系统分析的研究和在水利工程中的应用
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摘要
同电气工程、机械工程等学科研究领域相比,土木工程则具有较大模糊性和随机性,随着该学科的继续发展,许多问题已可通过系统分析的研究得到确定性的结果,并逐渐向最优化方法分析确定结论方向发展,可见系统分析在土木工程理论研究和工程应用中将会发挥越来越重要的作用。
系统分析的研究包括5部分。研究应用在水利工程方面。
1.系统建模-混合Lotka-Volterra模型
将Lotka-Volterra竞争模型与互利模型混合,得到混合的Lotka-Volterra模型。种群间的关系,表现为一个周期内一段时期竞争,一段时期互利。并证明了混合模型正平衡点的局部渐进稳定性和全局稳定性。
2.系统预测-考虑模糊区域的灰色马尔可夫链应用于防洪堤水平位移预测
应用灰色系统理论和模糊数学的方法,建立了考虑模糊区域的灰色马尔可夫链式预测模型。
3.非线性优化算法-工程结构可靠度计算
给出满足响应面法的功能函数求解结构可靠度C++程序。
应用划分网格法与避免了维数灾的粗格子点法求解几何可靠度;通过并行粗格子点法求解可靠度。
在大型工程结构分析中,应用几何可靠度求解,作为约束条件的结构功能函数较复杂或结构功能函数是隐式时,有必要采用罚函数将约束的优化问题转化为无约束的优化问题。从结构可靠度几何意义及惩罚函数的作用出发,分析了惩罚结构非极限状态可能出现的欺骗性。提出应用结构失效区域的变量来求解几何可靠度,得到一个不需引入惩罚函数的无约束优化问题。
4.系统仿真-仿真算法
自然界物种优胜劣汰,适者生存。在相互竞争的多个种群中,必然有某一个种群,其群内的个体具有最大的多样性(Most Diverse Population,MDP)。这个群我们称之为MDP群。在每个种群内,当前每一代个体根据以下因素更新自己:个体自身情况、群内最优个体、群外最优个体(也可取最优个体)、MDP群内随机个体、个体多样性较优群(此种群判断识别的个体多样性最优群)内随机个体。实现群个体的适应性与种群的个体多样性的双重竞争。种群个体适应性强,个体多样性强,种群产生更多的个体。在“双重竞争”寻优机制的作用下,逐步逼近最优个体。
模仿栖息地破坏下种群对环境的适应,提出栖息地破坏群竞争算法。
在GA个体选择策略中,Holland提出赌轮盘的个体选择策略,群优秀个体被选中机率较大。DHCPA采用智能个体选择策略:当群个体较少时,下一代产生优秀个体的几率小,这样会导致算法收敛速度慢,所以我们采用提高选中群内优个体概率的方法。当群个体较多时,我们采用降低选中群内优个体概率的方法,避免陷入局部最优。
智能的选择策略选中优个体的概率逐代提高。
迭代初期,由于栖息地破坏,群个体逐渐减少,淘汰了群内劣势个体加快收敛;随着种群对栖息地破坏适应能力增强,群个体增加,避免陷入局部最优,群个体适应性和群个体多样性决定了各群个体的增加快慢。
改进PSO算法的惯性权重。惯性权重不仅考虑了随代数纵向线性变化,也根据当前和迄今粒子的适应度重排序横向线性变化。横向线性变化上限不变,下限逐渐减小,使得线性变化数值范围随代数逐渐增大。惯性权重随着代数逐渐取负,并且适应度差的粒子取负的几率更大。
5.系统评价-层次分析法
n阶比较判断矩阵,通过选择判断矩阵n-1个元素a_(ij),a_(jk),…,a_(1m),a_(mn)得到所有不同权重向量[w_i,w_j,w_k,…w_1,w_m,w_n]~T,组成权重向量集合。通过最小二乘法评价集合内权重向量一致性,部分一致性最差权重向量对应权重求和得到的权重向量,通过求解广义偏差函数的最小二乘问题修正此权重向量。最终判断阵权重向量由修正的权重向量与未修正权重向量决定。
应用于防洪堤水平位移预测、临界水深计算、工程结构可靠度计算和土坝边坡稳定分析。
Compare with such as Electrical Engineer and Mechanical Engineer etc discipline research areas.Civil Engineer has large fuzzy and random nature,by the development of discipline continue,Through system analysis the many problem's research can obtain certain results,so use Optimization analysing and determining conclusion will develop gradually.It is illustrate the system analysis produce more and more important affection at civil engineer theory research and project application.
The research of system analysis includes 5 parts. And give many calculated examples.
1. set up system's mode-Hybrid Lotka-Volterra mode
Integrat Lotka-Volterra competition model with mutually beneficial model,obtain Hybrid Lotka-Volterra mode .The relationship of population: It is represent a cycle of competition for a period of time and mutual benefit for a period of time, And prove that the model Equilibrium point's local progressive stability and global stability.
2. system prediction- Thinking about fuzzy region and application of grey model A.A.Mapkob in prediction of flood embankment horizontal displacement
Useing grey system theory and fuzzy mathematics method,establish the thinking about fuzzy region grey model A.A.Mapkob.
3. nonlinear optimization algorithm- calculating structure reliability engineering
Giving C++ procedures for calculating structural reliability,and the performance function which Meet the Response Surface Method.
The article also put forward a proposal use divided mesh method and coarse divided mesh method which can avoids dimensional disaster when calculating the geometric reliability.Useing parallel coarse divided mesh method to calculating the geometric reliability.
Structure analysis of the major projects when application of geometric reliability,the structure function which as constraint more complex or is an implicit. It is necessary to use penalty function change constrained optimization into non-constrained optimization problem.It had analysed possible cheats of penalty un-ultimate state. It has proposes use structure fail area variable to calculate geometric reliability,obtain a un-introduce penalty function's non-constrained optimization problem.
4. System simulation- Simulation Algorithm
The natural species survival of the fittest.The competition of many populations,it must have a certain population, the most diversity of individuality population(MDP). This population we call the MDPAccording to the following factors to update each population's individualities at every generation:self, the population's best individuality, other population's best individuality (it also can use the best individuality), MDP random individuality, the More Diverse population(This population to identify the most diverse population by itself) random individuality.The realization of the double competition at the individuality survival of the fittest and the individual diversity of populations. The population who have better adaptability and better diversity of individualities will generate more individuality. At the "double competition" optimization mechanism,it will gradually approach the best solution.
When imitate the destroyed habitat the populations adapt themselves gradually by generation, obtain the destroyed habitat CPA-DHCPA.
In genetic algorithm individual select strategy, Holland proposed use the roulette gambling strategy of individual selection.So the better individualities greater probability of being selected.At DHCPA use the smart individual select strategy. When the small size of population,better individualities in a small probability at the next generation, this will lead to CPA convergence rate become slow, so we enhance the selected probability of better individualities. When the large size of population, so we reduce the selected probability of better individualities.
The smart individual select strategy the probability of select the better individualities increase gradually by generation.
At the initial iteration, due to the habitat destruction, size of population gradually reduce and eliminate the inferior individualities of population to accelerate convergence; With the population enhance the ability of well-being toward habitat destruction, increase size of population,so the population searching to avoid a local optimum, The adaptability and diversity of individualities of the population has decided to the increase speed of the population size.
It has modified PSO inertia weight.The inertia weight not only think about its longitudinal linear change by generation; but also think about current and up to now best results of particles adaptation sequence's lateral linear change which rearrange by adaptation good or bad. The lateral linear upper bound un-change and lower bound become small,so the lateral linear range expend gradually.The inertia weight will generate more negative value by generation increasing.
5. System evaluation-AHP
The n order judgment matrix, through select n-1 elements a_(ij), a_(jk),…, a_(lm), a_(mn) to obtain all different weight vectors [w_i, W_j, w_k,…, W_l, w_m, w_n] .To form the weight vector assemblage.Evaluate consistency weight vector in assemblage,the weight vector which is summation part of worse consistency weight vector, through GLSM correct this weight vector. Correct weight vector and un-correct weight vector population to decide final judgment matrix weight vector.
And application such as prediction of flood embankment horizontal displacement ,calculation of critical water depth problem, calculating structure reliability and earth dam Slope Stability Analysis.
系统分析的研究包括5部分。研究应用在水利工程方面。
1.系统建模-混合Lotka-Volterra模型
将Lotka-Volterra竞争模型与互利模型混合,得到混合的Lotka-Volterra模型。种群间的关系,表现为一个周期内一段时期竞争,一段时期互利。并证明了混合模型正平衡点的局部渐进稳定性和全局稳定性。
2.系统预测-考虑模糊区域的灰色马尔可夫链应用于防洪堤水平位移预测
应用灰色系统理论和模糊数学的方法,建立了考虑模糊区域的灰色马尔可夫链式预测模型。
3.非线性优化算法-工程结构可靠度计算
给出满足响应面法的功能函数求解结构可靠度C++程序。
应用划分网格法与避免了维数灾的粗格子点法求解几何可靠度;通过并行粗格子点法求解可靠度。
在大型工程结构分析中,应用几何可靠度求解,作为约束条件的结构功能函数较复杂或结构功能函数是隐式时,有必要采用罚函数将约束的优化问题转化为无约束的优化问题。从结构可靠度几何意义及惩罚函数的作用出发,分析了惩罚结构非极限状态可能出现的欺骗性。提出应用结构失效区域的变量来求解几何可靠度,得到一个不需引入惩罚函数的无约束优化问题。
4.系统仿真-仿真算法
自然界物种优胜劣汰,适者生存。在相互竞争的多个种群中,必然有某一个种群,其群内的个体具有最大的多样性(Most Diverse Population,MDP)。这个群我们称之为MDP群。在每个种群内,当前每一代个体根据以下因素更新自己:个体自身情况、群内最优个体、群外最优个体(也可取最优个体)、MDP群内随机个体、个体多样性较优群(此种群判断识别的个体多样性最优群)内随机个体。实现群个体的适应性与种群的个体多样性的双重竞争。种群个体适应性强,个体多样性强,种群产生更多的个体。在“双重竞争”寻优机制的作用下,逐步逼近最优个体。
模仿栖息地破坏下种群对环境的适应,提出栖息地破坏群竞争算法。
在GA个体选择策略中,Holland提出赌轮盘的个体选择策略,群优秀个体被选中机率较大。DHCPA采用智能个体选择策略:当群个体较少时,下一代产生优秀个体的几率小,这样会导致算法收敛速度慢,所以我们采用提高选中群内优个体概率的方法。当群个体较多时,我们采用降低选中群内优个体概率的方法,避免陷入局部最优。
智能的选择策略选中优个体的概率逐代提高。
迭代初期,由于栖息地破坏,群个体逐渐减少,淘汰了群内劣势个体加快收敛;随着种群对栖息地破坏适应能力增强,群个体增加,避免陷入局部最优,群个体适应性和群个体多样性决定了各群个体的增加快慢。
改进PSO算法的惯性权重。惯性权重不仅考虑了随代数纵向线性变化,也根据当前和迄今粒子的适应度重排序横向线性变化。横向线性变化上限不变,下限逐渐减小,使得线性变化数值范围随代数逐渐增大。惯性权重随着代数逐渐取负,并且适应度差的粒子取负的几率更大。
5.系统评价-层次分析法
n阶比较判断矩阵,通过选择判断矩阵n-1个元素a_(ij),a_(jk),…,a_(1m),a_(mn)得到所有不同权重向量[w_i,w_j,w_k,…w_1,w_m,w_n]~T,组成权重向量集合。通过最小二乘法评价集合内权重向量一致性,部分一致性最差权重向量对应权重求和得到的权重向量,通过求解广义偏差函数的最小二乘问题修正此权重向量。最终判断阵权重向量由修正的权重向量与未修正权重向量决定。
应用于防洪堤水平位移预测、临界水深计算、工程结构可靠度计算和土坝边坡稳定分析。
Compare with such as Electrical Engineer and Mechanical Engineer etc discipline research areas.Civil Engineer has large fuzzy and random nature,by the development of discipline continue,Through system analysis the many problem's research can obtain certain results,so use Optimization analysing and determining conclusion will develop gradually.It is illustrate the system analysis produce more and more important affection at civil engineer theory research and project application.
The research of system analysis includes 5 parts. And give many calculated examples.
1. set up system's mode-Hybrid Lotka-Volterra mode
Integrat Lotka-Volterra competition model with mutually beneficial model,obtain Hybrid Lotka-Volterra mode .The relationship of population: It is represent a cycle of competition for a period of time and mutual benefit for a period of time, And prove that the model Equilibrium point's local progressive stability and global stability.
2. system prediction- Thinking about fuzzy region and application of grey model A.A.Mapkob in prediction of flood embankment horizontal displacement
Useing grey system theory and fuzzy mathematics method,establish the thinking about fuzzy region grey model A.A.Mapkob.
3. nonlinear optimization algorithm- calculating structure reliability engineering
Giving C++ procedures for calculating structural reliability,and the performance function which Meet the Response Surface Method.
The article also put forward a proposal use divided mesh method and coarse divided mesh method which can avoids dimensional disaster when calculating the geometric reliability.Useing parallel coarse divided mesh method to calculating the geometric reliability.
Structure analysis of the major projects when application of geometric reliability,the structure function which as constraint more complex or is an implicit. It is necessary to use penalty function change constrained optimization into non-constrained optimization problem.It had analysed possible cheats of penalty un-ultimate state. It has proposes use structure fail area variable to calculate geometric reliability,obtain a un-introduce penalty function's non-constrained optimization problem.
4. System simulation- Simulation Algorithm
The natural species survival of the fittest.The competition of many populations,it must have a certain population, the most diversity of individuality population(MDP). This population we call the MDPAccording to the following factors to update each population's individualities at every generation:self, the population's best individuality, other population's best individuality (it also can use the best individuality), MDP random individuality, the More Diverse population(This population to identify the most diverse population by itself) random individuality.The realization of the double competition at the individuality survival of the fittest and the individual diversity of populations. The population who have better adaptability and better diversity of individualities will generate more individuality. At the "double competition" optimization mechanism,it will gradually approach the best solution.
When imitate the destroyed habitat the populations adapt themselves gradually by generation, obtain the destroyed habitat CPA-DHCPA.
In genetic algorithm individual select strategy, Holland proposed use the roulette gambling strategy of individual selection.So the better individualities greater probability of being selected.At DHCPA use the smart individual select strategy. When the small size of population,better individualities in a small probability at the next generation, this will lead to CPA convergence rate become slow, so we enhance the selected probability of better individualities. When the large size of population, so we reduce the selected probability of better individualities.
The smart individual select strategy the probability of select the better individualities increase gradually by generation.
At the initial iteration, due to the habitat destruction, size of population gradually reduce and eliminate the inferior individualities of population to accelerate convergence; With the population enhance the ability of well-being toward habitat destruction, increase size of population,so the population searching to avoid a local optimum, The adaptability and diversity of individualities of the population has decided to the increase speed of the population size.
It has modified PSO inertia weight.The inertia weight not only think about its longitudinal linear change by generation; but also think about current and up to now best results of particles adaptation sequence's lateral linear change which rearrange by adaptation good or bad. The lateral linear upper bound un-change and lower bound become small,so the lateral linear range expend gradually.The inertia weight will generate more negative value by generation increasing.
5. System evaluation-AHP
The n order judgment matrix, through select n-1 elements a_(ij), a_(jk),…, a_(lm), a_(mn) to obtain all different weight vectors [w_i, W_j, w_k,…, W_l, w_m, w_n] .To form the weight vector assemblage.Evaluate consistency weight vector in assemblage,the weight vector which is summation part of worse consistency weight vector, through GLSM correct this weight vector. Correct weight vector and un-correct weight vector population to decide final judgment matrix weight vector.
And application such as prediction of flood embankment horizontal displacement ,calculation of critical water depth problem, calculating structure reliability and earth dam Slope Stability Analysis.
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[4]刘蜀阳,张学良,孙大刚,林慕义,温淑花.基于极坐标复运算的粒子群优化算法[J].系统仿真学报.2006年.07期.
[5]王俊伟,汪定伟.一种带有梯度加速的粒子群算法[J].控制与决策.2004年.11期.
[6]李婷,赖旭芝,吴敏.粒子群优化新算法的最优潮流求解[J].中南大学学报(自然科学版),2007,38(1):133-137.
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[9]张文修,梁怡.遗传算法的数学基础(第1版和第2版)[M].西安.西安交通大学出版社.2003.5.
[10]Baker,J.Reducing bias and inefficiency in the selection algorithm,in Grefenstette[266],pp.14-21.
[11]冯骏,薛云灿,江金龙.一种新的改进粒子群算法研究[J].河海大学常州分校学报,2005,20(1):10-13.
[1]Kennedy J,Eberhart R C.Particle swarm optimization[A].In:Proc.IEEE Int.Conf.on Neural Networks[C].Piscataway,NJ:IEEE Press,1995.1942-1948.
[2]张文修,梁怡.遗传算法的数学基础(第1版和第2版)[M].西安.西安交通大学出版社.2003.5.
[3]Baker,J.Reducing bias and ineffidency in the selection algorithm,in Grefenstette[266],pp.14-21.
[4]冯骏,薛云灿,江金龙.一种新的改进粒子群算法研究[J].河海大学常州分校学报,2005,20(1):10-13.
[5]赵明阶,何光春,王多垠.边坡工程处治技术[M].北京:人民交通出版社.2003.
[6]张慧,李立增,王成华.粒子群算法在确定边坡最小安全系数中的应用[J].石家庄铁道学院学报.2004.17(2):1-4.
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[8]麻荣永.土石坝风险分析方法及应用[M].北京:科学出版社,2004.
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[2]金菊良,魏一鸣,丁晶.基于改进层次分析法的模糊综合评价模型[J].水利学报,2004,35(3):65-71.
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