基于广义灰色模型的极限承载力建模与预测研究
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摘要
极限承载力预测是岩土工程中重要的课题之一。确定极限承载力的方法很多,采用未破坏静载荷实验数据预测极限承载力因为简单、实用、经济而成为研究热点。由于极限承载力是一个受多因素影响的系统,其影响因素的显著特点是数据的多变性、参数的不确定性和数据的不完备性,所以采用以信息不完全系统为研究目标的灰色系统理论进行极限承载力研究是科学合理的。本文主要以单桩和锚杆极限承载力的预测进行研究和理论验证。
目前关于灰色系统理论在极限承载力上的应用主要停留在GM(1,1)模型上。GM(1,1)模型主要适用于等间距且较光滑的序列,但实际工程中由于受到多种因素的影响,数据序列形式复杂多变,所以必须提出新的灰色模型来满足多种形式序列的建模。本文正是从实际问题出发,在基于广义累加的基础上改进和提出了非等间隔GM(1,1)模型、(非)等间隔含跳跃点GM(1,1)模型和(非)等间隔阶段型GM(1,1)模型,分析这些模型的累加生成矩阵的表示方法、性质以及参数空间等。此外对GM(1,1)幂模型进行了深入的研究,分析了模型的参数空间、解的形式、曲线的形状和性质以及求解方法等。
在岩土工程中广泛存在着优化问题。灰色优化是灰色系统理论中一个重要部分,本文对灰色多目标线性规划和灰色双层线性规划进行了研究。提出了一些新的概念、对其性质以及解法进行了研究。
灰色预测模型一个主要特点就是简单实用,而粒子群算法也是由于理论简单、易于操作而广泛应用,所以本文采用粒子群算法求解灰色模型。作为一种智能进化算法,粒子群算法也存在“早熟”的弊病。为此本文提出了多种群粒子群算法(MSPSO)、多极值粒子群算法(MBPSO)和多种群多极值粒子群算法(MSBPSO),通过种群之间的信息共享以及极值之间的相互竞争,大大提高了算法的搜索效率。
采用基于粒子群优化算法参数辨识的灰色预测模型进行单桩和锚杆的极限承载力预测。对每个实例采用不同的预测模型进行建模,仿真结果显示,对同一组实验数据,采用改进的模型建模误差都比原始GM(1,1)模型小,其中GM(1,1)幂模型的误差是最小的。主要是因为GM(1,1)幂模型的解有多种曲线形式,所以可以满足多种形式的序列建模。实例说明本文改进和提出的灰色预测模型可以很好的解决极限承载力预测的问题。采用改进的粒子群算法求解灰色优化模型,并用于承载力研究中,获得了很好的效果。
采用Visual Basic程序语言编制了《基于广义灰色模型的极限承载力预测软件》系统,该系统包括本文研究的各种预测模型,可以实现预测、仿真、分析等功能,操作简单方便。
本课题来源为教育部高等学校博士点基金项目:基于广义累加灰生成的极限承载力建模与预测研究(200804970005)。
The prediction of the ultimate bearing capacity is an important program in the geotechnical engineering.There are many ways to get the ultimate bearing capacity now.Out of them the predicted method is a hot spot because of its simpleness, practicability and economy.It refers to use the data from the no-destroy static load test to model and predict the ultimate bearing capacity.The ultimate bearing capacity is a system interfered by many factors.The factors' great characteristics are data's polytropy and imperfection,parameter's uncertainty.The gray system theory's research objective is the system with incomplete information.So it is reasonable to study the ultimate bearing capacity.In this paper we only study the single pile's and bolt's ultimate bearing capacity.
At present only the GM(1,1) is used to predict the ultimate bearing capacity.As a classical model in the gray system,the GM(1,1) has some disadvantages itself.For example,the model is only fit for the smooth and equidistant sequence.In practical engineering,because of many factors' interfere,the sequences are complicated and polytropic.So a great task is to improve and put forward some new models to satisfy the sequences.This paper,practically,improved and put forward some new models based on the generalized accumulated generating operation.They are non-equidistant GM(1,1),non-equidistant and equidistant GM(1,1) with jump point and non-equidistant and equidistant GM(1,1) with multi-stage.We analyze the models' accumulated generating methods,properties and parameter space.GM(1,1) power model is studied further.We analyze the model's parameter space,curve's shape and properties,solufion's form and method.
Gray optimization model is an important part of the gray system theory.In this paper we study the gray multi-objective linear programming(GMLP) and gray bi-level linear programming(GBLP).Some concepts are put forward.The properties and solution are studied.
Gray model's great characteristic is simple and applied.And the particle swarm optimization(PSO) also has the advantages such as comparative simplicity,easy operation,and has been used in many fields.So we use PSO to solve the gray model's parameters.As one computation techniques,PSO also has the disadvantage of premature convergence.So we improve PSO and put forward Multi-Swarm PSO (MSPSO),Multi-Best PSO(MBPSO) and Multi-Swarm and Multi-Best PSO (MSBPSO).The searching efficiency is improved greatly by information sharing between swarms and mutual competition between best values.
In this paper,the gray models based on MSBPSO are used to predict the ultimate bearing capacity of single pile and bolt.For every example we use different models. The simulation results show that the new models' errors are smaller than GM(1,1)'s and the GM(1,1) power model is the best.It is because it has many forms of curve. So it can satisfy many forms of sequences' models.The examples show that the new models can solve the prediction of the ultimate bearing capacity preferably.We also use MSBPSO to solve the gray optimization models(GMLP,GBLP) about the bearing capacity and the effects are very good.
In this paper the Visual Basic language is used to design the software system "Prediction of the Ultimate Bearing Capacity Based on the Generalized Gray Model". The system contains each model improved and put forward in this paper.At the same time the system operates easily and has the functions of prediction,simulation and analysis.It would play a contributive role in generalizing the theory studied in the paper.
This dissertation was from Specialized Research Fund for the Doctoral Program of Higher Education of China:Study on Modeling and Prediction of the Ultimate Bearing Capacity Based on the Generalized Accumulated Generating Operation (N0.200804970005).
目前关于灰色系统理论在极限承载力上的应用主要停留在GM(1,1)模型上。GM(1,1)模型主要适用于等间距且较光滑的序列,但实际工程中由于受到多种因素的影响,数据序列形式复杂多变,所以必须提出新的灰色模型来满足多种形式序列的建模。本文正是从实际问题出发,在基于广义累加的基础上改进和提出了非等间隔GM(1,1)模型、(非)等间隔含跳跃点GM(1,1)模型和(非)等间隔阶段型GM(1,1)模型,分析这些模型的累加生成矩阵的表示方法、性质以及参数空间等。此外对GM(1,1)幂模型进行了深入的研究,分析了模型的参数空间、解的形式、曲线的形状和性质以及求解方法等。
在岩土工程中广泛存在着优化问题。灰色优化是灰色系统理论中一个重要部分,本文对灰色多目标线性规划和灰色双层线性规划进行了研究。提出了一些新的概念、对其性质以及解法进行了研究。
灰色预测模型一个主要特点就是简单实用,而粒子群算法也是由于理论简单、易于操作而广泛应用,所以本文采用粒子群算法求解灰色模型。作为一种智能进化算法,粒子群算法也存在“早熟”的弊病。为此本文提出了多种群粒子群算法(MSPSO)、多极值粒子群算法(MBPSO)和多种群多极值粒子群算法(MSBPSO),通过种群之间的信息共享以及极值之间的相互竞争,大大提高了算法的搜索效率。
采用基于粒子群优化算法参数辨识的灰色预测模型进行单桩和锚杆的极限承载力预测。对每个实例采用不同的预测模型进行建模,仿真结果显示,对同一组实验数据,采用改进的模型建模误差都比原始GM(1,1)模型小,其中GM(1,1)幂模型的误差是最小的。主要是因为GM(1,1)幂模型的解有多种曲线形式,所以可以满足多种形式的序列建模。实例说明本文改进和提出的灰色预测模型可以很好的解决极限承载力预测的问题。采用改进的粒子群算法求解灰色优化模型,并用于承载力研究中,获得了很好的效果。
采用Visual Basic程序语言编制了《基于广义灰色模型的极限承载力预测软件》系统,该系统包括本文研究的各种预测模型,可以实现预测、仿真、分析等功能,操作简单方便。
本课题来源为教育部高等学校博士点基金项目:基于广义累加灰生成的极限承载力建模与预测研究(200804970005)。
The prediction of the ultimate bearing capacity is an important program in the geotechnical engineering.There are many ways to get the ultimate bearing capacity now.Out of them the predicted method is a hot spot because of its simpleness, practicability and economy.It refers to use the data from the no-destroy static load test to model and predict the ultimate bearing capacity.The ultimate bearing capacity is a system interfered by many factors.The factors' great characteristics are data's polytropy and imperfection,parameter's uncertainty.The gray system theory's research objective is the system with incomplete information.So it is reasonable to study the ultimate bearing capacity.In this paper we only study the single pile's and bolt's ultimate bearing capacity.
At present only the GM(1,1) is used to predict the ultimate bearing capacity.As a classical model in the gray system,the GM(1,1) has some disadvantages itself.For example,the model is only fit for the smooth and equidistant sequence.In practical engineering,because of many factors' interfere,the sequences are complicated and polytropic.So a great task is to improve and put forward some new models to satisfy the sequences.This paper,practically,improved and put forward some new models based on the generalized accumulated generating operation.They are non-equidistant GM(1,1),non-equidistant and equidistant GM(1,1) with jump point and non-equidistant and equidistant GM(1,1) with multi-stage.We analyze the models' accumulated generating methods,properties and parameter space.GM(1,1) power model is studied further.We analyze the model's parameter space,curve's shape and properties,solufion's form and method.
Gray optimization model is an important part of the gray system theory.In this paper we study the gray multi-objective linear programming(GMLP) and gray bi-level linear programming(GBLP).Some concepts are put forward.The properties and solution are studied.
Gray model's great characteristic is simple and applied.And the particle swarm optimization(PSO) also has the advantages such as comparative simplicity,easy operation,and has been used in many fields.So we use PSO to solve the gray model's parameters.As one computation techniques,PSO also has the disadvantage of premature convergence.So we improve PSO and put forward Multi-Swarm PSO (MSPSO),Multi-Best PSO(MBPSO) and Multi-Swarm and Multi-Best PSO (MSBPSO).The searching efficiency is improved greatly by information sharing between swarms and mutual competition between best values.
In this paper,the gray models based on MSBPSO are used to predict the ultimate bearing capacity of single pile and bolt.For every example we use different models. The simulation results show that the new models' errors are smaller than GM(1,1)'s and the GM(1,1) power model is the best.It is because it has many forms of curve. So it can satisfy many forms of sequences' models.The examples show that the new models can solve the prediction of the ultimate bearing capacity preferably.We also use MSBPSO to solve the gray optimization models(GMLP,GBLP) about the bearing capacity and the effects are very good.
In this paper the Visual Basic language is used to design the software system "Prediction of the Ultimate Bearing Capacity Based on the Generalized Gray Model". The system contains each model improved and put forward in this paper.At the same time the system operates easily and has the functions of prediction,simulation and analysis.It would play a contributive role in generalizing the theory studied in the paper.
This dissertation was from Specialized Research Fund for the Doctoral Program of Higher Education of China:Study on Modeling and Prediction of the Ultimate Bearing Capacity Based on the Generalized Accumulated Generating Operation (N0.200804970005).
引文
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