不确定条件下桥梁结构损伤识别及状态评估的模糊计算方法研究
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摘要
随着现代经济的高速发展，在役桥梁所承受的交通荷载日益增加，外部恶劣环境导致材料不断老化，桥梁结构容易出现累积损伤，进而导致承载能力不足。因此，对桥梁结构进行损伤识别及状态评估，及时掌握桥梁的健康状态，对保障结构的安全运营，提高桥梁服役寿命，减少垮塌事故的发生，具有重要的社会及经济价值。
然而，在实际工程结构损伤识别及状态评估中，不可避免的会受到不确定性因素的影响，如外界环境、测量噪声、人为主观因素等。这些不确定性因素的存在阻碍了现有损伤识别及状态评估技术的实际应用进程，降低了识别及评估结果的可靠性。因此，如何在计算过程中，考虑并剔除不确定性因素的影响，对促进桥梁结构损伤识别及状态评估技术的工程实用化，具有重要的现实意义。
本文结合国家高技术研究发展计划（863计划）“季节冰冻区大范围道路灾害参数监测与辨识预警系统研究”项目，针对参数误差及信息缺失、温度、基准模型信息缺失以及人为主观因素等不确定性状况，基于模糊贴近度、模糊神经网络、模糊推理、模糊聚类等模糊计算方法，提出了具备较强鲁棒性的损伤识别及状态评估技术。本文开展的具体研究工作如下：
1.针对噪声及测试自由度不完整等引起的参数误差及信息不完备状况，提出了桥梁结构损伤识别的模糊贴近度方法。该方法以改进的振型比值为识别参数，分别选取K型抛物线及钟形函数作为输入、输出参数隶属度函数，通过建立结构损伤状态及损伤特征向量之间的对应关系，构建损伤识别知识库。通过计算测试样本与知识库中规则之间的模糊贴近度，基于择近原则，实现结构损伤定位及状态辨识。在原始数据中添加高斯分布随机数来模拟噪声，以节点振型数据的缺失模拟信息不完备状况，多片简支梁桥的数值模拟分析验证了该方法在参数误差及信息缺失状况下的损伤识别效果。以跨径1.5米槽梁作为室内试验模型，验证了模糊贴近度方法的实际应用效果。
2.针对温度改变引起的模态参数非正常变化，提出了一种能够剔除温度效应的桥梁结构损伤识别模糊神经网络方法。该方法通过结构弹性模量的改变对温度效应进行模拟，以归一化温度及均匀荷载面曲率作为模糊神经网络的输入参数，通过自适应训练，自动生成if then规则库。对简支梁桥的数值模拟分析验证了该方法的有效性，结果表明，均匀荷载面参数具备良好的损伤辨识能力，模糊神经网络可以实现测试样本的自适应损伤辨识，能够完成桥梁结构损伤识别中温度效应的有效剔除。
为了更好地说明模糊神经网络方法的有效性，通过构造向量相似度计算公式，对BP神经网络方法以及ANFIS方法的识别精度进行了对比分析。结果表明，ANFIS方法测试样本的期望输出与实际输出相似度更高，识别结果更准确。
3.考虑到在役桥梁基准模型数据不可得或仿真误差较大容易导致损伤识别方法失效，基于模态曲率、切比雪夫多项式及模糊推理理论，提出了一种不依赖基准模型信息的桥梁结构损伤识别方法。
该方法在损伤结构节点振型数据的基础上，通过二次中心差分得到相应的模态曲率值MSC d；在此基础上，选取特征节点的MSC d值，通过切比雪夫多项式拟合得到结构未损情况下的模态曲率值MSC u；通过MSC d与MSC u，计算得到结构损伤前后的模态曲率差值MCD，从而实现结构的损伤位置识别。以归一化的MCD作为模糊推理系统的输入参数，实现结构的损伤程度识别。对简支梁桥的数值模拟分析验证了该方法的有效性，结果表明，基于切比雪夫多项式拟合得到的模态曲率差，能够实现准确的损伤定位；以模态曲率差值为损伤识别参数构造的模糊推理系统，可以实现结构的损伤状态辨识。选取槽梁为室内试验模型，验证了本文所提出方法的实际应用效果。
4.针对现有桥梁状态评估方法容易受到人为主观因素的影响，本文以桥梁现场实测数据为基础，提出了一种基于模糊聚类的无监督式桥梁上部结构状态评估方法。该方法首先通过现场实测参数构建桥梁耐久性及安全性评价指标体系，分别考虑和不考虑指标权重影响，选取一定数量的实桥健康监测数据为聚类样本，通过计算得到样本的模糊相似矩阵及模糊等价矩阵，选取不同的阈值形成动态聚类图，基于F统计量分析确定最佳分类。该聚类结果视为桥梁安全性及耐久性状态评估的样本库，将同一类桥梁相应指标的平均值视为该类别的近似中心，通过计算未知桥梁状态数据与该中心之间的模糊贴近度，依据择近原则，对待评估桥梁的状态进行分析评价。分别选取长春赛德大桥及吉林省南坪（茂山）国境桥作为桥梁安全性及耐久性评估的实体工程，验证本文提出模糊聚类方法的有效性。
With the rapid development of modern economy, the traffic load that bridge in servicehas to bear increases gradually. Meanwhile, external harsh environment leads to materials’continuously aging problem, accompany with the easy occurrence of cumulative damage forbridge structure, so as to result in the insufficient carrying capacity. Therefore, it is of greatsocial and economic value to guarantee the safety operation of the structure, promote thebridge service life and reduce the occurrence rate of collapse accidents when taking thedamage identification and condition assessment of bridge structure into account, and timelygrasping the bridge damage location and degree as well as evaluating the bridge safety anddurability conditions.
However, in the process of actual structural damage identification and conditionassessment, it is inevitably affected by some uncertainties, such as the external environment,the measure noise, subjective factors and so on. The existence of these uncertainties hindersthe practical application process of the existing damage identification and conditionassessment technologies so as to reduce the reliability of the identification and assessmentresults. Thus, how to consider and net out the effect of uncertainties in the calculationprocess has an important practical significance for promoting the engineering application ofthe damage identification and condition assessment technology.
Aiming at the uncertainties, such as parameter error, information missing, temperature,information missing of the reference model, as well as subjective factors and so on, thispaper puts forward the damage identification and state assessment techniques with strongrobustness, based on fuzzy nearness, fuzzy neural network, fuzzy logic, fuzzy clustering andsome other fuzzy calculation methods. The specific research work is shown as follows:
1. Aiming at the condition of parameter errors and information missing caused bynoise and incomplete test degree of freedom, this paper proposes fuzzy nearness-based method in damage identification of bridge structure by taking simply supported beam bridgeas the research object. This approach takes the improved vibrator ratio as damageidentification parameters with K-type parabolic and Bell-shaped function as membershipfunction of input and output parameters, respectively, so as to builds the damageidentification knowledge base by establishing a correspondence between structural damagestate and damage eigenvectors. The structural damage localization and damage stateidentification are realized by calculating the regular fuzzy approach degree between testsamples and knowledge base, according to approximate principle. By adding Gaussiandistribution random number into raw data to simulate noise and with missing node modedata simulating incomplete information condition, numerical simulation analysis ofmulti-girder simply supported beam bridge proves good effect in the damage identificationof single-location and multi-location under the condition of parameter errors andinformation missing. Slot beam with span1.5m is selected as the indoor test model toproves the practical application effect of FNBDI method.
2. Aiming at the abnormal changes of modal parameters caused by temperature change,this paper proposes a fuzzy neural network approach that can eliminate the temperatureeffects in the damage identification of bridge structure. This method simulates thetemperature effect with the changes of structural elastic modulus and based on the modalfrequencies and vibration data of the structure, the corresponding structure uniform loadsurface and its curvature value are calculated. The uniform load curvature differences beforeand after the structural damage are taken as the damage identification parameters. Besides,the if thenrule base is automatically generated through adaptive training. This paperregards the normalized temperature and the uniform load surface curvature as the inputparameters of fuzzy neural network, and the numerical simulation analysis of simplysupported beam bridge verifies the effectiveness of the method.
In order to better illustrate the effectiveness of the fuzzy neural network method, BPneural network is selected as the damage identification algorithm with frequency changesquare ratio and frequency change value regarded as the identification parameters of thedamage location and degree, respectively. By constructing vector similarity formula, this paper comparatively analyzes the identification accuracy between BP neural network andANFIS method. The result indicates that the similarity between the desired output and theactual output of testing samples with the ANFIS method is higher and the identificationresult is more accurate.
3. Considering that the baseline model data of existing bridge is not available or thesimulation error is larger, it will lead to the failure of the damage identification method. Thischapter proposes a bridge structural damage identification method, based on modalcurvature, the Chebyshev polynomial and fuzzy reasoning theory without consideringbaseline model information.
This method obtains the corresponding modal curvature valuesMSC dthroughsecond central differencing method on the basis of the node mode data of damage structure.According to this, we select theMSC dvalue of the feature node and get the modalcurvature valueMSC uwithout damage by Chebyshev polynomial fitting. By calculatingthe modal curvature difference MCD before and after the structural damage throughMSC dandMSC u, the structural damage location identification can be realized. Thedamage degree identification of bridge structure is realized by making the normalizedMCD as the input parameters of fuzzy reasoning system. The numerical simulationanalysis of simply supported beam bridge has verified the effectiveness of this method andthe results show that the calculated modal curvature difference of the single-location andmulti-location that is not dependent on the benchmark model data, is able to achieveaccurate damage positioning. Taking the normalized modal curvature difference of therelevant nodes as input parameters of fuzzy systems, we respectively construct fuzzyreasoning system of single-location and multi-location damage identification, so as toguarantee the damage identification results of the test samples are equipped with goodaccuracy. Selecting slot beam as indoor test model and taking the mid-span unit damageidentification for example, the effectiveness of the method proposed in this paper is verifiedby the measured first modal shape data.
4. Since state assessment methods of the existing bridge are easily influenced by subjective factors, this paper proposes a unsupervised bridge superstructure state assessmentmethod based on fuzzy clustering according to bridge field measured data. Firstly, thismethod builds the durability and safety evaluation index system of bridges based on fieldmeasured parameters. And then, considering or not considering the index weight effectseparately, we select a certain number of bridge health monitoring data as clusteringsamples to obtain the fuzzy similarity matrix and fuzzy equivalent matrix of samples bycalculating. Finally, we select a different threshold to form a dynamic clustering map anddetermine the best classification based on statistic analysis. The clustering result is regardedas a sample base of bridge safety and durability state assessment. Taking the average of thecorresponding indicators of the same type bridges as the approximate center of this category,this method can analyze and evaluate the bridge state for assessment on the basis ofselecting the near principle by calculating the fuzzy nearness between the unknown bridgestate data and the center’s. This paper selects the Saide bridge and the border bridge inNanping (maoshan) in Jilin Province as the physical works of the bridge safety anddurability assessment to verify the effectiveness of fuzzy clustering method referred above.
然而，在实际工程结构损伤识别及状态评估中，不可避免的会受到不确定性因素的影响，如外界环境、测量噪声、人为主观因素等。这些不确定性因素的存在阻碍了现有损伤识别及状态评估技术的实际应用进程，降低了识别及评估结果的可靠性。因此，如何在计算过程中，考虑并剔除不确定性因素的影响，对促进桥梁结构损伤识别及状态评估技术的工程实用化，具有重要的现实意义。
本文结合国家高技术研究发展计划（863计划）“季节冰冻区大范围道路灾害参数监测与辨识预警系统研究”项目，针对参数误差及信息缺失、温度、基准模型信息缺失以及人为主观因素等不确定性状况，基于模糊贴近度、模糊神经网络、模糊推理、模糊聚类等模糊计算方法，提出了具备较强鲁棒性的损伤识别及状态评估技术。本文开展的具体研究工作如下：
1.针对噪声及测试自由度不完整等引起的参数误差及信息不完备状况，提出了桥梁结构损伤识别的模糊贴近度方法。该方法以改进的振型比值为识别参数，分别选取K型抛物线及钟形函数作为输入、输出参数隶属度函数，通过建立结构损伤状态及损伤特征向量之间的对应关系，构建损伤识别知识库。通过计算测试样本与知识库中规则之间的模糊贴近度，基于择近原则，实现结构损伤定位及状态辨识。在原始数据中添加高斯分布随机数来模拟噪声，以节点振型数据的缺失模拟信息不完备状况，多片简支梁桥的数值模拟分析验证了该方法在参数误差及信息缺失状况下的损伤识别效果。以跨径1.5米槽梁作为室内试验模型，验证了模糊贴近度方法的实际应用效果。
2.针对温度改变引起的模态参数非正常变化，提出了一种能够剔除温度效应的桥梁结构损伤识别模糊神经网络方法。该方法通过结构弹性模量的改变对温度效应进行模拟，以归一化温度及均匀荷载面曲率作为模糊神经网络的输入参数，通过自适应训练，自动生成if then规则库。对简支梁桥的数值模拟分析验证了该方法的有效性，结果表明，均匀荷载面参数具备良好的损伤辨识能力，模糊神经网络可以实现测试样本的自适应损伤辨识，能够完成桥梁结构损伤识别中温度效应的有效剔除。
为了更好地说明模糊神经网络方法的有效性，通过构造向量相似度计算公式，对BP神经网络方法以及ANFIS方法的识别精度进行了对比分析。结果表明，ANFIS方法测试样本的期望输出与实际输出相似度更高，识别结果更准确。
3.考虑到在役桥梁基准模型数据不可得或仿真误差较大容易导致损伤识别方法失效，基于模态曲率、切比雪夫多项式及模糊推理理论，提出了一种不依赖基准模型信息的桥梁结构损伤识别方法。
该方法在损伤结构节点振型数据的基础上，通过二次中心差分得到相应的模态曲率值MSC d；在此基础上，选取特征节点的MSC d值，通过切比雪夫多项式拟合得到结构未损情况下的模态曲率值MSC u；通过MSC d与MSC u，计算得到结构损伤前后的模态曲率差值MCD，从而实现结构的损伤位置识别。以归一化的MCD作为模糊推理系统的输入参数，实现结构的损伤程度识别。对简支梁桥的数值模拟分析验证了该方法的有效性，结果表明，基于切比雪夫多项式拟合得到的模态曲率差，能够实现准确的损伤定位；以模态曲率差值为损伤识别参数构造的模糊推理系统，可以实现结构的损伤状态辨识。选取槽梁为室内试验模型，验证了本文所提出方法的实际应用效果。
4.针对现有桥梁状态评估方法容易受到人为主观因素的影响，本文以桥梁现场实测数据为基础，提出了一种基于模糊聚类的无监督式桥梁上部结构状态评估方法。该方法首先通过现场实测参数构建桥梁耐久性及安全性评价指标体系，分别考虑和不考虑指标权重影响，选取一定数量的实桥健康监测数据为聚类样本，通过计算得到样本的模糊相似矩阵及模糊等价矩阵，选取不同的阈值形成动态聚类图，基于F统计量分析确定最佳分类。该聚类结果视为桥梁安全性及耐久性状态评估的样本库，将同一类桥梁相应指标的平均值视为该类别的近似中心，通过计算未知桥梁状态数据与该中心之间的模糊贴近度，依据择近原则，对待评估桥梁的状态进行分析评价。分别选取长春赛德大桥及吉林省南坪（茂山）国境桥作为桥梁安全性及耐久性评估的实体工程，验证本文提出模糊聚类方法的有效性。
With the rapid development of modern economy, the traffic load that bridge in servicehas to bear increases gradually. Meanwhile, external harsh environment leads to materials’continuously aging problem, accompany with the easy occurrence of cumulative damage forbridge structure, so as to result in the insufficient carrying capacity. Therefore, it is of greatsocial and economic value to guarantee the safety operation of the structure, promote thebridge service life and reduce the occurrence rate of collapse accidents when taking thedamage identification and condition assessment of bridge structure into account, and timelygrasping the bridge damage location and degree as well as evaluating the bridge safety anddurability conditions.
However, in the process of actual structural damage identification and conditionassessment, it is inevitably affected by some uncertainties, such as the external environment,the measure noise, subjective factors and so on. The existence of these uncertainties hindersthe practical application process of the existing damage identification and conditionassessment technologies so as to reduce the reliability of the identification and assessmentresults. Thus, how to consider and net out the effect of uncertainties in the calculationprocess has an important practical significance for promoting the engineering application ofthe damage identification and condition assessment technology.
Aiming at the uncertainties, such as parameter error, information missing, temperature,information missing of the reference model, as well as subjective factors and so on, thispaper puts forward the damage identification and state assessment techniques with strongrobustness, based on fuzzy nearness, fuzzy neural network, fuzzy logic, fuzzy clustering andsome other fuzzy calculation methods. The specific research work is shown as follows:
1. Aiming at the condition of parameter errors and information missing caused bynoise and incomplete test degree of freedom, this paper proposes fuzzy nearness-based method in damage identification of bridge structure by taking simply supported beam bridgeas the research object. This approach takes the improved vibrator ratio as damageidentification parameters with K-type parabolic and Bell-shaped function as membershipfunction of input and output parameters, respectively, so as to builds the damageidentification knowledge base by establishing a correspondence between structural damagestate and damage eigenvectors. The structural damage localization and damage stateidentification are realized by calculating the regular fuzzy approach degree between testsamples and knowledge base, according to approximate principle. By adding Gaussiandistribution random number into raw data to simulate noise and with missing node modedata simulating incomplete information condition, numerical simulation analysis ofmulti-girder simply supported beam bridge proves good effect in the damage identificationof single-location and multi-location under the condition of parameter errors andinformation missing. Slot beam with span1.5m is selected as the indoor test model toproves the practical application effect of FNBDI method.
2. Aiming at the abnormal changes of modal parameters caused by temperature change,this paper proposes a fuzzy neural network approach that can eliminate the temperatureeffects in the damage identification of bridge structure. This method simulates thetemperature effect with the changes of structural elastic modulus and based on the modalfrequencies and vibration data of the structure, the corresponding structure uniform loadsurface and its curvature value are calculated. The uniform load curvature differences beforeand after the structural damage are taken as the damage identification parameters. Besides,the if thenrule base is automatically generated through adaptive training. This paperregards the normalized temperature and the uniform load surface curvature as the inputparameters of fuzzy neural network, and the numerical simulation analysis of simplysupported beam bridge verifies the effectiveness of the method.
In order to better illustrate the effectiveness of the fuzzy neural network method, BPneural network is selected as the damage identification algorithm with frequency changesquare ratio and frequency change value regarded as the identification parameters of thedamage location and degree, respectively. By constructing vector similarity formula, this paper comparatively analyzes the identification accuracy between BP neural network andANFIS method. The result indicates that the similarity between the desired output and theactual output of testing samples with the ANFIS method is higher and the identificationresult is more accurate.
3. Considering that the baseline model data of existing bridge is not available or thesimulation error is larger, it will lead to the failure of the damage identification method. Thischapter proposes a bridge structural damage identification method, based on modalcurvature, the Chebyshev polynomial and fuzzy reasoning theory without consideringbaseline model information.
This method obtains the corresponding modal curvature valuesMSC dthroughsecond central differencing method on the basis of the node mode data of damage structure.According to this, we select theMSC dvalue of the feature node and get the modalcurvature valueMSC uwithout damage by Chebyshev polynomial fitting. By calculatingthe modal curvature difference MCD before and after the structural damage throughMSC dandMSC u, the structural damage location identification can be realized. Thedamage degree identification of bridge structure is realized by making the normalizedMCD as the input parameters of fuzzy reasoning system. The numerical simulationanalysis of simply supported beam bridge has verified the effectiveness of this method andthe results show that the calculated modal curvature difference of the single-location andmulti-location that is not dependent on the benchmark model data, is able to achieveaccurate damage positioning. Taking the normalized modal curvature difference of therelevant nodes as input parameters of fuzzy systems, we respectively construct fuzzyreasoning system of single-location and multi-location damage identification, so as toguarantee the damage identification results of the test samples are equipped with goodaccuracy. Selecting slot beam as indoor test model and taking the mid-span unit damageidentification for example, the effectiveness of the method proposed in this paper is verifiedby the measured first modal shape data.
4. Since state assessment methods of the existing bridge are easily influenced by subjective factors, this paper proposes a unsupervised bridge superstructure state assessmentmethod based on fuzzy clustering according to bridge field measured data. Firstly, thismethod builds the durability and safety evaluation index system of bridges based on fieldmeasured parameters. And then, considering or not considering the index weight effectseparately, we select a certain number of bridge health monitoring data as clusteringsamples to obtain the fuzzy similarity matrix and fuzzy equivalent matrix of samples bycalculating. Finally, we select a different threshold to form a dynamic clustering map anddetermine the best classification based on statistic analysis. The clustering result is regardedas a sample base of bridge safety and durability state assessment. Taking the average of thecorresponding indicators of the same type bridges as the approximate center of this category,this method can analyze and evaluate the bridge state for assessment on the basis ofselecting the near principle by calculating the fuzzy nearness between the unknown bridgestate data and the center’s. This paper selects the Saide bridge and the border bridge inNanping (maoshan) in Jilin Province as the physical works of the bridge safety anddurability assessment to verify the effectiveness of fuzzy clustering method referred above.
引文
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