pump blade shape was parameterized by cubic Bezier curve. The Latin hypercube design method was employed to supply the necessary samples for producing the perturbations of blade wrap angle, and blade angle at inlet and outlet. The hydraulic efficiency and head were optimized by NSGA-II and RBF hybrid algorithm. The Pareto-optimal solutions were obtained. In order to further illustrate the relationship between the centrifugal pump blade shape and its hydraulic performance, the POD method was used to discover the effects of optimized blade shape to the flow solutions. For the optimization of centrifugal pump MH48-12.5, blade shape and relative velocity field in impeller from Pareto-optimal solutions were analyzed. The results demonstratethat larger blade angle and smaller wrap angle increase the average kinetic energy in impeller, resulting in higher pump head design. Smaller blade angle and larger wrap angle decrease the velocity gradient from the pressure side to suction side, resulting in smaller hydraulic loss and higher efficiency design.

Optimization of tire tread pattern based on flow characteristics to improve hydroplaning resistance

Tire tread pattern is a crucial parameter to prevent hydroplaning. In this study, numerical modeling was used to investigate tire hydroplaning based on flow–structure interaction. The empirical model of hydroplaning speed published in the literature was used to validate the computational model. Analysis of water flow velocity and turbulent flow energy revealed that lateral grooves of the tire significantly influenced water drainage capacity. Based on the relationship between water flow vector and lateral groove shape, a combination of Kriging surrogate model and simulated annealing algorithm was used to optimize lateral groove design to minimize hydrodynamic lift force. Four geometry parameters of lateral grooves were selected as the design variables. Based on design of experiment principle, 12 simulation cases based on the optimal Latin hypercube design method were used to analyze the influence of design variables on hydrodynamic lift force. The surrogate model was optimized by the simulated annealing algorithm to optimize tire tread pattern. The results indicated that at the same water flow speed, the optimized lateral grooves can reduce hydrodynamic lift force by 14.05% and thus greatly improve safety performance of the tire. This study proves the validity and applicability of using numerical modeling for solving the complex design of tire tread pattern and optimization problem.