下载文档原格式
Pvsyst 后台参数的翻译 Grid-connected systempre-sizing 并网系统初步设置Monocrystalline module efficiency 单晶组件效率Polycrystalline efficiency 多晶组件效率Thin film efficiency 薄膜组件效率Free standing temperature correction 自由安装温度纠正系数Roof ventilated temperature correction 屋顶通风温度纠正系数No ventilation temperature correction 无通风温度纠正系数Ohmic wiring loss mismatch loss correction 线缆欧姆损失，失配损失纠正系数 IAM incidene angle modifier correction 入射角改变纠正系数Inverter average efficiency 逆变器平均效率Stand-alone systempre-sizing 独立系统初步设计Stand-alone:pv-array=>battery globa efficiency 阵列到电池整体效率 Batterycharge/discharge energy efficiency 电池充放电能量效率Soc minimum threshold 荷电率最小阈值Battery capacity:C100/C10 ratio100 小时率比10小时率系数Generatorefficiency(15%=1.5kwh/liter)发电机效率Pumping:pv-array daily effic(optical,thermal ,etc) 光伏水泵方阵综合效率(光，热等) Matching effic（thresh.andmppt loss）direct coupling 直接耦合匹配效率（阈值及最大跟踪损失）Matching effic（thresh.andmppt loss）with booster升压耦合匹配效率（阈值及最大跟踪损失）Matching effic（thresh.andmppt loss）cascading级联匹配效率（阈值及最大跟踪损失）Global effic.with fixed V DC converter 固定电压直流变换器耦合的综合效率Global effic.withmppt converter mppt 逆变器耦合综合效率DC-positive displacement pump efficiency 直流容积泵效率AC-positive displacement pump efficiency 交流容积泵效率Centrifugal pump efficiency 离心泵效率Oversizing{(pv field stc-losses)/pump power} 裕度（光伏阵列/泵功率）Specific pre-sizing costs(all systems) 所有系统初步设计价格Loan duration(=sexpected system lifetime) 系统寿命25 yearScale exponential factor(mouning and maintenance)规模指数因子0.6Systemdesign parameters 系统设计参数Minimum temperature for inverter Vmax design（需相应改动）逆变器最大电压设计使用的最低温度Winter operating temp.for inverter VmppMax design（需相应改动）逆变器跟踪最大电压值设计冬季运行温度Usual operating temperature at r1000W/m（需相应改动）平常运行温度Summer operating temp.for inverter VmppMin design（需相应改动）逆变器跟踪最小电压值设计夏季运行温度Voltage initial degradation amorphous 非晶硅初期压降Voltage initial degradation,microcrystalline 微晶硅初期压降Voltage initial degradation.CdTe 碲化镉太阳能组件初期压降Heat loss factor free mounting 自由安装式热损失因子Heat loss factor semi integrated 半集成式热损失因子Heat loss factor fully integrated 集成式热损失因子Heat loss factor according to wind velocity 根据风速定义的热损失因子Heat loss factor max./min. value 热损失最大/最小值Incidence angle modifier bo parameter 入射角改变纠正系数Copper Resistivity(at T=50 度)铜电阻率Aluminium Resistivity(at T=50 度)铝电阻率Max. wire section for specific admissible current对特定电流最大可接受线缆截面积Max. admissible current derating factor最大可允许电流衰减Default wiring resistance loss ratio at STC标况下默认线阻损失率Array resitance voltage drop at STC标况下阵列阻耗压降Irrad.absorption coefficient for tarray calculation阵列计算用辐射吸收系数Module dfficiency for temp.array calculation阵列计算用组件效率Series diode voltage drop二极管压降External transfo:iron losses外置变压器铁损External transfo:resist losses at STC外置变压器铜损Light soaking gain factor光辐照增益系数Default module quality factor默认组件质量因数Module quality loss:tolerance fraction组件质量因数公差LIDloss factorLID损失因子Default array mismatch power loss,crystalline默认阵列功率失配损失，晶硅组件Default array mismatch power loss, amorphous默认阵列功率失配损失，非晶硅Default array mismatch voltage loss ,crystalline默认阵列电压失配损失，晶硅组件Default array mismatch voltage loss , amorphous默认阵列电压失配损失，非晶硅Default soiling loss,yearly average默认年平均脏污损失Default unavailability loss默认无效损失Module strings shading ratio组串阴影率Module strings thin film shading ratio组串薄膜阴影率Grid inverter oversizing array/inverter nominal power并网阵列功率/逆变器裕度值SolaredgePnom ratio sizing,0=STC,1=real conditionsSolaredge功率比定型0=标况，1=真实条件Nominal medium voltage grid默认中压网络DC grid:arrayVnom/system Vnom ratio直流网：组件电压/系统电压Average pumping hours during a clear day晴空下平均抽水时间Pumps lifetime(economical evaluation)水泵寿命Fuel price (economical evaluation)燃油价格Flowrate oversizing accounting for average days平均流量裕度值Array current /pumps nominal current阵列电流/泵额定电流Detailed simulation verification conditions详细模拟检定条件Measured meteo in coll.plane:max.orientation difference吸收平面测量数据最大方位差Shading:max.orientation difference shaded #1-pv array遮光：遮光#1 阵列最大方位差Shading:max.orientation difference between shading planes遮光：遮光平面允许最大方位差Shadings with heterogeneous field:max.angle difference异形区域遮光最大角度差Helios3D:max.angle between palnes Helios3D:平面间最大角度差Shading:absolutemin.shading/field area ratio遮光：3D区域/系统定义区域绝对极小值Shading:warningmin. shading/field area ratio遮光：3D区域/系统定义区域禁告极小值Shading:warningmax.shading/field area ratio遮光：3D区域/系统定义区域禁告极大值Shading:absolutemax.shading/field area ratio遮光：3D区域/系统定义区域绝对极大值the inverter power is strongly oversized逆变器功率值严重过大the inverter power is slightly oversized逆变器功率值轻微过大acceptable overload loss for design可接受设计过载损失limit overload loss for design设计过载损失限值pv array/battery pack voltage：光伏阵列/蓄电池电压strongly undersized/oversized光伏阵列/蓄电池电压严重过小/过大slightly undersized/oversized光伏阵列/蓄电池电压轻微过小/过大pv array/regulator voltage：光伏阵列/控制器电压pv array/ regulator power：光伏阵列/控制器功率the battery pack capacity is perhaps：电池组容量the pv array power is slightly undersized/oversized阵列容量轻微过小/过大the pv array power is strongly undersized/oversized阵列容量严重过小/过大the pumping flowrate is strongly undersized/oversized水泵流量严重过小/过大the pumping flowrate is slightly undersized/oversized水泵流量轻微过小/过大pumping: the array voltage is strongly undersized/oversized阵列电压严重过小/过大pumping: the array voltage is slightly undersized/oversized阵列电压轻微过小/过大pumping: the array current is strongly undersized/oversized 阵列电流严重过小/过大pumping: the array current is slightlyundersized/oversized阵列电流轻微过小/过大光伏组件：EGap-Si-Mono单晶硅禁带宽度EGap -Si-poly多晶硅禁带宽度EGapa-Si:H tandem双结氢化非晶硅禁带宽度EGapa-si:H triple三结氢化非晶硅禁带宽度EGapucSia-Si:H微晶硅氢化非晶硅双结电池禁带宽度EGapCdTe碲化镉薄膜电池禁带宽度EGap CIS铜铟硒(CIS)薄膜电池禁带宽度EGap CSG：CSG （CrystaIIineSiIiconONGIass）电池禁带宽度EGap HIT异质结太阳能电池禁带宽度EGapAsGa砷化钾太阳能电池禁带宽度EGap Galnp2/GaAs/GeGalnp2/GaAs/Ge 三结太阳能电池禁带宽度EGap Not Registered未定义电池禁带宽度Built-in voltage for amorphous tripple，add to Vmp非晶硅三结太阳能电池峰值电压Built-in voltage for amorphous single非晶硅单结太阳能电池峰值电压Built-in voltage for amorphous tandem非晶硅双结太阳能电池峰值电压Crystalline:Rsho/Rsh default multiplier value晶硅：Rsho/Rsh默认乘数值Amorphous:Rsho/Rsh default multiplier value非晶硅：Rsho/Rsh默认乘数值RShexp exponential parameterRShexp 指数Thin films:Pmpp Temperature coefficient薄膜：峰值功率温度系数Gamma defult for Rserie optimization Si-poly多晶硅串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization Si-mono单晶硅串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization a-Si:H tandem氢化非晶硅双结电池串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization a-Si:H triple氢化非晶硅三结电池串联电阻最优化默认Gamma 值defult for RSerie optimization ucSia-Si:H多晶硅串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization CdTe碲化镉薄膜电池串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization CIS铜铟硒(CIS)薄膜电池串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization CSGCSG （CrystaIIineSiIiconONGIass）电池串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization HIT异质结太阳能电池串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization AsGa砷化钾串联电阻最优化默认Gamma 值Gamma defult for RSerie optimization Galnp2/GaAs/GeGalnp2/GaAs/Ge 串联电阻最优化默认Gamma 值Gamma defult for RSerieoptimization,unregistered未定义太阳能电池串联电阻最优化默认Gamma 值Min lo value for Galnp2/GaAs/Ge：Galnp2/GaAs/Ge 最小lo 值Min lo value for all others：其他电池的最小lo 值Min./Max.VmppCell,Si- Crystalline：晶硅最小/最大峰值电压Min./Max.VmppCell,a-Si:Htandem：双结氢化非晶硅最小/最大峰值电压Min./Max.VmppCell,a-Si:Htriple junction：三结氢化非晶硅最小/最大峰值电压Min./Max.VmppCell,ucSia-Si:H：微晶硅氢化非晶硅双结电池最小/最大峰值电压Vmpp Cell, ucSia-Si:H：微晶硅氢化非晶硅双结电池最大峰值电压Min./Max.Vmpp Cell, CdTe：碲化镉薄膜电池最小/最大峰值电压Min./Max.Vmpp Cell, CIS：铜铟硒(CIS)薄膜电池最小/最大峰值电压Min./Max.VmppCell,CSG：CSG（CrystaIIineSiIiconONGIass）最小/最大峰值电压Min./Max.Vmpp Cell, HIT：异质结太阳能电池最小/最大峰值电压Min./Max.Vmpp Cell, AsGa：砷化钾太阳能电池最小/最大峰值电压Min./Max.Vmpp Cell,Galnp2/GaAs/Ge：Galnp2/GaAs/Ge三结太阳能电池最小/最大峰值电压Min./Max.Vmpp Cell, unregistered：未定义电池最小峰值电压Max. Imp/Isc ratio：Imp/Isc 最大比值Max.Vmp/Isc ratio：Vmp/Isc 最大比值Max.mulsc/Isc ratio：mulsc/Isc 最大比值Max.Pmpp deviation{at STC}by respect to Pnom：标况与实际情况下功率误差Rshun min calculation:securitycoeff.vs MPP：并联电阻电小值计算：mpp 安全系数Rserie default calculation:Min./Max.RSerie/RSmax ratio串联电阻默认计算：最大/最小RSerie/RSmax 比值D2/MuTaucalculation:Max. RSerie/RSmax ratioD2/MuTau 计算：Max. RSerie/RSmax 比值Amorphous Recombin.loss factor: 非晶硅复合损失因子：D2/MuTau default valueD2/MuTau 默认值By-pass diode resistance{10mv/A}：旁路二极管电阻efaultBRev parameter ratio：默认BRev 参数率Regulators and convertersVoltage drop for C10 current：10 小时率下压降Charging triggering OFF：充电截止电压阈值，关闭阈值open batteries：开口式蓄电池sealed batteries：密封式蓄电池AGM batteries：蓄电池Ni-Cd batteries：蓄电池Charging triggering ON again：充电开启电压阀值Discharging triggering OFF：放电截止电压阈值Discharging triggering ON again：放电截止电压阈值Back-up generator triggering ON again：备用发电机开启阈值Back-up generator triggering OFF：备用发电机关闭阈值Temper. Coefficient (per element)温度系数（单格）Reference temperature for these thresholds对这些阈值的参考温度Minimum hysteresis for swiching(per element)切换时最小磁滞（单格）Initial SOC for simulation仿真初始荷电状态MPPT converters:power thresh./pnom lower limit：MPPT 逆变器：功率阈值/正常功率下限值MPPT converters:defaultmax.efficiency：MPPT 逆变器：默认最大效率MPPT converters:defaultEURO.efficiency：MPPT 逆变器：默认最大欧洲效率Normalized resistance factor：标准化电阻因数Max./Minimum value of the max.effciency：最大效率的最大/最小值Minimum efficiency difference max –EURO：最小欧洲效率的偏差值Max. efficiency difference max –EURO：最大欧洲效率的偏差值Minimum difference between legal and solar time：法定时间和太阳时间的最小差值Max. difference between legal and solar time：法定时间和太阳时间的最大差值Minimum monthly ambient temperature：最小月环境温度Lower/Upper limit for monthly clearness index kt：月晴空指数下限/上限Best Ktcc days have slightly high/low values：最佳Ktcc日微高值/低值Best Ktcc days have strongly high/low values：最佳Ktcc日极高值/低值Best Ktcc :number of exception days：最佳Ktcc 日微高值Limit for kbeam in transposition：转置时kbeam 的限制Limit for global horiz.in retro-transposition：反转录时全景的限制Lower limit for monthly diffuse/Global：月漫反射/全局辐射下限值Default wind velocity：默认风速Horizon:characteristic height for albedo factor extinction：地平线：反色率因子无效特征高度Horizon:max.mumber of points in printed table：地平线：在打印的表格中点的最大数量Site altitude limit：地理海拔限制Project site-meteomax. distance：工程气象地点最大距离Economic evaluation:loan duration(=expected lifetime)：经济评估：系统寿命Minimum piece kwh for enabling tariff：每度电最小税收Max. price kwh for enabling tariff：每度电最大税收Shadings:sun contrast for real objects：真实物体的太阳对照Shading animation:delay between steps：阴影动画，延迟间隔。
前言●Isight 5.5简介笔者自2000年开始接触并采用Isight软件开展多学科设计优化工作，经过12年的发展，我们欣喜地看到优化技术已经深深扎根到众多行业，帮助越来越多的中国企业提高产品性能和品质、降低成本和能耗，取得了可观的经济效益和社会效益。
作为工程优化技术的优秀代表，Isight 5.5软件由法国Dassault/Simulia公司出品，能够帮助设计人员、仿真人员完成从简单的零部件参数分析到复杂系统多学科设计优化（MDO, Multi-Disciplinary Design Optimization）工作。
Isight将四大数学算法（试验设计、近似建模、探索优化和质量设计）融为有机整体，能够让计算机自动化、智能化地驱动数字样机的设计过程，更快、更好、更省地实现产品设计。
毫无疑问，以Isight为代表的优化技术必将为中国经济从“中国制造”到“中国创造”的转型做出应有的贡献！●本书指南Isight功能强大，内容丰富。
本书力求通过循序渐进，图文并茂的方式使读者能以最快的速度理解和掌握基本概念和操作方法，同时提高工程应用的实践水平。
全书共分十五章，第1章至第7章为入门篇，介绍Isight的界面、集成、试验设计、数值和全局优化算法；第8章至第13章为提高篇，全面介绍近似建模、组合优化策略、多目标优化、蒙特卡洛模拟、田口稳健设计和6Sigma品质设计方法DFSS（Design For 6Sigma）的相关知识。
本书约定在本书中，【AA】表示菜单、按钮、文本框、对话框。
如果没有特殊说明，则“单击”都表示用鼠标左键单击，“双击”表示用鼠标左键双击。
在本书中，有许多“提示”和“试一试”，用于强调重点和给予读者练习的机会，用户最好详细阅读并亲身实践。
本书内容循序渐进，图文并茂，实用性强。
适合于企业和院校从事产品设计、仿真分析和优化的读者使用。
在本书出版过程中，得到了Isight发明人唐兆成（Siu Tong）博士、Dassault/Simulia （中国）公司负责人白锐、陈明伟先生的大力支持，工程师张伟、李保国、崔杏圆、杨浩强、周培筠、侯英华、庞宝强、胡月圆、邹波等参与撰写，李鸽、杨新龙也为本书提供了宝贵的建议和意见，在此向所有关心和支持本书出版的人士表示感谢。
算术优化算法的参数
算术优化算法（Arithmetic Optimization，AO）是一种优化算法，用于在数学和计算领域中解决各种优化问题。
算术优化算法通常使用启发式方法来寻找问题的最优解，它通过迭代搜索空间来逐步逼近最优解。
算术优化算法的参数包括：
1. 迭代次数：算术优化算法通常需要进行多次迭代才能找到最优解。
迭代次数决定了算法的搜索深度和时间成本。
2. 搜索策略：算术优化算法通常采用一种启发式搜索策略，如模拟退火、遗传算法、粒子群优化等。
搜索策略决定了算法的搜索方向和效率。
3. 目标函数：算术优化算法通常需要针对特定的目标函数进行优化。
目标函数是指需要优化的数学表达式，它描述了问题的最优解。
4. 初始解：算术优化算法通常从一个初始解开始搜索。
初始解的选择会影响算法的搜索效率和结果。
5. 停止条件：算术优化算法通常需要设置停止条件，以确定何时停止搜索。
停止条件可以是达到预设的最大迭代次数、找到满足一定精度要求的解等。
需要注意的是，算术优化算法的具体参数可能会因问题类型和具体应用而有所不同。
因此，在实际应用中，需要根据具体问题选择合适的参数并进行实验和调整，以获得最佳的优化效果。
pytorch优化器（optim）不同参数组,不同学习率设置的操作optim 的基本使⽤for do:1. 计算loss2. 清空梯度3. 反传梯度4. 更新参数optim的完整流程cifiron = nn.MSELoss()optimiter = torch.optim.SGD(net.parameters(),lr=0.01,momentum=0.9)for i in range(iters):out = net(inputs)loss = cifiron(out,label)optimiter.zero_grad() # 清空之前保留的梯度信息loss.backward() # 将mini_batch 的loss 信息反传回去optimiter.step() # 根据 optim参数和梯度更新参数 w.data -= w.grad*lr⽹络参数默认使⽤统⼀的优化器参数如下设置⽹络全局参数使⽤统⼀的优化器参数optimiter = torch.optim.Adam(net.parameters(),lr=0.01,momentum=0.9)如下设置将optimizer的可更新参数分为不同的三组，每组使⽤不同的策略optimizer = torch.optim.SGD([{'params': other_params},{'params': first_params, 'lr': 0.01*args.learning_rate},{'params': second_params, 'weight_decay': args.weight_decay}],lr=args.learning_rate,momentum=args.momentum,)我们追溯⼀下构造Optim的过程为了更好的看整个过程，去掉了很多条件判断语句，如 >0 <0# ⾸先是⼦类Adam 的构造函数class Adam(Optimizer):def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,weight_decay=0, amsgrad=False):defaults = dict(lr=lr, betas=betas, eps=eps,weight_decay=weight_decay, amsgrad=amsgrad)'''构造了参数params，可以有两种传⼊格式,分别对应1. 全局参数 net.parameters()2. 不同参数组 [{'params': other_params},{'params': first_params, 'lr': 0.1*lr}]和 <全局> 的默认参数字典defaults'''# 然后调⽤⽗类Optimizer 的构造函数super(Adam, self).__init__(params, defaults)# 看⼀下 Optim类的构造函数只有两个输⼊ params 和 defaultsclass Optimizer(object):def __init__(self, params, defaults):torch._C._log_api_usage_once("python.optimizer")self.defaults = defaultsself.state = defaultdict(dict)self.param_groups = [] # ⾃⾝构造的参数组，每个组使⽤⼀套参数param_groups = list(params)if len(param_groups) == 0:raise ValueError("optimizer got an empty parameter list")# 如果传⼊的net.parameters()，将其转换为字典if not isinstance(param_groups[0], dict):param_groups = [{'params': param_groups}]for param_group in param_groups:#add_param_group 这个函数,主要是处理⼀下每个参数组其它属性参数(lr,eps)self.add_param_group(param_group)def add_param_group(self, param_group):# 如果当前参数组中不存在默认参数的设置，则使⽤全局参数属性进⾏覆盖'''[{'params': other_params},{'params': first_params, 'lr': 0.1*lr}]如第⼀个参数组只提供了参数列表，没有其它的参数属性，则使⽤全局属性覆盖，第⼆个参数组则设置了⾃⾝的lr为全局 (0.1*lr)'''for name, default in self.defaults.items():if default is required and name not in param_group:raise ValueError("parameter group didn't specify a value of required optimization parameter " +name)else:param_group.setdefault(name, default)# 判断是否有⼀个参数出现在不同的参数组中，否则会报错param_set = set()for group in self.param_groups:param_set.update(set(group['params']))if not param_set.isdisjoint(set(param_group['params'])):raise ValueError("some parameters appear in more than one parameter group")# 然后更新⾃⾝的参数组中self.param_groups.append(param_group)⽹络更新的过程(Step)具体实现1、我们拿SGD举例，⾸先看⼀下，optim.step 更新函数的具体操作2、可见，for group in self.param_groups，optim中存在⼀个param_groups的东西，其实它就是我们传进去的param_list，⽐如我们上⾯传进去⼀个长度为3的param_list,那么 len(optimizer.param_groups)==3 , ⽽每⼀个 group ⼜是⼀个dict, 其中包含了每组参数所需的必要参数optimizer.param_groups:长度2的list，optimizer.param_groups[0]：长度6的字典3、然后取回每组所需更新的参数for p in group['params'] ,根据设置计算其正则化及动量累积，然后更新参数 w.data -= w.grad*lrdef step(self, closure=None):loss = Noneif closure is not None:loss = closure()for group in self.param_groups:# 本组参数更新所必需的参数设置weight_decay = group['weight_decay']momentum = group['momentum']dampening = group['dampening']nesterov = group['nesterov']for p in group['params']: # 本组所有需要更新的参数 paramsif p.grad is None: # 如果没有梯度则直接下⼀步continued_p = p.grad.data# 正则化及动量累积操作if weight_decay != 0:d_p.add_(weight_decay, p.data)if momentum != 0:param_state = self.state[p]if 'momentum_buffer' not in param_state:buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()else:buf = param_state['momentum_buffer']buf.mul_(momentum).add_(1 - dampening, d_p)if nesterov:d_p = d_p.add(momentum, buf)else:d_p = buf# 当前组学习参数更新 w.data -= w.grad*lrp.data.add_(-group['lr'], d_p)return loss如何获取指定参数1、可以使⽤d_parameters() 取回所有参数，然后设定⾃⼰的筛选规则，将参数分组2、取回分组参数的id map(id, weight_params_list)3、取回剩余分特殊处置参数的id other_params = list(filter(lambda p: id(p) not in params_id, all_params))all_params = model.parameters()weight_params = []quant_params = []# 根据⾃⼰的筛选规则将所有⽹络参数进⾏分组for pname, p in d_parameters():if any([pname.endswith(k) for k in ['cw', 'dw', 'cx', 'dx', 'lamb']]):quant_params += [p]elif ('conv' or 'fc' in pname and 'weight' in pname):weight_params += [p]# 取回分组参数的idparams_id = list(map(id, weight_params)) + list(map(id, quant_params))# 取回剩余分特殊处置参数的idother_params = list(filter(lambda p: id(p) not in params_id, all_params))# 构建不同学习参数的优化器optimizer = torch.optim.SGD([{'params': other_params},{'params': quant_params, 'lr': 0.1*args.learning_rate},{'params': weight_params, 'weight_decay': args.weight_decay}],lr=args.learning_rate,momentum=args.momentum,)获取指定层的参数id# # 以层为单位，为不同层指定不同的学习率# ## 提取指定层对象special_layers = t.nn.ModuleList([net.classifiter[0], net.classifiter[3]])# ## 获取指定层参数idspecial_layers_params = list(map(id, special_layers.parameters()))print(special_layers_params)# ## 获取⾮指定层的参数idbase_params = filter(lambda p: id(p) not in special_layers_params, net.parameters())optimizer = t.optim.SGD([{'params': base_params},{'params': special_layers.parameters(), 'lr': 0.01}], lr=0.001)补充：【pytorch】筛选冻结部分⽹络层参数同时设置有参数组的时候该怎么办？在进⾏神经⽹络训练的时候，常常需要冻结部分⽹络层的参数，不想让他们回传梯度。
Optimization Design of Vibrating Screen Damping Spring Based on Multi-objectiveGenetic AlgorithmYang NaMechanical and electrical technology departmentXijing University,Shaanxi Xi'an ,Chinae-mail:****************Shang MiaoMechanical and electrical technology departmentXijing University,Shaanxi Xi'an ,Chinae-mail:****************Abstract—The damping spring plays an important role in the design of the vibrating screen. In view of the problems existing in the design of the vibration damper, the multi-objective genetic algorithm is used to select the relevant design variables of the damping spring, and the objective function and the constraint conditions are established to obtain the optimal solution. Finally, the practicality of the algorithm is verified by practical application.Keywords-Vibrating screen; vibration damper; multi objective genetic algorithm; optimum designI.I NTRODUCTIONIn recent years, the development direction of the vibrating screen in coal mining industry is gradually tending to light and high strength, and the stiffness and strength of the vibration screen is an important design index to ensure the efficiency of the vibration sieve, and is also a main content of the vibration analysis[1]. In order to strengthen the strength and reliability of the spring, the spring is generally used to increase the spring, but this will increase the quality of the spring, not only affect the vibration sieve vibration trajectory, but also lead to rising costs. In order to design a more practical damping spring, some related optimization algorithms have been used in the literature.For example [2], [3] used the fuzzy algorithm and particle swarm algorithm, but two references used the single objective optimization, and engineering practice often encounters in multiple criteria and multiple targets situation, also genetic algorithm with the traditional algorithm has a essential difference, genetic algorithm starting from the entire population, and the traditional optimization algorithm starting to a single point, so genetic algorithm don't need complementary information or knowledge, and has a higher search efficiency.Therefore, the multi objective genetic algorithm is used to optimize the design of the vibration damper spring to achieve a better effect.II.THE CONCEPT OF MULTI OBJECTIVEOPTIMIZATIONThe problem of Multi objective optimization design (Optimization Multi-objective) is a common situation in engineering practice, sometimes it is necessary to achieve the optimal problem of multiple targets in a given region. For example, vibration sieve spring, the general design of the cost of the minimum, the maximum safety factor, and the best vibration trajectory, but a parameter changes, the other parameters will be changed, resulting in conflict. This kind of optimization problem with more than one objective value is called the multi-objective optimization problem. The mathematical model of multi objective optimization is generally expressed by the following formula,12min()[(),(),...,()]..TnmV f x f x f x f xs t x XX R⎧-=⎪∈⎨⎪⊆⎩(1)In the equation (1),V-min said vector minimization, even Vector objective function in which each sub objective function is to minimize as much as possible.III.MULYI OBJECTIVE OF GENETIC ALGORITHM BASED ON HYBID METHODWith the research of multi-objective genetic algorithm, many scholars have put forward a variety of algorithms, such as the weight coefficient transformation method, the parallel selection method, the permutation method, the shared function method and so on. But each algorithm has some disadvantages, such as the parallel selection method can be divided into a variety of groups to search for a common search so that the search efficiency is reduced by [4]. In this paper, by using the hybrid method, the parallel selection method and the shared function method are combined, and the characteristics of the two algorithms are optimized. The basic idea of the hybrid method is that the main body of the selection operator uses the coordinate method, according to the number of sub objective functions of the multi-objective optimization problem, the whole population is divided into some sub groups, and then the corresponding generation of the next generation. Pareto optimal individual to retain, do not let it participate in the crossover, mutation operations, but it will be retained directly to the next generation. Finally, the sharing function method is used to deal with an individual X, in which the number of species and the degree of similarity in the vicinity of it can be measured, which is called the niche [5],[(,Y)]XY nm s d X≤=∑(2)International Conference on Education, Management, Computer and Society (EMCS 2016)In the equation (2), s(d) is a shared function, which is a monotonically decreasing function of the distance between the individual and the D. D (X, Y) can be defined as individual X, Y between the Hamming distance. Niche technology is an effective method to avoid local convergence and premature convergence in genetic algorithm, and to maintain population diversity [6]. Each individual niche is computed, the niche of the small number of individuals can have more chance of being selected, so as to better genetic to the next generation, which is similar to a lesser degree of individual can have a better opportunity to be inherited to the next generation, increase the diversity of the population. Algorithm flow chart is shown in Figure 1.Figure 1. Algorithm flow chartIV. PROOF OF ALGORITHMIn order to verify the feasibility of the hybrid genetic algorithm, this paper uses a multi-objective optimization example with two optimization objectives to verify the feasibility of the algorithm,min f1=300/x+500/y+300/(100-x-y)min f2=30(300/x-3)+12(500/y-5)+ (3-1) (300/(100-x-y)-3)X y, S.T. is an integer, and x+y<100Among them, the optimal Pareto values obtained as shown in Figure 1, x, Y values shown in Figure 3, can be seen from Figure 1 because of the mixed method, using the niche technology, so the distribution of the optimal Pareto value is more uniform, figure 2 is the corresponding x, y value of the coordinate.Figure 2. optimal Pareto valueFigure 3. x, y value of the corresponding coordinatesV. A PPLICATIONSCylindrical coil spring structure shown in Figure 4, the spring working load F = 680N, the working stroke h = 16.59mm, the operating frequency fr = 25Hz, requires N ≥106 life cycles. Spring materials used 50CrVA,allowable stress [τ] = 405MPa. Structural requirements shown in Table 2, check the relevant design manual know, spring is the material density ρ = 7.5 × 10-6Kg / mm3, the curvature of the spring coefficient K = 1.6 / C0.14, in this instance to the structure of the lightest weight, minimum spring free height and the natural frequencies of the three Figure 4. helical springs ChartTable I Simulation parametersTake spring wire diameter d, diameter D2 and n is the number of turns of work the three design parameters as design variables, equation as follows,1223x d x x D x n ⎡⎤⎡⎤⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦ (4-1)Respectively structure the lightest weight, theminimum spring free height and the natural frequencies of the highest objective function, the formula is as follows,4211232131623231() 1.814810( 1.8)()( 1.3)18.25() 2.80910/r f x x x x f x x x f x f x x x ---⎧=⨯+⎪=++⎨⎪==⨯⎩(4-2) Where, f1 (x) on behalf of a spring structural weight; f2 (x) on behalf of free height of the spring; f3 (x) on behalf of the natural frequencies of the spring. Finally, the establishment of constraints, constraints, the following equation. Of which the first five to performance constraints, after 6 as boundary conditions, it can be seen which is a 11 dimensional nonlinear constraints objective optimization design problem,30.862.86121221331252412354351236171812912() 2.770610/4050()6/0()( 1.3)18.25 5.30()250 3.5610/()0()680 1.65910/()0() 2.50()9.50()300()60g x x x g x x x g x x x x g x x x x g x x x x g x x g x x g x x x g x x x =⨯-≤=-≤=++-≤=-⨯≤=-⨯≤=-≤=-≤=--≤=+-1031130g ()30()60x x g x x ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪≤⎪⎪=-≤⎪=-≤⎪⎩(4-3) Wherein, g1 (x) is the intensity of the constraint condition; g2 (x) is a spring index constraints; g3 (x) is a spring stability constraints; g4 (x) is a spring to prevent the resonance constraints; g5 (x) is a spring g6 (x) is a spring wire diameter lower;; stiffness constraints g7 (x) is a spring wire diameter upper limit; g8 (x) spring diameter limit; g9 (x) for the upper limit of the spring diameter; g10 (x) for the spring working g11 (x) for the spring working laps ceiling; the minimum number of laps. Optimized results are shown in Table 3 and Table 4. Figs. 5 and 6, respectively, over the plane Pareto point set and theobjective function,Figure 5. Pareto Point SetFigure 6. Over planeVI. C ONCLUSIONSIn this paper, the use of vibration sieve spring as an example, the use of multi-objective genetic algorithm to optimize the design of the spring, not only to improve the shortcomings of traditional design, but also to design parameters for a variety of choices. In this paper, the weight is light, the free height and the natural frequency are the design parameters, and the main parameters of the spring can be optimized according to the spring in different conditions, so as to improve the design efficiency, reduce the cost and so on.R EFERENCES[1] Guo Xiao Ling, Yang Jie. Dynamic analysis and optimum designof large vibrating screen [J]. coal technology[2] Noble, and I. N. Sneddon, “On certain integrals of Lipschitz -Hankel type in volving products of Bessel functions,” Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955. (references) [3] J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed.,vol. 2. Oxford: Clarendon, 1892, pp.68–73.[4] I. S. Jacobs and C. P. Bea n, “Fine particles, thin films andexchange anisotropy,” in Magnetism, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academic, 1963, pp. 271–350. [5] K. Elissa, “Title of paper if known,” unpublished.[6] Parsopoulos K E ，Tasoulis D K ，Pavlidis N G ，et al Vectorevaluated differential evolution for multiobjective optimizatin[C].Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2004)，Portland ，USA ，2004，204-211．Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, “Ele ctron[7] spectroscopy studies on magneto-optical media and plasticsubstrate interface,” IEEE Transl. J. Magn. Japan, vol. 2, pp. 740–741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].[8] spectroscopy studies on magneto-optical media and plasticsubstrate interface,” IEEE Transl. J. Magn. Japan, vol. 2, pp. 740–741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].。
workbench中topology optimization详解Topology optimization is a technique used in engineering design to determine the optimal distribution of material within a given design space in order to meet specific performance objectives. This technique is commonly used in various industries, including aerospace, automotive, and manufacturing.In Workbench, topology optimization can be performed using the Topology Optimization tool. This tool is part of the DesignModeler module and allows engineers to define design criteria and constraints, run optimization simulations, and analyze the results.Here is a step-by-step guide to performing topology optimization in Workbench:1. Create a geometric model: Start by creating a CAD model of the part or structure you want to optimize. This can be done using the DesignModeler module in Workbench. Import or create the geometry and define the necessary details such as dimensions, features, and boundary conditions.2. Define design criteria: Next, you need to define the design criteria or performance objectives for the optimization. This includes specifying the stiffness, weight, or other characteristics that you want to achieve. You can also define constraints such as minimum and maximum volume fractions, or allowable displacement limits.3. Assign material properties: Specify the material properties forthe model. This includes properties such as Young's modulus, Poisson's ratio, and density. You can either choose from a predefined material library or enter custom values.4. Set up the optimization study: In the Workbench Project Schematic, add the Topology Optimization tool to the project and connect it to other required modules such as Meshing and Analysis. Define the optimization objectives, constraints, and study parameters such as maximum iterations and convergence criteria.5. Generate mesh: Generate a finite element mesh for the model using the Meshing tool. Optimal mesh density is crucial for accurate results.6. Run the optimization simulation: Once the mesh is generated, start the optimization simulation. The Topology Optimization tool will iteratively modify the material distribution within the design space to optimize the performance objectives while satisfying the defined constraints. The simulation may take several iterations to converge, depending on the complexity of the problem.7. Analyze the results: Once the simulation is complete, analyze the optimized results. Workbench provides various visualization tools to observe the distribution of material within the optimized design, as well as other metrics such as displacement, stress, and strain. You can evaluate whether the performance objectives and constraints are met and make any necessary refinements to the design.8. Refine and finalize the design: Based on the optimization results,refine the design if needed. This may involve modifying the geometry, adjusting the optimization criteria, or rerunning the simulation with different settings. Iterate this process until you achieve the desired design performance.Overall, topology optimization in Workbench allows engineers to explore a wide range of design possibilities and discover optimized solutions with improved performance and reduced weight. It helps optimize the use of material, reduce development time, and improve the overall efficiency of the design process.。
毕业论文外文文献译文题目：：先进的数控系统在加工过程中的进给率优化题目学生：学号：200905010331院（系）：机电工程学院专业：机械设计制造及其自动化指导教师：张斌2013年6月5日先进的数控系统在加工过程中的进给率优化Firman Ridwan,Xun Xu摘要：严格的质量要求和严格的客户需求是更普遍的，是适应性强的和可互操作的新一代机床控制器的发展背后的主要推力。
一些国际标准，如STEP和STEP-NC的发展，为智能数控加工提出了一个原景。
本文提出了STEP-NC的功能的机器状态监控（MCM）的实施。
该系统允许在加工过程中的优化，以缩短加工时间，提高产品质量。
在系统中，optiSTEP NC，AECopt的控制器和基于知识的评估模块（KBE）已经制定出来的optiSTEP-NC系统的目的是执行最初的进给速率优化基于STEP-NC的数据，以协助工艺人员在分配适当的加工参数。
AECopt作为打算提供自适应和自动优化工序加工过程中的策划者和加工环境之间的连接。
KBE MTConnect负责获得加工在。
优化之前进行加工操作过程中或之后，收集数据和监测如机械振动，加速度和加加速度，切割功率和进给速率。
关键词：数控（CNC），STEP-NC的进给率优化，监测1介绍多年来，计算机数控机床（CNC）已经开发到加工高精密产品的能力。
支持数控发展的技术之一是机器状态监控（MCM）。
在这样做时，机床通过传感元件，信号调节器件，信号处理算法和信号解释的监督。
数控机床的实时监控，各种智能功能，如自适应控制，重新生成优化的数据集和先进的优化模型已经开发和实施。
以这种方式，不同的加工过程中的异常可以在早期阶段检测到，保证了更安全的加工环境。
动用MCM机床在加工过程中减少了需要人为干预和允许的机床的自动监督。
然而，挑战依然存在，在应对频繁的设计修改，市场需求的产品如质量和更短的时间更严格。
此外，加工一直以客户为中心，而不是制造商驱动。
导数法求解最优化模型代码最优化模型是一种数学模型，用于在满足一定约束条件的情况下，寻找一组变量的值，使目标函数达到最优值。
使用导数法求解最优化模型需要对目标函数进行求导，并通过导数的正负性来确定函数的单调性，从而找到最优解。
以下是一个简单的 Python 代码示例，演示了如何使用导数法求解一个一元函数的最优化问题：pythondef find_maxima(f, df, x0, tol=1e-6):"""使用导数法求解函数的最大值。
参数：f (callable)：目标函数。
df (callable)：目标函数的导数。
x0 (float)：初始点。
tol (float)：迭代停止的容差范围，默认为 1e-6。
返回：float：函数的最大值。
"""x = x0fx = f(x)dfx = df(x)while abs(dfx) > tol:if dfx > 0:x = x - tol * dfxelse:x = x + tol * dfxfx = f(x)dfx = df(x)return fx# 定义目标函数和导数def f(x):return x ** 2 - 2 * xdef df(x):return 2 * x - 2# 调用 find_maxima 函数求解最大值x0 = 0max_value = find_maxima(f, df, x0)print("最大值为：", max_value)```在上述代码中，`find_maxima` 函数接受目标函数`f`、目标函数的导数 `df`、初始点 `x0` 和容差范围 `tol` 作为参数。
在函数内部，通过不断迭代更新`x` 的值，使目标函数的导数趋近于 0，从而找到函数的最大值。
请注意，上述代码仅演示了求解一元函数最大值的情况。
如果是多元函数的最优化问题，需要使用更复杂的方法，如牛顿法、梯度下降法等。
Parameter optimization of a multi-pass milling process using non-traditional optimization algorithmsR.Venkata Rao a ,*,P.J.Pawar ba Department of Mechanical Engineering,S.V.National Institute of Technology,Ichchanath,Surat,Gujarat –395007,IndiabDepartment of Production Engineering,K.K.Wagh Institute of Engineering Education and Research,Nashik –422003,Maharashtra,India1.IntroductionIn today’s manufacturing environment many large industries have attempted to introduce the flexible manufacturing system (FMS)as a strategy to adapt to the ever-changing competitive market requirement.The flexible manufacturing system involves highly automated and computer controlled machines.Due to high capital and machining costs,there is an economic need to operate these machines as efficiently as possible in order to obtain the required pay back.The success of the machining operation depends on the selection of machining process parameters.Proper selection of process parameters play a significant role to ensure quality of product,to reduce the machining cost,to increase productivity in computer controlled machining processes and to assist in computer aided process planning.However,determina-tion of optimum process parameters of any machining process is usually a difficult task where the following aspects are required:knowledge of manufacturing process,empirical equations to develop realistic constraints,specification of machine tool capabilities,development of effective optimization criteria,and knowledge of mathematical and numerical optimization techni-ques.A human process planner selects machining process para-meters using his own experience or from the handbooks.But these parameters do not give optimal result.Various optimization strategies and algorithms ranging from elementary numerical search methods to more systematic approaches employing non-traditional techniques for optimization of process parameters in case of single pass milling operation had been reported in the literature.However,as multi-pass operations are often preferred to single pass operations for economic reasons,recent efforts have been directed towards determination of optimal machining conditions for multi-pass operations.Traditionally,mathematical programming techniques like linear programming,method of feasible direction,dynamic programming and geometric programming had been used to solve optimization problems in milling.However,these traditional methods of optimization do not fare well over a broad spectrum of problem domains.Moreover,traditional techniques may not be robust.Numerous constraints and multiple passes make machin-ing optimization problems complicated and hence these techni-ques are not ideal for solving such problems as they tend to obtain a local optimal solution.Considering the drawbacks of traditional optimization techni-ques,attempts are being made to optimize the machining problem using evolutionary optimization techniques.Evolutionary compu-tation consists of a variety of methods including optimization paradigms that are based on evolution mechanisms such asApplied Soft Computing 10(2010)445–456A R T I C L E I N F O Article history:Received 7February 2009Received in revised form 9May 2009Accepted 2August 2009Available online 8August 2009Keywords:Multi-pass millingProcess parameters optimization Artificial bee colonyParticle swarm optimization Simulated annealingA B S T R A C TThe effective optimization of machining process parameters affects dramatically the cost and production time of machined components as well as the quality of the final products.This paper presents optimization aspects of a multi-pass milling operation.The objective considered is minimization of production time (i.e.maximization of production rate)subjected to various constraints of arbor strength,arbor deflection,and cutting power.Various cutting strategies are considered to determine the optimal process parameters like the number of passes,depth of cut for each pass,cutting speed,and feed.The upper and lower bounds of the process parameters are also considered in the study.The optimization is carried out using three non-traditional optimization algorithms namely,artificial bee colony (ABC),particle swarm optimization (PSO),and simulated annealing (SA).An application example is presented and solved to illustrate the effectiveness of the presented algorithms.The results of the presented algorithms are compared with the previously published results obtained by using other optimization techniques.ß2009Elsevier B.V.All rights reserved.*Corresponding author.Tel.:+912612201661;fax:+912612201571.E-mail address:ravipudirao@ (R.Venkata Rao).Contents lists available at ScienceDirectApplied Soft Computingj o ur n a l ho m e pa g e :w w w.e l s e vi e r.c om /l o ca t e /as o c1568-4946/$–see front matter ß2009Elsevier B.V.All rights reserved.doi:10.1016/j.asoc.2009.08.007biological genetics and natural selection.These methods use the fitness information instead of the functional derivatives making them more robust and effective.Most commonly used non-traditional optimization technique is genetic algorithm (GA).However,GA provides a near optimal solution for a complex problem having large number of variables and constraints as in the case of multi-pass milling process optimization.This is mainly due to difficulty in determination of optimum controlling parameters such as population size,crossover rate and mutation rate.Therefore,the efforts are continuing to use more recent optimization algorithms,which are more powerful,robust and able to provide accurate solution.Artificial bee colony (ABC)algorithm developed by Karaboga [1]and Karaboga and Basturk [2,3]is one of the most recent algorithms and no effort has been yet made for optimization of process parameters of any of the machining processes by using this algorithm.Hence,in this paper an attempt is made to apply the artificial bee colony algorithm (ABC).For comparison purpose ,other non-traditional methods of optimization such as particle swarm optimization (PSO)and simulated annealing (SA)algorithms have also been tried for optimization of process parameters of multi-pass milling opera-tion.Particle swarm optimization has been successfully applied to some manufacturing processes such as pulsed laser micromachin-ing,electro-chemical machining,friction welding,boring,milling,etc.by various researchers [4–7,19].2.Review of literature on multi-pass milling process optimizationMilling is the machining process in which the metal is removed by a rotating multiple tooth cutter.Fig.1shows the milling operation.As the cutter rotates,each tooth removes a small amount of material from the advancing work for each spindle revolution.The relative motion between cutter and the work piece can be in any direction and hence surfaces having any orientation can be machined in ling operation can be performed in a single pass or in multiple passes.Multi-pass operations are often preferred to single pass operations for economic reasons and are generally used to machine stocks that cannot be removed in a single pass.Various investigators have presented optimization techniques,both traditional and non-traditional,for optimization of multi-pass milling operation.Shin and Joo [8]used the dynamic programming optimization method for milling process parameter optimization.However,forthe optimization problem involving large amount of independent parameters with a wide range of values such as the cutting parameters in milling operation,the use of dynamic programming is limited.Wang [9]used a neural network based approach to optimize milling process parameters.However,optimization by using neural networks may often ends in local minima or fails to converge on a result.Tolouei-Rad and Bidhendi [10]used the method of feasible direction and considered maximization of profit rate as an objective function in milling operation.The feasible solution denotes the local minimum of the problem.However,this local minimum need not be the global one unless the problem is convex programming problem.Optimization model developed in their work was non-convex.Sonmez et al.[11]studied multi-pass milling operation based on the maximum production rate criterion and used an algorithm adopted from the study of Agapiou [12]which was presented for the multi-pass turning operations.Although the results showed significant improvement over handbook recommendations,the optimization techniques used in their work (dynamic program-ming and using geometric programming)either tend to result in local minima or take a long time to converge on a reasonable result.Shunmugam et al.[13]used genetic algorithm (GA)for milling process parameter optimization with total production cost as the objective function.Although GA has advantages over the traditional techniques,the successful application of GA depends on the population size or the diversity of individual solutions in the search space.If GA cannot hold its diversity well before the global optimum is reached,it may prematurely converge to a local optimum.Although maintaining diversity is the predominant concern of GA,it also reduces the performance of GA [3,14].Lui and Wang [15]modified the genetic algorithm by defining and changing the operating domain and used for optimization of milling parameters.The results and the convergence speed of their approach were better than that of genetic algorithm.Wang et al.[16]presented a new hybrid approach,named genetic simulated annealing (GSA)and parallel genetic simulated annealing (PGSA),based on genetic algorithm and simulated annealing to find optimal machining parameters in milling operations.They pointed out that the results obtained were found to be better than those of genetic algorithm and geometric programming.Baskar et al.[17]considered a specific case in milling operation and solved the same by using three different non-traditional optimization techniques comprising a genetic algorithm,local hill climbing and memetic algorithm.Onwubolu [18]presented a new optimization technique based on tribes for determination of the cutting parameters in multi-pass milling operations.Although the results obtained in his work using tribes showed significant improvement over other traditional and non-traditional algorithms,but the results are not valid as some of the constraints in the solution obtained are violated.This is explained in the present work in Section 5.Yildiz [19]developed a new hybrid optimization approach by hybridizing the immune algorithm with hill climbing local search algorithm to maximize the total profit rate in milling operations.Zarei et al.[20]presented a harmony search (HS)algorithm to determine the optimum cutting parameters for multi-pass face-milling.The present study is mainly focused on optimization of process parameters of multi-pass milling operations considering mini-mization of total production time as the objective function (i.e.maximization of production rate)with constraints of arbor strength,arbor deflection and cutting power.Feed per tooth,speed and depth of cut are considered as process parameters.The upper and lower bounds of the process parameters are also included in thestudy.ling operation.R.Venkata Rao,P.J.Pawar /Applied Soft Computing 10(2010)445–456446The next section presents an optimization model of multi-pass milling process.3.Optimization model of multi-pass milling processThe optimization model of milling process formulated in the present work is based on the analysis given by Sonmez et al.[11]. The decision variables(i.e.process parameters)considered for this model are feed per tooth(f z),cutting speed(V)and depth of cut(a). The objective function and the constraints are formulated as discussed in the following sections.3.1.Objective functionFor a milling operation the total production time(T pr)is composed of the following items:(a)Machine preparation time(T p)as given by Eq.(1)T p¼T sN b(1)where T s=set-up time and N b=total number of components ina produced batch.(b)Loading–unloading time(T L).(c)Process adjusting and quick return time(T a).(d)Machining time(T m).(e)Tool changing time per component(T c),which is given byEq.(2).T c¼T d T mT(2)where T d=time for changing a dull cutting edge or tool and T=tool life.For a single pass milling operation the total production time (T pr)is the sum of the above time elements and can be written as T pr¼T pþT LþT aþT mþT c(3) orT pr¼T sN bþT LþT aþT mþT dT mT(4)For a multi-pass operation,Eq.(4)becomesT pr¼T sb þT LþX N pi¼1T aiþT miþT dT mi(5)where N p=total number of passes and subscript i denotes i th pass.For a particular milling operation,the machining time is given asT m¼Lf(6)where L=length of cut,f=feed rate=f z zN.f z=feed per tooth, z=number of teeth on milling cutter,and N=spindle speed in rpm.N is given by equation:N¼1000ÂVp(7)where D=cutter diameter,V=cutting speed.Tool life can be determined by using the formula given by Eq.(8).T¼C1=mv Db v=mÂðBmB h B p B tÞ1=mV1=m a a v=m f z v a v r Z n v=m l v s(8)where a=depth of cut,a r=width of the cut,B m,B k,B p,B t=correction coefficients,m,e v,u v,r v,n v,q v,b v,=exponents,C v=process constant,l s=cutting inclination angle.On substituting Eqs.(6)–(8)in Eq.(5),the objective function for multi-pass milling operation is expressed as given by Eq.(9).T pr¼T sbþT LþN p T aþX N pi¼1p DLzi iþT d p LVð1=mÀ1Þia e v=mifðu v=mÀ1Þzia r v=mrzðn v=mÀ1Þl q v=ms1000ÂC v Dðb v=mÀ1ÞÂðB m B h B p B tÞ1=m(9) 3.2.ConstraintsFollowing three constraints are considered in this optimization model.3.2.1.Arbor strengthThe arbor is subjected to torsion from the action of resistance to cutting.Therefore,the selected values of process parameters should ensure that the arbor is safe from strength point of view.F sÀF c!0(10) whereMean peripheral cutting force¼F c¼C z p a r zD b z a e z f u z z(11) where C zp=process constants,and b z,e z,and u z are exponents. Permissible force for arbor strengthðkgÞ¼F s¼0:1k b d3a0:08L aþ0:65ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið0:25L aÞ2þð0:5a DÞ2q(12)where k b=permissible bending strength of arbor,d a=arbor diameter,L a=arbor length between supports,a=k b/(1.3k t),and k t=permissible torsional strength of arbor.3.2.2.Arbor deflectionThe selected values of process parameters should be checked for arbor deflection as given by Eq.(13).F dÀF c!0(13) wherePermissible force for arbor deflectionðkgÞ¼F d¼4Eed4aa(14) where E=modulus of elasticity of arbor material and e=permis-sible value of arbor deflection.For roughing operation e=0.2mm and forfinishing operation e=0.05mm.3.2.3.PowerPower required for the cutting operation should not exceed the effective power transmitted to cutting point by the machine tool. This is ensured by Eq.(15).P cÀF c V6120!0(15) where P c=cutting power(kW)=P m h,P m=nominal motor power, and h=overall efficiency.3.3.Process parametersThe three process parameters and their bounds considered in this work are given in the following sections.3.3.1.Feed per toothThe optimum feed must be in the range determined by maximum and minimum values of the feed rates of the machine.f zminf z f zmax(16)R.Venkata Rao,P.J.Pawar/Applied Soft Computing10(2010)445–456447wheref zmin ¼f minzN max(17)f zmax ¼f maxmin(18)where f max=maximum spindle feed rate(mm/min),f min=mini-mum spindle feed rate(mm/min),N max=maximum spindle speed, and N min=minimum spindle speed.3.3.2.Cutting speedThe optimum cutting speed must be in the range determined by maximum spindle speed(N max)and minimum spindle speed(N min) of the machine.V min V V max(19) whereV max¼p DN max1000(20)V min¼p DN min(21)3.3.3.Depth of cutFor a milling operation the upper and lower bounds for depth of cut are as specified by Eq.(22).a min a a maxðmmÞ(22) where a min is the minimum depth of cut and a max is the maximum depth of cut.The above optimization model with the given process para-meters,objective function and the constraints is considered in the present work for multi-pass milling process using non-traditional optimization algorithms such as ABC,PSO and SA.These algorithms are explained briefly in the following sections.4.Presented non-traditional optimization algorithmsThree non-traditional optimization algorithms are considered in the present work for multi-pass milling process parameter optimization and are described in the following sections.4.1.Artificial bee colony algorithmA branch of nature inspired algorithms,called swarm intelli-gence,is focused on insect behavior in order to develop some meta-heuristics which can mimic insect’s problem solution abilities. Interaction between insects contributes to the collective intelli-gence of the social insect colonies.These communication systems between insects have been adapted to scientific problems for optimization.The foraging behavior,learning,memorizing and information sharing characteristics of honeybees have recently been one of the most interesting research areas in swarm intelligence.Artificial bee colony(ABC)algorithm is developed to model the intelligent behaviors of honeybee swarms[1–3].The honeybee swarms consists of two essential components(i.e.food sources and foragers)and defines two leading modes of the behavior(i.e.recruitment to a nectar source and abandonment of a source).4.1.1.Food sourcesThe value of a food source depends on different parameters such as its proximity to the nest,richness of energy and ease of extracting this energy.For the simplicity,the‘‘profitability’’of a food source can be represented with a single quantity.4.1.2.ForagersForagers can be unemployed,employed or experienced.4.1.2.1.Unemployed foragers.If it is assumed that a bee has no knowledge about the food sources in the searchfield,bee initializes its search as an unemployed forager.There are two possibilities for an unemployed forager:Scout bee:If the bee starts searching spontaneously without any knowledge,it will be a scout bee.The percentage of scout bees varies from5%to30%according to the information into the nest. The mean number of scouts averaged over conditions is about10%. Recruit:If the unemployed forager attends to a waggle dance done by some other bee,the bee will start searching by using the knowledge from waggle dance.4.1.2.2.Employed foragers.When the recruit beefinds and exploits the food source,it will raise to be an employed forager who memorizes the location of the food source.After the employed foraging bee loads a portion of nectar from the food source,it returns to the hive and unloads the nectar to the food area in the hive.There are three possible options related to residual amount of nectar for the foraging bee.If the nectar amount decreased to a low level or exhausted,foraging bee abandons the food source and become an unemployed bee.If there are still sufficient amount of nectar in the food source,it can continue to forage without sharing the food source information with the nest mates or it can go to the dance area to perform waggle dance for informing the nest mates about the same food source.The probability values for these options highly related to the quality of the food source.4.1.2.3.Experienced foragers.These types of foragers use their historical memories for the location and quality of food sources.This type of forages can be an inspector,which controls the recent status of food source already discovered.It can also be a reactivated forager by using the information from waggle dance.It tries to explore the same food source discovered by self if there are some other bees confirm the quality of same food source.It can also be scout bee to search new patches if the whole food source is exhausted.It can also be a recruit bee,which is searching a new food source declared in dancing area by another employed bee.Communication among bees related to the quality of food sources occurs in the dancing area.The related dance is called waggle dance.Since information about all the current rich sources is available to an onlooker on the dancefloor,she probably could watch numerous dances and choose to employ herself at the most profitable source.There is a greater probability of onlookers choosing more profitable sources since more information is circulating about the more profitable sources.Employed foragers share their information with a probability,which is proportional to the profitability of the food source,and the sharing of this information through waggle dancing is longer in duration.Hence, the recruitment is proportional to profitability of a food source.The flowchart of ABC algorithm is shown in Fig.2[21].The steps of ABC algorithm are explained in Section5.4.2.Particle swarm optimization algorithmParticle swarm optimization(PSO)is an evolutionary computa-tion technique developed by Kennedy and Eberhart[22].It exhibits common evolutionary computation attributes including initializa-tion with a population of random solutions and searching for optima by updating generations.Potential solutions,calledR.Venkata Rao,P.J.Pawar/Applied Soft Computing10(2010)445–456 448particles,are then ‘‘flown’’through the problem space by following the current optimum particles.The updates of the particles are accomplished as per the following equations:V i þ1¼wV i þc 1r 1ðpBest i ÀX i Þþc 2r 2ðgBest i ÀX i Þ(23)X i þ1¼X i þV i þ1(24)Eq.(23)calculates a new velocity (V i+1)for each particle (potential solution)based on its previous velocity,the best location it has achieved (pBest )so far,and the global best location (gBest ),the population has achieved.Eq.(24)updates individual particle’s position (X i )in solution hyperspace.The two random numbers r 1and r 2in Eq.(23)are independently generated in the range [0,1].The acceleration constants c 1and c 2in Eq.(23)represent the weighting of the stochastic acceleration terms that pull each particle towards pBest and gBest positions.c 1represents the confidence the particle has in itself (cognitive parameter)and c 2represents the confidence the particle has in swarm (social parameter).Thus,adjustment of these constants changes the amount of tension in the system.The inertia weight w plays animportant role in the PSO convergence behavior since it is employed to control the exploration abilities of the swarm.To achieve the dimensional consistency of Eqs.(23)and (24),the dimension of the term cr in Eq.(23)could be taken as (time)À2.This way,the second and the third terms in Eq.(23)assume the dimension of acceleration.To get the correct dimension of velocity,as required by the left hand side,one needs to multiply them by D t ,the time step,which becomes unity in the present case,denoting changes from iteration i to i +1.Similarly,the second term in Eq.(24)assumes the correct dimension when taken as V i+1D t .However,the present form results through the implicit assumption that D t equals 1[23,24].4.3.Simulated annealing algorithmSimulated annealing is a probabilistic hill climbing soft computing algorithm.The methodology of simulated annealing algorithm is described below.If i is the current configuration with cost C (i )then using the Metropolis algorithm [25],we can say that the probabilityofFig.2.Flowchart of the ABC algorithm [20].R.Venkata Rao,P.J.Pawar /Applied Soft Computing 10(2010)445–456449accepting j as next configuration depends on the difference in the function value at these two points or on D C=C(j)ÀC(i)and is calculated using the Boltzman probability distribution:Pr f new¼j j current¼i g¼1if D C0eÀD C=T otherwise(25)The nest section provides an application example to demon-strate and validate the application of the presented ABC,PSO and SA algorithms.5.Application exampleNow an application example is considered to demonstrate and validate the presented ABC,PSO and SA algorithms for the optimization of process parameters of the multi-pass milling operation.The example is based on the model developed by Sonmez et al.[11].Specifications of the required parameters and values of the constants considered by Sonmez et al.[11]and used in the present work are as follows:Type of machining:plain milling.Motor power(P m)=5.5kW,efficiency,h=0.7.Arbor diameter,d a=27mm,arbor length between supports, L a=210mm.Permissible bending stress of arbor,k b:140MPa.Permissible torsional stress of arbor,k t:120MPaModulus of elasticity of arbor material,E=200GPa.Spindle speed range:(31.5–2000)rpm,feed rate range:(14–900)mm/min.Tool material:HSS,tool diameter,D=63mm,number of teeth, z=8.Material:structural carbon steel(C#0.6%).Tensile strength:750MPa,Brinell hardness number=150.Length of cut,L a=160mm,width of cut,a r=50mm,depth of cut,a=5mm.Loading and unloading time of one work piece,T L=1.5min.Set-up time offixtures and machine tool,T s=10min.Tool change time,T c=5min.Process adjusting and quick return time,T a=0.1(min/part).Lot size(number of parts in the batch),N b=100.Cutting inclination=308.Constants:B m=1,B k=1,B p=0.8,B t=0.8,m=0.33,e v=0.3, u v=0.4,r v=0.1,n v=0.1,q v=0,C v=35.4,b v=0.45,C zp=68.2,b z=À0.86,e z=0.86,and u z=0.72.f zmin ¼f minzN max¼148Â2000¼0:000875ðmm=toothÞf zmax ¼f maxzN min¼9008Â31:5¼3:571ðmm=toothÞThus,0:000875f z3:571(26)V max¼p DN max1000¼pÂ63Â20001000¼395:84ðm=minÞV min¼p DN min1000¼pÂ63Â31:51000¼6:234ðm=minÞThus,6:234V395:84ðm=minÞ(27) For a milling operation the upper and lower bounds for depth of cut are as specified by Eq.(28).0:5a4ðmmÞ(28)5.1.Optimization using artificial bee colony algorithmFollowing steps are used for optimization of multi-pass milling operation using presented artificial bee colony algorithm.5.1.1.Step1:parameter selectionAs discussed in the description of ABC algorithm,food source represents a possible solution to the problem of minimization of production time in the present work.The number of initial solutions(i.e.the number of food sources)considered in this work isfive.The value of each food source depends on thefitness value of the objective function given by Eq.(9).For every food source there is only one employed bee (employed forager).In other words,the number of employed bees is equal to number of food sources.Hence,in the present work number of employed bees is considered to befive.It can be observed from Fig.3that even though the number of employed bees increases from5to10,the convergence rate of the algorithm slightly increases,however it does not affect thefinal solution. Moreover,computational efforts increase as number of employed bees increases.From this point of view the selection of the number of employed bee(equal tofive)is appropriate.The unemployed forager can be scout or an onlooker bee.The number of onlooker bees must be greater than the number of employed bees.The effect of number of onlooker bees on the convergence of solution is shown in Fig.4.It is observed that as the number of onlooker bees and hence the population size increases,the algorithm performs better in terms of convergence rate.However,after a sufficient number of onlooker bees,any increment in the value doesnot Fig.3.Effect of number of employed bees(n e)on convregence rate for roughmilling. Fig.4.Effect of number of onlooker bees(n o)on convregence rate for rough milling.R.Venkata Rao,P.J.Pawar/Applied Soft Computing10(2010)445–456 450。
