土压平衡盾构行星减速器的多目标稳健优化
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摘要
从土压平衡盾构(Earth-pressure-balance shield machine，EPBSM)刀盘所需力矩着手，探讨其大功率行星减速器(Planetary gear reducer，PGR)的载荷均衡与分配，从而为行星减速器的优化界定“土压平衡盾构”环境。同时，在行星减速器的4大构件(轮系、轴、行星架及箱体)中，因轮系是个全局性的“统帅”，故可采取对各构件分别加以优化的方式来实现整机的最优化。为此，就可遵照稳健设计的要求，分别建立其多目标的数力模型，从当今颇受关注的计算智能(Computationalintelligence，CI)中挑选出一种或几种算法并加以改进，使之成为或再融合成一种收敛性更好的新算法之后，再用来求解所建模型。最后，对优化后的行星减速器作仿真试验。其具体的原因、方法、原理及效果依次如下：
为克服灰色理论本身的固有缺陷与粒子群优化(Particle swarm optimization，PSO)算法在求解整数或混合整数规划过程中出现的问题，将方差的概念引入灰色关联度，提出可靠灰色关联度的概念及计算公式，并通过圆整粒子的初始位置与每次飞行速度，以使PSO算法满足求解过程中对整数解的要求。然后，将可靠灰色关联度作为变异策略来驾驭PSO算法，并详尽阐述其算法机理与流程，从而为复杂非线性约束条件下求解多目标混合整数规划问题提供一套切实可行的便捷方法。建立盾构三级行星减速器的轮系在满足配齿、变位系数、干涉、强度、等强度、等寿命等约束条件下其体积最小、效率最高、接触强度与弯曲强度可靠性最高的四目标函数的数力模型，再运用上述可靠灰色PSO算法编写MATLAB程序来求解所建数力模型。研究表明：1)与惩罚函数法(Penalty function method，PFM)相比(见P29-31)，所提算法有更快的收敛速度；2)该算法的泛化能力不但解决了该行星减速器原第三级强度偏弱的问题，而且在保证高可靠性条件下，使轮系体积减少11.55%，效率提高0.56%，传动比提高3.67%，各级强度与寿命基本相等。
鉴于现有免疫遗传算法(Immune genetic algorithm，IGA)其收敛性不理想的问题，剖析其理论体系本身存在的6大不足，并提出6条全新的策略，以加快算法的收敛。同时，阐明实码抗体与变量向量之间的关系，用图形直观描述复杂的算法机理，以便于对IGA的理解与实际操作；将可靠性分析的随机摄动法与其灵敏度分析结合起来，导出随机参数的概率分布为任意形状的机械零件计算其可靠度及灵敏度的函数表达式，由此创建行星减速器其轴的可靠度对设计变量的灵敏度最低与体积最小的两目标数力模型；提出实现目标函数值之间保持动态平衡的全新模型，顺利实现上述两目标函数与像集法的对接；最后，编写所改进IGA的MATLAB程序对该减速器的轴进行优化。结果表明：该算法的鲁棒性不仅使行星减速器轴的总体积减小13.65%，与改进前相比，所提IGA有更快的收敛速度与更高的收敛精度(见P50-51)。
为解答实际工程中变量相关情况下的高维小概率失效问题，将子集模拟、Monte Carlo法与重要抽样法结合起来，根据重要抽样的概率密度函数获取的相关变量的样本点来构造中间失效事件，从而将小失效概率转化为一条由一系列易于求解的较大条件失效概率的连乘积组成的杂交马尔可夫链，并直接抽取相关样本点来高效模拟结构的可靠性灵敏度。由此创建盾构行星减速器的三个行星架其失效概率对各变量均值、方差(包括相关系数)的可靠性灵敏度最低及体积最小的多目标优化问题，并提出多目标协同优化的思想。同时，针对可靠性灵敏度作为目标函数因误差导致多目标协同优化难以收敛的问题，提出利用误差的思想与方法；为加速遗传算法(Genetic algorithm，GA)与PSO算法的收敛，提出克隆与进化同时并举的精英策略及在相似个体之间进行交配的思想，并用此GA得到的优秀个体与PSO算法杂交，以实现种群续代更新的同时，进一步提高算法的收敛性；最后，运用上述算法对所建数力模型进行求解，结果表明：1)所提直接抽取相关样本的HMC能很好地模拟相关变量的可靠性及其灵敏度，免除了变量独立化过程反复转换的繁琐；2)所提杂交GA-PSO协同算法较GA与PSO算法有更快的收敛速度(见P79-81)，当相关系数为0.7时，可使三个行星架的总体积减小7.06%；3)证实了将可靠性灵敏度作为目标函数时所提利用误差的思想与方法的可行性与正确性。
为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性及灵敏度的问题，融合鞍点估计与线抽样法的优点，结合二分法的特点与黄金分割法的求解效率，提出基于黄金分割二分法的鞍点线抽样法，即可在标准化变量空间中沿重要线抽样方向利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点，从而将结构的失效概率转化为一系列线性功能函数失效概率的平均值，由此求出可靠性灵敏度，从而导出行星减速器的三级箱体其失效概率对基本变量均值与方差的可靠性灵敏度及结构轻量化的多目标优化问题；为提高算法的收敛性，对PSO算法与混合蛙跳算法(Shuffled frog-leaping algorithm，SFLA)进行改进，使前者变为自适应PSO(Self-adaptive PSO, SAPSO)算法后再与改进后的SFLA进行杂交，从而导致了杂交SAPSO-SFLA的产生，然后用来求解上述多目标问题。研究表明：1)基于黄金分割二分法的鞍点线抽样法在求解复杂非线性功能函数的可靠性及灵敏度时精度高，速度快；2)与SAPSO和SFLA相比，所提杂交SAPSO-SFLA不仅具有更快的收敛速度(见P106-108)，其鲁棒性还能使该三级箱体体积减小8.42%。
从行星减速器4大构件的优化可得出：1)上述所建4大数力模型与所提4大计算智能的泛化能力不仅解决了盾构原行星减速器第三级强度偏弱的问题，在保证高可靠性条件下，还可使整个行星减速器的体积减小21.58%，效率提高0.56%，传动比提高3.67%；2)当用轮系的体积减小率来近似预估整个行星减速器的体积减小情况时，其实际效果是轮系体积减小量的5.12倍。此外，仿真试验表明，优化后的行星减速器其各项指标均满足要求，可靠性较好。
The torque that drives the cutterhead of the Earth-pressure-balance shield machine(EPBSM) is first analyzed, and the load equilibrium and allocation of high-capacitythree-stages planetary gear reducer (PGR) are discussed to define the environment ofEPBSM for optimizing the PGR. For its4major elements, that is gear train, shaft,planetary carrier and gearbox, the gear train is a global commander so that the PGR canbe optimized by optimizing each constituent, their mathematical&mechanical modelsof multiple objectives are thus constructed according to the robust design demands. Inthe meanwhile, one or more very interesting algorithms that are selected from thecomputational intelligence (CI) are modified to become or be even combined to a newalgorithm that has better convergence than ever, and then they are used to solve themodels above.At last, the simulation test for the optimized PGR are done.The concretereason, methods, principles and effectiveness are successively as follows.
To overcome the intrinsic defect of the grey theory in itself and the appearingproblem of particle swarm optimization (PSO) algorithm when it is used to slove theinteger or mixed one programming problems, the sigma is introduced into greyrelational degree, the notion of the reliably grey relational degree(RGRD) is put forward.For PSO algorithm, the demand of the integer solution is met by rounding their initialposition and speed of each flight in the course of answering the problems. The RGRD isacted as the alternation strategy to control PSO, and their mechanism and processes areillustrated to provide a practical and convenient method for multi-objective integer ormixed one programming problems subject to complex non-linear conditions. Themathematical models are constructed for three-stage PGR in EPBSM with4objectivefunctions, that is to make its volume smallest, its efficiency highest and the reliability ofits contacting and bending strength highest, which are subject to the conditions such asteeth, modification coefficient, interference, strength, equal strength, equal life etc,which are solved by MATLAB programming language that applied the reliably greyPSO algorithm. The research results show that1) the strength and lifetime in everystage are basically equal under the conditions of ensuring high reliability, and thevelocity of the proposed algorithm is faster than that of the penalty function method(PFM)(see P29-31),2) the generalization ability not only resolves the strength problemthat there is a little weak in the original3rdstage of the PGR, but decreases the gear train volume by11.55%and increases its efficiency by0.56%and its transmission ratio by3.67%.
In view of the dissatisfactory convergence of the current immune genetic algorithm(IGA),6inherent drawbacks are found which existing in the current rationale of IGA.For these reasons,6new strategies which are corresponding to the drawbacks above areproposed to accelerate its convergence. The relationship between real-coded antibodiesand variables vector is illustrated, and the complicated algorithm mechanism isintuitively described by the figure, which make us understood easily and practicallyoperate on IGA. The stochastic perturbation method of the reliability is combined withits sensitivity analysis to deduce their function formulas on mechanical parts whoseprobability distributions of random parameters are arbitrary shape so that thetwo-objective mathematical models are created on minimizing the reliability sensitivityof the shafts of3-stage PGR in EPBSM with respect to design variables and theirvolume. A new model is proposed that can realize the dynamic balance betweenobjectives, by which the objectives are smoothly combined with the image set method.Finally, the shafts are optimized by means of the MATLAB programs languages thatapply the modified IGA above. The results show that the robustness of the improvedIGA not only decreases the total volume of shafts of the PGR by13.65%, but also itsconvergent velocity and accuracy are superior to that of the unimproved IGA (seeP50-51).
In the practical engineering, to answer the small failure probabilities withhigh-dimensional correlated variables, the subset simulation (SS) is combined togetherwith the Monte Carlo simulation and importance sampling (IS) method. The samplesfrom the probability density functions (PDF) of the importance sampling are used toconstruct the intermediate failure events, by which the small failure probabilities areturned into a hybrid Markov chain (HMC), which is a continuous product made of aseries large failure probability or conditional failure probability (CFP) which is easilyanswered, on which the structural reliability sensitivity (RS) can be efficiently simulatedby directly obtaining the samples with correlated ones.Multi-objectives optimizationmodels are established about minimizing the RS of failure probability of the3planetarycarriers of the PGR with respect to the variable mean, variance (including the correlatedcoefficient between them) respectively and volume etc, and the collaborativeoptimization idea for multi-objectives is put forward, in the meantime, in view of theproblem that it is difficult to converge for multi-objectives to be collaboratively optimized because of the errors when the RS is used as an objective function, the ideaand method that utilize the errors are proposed. To increase the convergent velocity ofgenetic algorithm (GA) and PSO, the elite strategy that have elitist cloned and to takepart in evolution simultaneously and the idea that have an individual to mate theindividual who is most similar to it are put forward. And the excellent individuals fromthe modified GA are hybridized with those individuals from PSO to update thepopulation and to further enhance their convergence. Finally, the3planetary carriers areoptimized according to the algorithm above, the results show that1) the SS of the ISwith correlated variables can highly simulate failure probability and its sensitivity,2)the convergent velocity of the collaborative algorithm of hybrid GA-PSO is superior tothat of the GA and PSO (see P79-81), it can reduce the total volume of the planet carriersby7.06%when the correlated coefficient is equal to0.7,3) it is confirmed that theproposed idea and method that utilize the errors are feasible and correct when the RSacts as objective function.
To solve the reliability and its sensitivity for structural system whose implicitnonlinear performance function (PF) are complicated, changeable and of non-normalvariables, the advantages of the saddlepoint approximation (SA) and line sampling (LS)are merged and the merits of dichotomy and the solution efficiency of the goldensection method are combined to propose the saddlepoint approximation-line samplingmethod (SA-LS) based on the dichotomy of the golden section point, namely, it is quickto find the zeropoint in PF corresponding to each sample along the important linesampling direction by the dichotomy above so that the structural failure probability canbe transformed into the mean of a series linear PF failure probability, and by whichreliability sensitivity can be solved, thus the multi-objectives are inferred about the RSof failure probability of the three-stage gearboxes of the PGR with respect to thevariables mean and variance and structural lightweight. To increase the convergence ofthe algorithm, after the PSO and shuffled frog-leaping algorithm (SFLA) are modifiedso that the former is changed into a self-adaptive PSO (SAPSO) algorithm, then it ishybridized with the improved SFLA to produce a new hybrid SAPSO-SFLA, and thehybrid algorithm is applied to answer the foregoing multi-objectives. Researches showthat1) the SA-LS method based on the dichotomy of the golden section point is of highprecision and fast velocity in solving the reliability and its sensitivity of thesophisticated nonlinear PF2) the convergence velocity of the proposed hybridSAPSO-SFLA is superior to that of the modified PSO and SFLA (see P106-108), and its robustness can decrease the volume of the gearboxes by8.42%.
As can be drawn from the optimization of the4main components of the PGR inthe EPBSM,1) the generalization of the constructed4mathematical&mechanicalmodels and the proposed4computational intelligence not only resolves the strengthproblem that there is a little weak in the original3rdstage of the PGR, but can decreasethe volume of the whole PGR by21.58%, and increase its efficiency and transmissionratio by0.56%and3.67%,respectively,2) The practicable volume decrease of the wholePGR is5.12than that of the gear train when the volume decrease rate of the gear train isapplied to approximately predict that of the whole PGR.What’s more, the simulationexperiment also prove that the each index of the optimized PGR meets the presetteddemand, and that its reliability is good.
为克服灰色理论本身的固有缺陷与粒子群优化(Particle swarm optimization，PSO)算法在求解整数或混合整数规划过程中出现的问题，将方差的概念引入灰色关联度，提出可靠灰色关联度的概念及计算公式，并通过圆整粒子的初始位置与每次飞行速度，以使PSO算法满足求解过程中对整数解的要求。然后，将可靠灰色关联度作为变异策略来驾驭PSO算法，并详尽阐述其算法机理与流程，从而为复杂非线性约束条件下求解多目标混合整数规划问题提供一套切实可行的便捷方法。建立盾构三级行星减速器的轮系在满足配齿、变位系数、干涉、强度、等强度、等寿命等约束条件下其体积最小、效率最高、接触强度与弯曲强度可靠性最高的四目标函数的数力模型，再运用上述可靠灰色PSO算法编写MATLAB程序来求解所建数力模型。研究表明：1)与惩罚函数法(Penalty function method，PFM)相比(见P29-31)，所提算法有更快的收敛速度；2)该算法的泛化能力不但解决了该行星减速器原第三级强度偏弱的问题，而且在保证高可靠性条件下，使轮系体积减少11.55%，效率提高0.56%，传动比提高3.67%，各级强度与寿命基本相等。
鉴于现有免疫遗传算法(Immune genetic algorithm，IGA)其收敛性不理想的问题，剖析其理论体系本身存在的6大不足，并提出6条全新的策略，以加快算法的收敛。同时，阐明实码抗体与变量向量之间的关系，用图形直观描述复杂的算法机理，以便于对IGA的理解与实际操作；将可靠性分析的随机摄动法与其灵敏度分析结合起来，导出随机参数的概率分布为任意形状的机械零件计算其可靠度及灵敏度的函数表达式，由此创建行星减速器其轴的可靠度对设计变量的灵敏度最低与体积最小的两目标数力模型；提出实现目标函数值之间保持动态平衡的全新模型，顺利实现上述两目标函数与像集法的对接；最后，编写所改进IGA的MATLAB程序对该减速器的轴进行优化。结果表明：该算法的鲁棒性不仅使行星减速器轴的总体积减小13.65%，与改进前相比，所提IGA有更快的收敛速度与更高的收敛精度(见P50-51)。
为解答实际工程中变量相关情况下的高维小概率失效问题，将子集模拟、Monte Carlo法与重要抽样法结合起来，根据重要抽样的概率密度函数获取的相关变量的样本点来构造中间失效事件，从而将小失效概率转化为一条由一系列易于求解的较大条件失效概率的连乘积组成的杂交马尔可夫链，并直接抽取相关样本点来高效模拟结构的可靠性灵敏度。由此创建盾构行星减速器的三个行星架其失效概率对各变量均值、方差(包括相关系数)的可靠性灵敏度最低及体积最小的多目标优化问题，并提出多目标协同优化的思想。同时，针对可靠性灵敏度作为目标函数因误差导致多目标协同优化难以收敛的问题，提出利用误差的思想与方法；为加速遗传算法(Genetic algorithm，GA)与PSO算法的收敛，提出克隆与进化同时并举的精英策略及在相似个体之间进行交配的思想，并用此GA得到的优秀个体与PSO算法杂交，以实现种群续代更新的同时，进一步提高算法的收敛性；最后，运用上述算法对所建数力模型进行求解，结果表明：1)所提直接抽取相关样本的HMC能很好地模拟相关变量的可靠性及其灵敏度，免除了变量独立化过程反复转换的繁琐；2)所提杂交GA-PSO协同算法较GA与PSO算法有更快的收敛速度(见P79-81)，当相关系数为0.7时，可使三个行星架的总体积减小7.06%；3)证实了将可靠性灵敏度作为目标函数时所提利用误差的思想与方法的可行性与正确性。
为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性及灵敏度的问题，融合鞍点估计与线抽样法的优点，结合二分法的特点与黄金分割法的求解效率，提出基于黄金分割二分法的鞍点线抽样法，即可在标准化变量空间中沿重要线抽样方向利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点，从而将结构的失效概率转化为一系列线性功能函数失效概率的平均值，由此求出可靠性灵敏度，从而导出行星减速器的三级箱体其失效概率对基本变量均值与方差的可靠性灵敏度及结构轻量化的多目标优化问题；为提高算法的收敛性，对PSO算法与混合蛙跳算法(Shuffled frog-leaping algorithm，SFLA)进行改进，使前者变为自适应PSO(Self-adaptive PSO, SAPSO)算法后再与改进后的SFLA进行杂交，从而导致了杂交SAPSO-SFLA的产生，然后用来求解上述多目标问题。研究表明：1)基于黄金分割二分法的鞍点线抽样法在求解复杂非线性功能函数的可靠性及灵敏度时精度高，速度快；2)与SAPSO和SFLA相比，所提杂交SAPSO-SFLA不仅具有更快的收敛速度(见P106-108)，其鲁棒性还能使该三级箱体体积减小8.42%。
从行星减速器4大构件的优化可得出：1)上述所建4大数力模型与所提4大计算智能的泛化能力不仅解决了盾构原行星减速器第三级强度偏弱的问题，在保证高可靠性条件下，还可使整个行星减速器的体积减小21.58%，效率提高0.56%，传动比提高3.67%；2)当用轮系的体积减小率来近似预估整个行星减速器的体积减小情况时，其实际效果是轮系体积减小量的5.12倍。此外，仿真试验表明，优化后的行星减速器其各项指标均满足要求，可靠性较好。
The torque that drives the cutterhead of the Earth-pressure-balance shield machine(EPBSM) is first analyzed, and the load equilibrium and allocation of high-capacitythree-stages planetary gear reducer (PGR) are discussed to define the environment ofEPBSM for optimizing the PGR. For its4major elements, that is gear train, shaft,planetary carrier and gearbox, the gear train is a global commander so that the PGR canbe optimized by optimizing each constituent, their mathematical&mechanical modelsof multiple objectives are thus constructed according to the robust design demands. Inthe meanwhile, one or more very interesting algorithms that are selected from thecomputational intelligence (CI) are modified to become or be even combined to a newalgorithm that has better convergence than ever, and then they are used to solve themodels above.At last, the simulation test for the optimized PGR are done.The concretereason, methods, principles and effectiveness are successively as follows.
To overcome the intrinsic defect of the grey theory in itself and the appearingproblem of particle swarm optimization (PSO) algorithm when it is used to slove theinteger or mixed one programming problems, the sigma is introduced into greyrelational degree, the notion of the reliably grey relational degree(RGRD) is put forward.For PSO algorithm, the demand of the integer solution is met by rounding their initialposition and speed of each flight in the course of answering the problems. The RGRD isacted as the alternation strategy to control PSO, and their mechanism and processes areillustrated to provide a practical and convenient method for multi-objective integer ormixed one programming problems subject to complex non-linear conditions. Themathematical models are constructed for three-stage PGR in EPBSM with4objectivefunctions, that is to make its volume smallest, its efficiency highest and the reliability ofits contacting and bending strength highest, which are subject to the conditions such asteeth, modification coefficient, interference, strength, equal strength, equal life etc,which are solved by MATLAB programming language that applied the reliably greyPSO algorithm. The research results show that1) the strength and lifetime in everystage are basically equal under the conditions of ensuring high reliability, and thevelocity of the proposed algorithm is faster than that of the penalty function method(PFM)(see P29-31),2) the generalization ability not only resolves the strength problemthat there is a little weak in the original3rdstage of the PGR, but decreases the gear train volume by11.55%and increases its efficiency by0.56%and its transmission ratio by3.67%.
In view of the dissatisfactory convergence of the current immune genetic algorithm(IGA),6inherent drawbacks are found which existing in the current rationale of IGA.For these reasons,6new strategies which are corresponding to the drawbacks above areproposed to accelerate its convergence. The relationship between real-coded antibodiesand variables vector is illustrated, and the complicated algorithm mechanism isintuitively described by the figure, which make us understood easily and practicallyoperate on IGA. The stochastic perturbation method of the reliability is combined withits sensitivity analysis to deduce their function formulas on mechanical parts whoseprobability distributions of random parameters are arbitrary shape so that thetwo-objective mathematical models are created on minimizing the reliability sensitivityof the shafts of3-stage PGR in EPBSM with respect to design variables and theirvolume. A new model is proposed that can realize the dynamic balance betweenobjectives, by which the objectives are smoothly combined with the image set method.Finally, the shafts are optimized by means of the MATLAB programs languages thatapply the modified IGA above. The results show that the robustness of the improvedIGA not only decreases the total volume of shafts of the PGR by13.65%, but also itsconvergent velocity and accuracy are superior to that of the unimproved IGA (seeP50-51).
In the practical engineering, to answer the small failure probabilities withhigh-dimensional correlated variables, the subset simulation (SS) is combined togetherwith the Monte Carlo simulation and importance sampling (IS) method. The samplesfrom the probability density functions (PDF) of the importance sampling are used toconstruct the intermediate failure events, by which the small failure probabilities areturned into a hybrid Markov chain (HMC), which is a continuous product made of aseries large failure probability or conditional failure probability (CFP) which is easilyanswered, on which the structural reliability sensitivity (RS) can be efficiently simulatedby directly obtaining the samples with correlated ones.Multi-objectives optimizationmodels are established about minimizing the RS of failure probability of the3planetarycarriers of the PGR with respect to the variable mean, variance (including the correlatedcoefficient between them) respectively and volume etc, and the collaborativeoptimization idea for multi-objectives is put forward, in the meantime, in view of theproblem that it is difficult to converge for multi-objectives to be collaboratively optimized because of the errors when the RS is used as an objective function, the ideaand method that utilize the errors are proposed. To increase the convergent velocity ofgenetic algorithm (GA) and PSO, the elite strategy that have elitist cloned and to takepart in evolution simultaneously and the idea that have an individual to mate theindividual who is most similar to it are put forward. And the excellent individuals fromthe modified GA are hybridized with those individuals from PSO to update thepopulation and to further enhance their convergence. Finally, the3planetary carriers areoptimized according to the algorithm above, the results show that1) the SS of the ISwith correlated variables can highly simulate failure probability and its sensitivity,2)the convergent velocity of the collaborative algorithm of hybrid GA-PSO is superior tothat of the GA and PSO (see P79-81), it can reduce the total volume of the planet carriersby7.06%when the correlated coefficient is equal to0.7,3) it is confirmed that theproposed idea and method that utilize the errors are feasible and correct when the RSacts as objective function.
To solve the reliability and its sensitivity for structural system whose implicitnonlinear performance function (PF) are complicated, changeable and of non-normalvariables, the advantages of the saddlepoint approximation (SA) and line sampling (LS)are merged and the merits of dichotomy and the solution efficiency of the goldensection method are combined to propose the saddlepoint approximation-line samplingmethod (SA-LS) based on the dichotomy of the golden section point, namely, it is quickto find the zeropoint in PF corresponding to each sample along the important linesampling direction by the dichotomy above so that the structural failure probability canbe transformed into the mean of a series linear PF failure probability, and by whichreliability sensitivity can be solved, thus the multi-objectives are inferred about the RSof failure probability of the three-stage gearboxes of the PGR with respect to thevariables mean and variance and structural lightweight. To increase the convergence ofthe algorithm, after the PSO and shuffled frog-leaping algorithm (SFLA) are modifiedso that the former is changed into a self-adaptive PSO (SAPSO) algorithm, then it ishybridized with the improved SFLA to produce a new hybrid SAPSO-SFLA, and thehybrid algorithm is applied to answer the foregoing multi-objectives. Researches showthat1) the SA-LS method based on the dichotomy of the golden section point is of highprecision and fast velocity in solving the reliability and its sensitivity of thesophisticated nonlinear PF2) the convergence velocity of the proposed hybridSAPSO-SFLA is superior to that of the modified PSO and SFLA (see P106-108), and its robustness can decrease the volume of the gearboxes by8.42%.
As can be drawn from the optimization of the4main components of the PGR inthe EPBSM,1) the generalization of the constructed4mathematical&mechanicalmodels and the proposed4computational intelligence not only resolves the strengthproblem that there is a little weak in the original3rdstage of the PGR, but can decreasethe volume of the whole PGR by21.58%, and increase its efficiency and transmissionratio by0.56%and3.67%,respectively,2) The practicable volume decrease of the wholePGR is5.12than that of the gear train when the volume decrease rate of the gear train isapplied to approximately predict that of the whole PGR.What’s more, the simulationexperiment also prove that the each index of the optimized PGR meets the presetteddemand, and that its reliability is good.
引文
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