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fgoalattainSolve multiobjective goal attainment problemsEquationFinds the minimum of a problem specified byx, weight, goal, b, beq, lb, and ub are vectors, A and Aeq are matrices, and c(x), ceq(x), and F(x) are functions that return vectors. F(x), c(x), and ceq(x) can be nonlinear functions.Syntaxx = fgoalattain(fun,x0,goal,weight)x = fgoalattain(fun,x0,goal,weight,A,b)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,... options)x = fgoalattain(problem)[x,fval] = fgoalattain(...)[x,fval,attainfactor] = fgoalattain(...)[x,fval,attainfactor,exitflag] = fgoalattain(...)[x,fval,attainfactor,exitflag,output] = fgoalattain(...)[x,fval,attainfactor,exitflag,output,lambda] = fgoalattain(...)Descriptionfgoalattain solves the goal attainment problem, which is one formulation for minimizing a multiobjective optimization problem.x = fgoalattain(fun,x0,goal,weight) tries to make the objective functions supplied by fun attain the goals specified by goal by varying x, starting at x0, with weight specified by weight.x = fgoalattain(fun,x0,goal,weight,A,b) solves the goal attainment problem subject to the linear inequalities A*x ≤ b.x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq) solves the goal attainment problem subject to the linear equalities Aeq*x = beq as well. Set A = [] and b = [] if no inequalities exist.x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub) defines a set of lower and upper bounds on the design variables in x, so that the solution is always in the range lb ≤ x ≤ ub.x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon) subjects the goal attainment problem to the nonlinear inequalities c(x) or nonlinear equality constraints ceq(x) defined in nonlcon. fgoalattain optimizes such that c(x) ≤ 0 and ceq(x) = 0. Set lb = [] and/or ub = [] if no bounds exist.x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,... options) minimizes with the optimization options specified in the structure options. Use optimset to set these options.x = fgoalattain(problem) finds the minimum for problem, where problem is a structure described in Input Arguments.Create the structure problem by exporting a problem from Optimization Tool, as described in Exporting to the MATLAB Workspace.[x,fval] = fgoalattain(...) returns the values of the objective functions computed in fun at the solution x.[x,fval,attainfactor] = fgoalattain(...) returns the attainment factor at the solution x.[x,fval,attainfactor,exitflag] = fgoalattain(...) returns a value exitflag that describes the exit condition of fgoalattain.[x,fval,attainfactor,exitflag,output] = fgoalattain(...) returns a structure output that contains information about the optimization.[x,fval,attainfactor,exitflag,output,lambda] = fgoalattain(...) returns a structure lambda whose fields contain the Lagrange multipliers at the solution x.Input ArgumentsFunction Arguments contains general descriptions of arguments passed into fgoalattain. This section provides function-specific details for fun, goal, nonlcon, options, weight, and problem:fun The function to be minimized. fun is a function that acceptsa vector x and returns a vector F, the objective functionsevaluated at x. The function fun can be specified as a functionhandle for a function file:x = fgoalattain(@myfun,x0,goal,weight)where myfun is a MATLAB function such asfunction F = myfun(x)F = ... % Compute function values at x.fun can also be a function handle for an anonymous function.x = fgoalattain(@(x)sin(x.*x),x0,goal,weight);If the user-defined values for x and F are matrices, they areconverted to a vector using linear indexing.To make an objective function as near as possible to a goalvalue, (i.e., neither greater than nor less than) use optimsetto set the GoalsExactAchieve option to the number of objectivesrequired to be in the neighborhood of the goal values. Suchobjectives must be partitioned into the first elements of thevector F returned by fun.If the gradient of the objective function can also be computedand the GradObj option is 'on', as set byoptions = optimset('GradObj','on')then the function fun must return, in the second outputargument, the gradient value G, a matrix, at x. The gradientconsists of the partial derivative dF/dx of each F at the pointx. If F is a vector of length m and x has length n, where n isthe length of x0, then the gradient G of F(x) is an n-by-m matrixwhere G(i,j) is the partial derivative of F(j) with respect tox(i) (i.e., the jth column of G is the gradient of the jthobjective function F(j)).goal Vector of values that the objectives attempt to attain. The vector is the same length as the number of objectives F returnedby fun. fgoalattain attempts to minimize the values in thevector F to attain the goal values given by goal.nonlcon The function that computes the nonlinear inequality constraints c(x) ≤ 0 and the nonlinear equality constraintsceq(x) = 0. The function nonlcon accepts a vector x and returnstwo vectors c and ceq. The vector c contains the nonlinearinequalities evaluated at x, and ceq contains the nonlinearequalities evaluated at x. The function nonlcon can bespecified as a function handle.x = fgoalattain(@myfun,x0,goal,weight,A,b,Aeq,beq,...lb,ub,@mycon)where mycon is a MATLAB function such asfunction [c,ceq] = mycon(x)c = ... % compute nonlinear inequalities at x.ceq = ... % compute nonlinear equalities at x.If the gradients of the constraints can also be computed andthe GradConstr option is 'on', as set byoptions = optimset('GradConstr','on')then the function nonlcon must also return, in the third andfourth output arguments, GC, the gradient of c(x), and GCeq,the gradient of ceq(x). Nonlinear Constraints explains how to"conditionalize" the gradients for use in solvers that do notaccept supplied gradients.If nonlcon returns a vector c of m components and x has lengthn, where n is the length of x0, then the gradient GC of c(x)is an n-by-m matrix, where GC(i,j) is the partial derivativeof c(j) with respect to x(i) (i.e., the jth column of GC is thegradient of the jth inequality constraint c(j)). Likewise, ifceq has p components, the gradient GCeq of ceq(x) is an n-by-pmatrix, where GCeq(i,j) is the partial derivative of ceq(j)with respect to x(i) (i.e., the jth column of GCeq is thegradient of the jth equality constraint ceq(j)).Passing Extra Parameters explains how to parameterize thenonlinear constraint function nonlcon, if necessary.options Options provides the function-specific details for the options values.weight A weighting vector to control the relative underattainment or overattainment of the objectives in fgoalattain. When thevalues of goal are all nonzero, to ensure the same percentageof under- or overattainment of the active objectives, set theweighting function to abs(goal). (The active objectives are theset of objectives that are barriers to further improvement ofthe goals at the solution.)When the weighting function weight is positive, fgoalattainattempts to make the objectives less than the goal values. Tomake the objective functions greater than the goal values, setweight to be negative rather than positive. To make an objectivefunction as near as possible to a goal value, use theGoalsExactAchieve option and put that objective as the firstelement of the vector returned by fun (see the precedingdescription of fun and options).problem objective Vector of objective functionsx0 Initial point for xgoal Goals to attainweight Relative importance factors of goalsAineq Matrix for linear inequality constraintsbineq Vector for linear inequality constraintsAeq Matrix for linear equality constraintsbeq Vector for linear equality constraintslb Vector of lower boundsub Vector of upper boundsnonlcon Nonlinear constraint functionsolver 'fgoalattain'options Options structure created with optimset Output ArgumentsFunction Arguments contains general descriptions of arguments returned by fgoalattain. This section provides function-specific details for attainfactor, exitflag, lambda, and output:attainfactor The amount of over- or underachievement of the goals. If attainfactor is negative, the goals have been overachieved;if attainfactor is positive, the goals have beenunderachieved.attainfactor contains the value of γ at the solution. Anegative value of γindicates overattainment in the goals.exitflag Integer identifying the reason the algorithm terminated.The following lists the values of exitflag and thecorresponding reasons the algorithm terminated.1 Function converged to a solutions x.4 Magnitude of the search direction lessthan the specified tolerance andconstraint violation less thanoptions.TolCon5 Magnitude of directional derivative lessthan the specified tolerance andconstraint violation less thanoptions.TolCon0 Number of iterations exceededoptions.MaxIter or number of functionevaluations exceeded options.FunEvals-1 Algorithm was terminated by the outputfunction.-2 No feasible point was found.lambda Structure containing the Lagrange multipliers at the solution x (separated by constraint type). The fields of thestructure arelower Lower bounds lbupper Upper bounds ubineqlin Linear inequalitieseqlin Linear equalitiesineqnonlin Nonlinear inequalitieseqnonlin Nonlinear equalitiesoutput Structure containing information about the optimization.The fields of the structure areiterations Number of iterations takenfuncCount Number of function evaluationslssteplength Size of line search step relative tosearch directionstepsize Final displacement in xalgorithm Optimization algorithm usedfirstorderopt Measure of first-order optimalityconstrviolation Maximum of constraint functionsmessage Exit messageOptionsOptimization options used by fgoalattain. You can use optimset to set or change the values of these fields in the options structure options. See Optimization Options for detailed information.DerivativeCheck Compare user-supplied derivatives (gradients ofobjective or constraints) to finite-differencingderivatives. The choices are 'on' or the default,'off'.Diagnostics Display diagnostic information about the functionto be minimized or solved. The choices are 'on' orthe default, 'off'.DiffMaxChange Maximum change in variables for finite-differencegradients (a positive scalar). The default is 0.1.DiffMinChange Minimum change in variables for finite-differencegradients (a positive scalar). The default is 1e-8. Display Level of display.∙'off' displays no output.∙'iter' displays output at each iteration, andgives the default exit message.∙'iter-detailed' displays output at eachiteration, and gives the technical exitmessage.∙'notify' displays output only if the functiondoes not converge, and gives the default exitmessage.∙'notify-detailed' displays output only if thefunction does not converge, and gives thetechnical exit message.∙'final' (default) displays just the finaloutput, and gives the default exit message.∙'final-detailed' displays just the finaloutput, and gives the technical exit message.FinDiffType Finite differences, used to estimate gradients, areeither 'forward' (default), or 'central'(centered). 'central' takes twice as many functionevaluations, but should be more accurate.The algorithm is careful to obey bounds whenestimating both types of finite differences. So, forexample, it could take a backward, rather than aforward, difference to avoid evaluating at a pointoutside bounds.FunValCheck Check whether objective function and constraintsvalues are valid. 'on' displays an error when theobjective function or constraints return a valuethat is complex, Inf, or NaN. The default, 'off',displays no error.GoalsExactAchieve Specifies the number of objectives for which it isrequired for the objective fun to equal the goal goal(a nonnegative integer). Such objectives should bepartitioned into the first few elements of F. Thedefault is 0.GradConstr Gradient for nonlinear constraint functions definedby the user. When set to 'on', fgoalattain expectsthe constraint function to have four outputs, asdescribed in nonlcon in the Input Arguments section.When set to the default, 'off', gradients of thenonlinear constraints are estimated by finitedifferences.GradObj Gradient for the objective function defined by theuser. See the preceding description of fun to seehow to define the gradient in fun. Set to 'on' tohave fgoalattain use a user-defined gradient of theobjective function. The default, 'off',causesfgoalattain to estimate gradients usingfinite differences.MaxFunEvals Maximum number of function evaluations allowed (apositive integer). The default is100*numberOfVariables.MaxIter Maximum number of iterations allowed (a positiveinteger). The default is 400.MaxSQPIter Maximum number of SQP iterations allowed (a positiveinteger). The default is 10*max(numberOfVariables,numberOfInequalities + numberOfBounds)MeritFunction Use goal attainment/minimax merit function if setto 'multiobj', the default. Use fmincon meritfunction if set to 'singleobj'.OutputFcn Specify one or more user-defined functions that anoptimization function calls at each iteration,either as a function handle or as a cell array offunction handles. The default is none ([]). SeeOutput Function.PlotFcns Plots various measures of progress while thealgorithm executes, select from predefined plots orwrite your own. Pass a function handle or a cellarray of function handles. The default is none ([]).∙@optimplotx plots the current point∙@optimplotfunccount plots the function count∙@optimplotfval plots the function value∙@optimplotconstrviolation plots the maximumconstraint violation∙@optimplotstepsize plots the step sizeFor information on writing a custom plot function,see Plot Functions.RelLineSrchBnd Relative bound (a real nonnegative scalar value) onthe line search step length such that the totaldisplacement in x satisfies|Δx(i)| ≤relLineSrchBnd· max(|x(i)|,|typicalx(i)|). This option provides control over themagnitude of the displacements in x for cases inwhich the solver takes steps that are considered toolarge. The default is none ([]).RelLineSrchBndDurat ion Number of iterations for which the bound specified in RelLineSrchBnd should be active (default is 1).TolCon Termination tolerance on the constraint violation,a positive scalar. The default is 1e-6.TolConSQP Termination tolerance on inner iteration SQPconstraint violation, a positive scalar. Thedefault is 1e-6.TolFun Termination tolerance on the function value, apositive scalar. The default is 1e-6.TolX Termination tolerance on x, a positive scalar. Thedefault is 1e-6.TypicalX Typical x values. The number of elements in TypicalXis equal to the number of elements in x0, thestarting point. The default value isones(numberofvariables,1). fgoalattain usesTypicalX for scaling finite differences forgradient estimation.UseParallel When 'always', estimate gradients in parallel.Disable by setting to the default, 'never'. ExamplesConsider a linear system of differential equations.An output feedback controller, K, is designed producing a closed loop systemThe eigenvalues of the closed loop system are determined from the matrices A, B, C, and K using the command eig(A+B*K*C). Closed loop eigenvalues must lie on the real axis in the complex plane to the left of the points [-5,-3,-1]. In order not to saturate the inputs, no element in K can be greater than 4 or be less than -4.The system is a two-input, two-output, open loop, unstable system, with state-space matrices.The set of goal values for the closed loop eigenvalues is initialized as goal = [-5,-3,-1];To ensure the same percentage of under- or overattainment in the active objectives at the solution, the weighting matrix, weight, is set to abs(goal).Starting with a controller, K = [-1,-1; -1,-1], first write a function file, eigfun.m.function F = eigfun(K,A,B,C)F = sort(eig(A+B*K*C)); % Evaluate objectivesNext, enter system matrices and invoke an optimization routine.A = [-0.5 0 0; 0 -2 10; 0 1 -2];B = [1 0; -2 2; 0 1];C = [1 0 0; 0 0 1];K0 = [-1 -1; -1 -1]; % Initialize controller matrixgoal = [-5 -3 -1]; % Set goal values for the eigenvalues weight = abs(goal); % Set weight for same percentagelb = -4*ones(size(K0)); % Set lower bounds on the controllerub = 4*ones(size(K0)); % Set upper bounds on the controller options = optimset('Display','iter'); % Set display parameter[K,fval,attainfactor] = fgoalattain(@(K)eigfun(K,A,B,C),...K0,goal,weight,[],[],[],[],lb,ub,[],options)You can run this example by using the demonstration script goaldemo. (From the MATLAB Help browser or the MathWorks™ Web site documentation, you can click the demo name to display the demo.) After about 11 iterations, a solution isActive inequalities (to within options.TolCon = 1e-006):lower upper ineqlinineqnonlin1 12 24K =-4.0000 -0.2564-4.0000 -4.0000fval =-6.9313-4.1588-1.4099attainfactor =-0.3863DiscussionThe attainment factor indicates that each of the objectives has been overachieved by at least 38.63% over the original design goals. The active constraints, in this case constraints 1 and 2, are the objectives that are barriers to further improvement and for which the percentage of overattainment is met exactly. Three of the lower bound constraints are also active.In the preceding design, the optimizer tries to make the objectives less than the goals. For a worst-case problem where the objectives must be as near to the goals as possible, use optimset to set the GoalsExactAchieve option to the number of objectives for which this is required.Consider the preceding problem when you want all the eigenvalues to be equal to the goal values. A solution to this problem is found by invoking fgoalattain with the GoalsExactAchieve option set to 3.options = optimset('GoalsExactAchieve',3);[K,fval,attainfactor] = fgoalattain(...@(K)eigfun(K,A,B,C),K0,goal,weight,[],[],[],[],lb,ub,[],... options)After about seven iterations, a solution isK =-1.5954 1.2040-0.4201 -2.9046fval =-5.0000-3.0000-1.0000attainfactor =1.0859e-20In this case the optimizer has tried to match the objectives to the goals. The attainment factor (of 1.0859e-20) indicates that the goals have been matched almost exactly.NotesThis problem has discontinuities when the eigenvalues become complex; this explains why the convergence is slow. Although the underlying methods assume the functions are continuous, the method is able to make stepstoward the solution because the discontinuities do not occur at the solution point. When the objectives and goals are complex, fgoalattain tries to achieve the goals in a least-squares sense.AlgorithmMultiobjective optimization concerns the minimization of a set of objectives simultaneously. One formulation for this problem, and implemented in fgoalattain, is the goal attainment problem of Gembicki[3]. This entails the construction of a set of goal values for the objective functions. Multiobjective optimization is discussed in Multiobjective Optimization.In this implementation, the slack variable γis used as a dummy argument to minimize the vector of objectives F(x) simultaneously; goal is a set of values that the objectives attain. Generally, prior to the optimization, it is not known whether the objectives will reach the goals (under attainment) or be minimized less than the goals (overattainment). A weighting vector, weight, controls the relative underattainment or overattainment of the objectives.fgoalattain uses a sequential quadratic programming (SQP) method, which is described in Sequential Quadratic Programming (SQP). Modifications are made to the line search and Hessian. In the line search an exact merit function (see [1] and [4]) is used together with the merit function proposed by [5]and [6]. The line search is terminated when either merit function shows improvement. A modified Hessian, which takes advantage of the special structure of the problem, is also used (see [1] and [4]). A full description of the modifications used is found in Goal Attainment Method in "Introduction to Algorithms." Setting the MeritFunction option to 'singleobj' withoptions = optimset(options,'MeritFunction','singleobj')uses the merit function and Hessian used in fmincon.See also SQP Implementation for more details on the algorithm used and the types of procedures displayed under the Procedures heading when the Display option is set to 'iter'.LimitationsThe objectives must be continuous. fgoalattain might give only local solutions.。
机器学习专业词汇中英⽂对照activation 激活值activation function 激活函数additive noise 加性噪声autoencoder ⾃编码器Autoencoders ⾃编码算法average firing rate 平均激活率average sum-of-squares error 均⽅差backpropagation 后向传播basis 基basis feature vectors 特征基向量batch gradient ascent 批量梯度上升法Bayesian regularization method 贝叶斯规则化⽅法Bernoulli random variable 伯努利随机变量bias term 偏置项binary classfication ⼆元分类class labels 类型标记concatenation 级联conjugate gradient 共轭梯度contiguous groups 联通区域convex optimization software 凸优化软件convolution 卷积cost function 代价函数covariance matrix 协⽅差矩阵DC component 直流分量decorrelation 去相关degeneracy 退化demensionality reduction 降维derivative 导函数diagonal 对⾓线diffusion of gradients 梯度的弥散eigenvalue 特征值eigenvector 特征向量error term 残差feature matrix 特征矩阵feature standardization 特征标准化feedforward architectures 前馈结构算法feedforward neural network 前馈神经⽹络feedforward pass 前馈传导fine-tuned 微调first-order feature ⼀阶特征forward pass 前向传导forward propagation 前向传播Gaussian prior ⾼斯先验概率generative model ⽣成模型gradient descent 梯度下降Greedy layer-wise training 逐层贪婪训练⽅法grouping matrix 分组矩阵Hadamard product 阿达马乘积Hessian matrix Hessian 矩阵hidden layer 隐含层hidden units 隐藏神经元Hierarchical grouping 层次型分组higher-order features 更⾼阶特征highly non-convex optimization problem ⾼度⾮凸的优化问题histogram 直⽅图hyperbolic tangent 双曲正切函数hypothesis 估值，假设identity activation function 恒等激励函数IID 独⽴同分布illumination 照明inactive 抑制independent component analysis 独⽴成份分析input domains 输⼊域input layer 输⼊层intensity 亮度/灰度intercept term 截距KL divergence 相对熵KL divergence KL分散度k-Means K-均值learning rate 学习速率least squares 最⼩⼆乘法linear correspondence 线性响应linear superposition 线性叠加line-search algorithm 线搜索算法local mean subtraction 局部均值消减local optima 局部最优解logistic regression 逻辑回归loss function 损失函数low-pass filtering 低通滤波magnitude 幅值MAP 极⼤后验估计maximum likelihood estimation 极⼤似然估计mean 平均值MFCC Mel 倒频系数multi-class classification 多元分类neural networks 神经⽹络neuron 神经元Newton’s method ⽜顿法non-convex function ⾮凸函数non-linear feature ⾮线性特征norm 范式norm bounded 有界范数norm constrained 范数约束normalization 归⼀化numerical roundoff errors 数值舍⼊误差numerically checking 数值检验numerically reliable 数值计算上稳定object detection 物体检测objective function ⽬标函数off-by-one error 缺位错误orthogonalization 正交化output layer 输出层overall cost function 总体代价函数over-complete basis 超完备基over-fitting 过拟合parts of objects ⽬标的部件part-whole decompostion 部分-整体分解PCA 主元分析penalty term 惩罚因⼦per-example mean subtraction 逐样本均值消减pooling 池化pretrain 预训练principal components analysis 主成份分析quadratic constraints ⼆次约束RBMs 受限Boltzman机reconstruction based models 基于重构的模型reconstruction cost 重建代价reconstruction term 重构项redundant 冗余reflection matrix 反射矩阵regularization 正则化regularization term 正则化项rescaling 缩放robust 鲁棒性run ⾏程second-order feature ⼆阶特征sigmoid activation function S型激励函数significant digits 有效数字singular value 奇异值singular vector 奇异向量smoothed L1 penalty 平滑的L1范数惩罚Smoothed topographic L1 sparsity penalty 平滑地形L1稀疏惩罚函数smoothing 平滑Softmax Regresson Softmax回归sorted in decreasing order 降序排列source features 源特征sparse autoencoder 消减归⼀化Sparsity 稀疏性sparsity parameter 稀疏性参数sparsity penalty 稀疏惩罚square function 平⽅函数squared-error ⽅差stationary 平稳性（不变性）stationary stochastic process 平稳随机过程step-size 步长值supervised learning 监督学习symmetric positive semi-definite matrix 对称半正定矩阵symmetry breaking 对称失效tanh function 双曲正切函数the average activation 平均活跃度the derivative checking method 梯度验证⽅法the empirical distribution 经验分布函数the energy function 能量函数the Lagrange dual 拉格朗⽇对偶函数the log likelihood 对数似然函数the pixel intensity value 像素灰度值the rate of convergence 收敛速度topographic cost term 拓扑代价项topographic ordered 拓扑秩序transformation 变换translation invariant 平移不变性trivial answer 平凡解under-complete basis 不完备基unrolling 组合扩展unsupervised learning ⽆监督学习variance ⽅差vecotrized implementation 向量化实现vectorization ⽮量化visual cortex 视觉⽪层weight decay 权重衰减weighted average 加权平均值whitening ⽩化zero-mean 均值为零Letter AAccumulated error backpropagation 累积误差逆传播Activation Function 激活函数Adaptive Resonance Theory/ART ⾃适应谐振理论Addictive model 加性学习Adversarial Networks 对抗⽹络Affine Layer 仿射层Affinity matrix 亲和矩阵Agent 代理 / 智能体Algorithm 算法Alpha-beta pruning α-β剪枝Anomaly detection 异常检测Approximation 近似Area Under ROC Curve／AUC Roc 曲线下⾯积Artificial General Intelligence/AGI 通⽤⼈⼯智能Artificial Intelligence/AI ⼈⼯智能Association analysis 关联分析Attention mechanism 注意⼒机制Attribute conditional independence assumption 属性条件独⽴性假设Attribute space 属性空间Attribute value 属性值Autoencoder ⾃编码器Automatic speech recognition ⾃动语⾳识别Automatic summarization ⾃动摘要Average gradient 平均梯度Average-Pooling 平均池化Letter BBackpropagation Through Time 通过时间的反向传播Backpropagation/BP 反向传播Base learner 基学习器Base learning algorithm 基学习算法Batch Normalization/BN 批量归⼀化Bayes decision rule 贝叶斯判定准则Bayes Model Averaging／BMA 贝叶斯模型平均Bayes optimal classifier 贝叶斯最优分类器Bayesian decision theory 贝叶斯决策论Bayesian network 贝叶斯⽹络Between-class scatter matrix 类间散度矩阵Bias 偏置 / 偏差Bias-variance decomposition 偏差-⽅差分解Bias-Variance Dilemma 偏差 – ⽅差困境Bi-directional Long-Short Term Memory/Bi-LSTM 双向长短期记忆Binary classification ⼆分类Binomial test ⼆项检验Bi-partition ⼆分法Boltzmann machine 玻尔兹曼机Bootstrap sampling ⾃助采样法／可重复采样／有放回采样Bootstrapping ⾃助法Break-Event Point／BEP 平衡点Letter CCalibration 校准Cascade-Correlation 级联相关Categorical attribute 离散属性Class-conditional probability 类条件概率Classification and regression tree/CART 分类与回归树Classifier 分类器Class-imbalance 类别不平衡Closed -form 闭式Cluster 簇/类/集群Cluster analysis 聚类分析Clustering 聚类Clustering ensemble 聚类集成Co-adapting 共适应Coding matrix 编码矩阵COLT 国际学习理论会议Committee-based learning 基于委员会的学习Competitive learning 竞争型学习Component learner 组件学习器Comprehensibility 可解释性Computation Cost 计算成本Computational Linguistics 计算语⾔学Computer vision 计算机视觉Concept drift 概念漂移Concept Learning System /CLS 概念学习系统Conditional entropy 条件熵Conditional mutual information 条件互信息Conditional Probability Table／CPT 条件概率表Conditional random field/CRF 条件随机场Conditional risk 条件风险Confidence 置信度Confusion matrix 混淆矩阵Connection weight 连接权Connectionism 连结主义Consistency ⼀致性／相合性Contingency table 列联表Continuous attribute 连续属性Convergence 收敛Conversational agent 会话智能体Convex quadratic programming 凸⼆次规划Convexity 凸性Convolutional neural network/CNN 卷积神经⽹络Co-occurrence 同现Correlation coefficient 相关系数Cosine similarity 余弦相似度Cost curve 成本曲线Cost Function 成本函数Cost matrix 成本矩阵Cost-sensitive 成本敏感Cross entropy 交叉熵Cross validation 交叉验证Crowdsourcing 众包Curse of dimensionality 维数灾难Cut point 截断点Cutting plane algorithm 割平⾯法Letter DData mining 数据挖掘Data set 数据集Decision Boundary 决策边界Decision stump 决策树桩Decision tree 决策树／判定树Deduction 演绎Deep Belief Network 深度信念⽹络Deep Convolutional Generative Adversarial Network/DCGAN 深度卷积⽣成对抗⽹络Deep learning 深度学习Deep neural network/DNN 深度神经⽹络Deep Q-Learning 深度 Q 学习Deep Q-Network 深度 Q ⽹络Density estimation 密度估计Density-based clustering 密度聚类Differentiable neural computer 可微分神经计算机Dimensionality reduction algorithm 降维算法Directed edge 有向边Disagreement measure 不合度量Discriminative model 判别模型Discriminator 判别器Distance measure 距离度量Distance metric learning 距离度量学习Distribution 分布Divergence 散度Diversity measure 多样性度量／差异性度量Domain adaption 领域⾃适应Downsampling 下采样D-separation （Directed separation）有向分离Dual problem 对偶问题Dummy node 哑结点Dynamic Fusion 动态融合Dynamic programming 动态规划Letter EEigenvalue decomposition 特征值分解Embedding 嵌⼊Emotional analysis 情绪分析Empirical conditional entropy 经验条件熵Empirical entropy 经验熵Empirical error 经验误差Empirical risk 经验风险End-to-End 端到端Energy-based model 基于能量的模型Ensemble learning 集成学习Ensemble pruning 集成修剪Error Correcting Output Codes／ECOC 纠错输出码Error rate 错误率Error-ambiguity decomposition 误差-分歧分解Euclidean distance 欧⽒距离Evolutionary computation 演化计算Expectation-Maximization 期望最⼤化Expected loss 期望损失Exploding Gradient Problem 梯度爆炸问题Exponential loss function 指数损失函数Extreme Learning Machine/ELM 超限学习机Letter FFactorization 因⼦分解False negative 假负类False positive 假正类False Positive Rate/FPR 假正例率Feature engineering 特征⼯程Feature selection 特征选择Feature vector 特征向量Featured Learning 特征学习Feedforward Neural Networks/FNN 前馈神经⽹络Fine-tuning 微调Flipping output 翻转法Fluctuation 震荡Forward stagewise algorithm 前向分步算法Frequentist 频率主义学派Full-rank matrix 满秩矩阵Functional neuron 功能神经元Letter GGain ratio 增益率Game theory 博弈论Gaussian kernel function ⾼斯核函数Gaussian Mixture Model ⾼斯混合模型General Problem Solving 通⽤问题求解Generalization 泛化Generalization error 泛化误差Generalization error bound 泛化误差上界Generalized Lagrange function ⼴义拉格朗⽇函数Generalized linear model ⼴义线性模型Generalized Rayleigh quotient ⼴义瑞利商Generative Adversarial Networks/GAN ⽣成对抗⽹络Generative Model ⽣成模型Generator ⽣成器Genetic Algorithm/GA 遗传算法Gibbs sampling 吉布斯采样Gini index 基尼指数Global minimum 全局最⼩Global Optimization 全局优化Gradient boosting 梯度提升Gradient Descent 梯度下降Graph theory 图论Ground-truth 真相／真实Letter HHard margin 硬间隔Hard voting 硬投票Harmonic mean 调和平均Hesse matrix 海塞矩阵Hidden dynamic model 隐动态模型Hidden layer 隐藏层Hidden Markov Model/HMM 隐马尔可夫模型Hierarchical clustering 层次聚类Hilbert space 希尔伯特空间Hinge loss function 合页损失函数Hold-out 留出法Homogeneous 同质Hybrid computing 混合计算Hyperparameter 超参数Hypothesis 假设Hypothesis test 假设验证Letter IICML 国际机器学习会议Improved iterative scaling/IIS 改进的迭代尺度法Incremental learning 增量学习Independent and identically distributed/i.i.d. 独⽴同分布Independent Component Analysis/ICA 独⽴成分分析Indicator function 指⽰函数Individual learner 个体学习器Induction 归纳Inductive bias 归纳偏好Inductive learning 归纳学习Inductive Logic Programming／ILP 归纳逻辑程序设计Information entropy 信息熵Information gain 信息增益Input layer 输⼊层Insensitive loss 不敏感损失Inter-cluster similarity 簇间相似度International Conference for Machine Learning/ICML 国际机器学习⼤会Intra-cluster similarity 簇内相似度Intrinsic value 固有值Isometric Mapping/Isomap 等度量映射Isotonic regression 等分回归Iterative Dichotomiser 迭代⼆分器Letter KKernel method 核⽅法Kernel trick 核技巧Kernelized Linear Discriminant Analysis／KLDA 核线性判别分析K-fold cross validation k 折交叉验证／k 倍交叉验证K-Means Clustering K – 均值聚类K-Nearest Neighbours Algorithm/KNN K近邻算法Knowledge base 知识库Knowledge Representation 知识表征Letter LLabel space 标记空间Lagrange duality 拉格朗⽇对偶性Lagrange multiplier 拉格朗⽇乘⼦Laplace smoothing 拉普拉斯平滑Laplacian correction 拉普拉斯修正Latent Dirichlet Allocation 隐狄利克雷分布Latent semantic analysis 潜在语义分析Latent variable 隐变量Lazy learning 懒惰学习Learner 学习器Learning by analogy 类⽐学习Learning rate 学习率Learning Vector Quantization/LVQ 学习向量量化Least squares regression tree 最⼩⼆乘回归树Leave-One-Out/LOO 留⼀法linear chain conditional random field 线性链条件随机场Linear Discriminant Analysis／LDA 线性判别分析Linear model 线性模型Linear Regression 线性回归Link function 联系函数Local Markov property 局部马尔可夫性Local minimum 局部最⼩Log likelihood 对数似然Log odds／logit 对数⼏率Logistic Regression Logistic 回归Log-likelihood 对数似然Log-linear regression 对数线性回归Long-Short Term Memory/LSTM 长短期记忆Loss function 损失函数Letter MMachine translation/MT 机器翻译Macron-P 宏查准率Macron-R 宏查全率Majority voting 绝对多数投票法Manifold assumption 流形假设Manifold learning 流形学习Margin theory 间隔理论Marginal distribution 边际分布Marginal independence 边际独⽴性Marginalization 边际化Markov Chain Monte Carlo/MCMC 马尔可夫链蒙特卡罗⽅法Markov Random Field 马尔可夫随机场Maximal clique 最⼤团Maximum Likelihood Estimation/MLE 极⼤似然估计／极⼤似然法Maximum margin 最⼤间隔Maximum weighted spanning tree 最⼤带权⽣成树Max-Pooling 最⼤池化Mean squared error 均⽅误差Meta-learner 元学习器Metric learning 度量学习Micro-P 微查准率Micro-R 微查全率Minimal Description Length/MDL 最⼩描述长度Minimax game 极⼩极⼤博弈Misclassification cost 误分类成本Mixture of experts 混合专家Momentum 动量Moral graph 道德图／端正图Multi-class classification 多分类Multi-document summarization 多⽂档摘要Multi-layer feedforward neural networks 多层前馈神经⽹络Multilayer Perceptron/MLP 多层感知器Multimodal learning 多模态学习Multiple Dimensional Scaling 多维缩放Multiple linear regression 多元线性回归Multi-response Linear Regression ／MLR 多响应线性回归Mutual information 互信息Letter NNaive bayes 朴素贝叶斯Naive Bayes Classifier 朴素贝叶斯分类器Named entity recognition 命名实体识别Nash equilibrium 纳什均衡Natural language generation/NLG ⾃然语⾔⽣成Natural language processing ⾃然语⾔处理Negative class 负类Negative correlation 负相关法Negative Log Likelihood 负对数似然Neighbourhood Component Analysis/NCA 近邻成分分析Neural Machine Translation 神经机器翻译Neural Turing Machine 神经图灵机Newton method ⽜顿法NIPS 国际神经信息处理系统会议No Free Lunch Theorem／NFL 没有免费的午餐定理Noise-contrastive estimation 噪⾳对⽐估计Nominal attribute 列名属性Non-convex optimization ⾮凸优化Nonlinear model ⾮线性模型Non-metric distance ⾮度量距离Non-negative matrix factorization ⾮负矩阵分解Non-ordinal attribute ⽆序属性Non-Saturating Game ⾮饱和博弈Norm 范数Normalization 归⼀化Nuclear norm 核范数Numerical attribute 数值属性Letter OObjective function ⽬标函数Oblique decision tree 斜决策树Occam’s razor 奥卡姆剃⼑Odds ⼏率Off-Policy 离策略One shot learning ⼀次性学习One-Dependent Estimator／ODE 独依赖估计On-Policy 在策略Ordinal attribute 有序属性Out-of-bag estimate 包外估计Output layer 输出层Output smearing 输出调制法Overfitting 过拟合／过配Oversampling 过采样Letter PPaired t-test 成对 t 检验Pairwise 成对型Pairwise Markov property 成对马尔可夫性Parameter 参数Parameter estimation 参数估计Parameter tuning 调参Parse tree 解析树Particle Swarm Optimization/PSO 粒⼦群优化算法Part-of-speech tagging 词性标注Perceptron 感知机Performance measure 性能度量Plug and Play Generative Network 即插即⽤⽣成⽹络Plurality voting 相对多数投票法Polarity detection 极性检测Polynomial kernel function 多项式核函数Pooling 池化Positive class 正类Positive definite matrix 正定矩阵Post-hoc test 后续检验Post-pruning 后剪枝potential function 势函数Precision 查准率／准确率Prepruning 预剪枝Principal component analysis/PCA 主成分分析Principle of multiple explanations 多释原则Prior 先验Probability Graphical Model 概率图模型Proximal Gradient Descent/PGD 近端梯度下降Pruning 剪枝Pseudo-label 伪标记Letter QQuantized Neural Network 量⼦化神经⽹络Quantum computer 量⼦计算机Quantum Computing 量⼦计算Quasi Newton method 拟⽜顿法Letter RRadial Basis Function／RBF 径向基函数Random Forest Algorithm 随机森林算法Random walk 随机漫步Recall 查全率／召回率Receiver Operating Characteristic/ROC 受试者⼯作特征Rectified Linear Unit/ReLU 线性修正单元Recurrent Neural Network 循环神经⽹络Recursive neural network 递归神经⽹络Reference model 参考模型Regression 回归Regularization 正则化Reinforcement learning/RL 强化学习Representation learning 表征学习Representer theorem 表⽰定理reproducing kernel Hilbert space/RKHS 再⽣核希尔伯特空间Re-sampling 重采样法Rescaling 再缩放Residual Mapping 残差映射Residual Network 残差⽹络Restricted Boltzmann Machine/RBM 受限玻尔兹曼机Restricted Isometry Property/RIP 限定等距性Re-weighting 重赋权法Robustness 稳健性/鲁棒性Root node 根结点Rule Engine 规则引擎Rule learning 规则学习Letter SSaddle point 鞍点Sample space 样本空间Sampling 采样Score function 评分函数Self-Driving ⾃动驾驶Self-Organizing Map／SOM ⾃组织映射Semi-naive Bayes classifiers 半朴素贝叶斯分类器Semi-Supervised Learning 半监督学习semi-Supervised Support Vector Machine 半监督⽀持向量机Sentiment analysis 情感分析Separating hyperplane 分离超平⾯Sigmoid function Sigmoid 函数Similarity measure 相似度度量Simulated annealing 模拟退⽕Simultaneous localization and mapping 同步定位与地图构建Singular Value Decomposition 奇异值分解Slack variables 松弛变量Smoothing 平滑Soft margin 软间隔Soft margin maximization 软间隔最⼤化Soft voting 软投票Sparse representation 稀疏表征Sparsity 稀疏性Specialization 特化Spectral Clustering 谱聚类Speech Recognition 语⾳识别Splitting variable 切分变量Squashing function 挤压函数Stability-plasticity dilemma 可塑性-稳定性困境Statistical learning 统计学习Status feature function 状态特征函Stochastic gradient descent 随机梯度下降Stratified sampling 分层采样Structural risk 结构风险Structural risk minimization/SRM 结构风险最⼩化Subspace ⼦空间Supervised learning 监督学习／有导师学习support vector expansion ⽀持向量展式Support Vector Machine/SVM ⽀持向量机Surrogat loss 替代损失Surrogate function 替代函数Symbolic learning 符号学习Symbolism 符号主义Synset 同义词集Letter TT-Distribution Stochastic Neighbour Embedding/t-SNE T – 分布随机近邻嵌⼊Tensor 张量Tensor Processing Units/TPU 张量处理单元The least square method 最⼩⼆乘法Threshold 阈值Threshold logic unit 阈值逻辑单元Threshold-moving 阈值移动Time Step 时间步骤Tokenization 标记化Training error 训练误差Training instance 训练⽰例／训练例Transductive learning 直推学习Transfer learning 迁移学习Treebank 树库Tria-by-error 试错法True negative 真负类True positive 真正类True Positive Rate/TPR 真正例率Turing Machine 图灵机Twice-learning ⼆次学习Letter UUnderfitting ⽋拟合／⽋配Undersampling ⽋采样Understandability 可理解性Unequal cost ⾮均等代价Unit-step function 单位阶跃函数Univariate decision tree 单变量决策树Unsupervised learning ⽆监督学习／⽆导师学习Unsupervised layer-wise training ⽆监督逐层训练Upsampling 上采样Letter VVanishing Gradient Problem 梯度消失问题Variational inference 变分推断VC Theory VC维理论Version space 版本空间Viterbi algorithm 维特⽐算法Von Neumann architecture 冯 · 诺伊曼架构Letter WWasserstein GAN/WGAN Wasserstein⽣成对抗⽹络Weak learner 弱学习器Weight 权重Weight sharing 权共享Weighted voting 加权投票法Within-class scatter matrix 类内散度矩阵Word embedding 词嵌⼊Word sense disambiguation 词义消歧Letter ZZero-data learning 零数据学习Zero-shot learning 零次学习Aapproximations近似值arbitrary随意的affine仿射的arbitrary任意的amino acid氨基酸amenable经得起检验的axiom公理，原则abstract提取architecture架构，体系结构；建造业absolute绝对的arsenal军⽕库assignment分配algebra线性代数asymptotically⽆症状的appropriate恰当的Bbias偏差brevity简短，简洁；短暂broader⼴泛briefly简短的batch批量Cconvergence 收敛，集中到⼀点convex凸的contours轮廓constraint约束constant常理commercial商务的complementarity补充coordinate ascent同等级上升clipping剪下物；剪报；修剪component分量；部件continuous连续的covariance协⽅差canonical正规的，正则的concave⾮凸的corresponds相符合；相当；通信corollary推论concrete具体的事物，实在的东西cross validation交叉验证correlation相互关系convention约定cluster⼀簇centroids 质⼼，形⼼converge收敛computationally计算(机)的calculus计算Dderive获得，取得dual⼆元的duality⼆元性；⼆象性；对偶性derivation求导；得到；起源denote预⽰，表⽰，是…的标志；意味着，[逻]指称divergence 散度；发散性dimension尺度，规格；维数dot⼩圆点distortion变形density概率密度函数discrete离散的discriminative有识别能⼒的diagonal对⾓dispersion分散，散开determinant决定因素disjoint不相交的Eencounter遇到ellipses椭圆equality等式extra额外的empirical经验；观察ennmerate例举，计数exceed超过，越出expectation期望efficient⽣效的endow赋予explicitly清楚的exponential family指数家族equivalently等价的Ffeasible可⾏的forary初次尝试finite有限的，限定的forgo摒弃，放弃fliter过滤frequentist最常发⽣的forward search前向式搜索formalize使定形Ggeneralized归纳的generalization概括，归纳；普遍化；判断（根据不⾜）guarantee保证；抵押品generate形成，产⽣geometric margins⼏何边界gap裂⼝generative⽣产的；有⽣产⼒的Hheuristic启发式的；启发法；启发程序hone怀恋；磨hyperplane超平⾯Linitial最初的implement执⾏intuitive凭直觉获知的incremental增加的intercept截距intuitious直觉instantiation例⼦indicator指⽰物，指⽰器interative重复的，迭代的integral积分identical相等的；完全相同的indicate表⽰，指出invariance不变性，恒定性impose把…强加于intermediate中间的interpretation解释，翻译Jjoint distribution联合概率Llieu替代logarithmic对数的，⽤对数表⽰的latent潜在的Leave-one-out cross validation留⼀法交叉验证Mmagnitude巨⼤mapping绘图，制图；映射matrix矩阵mutual相互的，共同的monotonically单调的minor较⼩的，次要的multinomial多项的multi-class classification⼆分类问题Nnasty讨厌的notation标志，注释naïve朴素的Oobtain得到oscillate摆动optimization problem最优化问题objective function⽬标函数optimal最理想的orthogonal(⽮量，矩阵等)正交的orientation⽅向ordinary普通的occasionally偶然的Ppartial 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Nov.2020Vol.37No.S Transactions of Nanjing University of Aeronautics and AstronauticsFBS Effect and Temperature Dependence in Trench⁃AssistedMultimode FiberZHANG Zelin1，2，LU Yuangang1，2*，XIE Youwen1，2，HUANG Jian1，2，ZHOU Lang1，2 1.Key Laboratory of Space Photoelectric Detection and Perception of Ministry of Industry and Information Technology，College of Astronautics，Nanjing University of Aeronautics and Astronautics，Nanjing211106，P.R.China；2.College of Science，Nanjing University of Aeronautics and Astronautics，Nanjing211106，P.R.China（Received13July2020；revised10September2020；accepted12September2020）Abstract:We propose the trench-assisted multimode fiber（TA-OM4）as a novel sensing fiber in forward Brillouin scattering（FBS）-based temperature sensor，due to its higher temperature sensitivity，better bending resistance and lower propagation loss，compared with the single mode fiber（SMF）and other sensing fibers.The FBS effect and acousto-optic interaction in TA-OM4are the first time to be demonstrated and characterized at1550nm theoretically and experimentally.A2.0km long TA-OM4is put into an oven to measure its temperature sensitivity，which can reach up to80.3kHz/℃，exceeding53%of SMF（52.4kHz/℃）.The simulated and experimental results verify that the TA-OM4may be a good candidate as the sensing fiber for the FBS-based temperature sensor.Key words：forward Brillouin scattering；acousto-optic interaction；optic-fiber sensor；temperature sensitivity；multimode fiberCLC number：TN29Document code：A Article ID：1005‐1120（2020）S‐0095‐070IntroductionStimulated Brillouin scattering（SBS）in opti‐cal fiber is a phenomenon caused by the interaction between a light wave and an acoustic wave，which is widely studied and employed in the field of distrib‐uted sensing［1-2］.Backward Brillouin scattering in‐duces high frequency shifts around10GHz which can be utilized in Brillouin optical time-domain sen‐sors and Brillouin laser.However，the forward Brill‐ouin scattering（FBS）have much lower frequency shift of several hundreds of mega Hertz，which can be used in several applications，such as temperature sensing，opto-mechanical chemical sensors，optical frequency comb and opto-mechanical laser［3-6］.Recently，the temperature sensors based on FBS have been proposed using the silica single mode fiber（SMF），high nonlinear fiber（HNLF）and photonics crystal fiber（PCF）［7-9］.However，the lower temperature sensitivity of SMF may limit its measurement pared with SMF，al‐though the HNLF and PCF have slightly lager tem‐perature sensitivities，their disadvantages of bad bending resistance，high cost and large propagation loss which are5.4dB/km of PCF and0.76dB/km of HNLF，respectively，can compromise their sens‐ing performance for future FBS-based temperature sensors in complex engineering application［8-9］.For‐tunately，the trench-assisted multimode fiber（TA-OM4），due to its low propagation loss（0.24dB/ km）which is similar to that of SMF（0.20dB/ km），excellent bending resistance and high back‐ward stimulated Brillouin scattering（BSBS）and modulation instability（MI）threshold，has been a good candidate as the sensing fiber in BSBS-based temperature sensors［10］.However，the characteristic of FBS process in TA-OM4at1550nm and its ap‐plications in FBS-based temperature sensors have*Corresponding author，E-mail address：*************.cn.How to cite this article:ZHANG Zelin，LU Yuangang，XIE Youwen，et al.FBS effect and temperature dependence in trench‐assisted multimode fiber［J］.Transactions of Nanjing University of Aeronautics and Astronautics，2020,37(S)：95‐101. http：///10.16356/j.1005‐1120.2020.S.012Vol.37 Transactions of Nanjing University of Aeronautics and Astronauticsnot been reported.In this paper，we theoretically and experimen‐tally investigate the acousto-optic interaction causedby FBS and FBS spectrum in TA-OM4.Further‐more，we have found that the largest strain coeffi‐cient in TA-OM4is about4.0kHz/με，which is sosmall that the frequency shift of FBS is not sensitiveto make acceptable strain measurement.Therefore，we only focus on its temperature dependence ofFBS in this pared with the temperatureresponse of FBS in SMF，we experimentally mea‐sure the FBS temperature response of TA-OM4.The highest temperature dependence of TA-OM4islinear with a coefficient of80.3kHz/℃，which is53%larger than that of SMF（52.4kHz/℃）.Thesimulated and experimental results show that theTA-OM4may be a good candidate as the sensing fi‐ber in FBS-based temperature sensors.1FBS Resonances in TA⁃OM41.1Theoretical description of FBS in optical fi⁃berThe acoustic modes responsible for FBS are ra‐dial dilatational modes（R0，m）and mixed torsional-radial modes（TR2，m）.The FBS is a typical opto-acoustic interaction，which can be described as thecoupling amplitude equations between optical fieldE（r，z，t）and acoustic wave for the displacementvector U（r，z，t）［11］∂2E ∂z2-n2effc2∂2E∂t2=1ε0c2∂2P NL∂t2(1)∂2U∂z2+Γ∂U∂t+V s2∇×(∇×U)-V l2∇(∇∙U)=Fρ(2) where P NL is the total nonlinear polarization，c the light velocity in vacuum，n eff the effective refractive index，ε0the vacuum permittivity，V l the longitudi‐nal acoustic velocity of the fiber，ρ0the density of fused silica，V s shear sound velocity of the fiber，andΓthe acoustic damping parameter.F=ε0[12γ12∇()E∙E+γ44(E∙∇)E]is the elec‐trostrictive driving term，andγ12andγ44are both the elements of the electrostrictive tensor for fused sili‐ca.By employing the finite element analysis（FEA）method and solving Eq.（1），we obtain the optical field E（r）.Moreover，by solving Eq.（2）with the appropriate boundary conditions，we difine the nor‐malized displacement distribution U m（r）in terms of Bessel functions J n（z），where n is the order of Bes‐sel functions.By usingρm(r)=-ρ0∇U m(r)，we obtain the density vibration caused by FBS.For the radial dilatational R0，m modes，the boundary condition corresponding to the free fiber surface can be written as(1-α2)J0(y)-α2J2(y)=0(3) whereαis the ratio between shear sound velocity and longitudinal acoustic velocity，and y m the m th zero of Eq.（3）.Furthermore，the central frequency of the m th acoustic mode can be expressed asf m=y m V lπd(4) where d is the cladding diameter of optical fiber.Similar to the Kerr effect in fiber，the opto-me‐chanical coefficient can be used to quantify the opto-acoustic interaction caused by FBS，which can be expressed as［6，12-13］γ(m)OM=k02πn2neff cρ0Q(m)E Q(m)pΓm f m(5) whereΓm is the linewidth of the m th resonant peak induced by FBS.The Q(m)E and Q(m)p are the elec‐trostrictive overlap and photo-elastic overlap，which determines the efficiency of stimulation of acoustic modes and describes the modification of the effec‐tive index by acoustic modes［13-14］，respectively.By solving Eqs.（1）—（5），the acoustic field distribu‐tion and FBS resonances can be obtained next.1.2Simulation and FBS spectrum in TA⁃OM4For TA-OM4，the diameters of the fiber core and cladding are50and125μm，respectively.The refractive index profile is given in Fig.1.The refrac‐tive index profile shows a quasi-quadratic distribu‐tion in the central region and has a trench-index pro‐file around the fiber core［10］.The three highest linear polarization（LP）modes are respectively LP01，96No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench-Assisted Multimode FiberLP11and LP21，and the corresponding intensity ratio of these three LP modes I01∶I11∶I21，is1∶0.14∶0.006. Considering the highest intensity ratio of LP01，the tiny coupling efficiency between LP01and other high-order modes and the single mode condition of most optical components［15］，it is enough to investigate the FBS process of TA-OM4corresponding to the fundamental mode LP01.By solving Eqs.（1）and（2），three excited acoustic modes are found and displayed in Fig.2. As it shown in Fig.2（a），taking R0，4mode as an example，the R0，m modes are the radial dilatational modes，which have the most efficient scattering ef‐ficiency and are independent of angular coordinate φ.Especially，the R0，m modes can induce refractive index changes so that the pure phase modulation will be also induced.Other acoustic modes are TR2，m acoustic modes，which are the mixed tor‐sional-radial modes.As it shown in Figs.2（b）and （c），different from R0，m modes，the TR2，m modes are doubly degenerated，which vary sinusoidally with angular coordinate2φ.Furthermore，the scat‐tering efficiency of TR2，m modes is much lower than that of R0，m modes.For the TR2，m（90°/0°）mode，its induced birefringent axes are parallel to the birefringent axes of TA-OM4，which does not induce the depolarized scattering but the polarized scattering and also cause pure phase modulation. For the TR2，m（45°/-45°）mode，the mode pat‐tern is rotated by45°.In this case pure phase modu‐lation will not occur，and the depolarized scattering is induced［16］.Fig.1Refractive index profile of TA-OM4and calculated three LP optical modes with the highestintensityFig.2Normalized transverse profile of acoustic modes excited by LP01optical mode in TA-OM497Vol.37Transactions of Nanjing University of Aeronautics and Astronautics Generally ，the overlap between optical modes and acoustic modes determines the shape of FBS resonances.Taking four acoustic modes （R 0，1to R 0，4）as examples ，the 2D mode profiles of longitu‐dinal optical fundamental mode LP 01and four acous‐tic modes are displayed in Fig.3.In order to experimentally investigate the FBS process in TA -OM4，we also measure the FBS spectrum by using a coherent detection ，which isshown in Fig.4.The light source （NKT Photonics ）is a 1550nm single -wavelength semiconductor la‐ser with linewidth 5kHz.The pump light propagat‐ing through the isolator （ISO ）is split into two branches by a 50/50coupler.The upper branch used as the pump light is amplified by an erbium -doped fiber amplifier （EDFA ，Amonics ）.A narrow bandpass filter （BPF ，AOS Photonics ）with 3.5GHz bandwidth is used to eliminate the amplified spontaneous emission （ASE ）noise induced by ED‐FA.A variable attenuator （VA ）is utilized to adjust the input power level to protect fiber components.The pump light is launched into 2.0km long TA -OM4（YOFC ）to obtain the FBS signal which beats with the reference light.Finally ，a 1.6GHz bandwidth photodetector （PD ，Thorlabs PDB480）is utilized to detect the beat signal ，which is ana‐lyzed by an electrical spectrum analyzer （ESA ，Tektronix RSA5126B ）and used to obtain the FBS spectrum.In our experiment ，the incident light power is 11.2mW.The measured FBS spectrum is shown in Fig.5.The measured FBS spectrum includes two parts.One part is from the R 0，m modes and the other is from the TR 2，m modes.However ，due to the ran‐dom change of polarization states along the TA -OM4，the FBS intensities induced by TR 2，m modes are much lower than those of R 0，m modes.As it shown in Fig.5，we can find that the fourth resonant peak with the highest intensity locates at 173.1MHz.By solving Eq.（5），we obtain the calculated opto -mechanical coefficient of R 0，4mode as 5.25（W∙km ）-1，which is slightly higher than that of SMF 5（W ∙km ）-1［6］.In Fig.6，two adjacent resonant peaksgenerated by R 0，m modes have equivalent frequency interval of 47.5MHz ，which can be verified by solv‐ing Eq.（4）.It is obvious that ，whatever resonant peaks intensity and frequency shift ，the calculated and experimental results are in good agreement.The largest difference of normalized intensity be‐tween calculated and experimental results are less than 5%，which are from the error of the estimated fiberparameters.Fig.32-D profiles of optical mode LP 01and acoustic modes R 0,1to R0,4Fig.4Experimental setup of measuring the FBS spectrum of TA -OM4Fig.5The measured FBS spectrum of TA -OM498No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench -Assisted Multimode Fiber 2TemperatureResponse inTA⁃OM4In order to evaluate whether the TA -OM4can be used as the novel sensing fiber in FBS -based tem ‐perature sensors ，we put both TA -OM4and SMF into an oven to measure their temperature sensitivi‐ties of R 0，m modes ，and results are shown in Fig.7.Seven different temperatures between -10℃to 50℃are measured with a temperatures step of 10℃.It is obvious that the temperature sensitivities increase linearly with an increase in m value of R 0，m modes ，whose trends are in accordance with that in Ref.［17］.The observed temperature coefficient of R 0，12in TA -OM4can reach 80.3kHz/℃，which is 53%larger than that of SMF （52.4kHz/℃）.Furthermore ，we also obtain the temperature sensitivities of spectral peaks corresponding to R 0，4（f 4=173.1MHz ）mode in TA -OM4and R 0，5（f 5=222.9MHz ）mode in SMF ，which exhibit the high‐est resonance intensity of all peaks.In Fig.8，the calibration temperature coefficient of TA -OM4（αTA‐OM4）can reach 31.9kHz/℃，which is much 41%larger than that of SMF （αSMF =22.6kHz/℃）.3ConclusionsFBS processes in TA -OM4are theoreticallyand experimentally investigated and the acousto -op‐tic interaction of TA -OM4at 1550nm are charac‐terized and demonstrated.We experimentally mea‐sure the FBS spectrum ，which is in good agreement with simulated results.The temperature sensitivities of R 0，m modes in TA -OM4are also measured ，which exceed 40%of SMF.The calculated and ex‐perimental results demonstrate that the TA -OM4could be a good sensing fiber in FBS -based tempera‐ture sensors ，with advantages of high temperature sensitivity ，good bending resistance and low propa‐gation loss.References［1］MATSUI T ，NAKAJIMA K ，YAMAMOTO F.Guided acoustic -wave brillouin scatteringcharacteris‐Fig.6Measured (green)and calculated (red)normal‐ized FBS resonant intensity in TA -OM4in‐duced by R 0,mmodesFig.7Measured temperature sensitivities of TA -OM4and SMF versus different R 0,m modes ，re‐spectivelyFig.8Temperature sensitivities of R 0,4mode in TA -OM4and R 0,5mode in SMF99Vol.37 Transactions of Nanjing University of Aeronautics and Astronauticstics of few-mode fiber［J］.Applied Optics，2015，54（19）：6093-6097.［2］BAO X，CHEN L.Recent progress in Brillouin scat‐tering based fiber sensors［J］.Sensors，2011，11（4）：4152-4187.［3］FU Y，FAN X，WANG B，et al.Discriminative mea‐surement of temperature and strain using stimulatedBrillouin scattering and guided acoustic-wave brillouinscattering［C］//2018Asia Communications and Photo‐nics Conference（ACPC）.Hangzhou：IEEE，2018：1-3.［4］CHOW D M，THEVENAZ L.Opto-acoustic chemi‐cal sensor based on forward stimulated Brillouin scat‐tering in optical fiber（Invited）［C］//Proceedings ofthe7th International Conference on Photonics（ICP）.［S.l.］：IEEE，2018：1-3.［5］BUTSCH A，KOEHLER J R，NOSKOV R E，et al.CW-pumped single-pass frequency comb genera‐tion by resonant optomechanical nonlinearity in 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fibers［J］.Journal of the Optical So‐ciety of America B，1995，12（9）：1651-1655.［17］CHUN Y D，SHANG L H，JING L L，et al.Simul‐taneous measurement on strain and temperature viaguided acoustic-wave Brillouin scattering in singlemode fibers［J］.Acta Physica Sinica，2016，65（24）.240702.1-240702.7.Acknowledgements This work was supported in part by the National Natural Foundation of China（Nos.61875086，61377086），the Aerospace Science Foundation of China （No.2016ZD52042），and Nanjing University of Aeronautics and Astronautics Ph.D.short-term visiting scholar project （No.190901DF08）.Authors Mr.ZHANG Zelin is currently a Ph.D.candidate of Optical Engineering at the Department of Applied Phys‐ics，Nanjing University of Aeronantics and Astronautics （NUAA）.His research focuses on distributed fiber sensors and nonlinear fiber optics.Prof.LU Yuangang is currently a professor in College of As‐tronautics at NUAA.His research focuses on distributed fi‐ber sensors，image processing and technology of photoelec‐trical detection.Author contributions Mr.ZHANG Zelin contributed to simulation by doing experiment and writing the manuscript. Prof.LU Yuangang designed and guided the study，and gave key opinions on the core issues.Mr.XIE Youwen and Mr.HUANG Jian conducted some related works about the experiments.Ms.ZHOU Lang conducted some related works about the simulation.Competing interests The author declare no competing interests.（Production Editor：XIA Daojia）100No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench-Assisted Multimode Fiber101沟道型折射率多模光纤的前向布里渊散射效应及其温度响应张泽霖1，2，路元刚1，2，谢有文1，2，黄剑1，2，周朗1，2（1.空间光电探测与感知工业和信息化部重点实验室，南京航空航天大学航天学院，南京211106，中国；2.南京航空航天大学理学院，南京211106，中国）摘要：提出了沟道型折射率多模光纤（TA‐OM4）可作为一种新型传感光纤应用于基于前向布里渊散射（FBS）的温度传感器中。
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多模态多目标优化算法多模态多目标优化算法（Multi-modal Multi-objective Optimization Algorithm）是一种用于解决多目标优化问题的算法。
在许多实际问题中，我们往往需要优化多个目标函数，而这些目标函数往往是相互矛盾的。
多模态多目标优化算法可以在解空间中寻找到多个非劣解，这些非劣解同时优化了多个目标函数，为决策者提供了一系列可行的解决方案。
多模态多目标优化算法的核心思想是将问题转化为一个多目标优化问题，并在解空间中寻找到一组非劣解。
与传统的单目标优化算法不同，多模态多目标优化算法不仅考虑了目标函数的优化，还考虑了解的多样性和分布性。
通过引入多样性和分布性的指标，多模态多目标优化算法可以在解空间中寻找到多个非劣解，这些非劣解分布在整个解空间中的不同模态中。
多模态多目标优化算法的基本流程如下：首先，初始化一组解，并计算每个解的目标函数值。
然后，根据多样性和分布性的指标，选择一组最优的解作为种群。
接下来，通过交叉和变异等遗传算子，对种群中的解进行操作，生成新的解，并计算每个解的目标函数值。
然后，根据多样性和分布性的指标，选择一组最优的解作为新的种群。
重复上述步骤，直到满足终止条件，得到一组非劣解。
多模态多目标优化算法的优势在于可以同时考虑多个目标函数，并寻找到多个非劣解。
这样，决策者可以根据自己的需求，选择最合适的解决方案。
另外，多模态多目标优化算法还具有较好的收敛性和多样性，可以在解空间中寻找到全局最优解和局部最优解。
然而，多模态多目标优化算法也存在一些挑战和问题。
首先，多模态多目标优化算法需要选择合适的多样性和分布性指标，以评估解的多样性和分布性。
不同的指标对解的评估结果可能存在差异，需要根据具体问题选择合适的指标。
其次，多模态多目标优化算法的计算复杂度较高，需要耗费大量的计算资源和时间。
因此，在实际应用中，需要根据问题的规模和复杂度选择合适的优化算法。
多模态多目标优化算法是一种有效的解决多目标优化问题的算法。
createnccmodel的参数说明createnccmodel是一个用于创建NCC（Neural Collaborative Filtering）模型的函数，该模型常用于推荐系统中。
下面将对createnccmodel的参数进行详细说明。
1. 参数一：user_num参数名：user_num参数类型：整数参数含义：用户数量说明：该参数表示参与推荐的用户数量，需要根据实际情况设定。
用户数量越多，模型的训练和推荐效果可能会更好，但也会增加计算和存储的成本。
2. 参数二：item_num参数名：item_num参数类型：整数参数含义：物品数量说明：该参数表示参与推荐的物品数量，需要根据实际情况设定。
物品数量越多，模型的训练和推荐效果可能会更好，但也会增加计算和存储的成本。
3. 参数三：latent_dim参数名：latent_dim参数类型：整数参数含义：潜在因子维度说明：该参数表示模型中潜在因子的维度，用于表示用户和物品的特征。
潜在因子维度越大，模型能够更好地捕捉用户和物品的特征，但也会增加模型的复杂度和训练时间。
4. 参数四：layers参数名：layers参数类型：列表参数含义：神经网络层数和每层的隐藏单元数说明：该参数表示神经网络的结构，列表中的元素依次表示每一层的隐藏单元数。
例如，[64,32,16]表示神经网络有3层，第一层隐藏单元数为64，第二层隐藏单元数为32，第三层隐藏单元数为16。
神经网络的结构可以根据实际情况进行调整，以提高模型的表达能力。
5. 参数五：num_classes参数名：num_classes参数类型：整数参数含义：分类数量说明：该参数表示推荐结果的分类数量，用于多分类问题。
例如，如果推荐结果分为10个类别，则num_classes为10。
如果是二分类问题，则num_classes为2。
6. 参数六：dropout_rate参数名：dropout_rate参数类型：浮点数参数含义：丢弃率说明：该参数表示在训练过程中随机丢弃神经元的比例，用于防止过拟合。
浙江理工大学学报（自然科学版），第37卷，第6期，20：17年月Journal of Zhejiang Sci-Tech U niversity(Natural Sciences)V o l.37，N o. 6，N ov.2017D Q I：10. 3969/j.issn. 1673-3851. 201 7. 11. 015多模态函数聚类后再创种群的并行搜索佳点集萤火虫算法方贤1,铁治欣1,李敬明2,高雄1(1.浙江理工大学信息学院，杭州310018;.合肥工业大学管理学院，合肥230009)摘要：萤火虫算法在求解多模态函数时，随着峰值个数的增加，往往需要更大的种群规模才能得到较为理想 的结果，而且初始种群是否均匀分布对结果也有很大影响。
针对萤火虫算法的这些不足，提出了一种多模态函数的 聚类后再创种群的并行搜索佳点集萤火虫算法。
该算法首先以数论佳点集的思想将萤火虫均匀分布于搜索空间 中，在粗糙搜索完成后，通过密度聚类算法进行捕峰操作，重新构造等同于峰值点数的各个平行空间；然后在各空间 中继续加入少量佳点集生成的萤火虫并行精细搜索，最终可获得各个平行空间的局部最优解以及整个空间的全局 最优解。
与其他算法在12个典型多模态函数中的测试结果进行对比，该算法总体上缩小了种群规模，加快了收效速 度，搜索精度更高，时间成本更低，稳定性能更好。
关键词：萤火虫算法；多模态函数；圭点集；密度聚类算法；并行搜索中图分类号：TP391.9文献标志码：A文章编号：1673-3851 (2017) 06-0843-080引言在工程技术、科学计算、经济管理等领域中，绝 大多数实际问题可以通过构建模型归结为函数优化问题。
其中，一些函数由于自身维数高、峰值点多、震荡严重等因素造成性态差。
采用传统的算法，如 D F P变尺度算法、P o w e ll方向加速法等，往往难以或无法找到全局最优解。
近年来随着智能计算学科的发展，一些仿生算法应运而生，如粒子群算法(particle swarm optimization,P S())、遗传算法(genetic algorithm,G A)、蚁群算法（ant clony optimization,AC O)、蜂群算法（artificial bee colony algorithm,A B C)、鱼群算法（artificial fish swarm algorithm,A F S A)等。
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多目标形貌优化方法研究李颖琎 昝建明 张松波长安汽车工程研究院CAE工程所多目标形貌优化方法研究Research on Multi-objective TopographyOptimization李颖琎 昝建明 张松波（长安汽车工程研究院CAE工程所，重庆401120）摘要: 工程界目前对拓扑优化和形貌优化问题的研究主要集中在单目标函数方面，但是在实际工程应用中，须同时考虑多个目标函数和多个约束的情况。
在多目标优化中，由于各目标之间很难同时达到最优化，各目标的最优解时常出现对立局面，所以要求一个全局最优解是很困难的。
本文利用折衷规划法结合平均频率法得到多目标优化的综合目标函数，可以有效地求解出多目标函数的最优解，从而为多目标优化提供解决方案。
本文以汽车地板加强件为例，分别进行了柔度最小化、固有频率最大化以及多目标的形貌优化，其结果显示多目标形貌优化方案较大地提高了部件本身的结构力学和NVH性能。
关键词: 多目标优化，形貌优化，柔度，固有频率，OptiStructAbstract: Single-objective optimization is the focus of topology optimization and topography optimization in engineering at present, but Multi-objective Optimization and multi-constraint must considered in practical application. It is hard to optimize every objective, because they are inconsistent usually. We can acquire the optimization solution by used OptiStruct（certainly must used the weighted method, compromise programming approach and mean frequency formulation）.With an example of a vehicle floor part, this paper is aim to minimize compliance and maximize the natural frequency. The results showed that the static and dynamic character was ameliorated.Key words: multi-objective optimization，topography optimization，compliance，natural frequency，OptiStruct1 概述形貌优化是一种形状最佳化的方法，即在板型结构中寻找最优的加强筋分布的概念方法，用于设计薄壁结构的强化压痕，在减轻结构重量的同时满足强度、频率等要求。
