大跨度桥梁具有阻尼比低、结构柔度大和质量轻等特点,它们在低风速下容易产生涡激共振现象。振动幅度过大会影响桥梁的正常运营,给行人和行车带来不便,同时也会带来桥梁结构强度破坏和疲劳损伤问题。涡激共振是大跨度桥梁抗风设计关键问题之一,对涡激共振的研究具有重要的理论意义和实际的工程应用价值。 本文通过大跨度桥梁主梁节段模型的风洞试验对涡激共振现象进行研究,采用机器学习的方法对涡振数据进行数据处理和分析,并采用多种优化算法对模型参数进行识别研究,这些研究拓宽了桥梁结构抗风思路。本文研究的主要内容如下: 1)涡振信号的信号处理分析理论研究。首先,根据试验信号的稀疏性,研究了信号的压缩感知重建,通过正交匹配追踪算法对一维试验信号进行压缩重建。其次,对试验信号进行傅里叶变换,通过信号的频谱,研究复杂信号的频率成分。接着,由于试验信号中不可避免地含有噪声,研究了基于小波分析的去噪方法。最后,通过相关分析,研究不同信号的相关程度。 2)风洞试验数据的理论分析与建模分析。Scanlan模型是应用广泛的单自由度模型,根据风洞试验数据对Scanlan模型进行残差分析,其残差具有非常显著的规律性,即残差与重构竖向涡激力(VIVF)存在二次关系,且与时间变量存在正弦关系。在分析潜在二次项与残差的关系中,发现位移与速度的交叉项与残差存在显著的线性关系,故提出一个改进的VIVF模型(RVIVFM),即通过向Scanlan模型中添加该二次交叉项。另一种建模则是试验数据驱动建模,采用监督学习的方法认真分析数据间的相互关系并构建一个假设函数,通过信号的频谱分析删除假设函数中对应频率成分不显著的项,再通过相关分析对假设函数优化,使假设函数中的自变量间不存在强相关以及自变量们与因变量保持中度或者中度以上相关,最终提出一种简单的基于监督学习新模型(SVIVFM)。虽然RVIVFM和SVIVFM创建的方法不同,这两种模型都能很好地刻画VIVF的特点。与RVIVFM相比, SVIVFM仅包含5个参数,SVIVFM更加简单有效。 3)基于凸优化的涡振模型参数识别算法。涡激共振是一个复杂流固耦合现象,其模型都是非线性。传统GTR/DTR方法是通过钝体的振动响应来识别VIVF模型参数,由于振幅小和试验中噪声的存在,该方法识别参数的正确性是有限的。为了提高参数识别的精度,采用最小二乘法来构建目标函数。该目标函数是非线性二次凸函数,可通过Levenberg-Marquardt迭代算法(LMA)来识别RVIVFM参数。但LMA算法在迭代中需要计算海森矩阵的逆矩阵,它的算法复杂度高,并且对初始值比较依赖。为了简单且有效地识别模型参数,提出一种基于模型退化的参数识别方法。由于在RVIVFM中瞬间升力项是非常小,将RVIVFM中的瞬间升力项退化为一个小的常数。退化后的RVIVFM是一个由非线性基函数组成的线性方程,采用解正规方程识别参数。 4)涡振模型参数识别的智能优化算法。 ·本文提出一种基于GA和LMA的混合算法(GALMA)。遗传算法(GA)具有很强的搜索能力,但在迭代后期收敛慢,而LMA具有很强的局部搜索能力却非常依赖初始解。GALMA利用GA算法产生一个合适的解,LMA将该解作为初始解来搜索最优解。GALMA的显著特点是不依赖初始值且搜索能力强。 ·本文提出一种基于自适应惯性权重的粒子群算法(NAPSO)。粒子的惯性权重能平衡算法的全局和局部搜索能力,在算法每次迭代时,每个粒子根据其自身的适应度来自适应地调整其惯性权重,这个策略保证种群的多样性和算法的稳定性。 ·本文提出一种改进的模拟退火算法(ISA)。由于涡激振动问题的特点,SA算法的接收概率一直为1,SA算法总是接收新的扰动解,使得SA算法一直处于动荡状态,很难收敛。ISA算法通过放大能量差使得接收概率在10%左右,既确保算法收敛又提供算法跳出局部最优值的可能性,再加上马尔科夫链的长度和新解产生规则的调整,ISA算法能高效地识别模型参数。 ·本文提出一种变尺度Logistics混沌算子的局部搜索和亮度自适应的萤火虫算法(FACLBV)。萤火虫算法(FA)是通过萤火虫间相互吸引来寻优的,在吸引过程中,萤火虫自身的亮度和移动中的局部搜索对寻优的能力有很大影响。为了提高算法效率,FACLBV算法萤火虫的初始亮度与其解空间的位置建立函数关系,也将Logistic混沌算子应于局部搜索并设定局部搜索的缩放因子用以控制搜索尺度。这种策略使得算法具良好的稳定性和收敛性,仿真结果显示算法的有效性。 5)非参数检验应用于算法性能分析,Wilcoxon符号秩检验和Friedman检验应用于PSO类和GA类的性能。此外,Friedman还检验了GALMA、NAPSO、ISA和FACLBV算法的性能。 综上所述,本文运用机器学习方法对涡振数据理论分析与数据处理,研究了单自由度涡振模型和多种优化的参数识别算法。未来还需要更多数据,进行大数据处理,提取不同几何形状的结构体在不同风速和攻击角下的自激力特征信息,构建更广义的涡振模型。应用更智能优化算法识别多自由度涡振模型的参数,更立体更广义地研究涡振中流体与结构体的交互作用。 关键词:大跨度桥梁,涡激共振,残差分析,机器学习,智能优化算法
Long-span bridges are prone to wind-induced vibration at low wind speed due to low damping, large flexibility and light weight. Large vibration amplitudes will affect the normal operation of the bridge, bring inconvenience to pedestrians and traffic, and result in structural strength damage and fatigue damage problems. Vortex-induced resonance (VIR) is one of the key problems in wind-resistant design of long-span bridges. Such research has important theoretical significance and practical engineering application value. In this paper, VIR phenomena of long-span bridges are studied by wind tunnel test. The data of VIR are analyzed by machine learning, and the identification of model parameters is studied by optimization algorithms. The main contents of this paper are as follows: 1)Theoretical analysis of VIR signals. Firstly, according to the sparsity of the experimental signals, the orthogonal matching pursuit algorithm is used to compress and reconstruct the one-dimensional experimental signals. Secondly, Fourier transform is used to study the frequency components of complex signals through the spectrum of signal. Then, the denoising method based on wavelet analysis is studied, because the experimental signals inevitably contain noise. Finally, the correlation degree of different signals is studied through correlation analysis. 2)Theoretical analysis and modeling analysis of wind tunnel experimental data. Scanlan model is a widely used single-degree-of-freedom model. According to the wind tunnel data, the residual analysis of Scanlan model has a very significant regularity, that is, there is a quadratic relationship between the residual and the reconstructed vertical vortex excitation force (VIVF), and there is a sinusoidal relationship with time. In the analysis of the relationship between the potential quadratic term and the residual, it is found that there is a significant linear relationship between the cross term of displacement and velocity and the residual. Therefore, an improved VIVF model (RVIVFM) is proposed, which adds the quadratic cross term to the Scanlan model. The other model is driven by experimental data. The supervised learning method is used to analyze the relationship between data and build a hypothesis function. Through the spectrum analysis of the signal, the items whose frequency components are not significant are deleted. Then the hypothesis function is optimized by correlation analysis. In this hypothesis, there is no strong correlation between independent variables, and independent variables are moderately or above correlated with the dependent variables. Finally, a simple supervised learning model (SVIVFM) is proposed. Although there are different ways to establish RVIVFM and SVIVFM, these two models depict the characteristics of VIVF well. Compared with RVIVFM, SVIVFM contains 5 parameters, so SVIVFM is simpler and more effective. 3)Parameter identification algorithm based on convex optimization. VIR is a complex fluid solid coupling phenomenon, so its models are nonlinear. The traditional GTR / DTR method identifies the parameters of VIVF model by the vibration response of blunt body. Because of the small amplitudes and the existence of noises in experiment, the correctness of this method is limited. In order to improve the accuracy of identified parameter, the least square method is used to establish the objective function. The objective function is a nonlinear quadratic convex function, and RVIVFM parameters can be identified by Levenberg-Marquardt algorithm (LMA). However, LMA needs to compute the inverse matrix of Hessian matrix in iterations, which has high computational complexity and is sensitive to the initial solution. In order to identify the model parameters simply and effectively, a parameter identification method based on model degradation is proposed. Because the instantaneous lift term in RVIVFM is very small, it is reduced to a small constant. The degenerated RVIVFM is a linear equation composed of nonlinear basis functions, so the parameters are identified by solving the normal equation. 4)our intelligent optimization algorithms for parameter identification of vortex vibration model. ·In this paper, a hybrid algorithm based on Genetic algorithm (GA) and LMA (GALMA) is proposed. GA has a strong searching ability, but it converges slowly in the late iterations, while LMA has a strong local searching ability and is sensitive to the initial solution. GALMA uses GA algorithm to generate a suitable solution. LMA uses the solution as the initial solution to search for the optimal solution. The main feature of GALMA is that it does not depend on the initial solution and has strong search ability. ·In this paper, a new adaptive particle swarm optimization algorithm based on inertia weight (NAPSO) is proposed. The inertia weight of each particle has important impact on the global and local search ability. Each particle adaptively adjusts its inertia weight according to its own fitness in last iteration of the algorithm. This strategy guarantees the diversity of the population and the stability of the algorithm. ·In this paper, an improved simulated annealing algorithm (ISA) is proposed. Because of the characteristics of vortex-induced vibration, the accepted probability of SA is always 1,and SA algorithm always receives new perturbation solutions. The strategy makes SA algorithm in a turbulent state and difficult to converge. ISA algorithm enlarges the energy difference so that the accepted probability is about 10%. The accepted probability not only ensures the convergence of the algorithm, but also provides the possibility of the algorithm jumping out of the local optimal value. In addition, the length of Markov chain and the rules of new solution generation are adjusted, these strategies make ISA algorithm identify model parameters efficiently. ·In this paper, a firefly algorithm based on mutative local chaotic search and adaptive initial brightness (FACLBV) is proposed. For the firefly algorithm, the brightness of fireflies and the local search have great influence on the ability of optimization. In order to improve the efficiency of FACLBV, the initial brightness of each firefly is related to its location of the solution space, the Logistic chaos operator is used to search locally, and the scaling factor of the local search is used to control the search scale. This strategy makes FACLBV has good stability and convergence, and the simulation results show the effectiveness of FACLBV 5)Nonparametric tests are applied to algorithm performance analysis, Wilcoxon's test and Friedman's test are applied to PSO and GA algorithms. In addition, Friedman' tests checks the performance of algorithms such as GALMA, NAPSO, ISA and FACLBV. In summary, this paper studies the single-degree-of-freedom (SDOF) VIVF model and a variety of optimized parameter identification algorithms. Big data processing needs more data in order to extract the self-excited force characteristics under different wind speeds and attack angles and build a more generalized vortex-induced vibration model. More intelligent optimization algorithms are applied to identify the parameters of the multi-degree-of-freedom VIV model, and the interaction between fluid and structure in vortex-induced vibration is studied by data mining. Key words: long-span bridge, vortex-induced resonance, residual analysis, supervised learning, intelligent optimization algorithm