Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Deep Learning Based Automatic Charging Identification and Positioning Method for Electric Vehicle

Electric vehicle charging identification and positioning is critically important to achieving automatic charging.In terms of the problem of automatic charging for electric vehicles,a dual recognition and positioning method based on deep learning is proposed.The method is divided into two parts:global recognition and localization and local recognition and localization.In the specific implementation process,the collected pictures of electric vehicle charging attitude are classified and labeled.It is trained with the improved YOLOv4 networkmodel and the corresponding detectionmodel is obtained.The contour of the electric vehicle is extracted by the BiSeNet semantic segmentation algorithm.The minimum external rectangle is used for positioning of the electric vehicle.Based on the location relationship between the charging port and the electric vehicle,the rough location information of the charging port is obtained.The automatic charging equipment moves to the vicinity of the charging port,and the camera near the charging gun collects pictures of the charging port.The model is detected by the Hough circle,the KM algorithmis used for featurematching,and the homography matrix is used to solve the attitude.The results show that the dual identification and location method based on the improved YOLOv4 algorithm proposed in this paper can accurately locate the charging port.The accuracy of the charging connection can reach 80%.It provides an effective way to solve the problems of automatic charging identification and positioning of electric vehicles and has strong engineering practical value.

Improved RRT^(∗)Algorithm for Automatic Charging Robot Obstacle Avoidance Path Planning in Complex Environments

A new and improved RRT∗algorithm has been developed to address the low efficiency of obstacle avoidance planning and long path distances in the electric vehicle automatic charging robot arm.This algorithm enables the robot to avoid obstacles,find the optimal path,and complete automatic charging docking.It maintains the global completeness and path optimality of the RRT algorithmwhile also improving the iteration speed and quality of generated paths in both 2D and 3D path planning.After finding the optimal path,the B-sample curve is used to optimize the rough path to create a smoother and more optimal path.In comparison experiments,the new algorithmyielded reductions of 35.5%,29.2%,and 11.7%in search time and 22.8%,19.2%,and 9%in path length for the 3D environment.Finally,experimental validation of the automatic charging of electric vehicles was conducted to further verify the effectiveness of the algorithm.The simulation experimental validation was carried out by kinematic modeling and building an experimental platform.The error between the experimental results and the simulation results is within 10%.The experimental results show the effectiveness and practicality of the algorithm.

Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties.To characterize the random-field uncertainties with a reduced set of random variables,the Karhunen-Lo`eve(K-L)expansion is adopted.The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization.Under dividing the design domain,the volume fraction of each preset gradient layer is extracted.Based on the ordered solid isotropic microstructure with penalization(Ordered-SIMP),a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer.The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions.Then,the method of moving asymptotes(MMA)is introduced to iteratively update the design variables.Several numerical examples are presented to verify the validity and applicability of the proposed method.The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions,and robust design structures are more stable than that indicated by the deterministic results.

Robust Topology Optimization of Vehicle Suspension Control Arm

A robust topology optimization design framework is developed to solve lightweight structural design problems under uncertain conditions. To enhance the calculation accuracy and flexibility of the statistical moments of robust analysis, number theory integral method is applied to sample point selection and weight assignment. Both the structure topology optimization and number theory integral methods are combined to form a new robust topology optimization method. A suspension control arm problem is provided as a demonstration of robust topology optimization methods under loading uncertainties. Based on the results of deterministic and robust topology optimization, it is demonstrated that the proposed robust topology optimization method can produce a more robust design than that obtained by deterministic topology optimization. It is also found that this new approach is easy to apply in the existing commercial topology optimization software and thus feasible in practical engineering problems.

A Comparison of Deterministic, Reliability-Based Topology Optimization under Uncertainties

Reliability and optimization are two key elements for structural design. The reliabilitybased topology optimization(RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach(the performance measure approach, PMA) and the decoupled approaches(the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method(SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique.The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity,accuracy and efficiency were drawn.

An Efficient Strategy for Non-probabilistic Reliability-Based Multi-material Topology Optimization with Evidence Theory

It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-probability uncertainty,the multi-material interpolation model is represented by the ordered rational approximation of mat erial properties(ordered RAMP).Combined with structural compliance minimization,the multi-material topology optimization with reliability constraints is established.The corresponding non-probability uncertainties are described by the evidence theory,and the uniformity processing method is introduced to convert the evidence variables into random variables.The first-order reliability method is employed to search the most probable point under the reliability index constraint,and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information.Therefore,the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format,followed by the ordered RAMP method to solve the optimization problem.Finally,through numerical examples of 2D and 3D structures,the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.