【作者】 张宁；

【导师】 沈水龙； 周安楠；

【作者基本信息】 上海交通大学 ， 土木工程， 2019， 博士

【摘要】 本研究主要针对既有的土体神经网络本构模型网络结构简单、学习能力较弱及模型表现不稳定的问题,应用数值试验、理论分析、实例分析和统计分析相结合的方法展开研究。研究重点探索以下问题:基于长短期记忆(LSTM)深度学习网络建立土体本构模型的可行性,神经网络本构模型中的小数值失准问题,LSTM深度学习网络训练过程收敛慢,LSTM深度学习网络本构模型的雅各比矩阵计算方法。本研究取得了如下创新性成果:(1)提出了基于LSTM深度学习网络的土体本构模型的建模方法。基于修正剑桥模型,利用数值试验方法建立了不同围压下的排水实验偏应力和轴应变基准数据集。基于基准数据集,综合分析了传统的前馈式、反馈式神经网络本构模型与LSTM深度学习本构模型的学习和泛化能力,结果表明LSTM深度学习网络本构模型具有更高的训练和预测精度,训练模型至收敛采用的迭代次数减少50%。LSTM深度学习网络本构模型能够输出符合实际土体力学行为的平滑应力应变曲线,模型表现稳定、结果波动小;发现既有神经网络模型存在的小样本数值失准和初值振荡的问题。基于数值试验方法建立了多参数组合的外推数据集,验证了LSTM深度学习本构模型具有较强的外推能力。(2)提出了采用均方相对误差(REMSE)代价函数解决神经网络本构模型中小数值样本失准问题的方法。采用定性和定量理论分析方法,发现导致小数值样本失准现象的原因是绝对误差类代价函数引起的梯度分配不均。采用理论分析和数值试验方法,探明了REMSE代价函数通过调整不同样本的梯度值以解决梯度分配不均的机理。基于基准数据集和外推数据集,验证了REMSE代价函数解决小数值样本失准问题和初值振荡问题的有效性,改进LSTM深度学习本构模型具有更强的外推能力。REMSE模型存在前期收敛速度较慢的问题,但其收敛速度衰减较慢。(3)提出了混合激活函数,加速LSTM深度学习网络的学习和收敛。针对REMSE模型前期收敛速度较慢的问题,基于双曲正切函数和线性函数提出混合激活函数的概念。基于MNIST手写字体数据集、Cifar 10图片分类数据集和PTB语言识别数据集,验证了混合激活函数能够在深层全连接前馈神经网络、深度卷积神经网络模型VGG16和深度LSTM模型的不同深度学习网络结构中起到较大的加速作用。针对混合激活函数,增大参数λ和线性项βx能够起到普遍性的加速作用,但具体的加速效果与网络本身的结构形式和尺寸相关。基于REMSE函数和混合激活函数,构造了改进的LSTM深度学习本构模型,对比分析发现改进的LSTM深度学习本构模型具有最优的学习能力和外推能力。(4)提出了改进LSTM深度学习本构模型并学习和预测粘土、粗粒土和饱和砂土塑性屈服行为。改进LSTM本构模型有效学习了不同力学参数对上海粘土应力应变行为的影响,准确预测了未知力学参数土样在位置应力条件下的塑性屈服行为。改进LSTM本构模型很好地学习和预测了主应力比对粗粒土在真三轴试验条件下的应力应变和应变之间的影响,其相对误差控制在3%以下。改进LSTM本构模型既能够学习饱和砂土在不同围压下的屈服破坏行为,又能够在保证大数值样本学习精确度的前提下,解决小数值样本的失准问题,其结果的所有误差水平均优于既有的嵌入式神经网络模型。(5)提出了LSTM深度学习本构模型的雅各比矩阵计算方法。推导LSTM深度学习本构模型的雅各比矩阵形式。采用轴对称应力状态下的线弹性模型,对比分析了线弹性模型应力应变数据与LSTM本构模型输出数据,以及LSTM本构模型输出数据与雅各比矩阵计算数据的差异,验证了雅各比矩阵与LSTM深度学习本构模型的等效性。基于修正剑桥模型数值试验,获取了多应力路径的排水和不排水三轴剪切实验数据,验证了LSTM深度学习本构模型的雅各比矩阵形式预测塑性屈服行为的有效性。更多还原

【Abstract】 In terms of the current weakness of shallow neural network on learning and generalizing nonlinear soil behaviors,this thesis investigates the learning and generalization performance of LSTM deep learning technique on soil behaviors by means of numerical experiments,theoretical analysis,measured data analysis and numerical simulation.In addition,the feasibility of combining LSTM deep learning technique and finite element method is discussed and attempted.The principal research and innovations is concluded as followings:1.Proposing constitutive modelling method based on LSTM deep learning technique.Numerical experiments of are applied to build the deviatoric stress-axial strain data base for clay under different confining pressure based on modified Cambridge model.Performance of traditional feedforward and feedback neural networks are compared with LSTM deep learning neural network on learning complicated stress-strain behavior.Experiment results illustrate the much more excellent capability of learning and generalization of LSTM deep learning technique with more accurate precision.What’s more,the convergence rate increase 50 percent correspondingly.The learning and prediction results of stress and strain are more smooth and consistent to the real stress-strain relationship for LSTM deep learning network,while results from traditional neural networks still fluctuate when the soil yield.However,common problems of imprecision to small values and numerical oscillation at initial state occur for both traditional neural networks and LSTM deep learning network.2.Proposing a new cost function method for common problems of impression and numerical oscillation.Based on qualitative and quantitative analysis,the mechanism of impression and numerical oscillation is interpreted as the unfair gradients for different values during back propagation of absolute errors(refered to MSE error).a new cost function named as REMSE based on relative error is proposed,while the mechanism of REMSE function on solving imprecision and numerical oscillation is verified by theoretical and numerical trials.It is also evidenced that the REMSE cost function figures out the impression and numerical oscillation problems of LSTM models for numerical stress-strain database.However,even though convergence rate decay slowly,the initial convergence rate of LSTM model with REMSE cost function is slightly slower than LSTM model with MSE cost functions.3.Proposing a new Combination unit to accelerate the training process of LSTM deep learning network.A Combination unit of hyperbolic tangent function and linear unit is proposed to accelerate the error backpropagation of neural networks.The validation of new Combination unit has been supported by experiments of common and typical deep neural networks working on benchmark datasets such as MNIST digit dataset,Cifar 10 pattern recognition dataset and Penn Treebank(PTB)dataset.Those typical deep networks include deep feedforward neural network,deep convolutional neural network VGG16 and deep LSTM neural network.It should be referred that the increasing parameterλand linear termβx accelerate the training process in all types of deep networks,while the scale of acceleration depends on the architecture and dimensions of networks.4.Proposing modified LSTM deep learning constitutive model successfully learning the stress-strain relationship of real coarse sand and saturated fined sands.The modified LSTM deep learning constitutive model successful learns and predicts the effect of second main stress on coarse sands under the real triaxial compressed condition.The relative errors of results are under 3 percent which is acceptable for engineering practice.Besides,the modified LSTM model accurately predicts the plastic behavior of saturated fined sands under different confining pressures.The modified LSTM model not only solves problems of imprecision and numerical oscillation on small value samples,but also performs very well on large value samples.All error indexes of results from modified LSTM model outperform those from traditional nested neural network.5.Proposing a Jacobian matrix of combining LSTM deep learning networks with finite element method for engineering practice.Deducing the Jacobian matrix of LSTM deep learning network aiming at applying the LSTM model in finite element method to solve engineering problems.The Jacobian matrix is evidenced by comparing with linear elastic model under plane strain state.The comparison results illustrate the relative error between Jacobian matrix and real elastic modulus is less than 3 percent.更多还原