This paper proposes a new methodology for moving force identification (MFI) from the responses of bridge deck. Based on the existing time domain method (TDM), the MFI problem eventually becomes ...solving the linear algebraic equation in the form Ax=b. The vector b is usually contaminated by an unknown error e generating from measurement error, which often called the vector e as ‘‘noise’’. With the ill-posed problems that exist in the inverse problem, the identification force would be sensitive to the noise e. The proposed truncated generalized singular value decomposition method (TGSVD) aims at obtaining an acceptable solution and making the noise to be less sensitive to perturbations with the ill-posed problems. The illustrated results show that the TGSVD has many advantages such as higher precision, better adaptability and noise immunity compared with TDM. In addition, choosing a proper regularization matrix L and a truncation parameter k are very useful to improve the identification accuracy and to solve ill-posed problems when it is used to identify the moving force on bridge.
•A truncated generalized singular value decomposition method is proposed for identifying force.•The regularization matrix L is introduced which can improve solving the ill-posed problems.•The truncation parameter k is introduced which can avoid noise disturbance and ensure robustness.•The proposed method has high precision, good adaptability and immunity of ill-posed problems.
Suspension bridges are flexible and vibration sensitive structures that exhibit complex and multi-modal vibration. Due to this, the usual vibration based methods could face a challenge when used for ...damage detection in these structures. This paper develops and applies a mode shape component specific damage index (DI) to detect and locate damage in a suspension bridge with pre-tensioned cables. This is important as suspension bridges are large structures and damage in them during their long service lives could easily go un-noticed. The capability of the proposed vibration based DI is demonstrated through its application to detect and locate single and multiple damages with varied locations and severity in the cables of the suspension bridge. The outcome of this research will enhance the safety and performance of these bridges which play an important role in the transport network.
•Damage detection in a suspension bridge is treated using vibration Characteristics.•Component specific damage indices (DIs) are developed and applied to detect damage•Vertical damage index can detect and locate damage in the suspension bridge cables•This damage index DIV performs well even in the presence of noise in modal data.•The dominant vibration mode being in the vertical direction DIV performs better
•The proposed method does not require eigenvalue analysis and optimization process.•The method can identify light damage with good accuracy with noise polluted data.•PCA is done for subsets ...separately hence main features are extracted precisely.•It is noted that method is able to detect multiple faults.•Networks trained with summation FRFs were better than the individual networks.
Pattern recognition is a promising approach for the identification of structural damage using measured dynamic data. Much of the research on pattern recognition has employed artificial neural networks (ANNs) and genetic algorithms as systematic ways of matching pattern features. The selection of a damage-sensitive and noise-insensitive pattern feature is important for all structural damage identification methods. Accordingly, a neural networks-based damage detection method using frequency response function (FRF) data is presented in this paper. This method can effectively consider uncertainties of measured data from which training patterns are generated.
The proposed method reduces the dimension of the initial FRF data and transforms it into new damage indices and employs an ANN method for the actual damage localization and quantification using recognized damage patterns from the algorithm. In civil engineering applications, the measurement of dynamic response under field conditions always contains noise components from environmental factors. In order to evaluate the performance of the proposed strategy with noise polluted data, noise contaminated measurements are also introduced to the proposed algorithm. ANNs with optimal architecture give minimum training and testing errors and provide precise damage detection results. In order to maximize damage detection results, the optimal architecture of ANN is identified by defining the number of hidden layers and the number of neurons per hidden layer by a trial and error method. In real testing, the number of measurement points and the measurement locations to obtain the structure response are critical for damage detection. Therefore, optimal sensor placement to improve damage identification is also investigated herein.
A finite element model of a two storey framed structure is used to train the neural network. It shows accurate performance and gives low error with simulated and noise-contaminated data for single and multiple damage cases. As a result, the proposed method can be used for structural health monitoring and damage detection, particularly for cases where the measurement data is very large. Furthermore, it is suggested that an optimal ANN architecture can detect damage occurrence with good accuracy and can provide damage quantification with reasonable accuracy under varying levels of damage.
Four new methods have been developed to overcome the ill-posed problems inherently existing in moving force identification (MFI) in previous studies. This paper is an extension of the work to ...evaluate the overall performance of these presented methods by numerical simulations and experiment verifications in laboratory. A simply-supported bridge and two types of moving forces are adopted to evaluate the identification accuracy and ill-posed immunity of these new approaches. Bending moment and acceleration responses are measured when the time-varying forces moving across the bridge deck at constant speed. Numerical simulations of both uniaxial and biaxial forces include 12 cases, which are used to compare the identification accuracy and ill-posed immunity of these methods in detail. Finally, a hinge supported steel beam model and a vehicle model were designed and fabricated in laboratory. Then a series of experimental studies on MFI with these four methods are performed in laboratory. Both numerical and experimental results show that these four approaches can accurately identify moving forces with strong robustness and ill-posed immunity. Moreover, the truncated generalized singular value decomposition (TGSVD) method has higher identification accuracy than the piecewise polynomial truncated singular value decomposition (PP-TSVD) method, and the modified preconditioned conjugate gradient (M-PCG) method has higher identification efficiency than the preconditioned least square QR-factorization (PLSQR) method. To summarize, if the first goal in MFI is to improve the identification accuracy, the TGSVD method is recommended due to its high identification accuracy and stability in different cases. If the first goal in MFI is to improve the identification efficiency, the M-PCG method is recommended due to its high identification efficiency and easy to determine the optimal number of iterations.
•Comparative studies have been carried out to evaluate the proposed four methods.•A guideline on selecting the best method for practical MFI has been provided.•Studies show that the PP-TSVD method is the worst among these four methods.•The TGSVD method is recommended for improving the identification accuracy.•The M-PCG method is recommended for improving the identification efficiency.
•Introducing a standard process of building a machine learning based settlement prediction model.•Hybrid meta-heuristic and machine learning algorithms is proposed.•Gini importance index is employed ...to investigate the importance of input parameters.
Machine learning (ML) algorithms have been gradually used in predicting tunneling-induced settlement, but there is no uniform process for establishing ML models and even obviously exists deficiency in the existing settlement prediction ML models. This study systematically demonstrates the process of application of machine learning (ML) algorithms in predicting tunneling-induced settlement. The whole process can be categorized into four phases: the selection of ML algorithms, the determination of optimum-hyper-parameters, the improvement in model robustness and sensitivity analysis. The prediction performance of five commonly used ML algorithms back-propagation (BPNN), general regression neural network (GRNN), extreme learning machine (ELM), support vector machine (SVM) and random forest (RF) was comprehensively compared. The results indicate that proposed hybrid intelligent algorithm with the integration of the meta-heuristic algorithm particle swarm optimization (PSO) and ML can effectively determine the global optimum hyper-parameters of ML algorithms. The mean prediction error of k-fold cross-validation sets defined as the fitness function of the PSO algorithm can improve the robustness of ML models. RF algorithm outperforms the remaining four ML algorithms in recognizing the evolution of tunneling-induced settlement. BPNN shows great extrapolation capability, so it is recommended to establish settlement prediction model if the existing datasets are small. Sensitivity analysis indicates the geological and geometric parameters are the most influential variables for the settlement.
•A preconditioned least square QR-factorization approach is developed for moving force identification.•The regularization matrix L is introduced to improve the ill-posed problems.•The number of ...iterations j is introduced to avoid noise disturbance and ensure the robustness.•Preconditioned least square QR-factorization approach is validated through numerical simulation.
This paper develops a novel method for moving force identification (MFI) called preconditioned least square QR-factorization (PLSQR) method. The algorithm seeks to reduce the impact of identification errors caused by unknown noise. The biaxial moving forces travel on a simply supported bridge at three different speeds is used to generate numerical simulations to assess the effectiveness and applicability of the algorithm. Results indicate that the method is more robust towards ill-posed problem and has higher identification precision than the conventional time domain method (TDM). In addition, the robustness and ill-posed immunity of PLSQR are directly affected by two kinds of regularization parameters, namely, number of iterations j and regularization matrix L. Compared with the standard form of least square QR-factorization (LSQR), i.e., the regularization matrix L being the identity matrix In, the PLSQR with the optimal number of iterations j and regularization matrix L has many advantages on MFI and it is more suitable for field trials due to better adaptability with type of sensors and number of sensors.
This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient ...(PCG) methods with a modified Gram-Schmidt algorithm. The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem. A simply supported beam model with biaxial time-varying forces is used to generate numerical simulations with various analysis scenarios to assess the effectiveness of the method. Evaluation results show that regularization matrix L and number of iterations j are very important influence factors to identification accuracy and noise immunity of M-PCG. Compared with the conventional counterpart SVD embedded in the time domain method (TDM) and the standard form of CG, the M-PCG with proper regularization matrix has many advantages such as better adaptability and more robust to ill-posed problems. More importantly, it is shown that the average optimal numbers of iterations of M-PCG can be reduced by more than 70% compared with PCG and this apparently makes M-PCG a preferred choice for field MFI applications.
•A modified preconditioned conjugate gradient (M-PCG) approach is developed for moving force identification.•The qualitative and quantitative selection rules about parameters that affect the accuracy of the M-PCG are proposed.•Compared with PCG, the computation efficiency of M-PCG is shown to be superior by introducing the modified Gram-Schmidt.•Advantages of M-PCG include higher precision, better adaptability and superior efficiency in solving the ill-posed problems.
•A preconditioned range restricted GMRES algorithm is developed for MFI.•It has significant advantages in both of the identification efficiency and accuracy.•The accuracy of the new method is very ...high in highly inaccurate measurement cases.•The new method is verified by numerical simulations and experimental studies.
Moving force identification (MFI) is a widely concerned inverse problem in structural dynamics and well-known as intrinsically existing ill-posedness. With the help of Arnoldi process and Krylov subspace method, the generalized minimal residual (GMRES) method can be improved to a range restricted generalized minimal residual (RRGMRES) method. Furthermore, by introducing the smoothing-norm preconditioning, a preconditioned range restricted generalized minimal residual (PRRGMRES) method is proposed to provide a stable solution to the ill-posed dynamic force identification problem. Simulations show that the novel method has significant improvement when compared to the classic time domain method and the RRGMRES method. In addition, to show the effectiveness and advantages of the proposed method, the PRRGMRES method is also compared with a newly-proposed regularization method named the preconditioned least square QR-factorization (PLSQR) method. Simulation results show that the PRRGMRES method has much better robustness and higher computational efficiency than the PLSQR method especially in dealing with highly inaccurate measurement cases. Finally, the accuracy and efficiency of the PRRGMRES method is verified by experimental studies. The PRRGMRES method has good performance in both overcoming ill-posed problems and improving computational efficiency, which should be of the highest priority in adoption for MFI.
•A method is proposed to indirectly measure displacements under dominant design loads by exerting several simple testing loads.•Proper testing loads can be quickly found and have far less loading ...points than design loads.•Proposed indirect method is more robust to resist measurement noise than traditional direct method.•Reason why proposed indirect method has better robustness is explained.
Structural stiffness of a real tension structure may degrade due to many factors, so the stiffness monitoring is very important. If the displacements under the dominant design loads are obtained, the stiffness state of the real structure can be intuitively assessed by a deformation checking process. However, exerting design loads on a real structure is neither efficient nor economical, because they usually have too many loading points. A method is hence proposed to indirectly measure the displacements under the design loads by merely exerting several simple testing loads. By utilizing the linear combination of several contributing eigenvectors to express the displacements, the problem of measuring displacements is transformed to that of measuring combinational coefficients of these contributing eigenvectors. The relationship between the combinational coefficients of the mutual contributing eigenvector of the design load and the testing load is set up firstly, with two basic conditions established. To satisfy the basic conditions, a strategy to decompose the design load and an algorithm to find proper testing loads are suggested. The numerical example of a cable net with two typical design loads is finally analyzed. Results illustrate that the proposed indirect method is effective, with three simple testing loads (no more than 3 loading points) found to replace the two design loads (181 loading points) in the on-site static testing. Besides, the proposed indirect method is more robust to resist the influence of measurement noise than the traditional direct method. The reason why the proposed indirect method has better robustness is also discussed.
Swarm intelligence algorithms and finite element model update technology are important issues in the field of structural damage detection. However, the complexity of engineering structural models ...normally leads to low computational efficiency and large detection errors in structural damage detection. To solve these problems, a simulated annealing-artificial hummingbird algorithm (SA-AHA) is proposed based on the artificial hummingbird algorithm (AHA). The Sobol sequence is used to improve the identification efficiency by optimizing the initial population distribution of the AHA. Then, the simulated annealing strategy is introduced to improve the detection accuracy by enhancing the global search ability of the AHA. In addition, a novel objective function is presented by combining modal flexibility residual, natural frequency residual, and trace sparse constraint of the structural model. Numerical simulations of a simply supported beam and a two-story rigid frame are carried out to verify the superiority of the proposed SA-AHA and the objective function. Simulation results demonstrate that the SA-AHA is better than the AHA in terms of damage computational efficiency and damage identification accuracy. Moreover, the new objective function can be more excellently applied to the SA-AHA than the previous one, which can be effectively used to locate and estimate the damage of the proposed SA-AHA in structure. Finally, experimental studies are carried out to verify the proposed method.
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