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.

Inverse design and realization of an optical cavity-based displacement transducer with arbitrary responses

Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis.A number of theories and methods have been successful in describing the optical response of a stratified optical cavity,while the inverse problem,especially the inverse design of a displacement sensitive cavity,remains a significant challenge due to the cost of computation and comprehensive performance requirements.This paper reports a novel inverse design methodology combining the characteristic matrix method,mixed-discrete variables optimization algorithm,and Monte Carlo method-based tolerance analysis.The material characteristics are indexed to enable the mixed-discrete variables optimization,which yields considerable speed and efficiency improvements.This method allows arbitrary response adjustment with technical feasibility and gives a glimpse into the analytical characterization of the optical response.Two entirely different light-displacement responses,including an asymmetric sawtooth-like response and a highly symmetric response,are dug out and experimentally achieved,which fully confirms the validity of the method.The compact Fabry-Perot cavities have a good balance between performance and feasibility,making them promising candidates for displacement transducers.More importantly,the proposed inverse design paves the way for a universal design of optical cavities,or even nanophotonic devices.

Removal of Pb(Ⅱ) from aqueous solution by magnetic humic acid/chitosan composites

A novel adsorbent named magnetic humic acid/chitosan composite(M-HA/Cs) was synthesized by decorating humic acid/chitosan composites with Fe_3O_4 nanoparticles. The adsorption capacity of M-HA/Cs was 1.5 times that of MCs. The effects of solution p H, initial concentration of Pb(Ⅱ) ions and adsorption temperature on Pb(Ⅱ) removal were examined in a batch system and further optimized using Box-Behnken analysis. The recommended optimum conditions are initial Pb(Ⅱ) concentration of 139.90 mg/L, initial pH of 4.98, and temperature of 43.97 oC. The adsorption processes could be well described by pseudo-second-order and Elovich models. Isotherm studies reveal that the adsorption process follows Sips and Temkin models. The thermodynamic study indicats that the adsorption process is spontaneous and exothermic. The potential mechanism of Pb(Ⅱ) on M-HA/Cs at pH 5 may be surface electrostatic attraction, coordination and hydrogen bonding.

MODELING, VALIDATION AND OPTIMAL DESIGN OF THE CLAMPING FORCE CONTROL VALVE USED IN CONTINUOUSLY VARIABLE TRANSMISSION

Associated dynamic performance of the clamping force control valve used in continuously variable transmission （CVT） is optimized. Firstly, the structure and working principle of the valve are analyzed, and then a dynamic model is set up by means of mechanism analysis. For the purpose of checking the validity of the modeling method, a prototype workpiece of the valve is manufactured for comparison test, and its simulation result follows the experimental result quite well. An associated performance index is founded considering the response time, overshoot and saving energy, and five structural parameters are selected to adjust for deriving the optimal associated performance index. The optimization problem is solved by the genetic algorithm （GA） with necessary constraints. Finally, the properties of the optimized valve are compared with those of the prototype workpiece, and the results prove that the dynamic performance indexes of the optimized valve are much better than those of the prototype workpiece.

System Reduction Using an LQR-Inspired Version of Optimal Replacement Variables

Optimal ReplacementVariables(ORV)is amethod for approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.An earlier version of ORV[1]had some issues,including limited accuracy and in some rare cases,instability.Here we present a newversion of ORV,inspired by the linear quadratic regulator problemof control theory,which provides better accuracy,a guarantee of stability and is in some ways easier to use.

Reduction of Linear Systems of ODEs with Optimal Replacement Variables

In this exploratory study,we present a new method of approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.The method has the following key elements:(i)put a(simple,ad-hoc)probability distribution on the phase space of the ODE;(ii)assert that a small set of replacement variables are to be unknown linear combinations of the not-of-interest variables,and let the variables of the reduced system consist of the variables-of-interest together with the replacement variables;(iii)find the linear combinations that minimize the difference between the dynamics of the original system and the reduced system.We describe this approach in detail for linear systems of ODEs.Numerical techniques and issues for carrying out the required minimization are presented.Examples of systems of linear ODEs and variable-coefficient linear PDEs are used to demonstrate the method.We show that the resulting approximate reduced system of ODEs gives good approximations to the original system.Finally,some directions for further work are outlined.

Dealing With the Constraints of Optimization by O. D.E. Method

In [1],a new method is presented,which uses O. D. E. method(i. e. ordinary differential equations method)for finding the local optima of the general constrained optimization. However, the discussion about the constraints handled is continued by the ordinary differential equations in this paper. It is proved that the solutions starting from the neighbourhood of a critical point of the differential equations given in this paper about part variables always converge to the feasible point of Eq. (1. 1).

Genetic Algorithm with Variable Length Chromosomes for Network Intrusion Detection

Genetic algorithm(GA) has received significant attention for the design and implementation of intrusion detection systems. In this paper, it is proposed to use variable length chromosomes(VLCs) in a GA-based network intrusion detection system.Fewer chromosomes with relevant features are used for rule generation. An effective fitness function is used to define the fitness of each rule. Each chromosome will have one or more rules in it. As each chromosome is a complete solution to the problem, fewer chromosomes are sufficient for effective intrusion detection. This reduces the computational time. The proposed approach is tested using Defense Advanced Research Project Agency(DARPA) 1998 data. The experimental results show that the proposed approach is efficient in network intrusion detection.

THE OPTIMAL VARIABLE SUCCESSIVE OVER RELAXATION (OVSOR) METHOD FOR THREE-DIMENSIONAL RESERVOIR SIMULATIONS

This present paper has proved the theorem of the Point Optimal Variable Successive Over Relaxation (OVSOR) method of the three-dimensional unsteady flow in the reservoir, and has put forward a formu- la for calculating optimal parameters for OVSOR which vary with space points and time points. Using this method, internal memory of computer is the smallest, calculating work is the smallest, and calculating funds are the smallest. It is very easy to operate on microcomputers for three-dimensional res- ervoir simulation. The method is stable and convergent even if the time steps are taken to be large (for example, one year). The same applies for space steps. It is applicable both for homogeneous, isotropic porous mediums and for heterogeneous, anisotropic porous medium. On IBM microcomputers with internal memory of 512 thousand bytes, 8000 grid points may be cal- culated for three-dimensional simulation. It takes only two minutes to get convergence for one time step. It may be extended to three-dimensional heat conduction equation and three-dimensional simulation of the ground water flow. It looks much more advantageous for two-dimensional simulation.

A novel fractional grey forecasting model with variable weighted buffer operator and its application in forecasting China's crude oil consumption

Oil is an important strategic material and civil energy.Accurate prediction of oil consumption can provide basis for relevant departments to reasonably arrange crude oil production,oil import and export,and optimize the allocation of social resources.Therefore,a new grey model FENBGM(1,1)is proposed to predict oil consumption in China.Firstly,the grey effect of the traditional GM(1,1)model was transformed into a quadratic equation.Four different parameters were introduced to improve the accuracy of the model,and the new initial conditions were designed by optimizing the initial values by weighted buffer operator.Combined with the reprocessing of the original data,the scheme eliminates the random disturbance effect,improves the stability of the system sequence,and can effectively extract the potential pattern of future development.Secondly,the cumulative order of the new model was optimized by fractional cumulative generation operation.At the same time,the smoothness rate quasi-smoothness condition was introduced to verify the stability of the model,and the particle swarm optimization algorithm(PSO)was used to search the optimal parameters of the model to enhance the adaptability of the model.Based on the above improvements,the new combination prediction model overcomes the limitation of the traditional grey model and obtains more accurate and robust prediction results.Then,taking the petroleum consumption of China's manufacturing industry and transportation,storage and postal industry as an example,this paper verifies the validity of FENBGM(1,1)model,analyzes and forecasts China's crude oil consumption with several commonly used forecasting models,and uses FENBGM(1,1)model to forecast China's oil consumption in the next four years.The results show that FENBGM(1,1)model performs best in all cases.Finally,based on the prediction results of FENBGM(1,1)model,some reasonable suggestions are put forward for China's oil consumption planning.