An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography

Electrical resistance tomography (ERT) reconstructs the conductivity distribution from the boundary changes of electrical measurements. The inverse problem of ERT is seriously ill-posed where regularization methods are needed to treat this ill-posedness. A proper choice of regularization parameter which controls the degree of smoothing is very important for these regularization methods. Although have been a variety of methods, such as L-curve method, to choose a reasonable parameter for the problem, these methods usually result in a scalar parameter which cannot distinctly express the spatial characteristic of the conductivity distribution. So a spatially adaptive regularization parameter choice method is proposed for regularizing the inverse problem of ERT based on Tikhonov regularization. Since large regularization parameters can stabilize and smoothen the solution, while small regularization parameters can approximate and sharpen the solution, the proposed method adaptively updates the regularization parameters during the iteration process and provides spatially varying parameter for each pixel of the reconstructed image. When the iteration is stopped, large regularization parameters for the smooth background region and small regularization parameters for the object region can be obtained. The method is discussed using simulated data for some typical conductivity distributions, and further applied to the analysis of real measurement data acquiring from the practical system. The results demonstrate that flexible regularization parameter vectors can be achieved for different distributions and the strength of regularization is adaptively provided for different regions in a specific distribution. The adaptive method achieves an efficient and reliable regularization solution and has outstanding performance in noise immunity especially in smooth background regions.     

Adaptive Tikhonov regularization for damage detection based on nonlinear model updating

This paper presents an adaptive regularization approach for solving the nonlinear model updating inverse problem. The discrimination of possible damaged elements and undamaged elements is done from results obtained in previous iterations via a new side condition which aims at (a) to limit the local change in damaged structural elements in each iteration; and (b) to force the variation of other undamaged elements close to zero. A thirty-one bar plane truss structure with multiple damages is studied. Results obtained from the proposed method are greatly improved over those obtained from the traditional Tikhonov regularization even with large noise contamination in the measurements.     

The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms

This paper reports studies on the influence of the regularization parameter and the first estimate on the performance of iterative image restoration algorithms. We discuss regularization parameter estimation methods that have been developed for the linear Tikhonov–Miller filter to restore images distorted by additive Gaussian noise. We have performed experiments on synthetic data to show that these methods can be used to determine the regularization parameter of non-linear iterative image restoration algorithms, which we use to restore images contaminated by Poisson noise. We conclude that the generalized cross-validation method is an efficient method to determine a value of the regularization parameter close to the optimal value. We have also derived a method to estimate the regularization parameter of a Tikhonov regularized version of the Richardson–Lucy algorithm.   These iterative image restoration algorithms need a first estimate to start their iteration. An obvious and frequently used choice for the first estimate is the acquired image. However, the restoration algorithm could be sensitive to the noise present in this image, which may hamper the convergence of the algorithm. We have therefore compared various choices of first estimates and tested the convergence of various iterative restoration algorithms. We found that most algorithms converged for most choices, but that smoothed first estimates resulted in a faster convergence.     

特征融合和模型自适应更新相结合的相关滤波目标跟踪

提出了一种基于自适应特征融合和自适应模型更新的相关滤波跟踪算法(CFT)。该算法在跟踪的训练阶段利用损失函数计算特征的自适应权重,在检测阶段对不同特征的响应图进行加权求和,从而实现了响应图层面的自适应特征融合。设计了自适应的模型更新策略,采用响应图的峰值旁瓣比判断是否发生遮挡或错误跟踪,据此决定是否在当前帧更新目标模型。在11个视频序列上对所提算法进行了实验,验证了所采用的自适应特征融合策略和自适应模型更新策略的有效性。与多个传统的采用单特征的相关滤波跟踪算法进行了比较,结果显示,所提算法的跟踪精度和成功率典型值分别提升了18.2%和11.5%。实验结果验证了特征融合和自适应模型更新对跟踪算法的改进具有指导意义。     

Consistent regularization of nonlinear model updating for damage identification

Even though many innovative methods have been proposed more recently, traditional sensitivity-based methods are still widely used for model updating and damage identification. Most publications, however, seem to lack rigorous mathematical treatment of some important details. A first observation is that few authors recognize the issue as an inverse problem that needs regularization. Without regularization, inherent measurement errors can lead to completely unrealistic results. Most authors who do use regularization apply it intuitively but inconsistently. In this paper, the two best-known regularization schemes—Tikhonov regularization and truncated singular value decomposition—are applied consistently to the nonlinear updating problem. Line search and stopping criteria known from numerical optimization are adapted to the regularized problem. The optimal regularization parameter is determined by generalized cross-validation. Numerical simulations are used to demonstrate the effects of some commonly encountered inconsistencies and to prove the superior behavior of the proposed algorithm. This algorithm is then successfully applied to a laboratory model with experimental data. Good agreement with actual crack patterns is observed.     

基于矩阵逼近的模型修正方法的研究

提出一种新的以试验振动和参数辨识的数据为参数,进行有限元分析模型修正的方法。该方法基于矩阵最佳逼近理论,运用Ｂａｙｅｓ估计原理来处理试验结果误差带来的试验模态可信度问题,求取分析模对试验获得的不完备模态的谱点的最佳逼近结果,最后获得质量阵的最小修正模型。     

Data fusion of acceleration and angular velocity for improved model updating

In the traditional finite element (FE) model updating, translational responses, such as acceleration, have generally been employed to identify the structural properties. However, the boundary conditions of a structure are associated with both translational and rotational DOFs. Thus, the combinational measurement of translational and rotational responses (e.g., angular velocity) would increase accuracy of FE model updating of structures, especially in identifying their boundary conditions. This paper proposes data fusion of translational and rotational responses for improved system identification using FE model updating technique. In the proposed method, the accelerometers and gyroscopes are installed in between and near the supports of a structure, respectively, and FE model updating is carried out using the natural frequencies, the translational mode shapes obtained from accelerations, and the rotational mode shapes obtained from angular velocities. Numerical and experimental verifications are carried out on simply-supported beam structures. The verifications show that the proposed FE model updating strategy based on the data fusion results in more accurate assessment of both structural properties and boundary conditions than the traditional FE model updating using translational responses only.     

Comparative study of damped FE model updating methods

Most of finite element (FE) model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs) and complex mode shapes. In this paper, a detailed comparison of two approaches of obtaining damped FE model updating methods are evaluated with the objective that the FRFs obtained from damped updated FE models is able to predict the measured FRFs accurately. In the first method, damped updating FE model is obtained by complex parameter-based updating procedure, which is a single-step procedure. In the second method, damped updated model is obtained by the FE model updating with damping identification, which is a two-step procedure. In the first step, mass and stiffness matrices are updated and in the second step, damping matrix is identified using updated mass and stiffness matrices, which are obtained in the previous step. The effectiveness of both methods is evaluated by numerical examples as well as by actual experimental data. Firstly, a study is performed using a numerical simulation based on fixed–fixed beam structure with non-proportional viscous damping model. The numerical study is followed by a case involving actual measured data for the case of F-shaped test structure. The updated results have shown that the complex parameter-based FE model updating procedure gives better matching of complex FRFs with the experimental data.     

具有泵浦噪声之光动力学系统自适应控制

以控制具有泵浦噪声的布拉格声光系统为例,研究了利用光动力学系统自适应参考模型控制技术用于控制具有泵浦噪声之光动力学系统的可行性.研究发现,由于此自适应控制技术以受控光动力学系统与其无泵浦噪声参考模型之输出差值作为反馈宗量,进而对光动力学系统之控制参数进行调整,故该技术在泵浦噪声出现时仍可消除光动力学系统控制参数的确定性扰动,因而特别适合于需要光动力学系统之运转稳定在某一具体动力学状态及按预定顺序进行转换情形下的控制.     

Updating non-linear components

The objective of the present investigations was updating of finite element (FE) models with local non-linearities, such as Coulomb friction, gaps, local plasticity. Parameters of non-linear elements in the input file of a FE code are updated by fitting simulated time history functions and the corresponding measurement data. The problem of estimating the initial values as well as the problem of increasing error between simulated and measured time history functions have been overcome by using the method of 'modal state observers'. State observers are known in control theory but are a new approach for FE analysis.The presented methods use least square algorithms with analytically and numerically calculated sensitivity matrices for the updating process. A program for updating on principle any parameter of the input file of a standard FE code is described. The only requirement is, that the parameters should have a significant influence on the measured time history function. All of the presented methods have been validated against test results.     

正则化参数自适应选取的声学CT温度场重建

声学CT温度场重建为不适定逆问题。正则化参数的选取对重建精度有重要影响。提出一种正则化参数自适应选取的温度场重建算法——ARPSM(adaptive regularization parameter selection by minimum change criterion)算法。该算法采用一种新的、称为最小变化法的正则化参数选取法,自适应地选取正则化参数,兼顾温度场细节重建和噪声抑制。模型温度场和实验室内均匀温度场的重建结果表明,与常用的L曲线法相比,最小变化法确定的正则化参数对应着更小的温度场重建误差。ARPSM算法具有较高的重建精度和较强的噪声抑制能力,可望用于仓储粮食温度分布监测等对重建质量有较高要求的应用场合。     

基于正则化与遗忘因子的极限学习机及其在故障预测中的应用

为了解决在线贯序极限学习机(OS-ELM)算法容易产生奇异矩阵、算法贯序更新过程中没有考虑训练样本时效性的问题,提出基于l2-正则化和自适应遗忘因子的OS-ELM(RFOS-ELM)算法。RFOS-ELM在初始阶段加入正则化机制,克服因矩阵奇异而降低OS-ELM泛化能力的缺点。在贯序更新阶段,RFOS-ELM通过引入自适应遗忘因子实时调整新旧训练样本所占比重,推导正则化条件下带遗忘因子RFOS-ELM的递推更新算法,提高其对动态变化系统的跟踪能力。某型无人机机载发射机故障预测实例表明,相比于传统OS-ELM和正则化OS-ELM算法,本文提出方法具有更高的预测精度。     

边缘保持正则化低码率压缩图像后处理算法

从图像恢复的角度,提出以正则化方法完成后处理任务。分析了正则化方法的模型,并给出了边缘保持的正则化函数所应具有的特性。从复杂性、健壮性和对边缘细节粒度控制的能力三个方面选择了相应的势能函数,然后以半二次正则化将能量函数进行转换,使其快速达到最小化。最后给出了整个交替迭代后处理算法的描述。该方法对图像边缘细节具有自适应性,并能较快地取得最小值。实验结果显示,该算法能有效地提高低码率压缩图像的客观质量和视觉效果。     

Finite element model updating and structural damage identification using OMAX data

The main limitations in the finite element (FE) model updating technique lie in the ability of the FE model to represent the true behavior of the structure (modelling problem), and in the ability to identify enough modal parameters with sufficient accuracy, especially for large structures that are tested in operational conditions (identification problem). In this paper, the identification problem is solved with an OMAX approach, where an artificial force is used in operational conditions and a structural model is identified that takes both the forced and the ambient excitation into account. From an extensive case study on a real three-span bridge, it is observed that, while updating the FE model using the experimental output-only data yields a good fit, discrepancies show up when the more extensive set of OMAX data is used for validation, or even for updating. It can be concluded that an OMAX approach not only increases the well-posedness of the updating problem, it also allows to detect potential inaccuracies in the FE model.     

A hybrid regularization method combining Tikhonov with total variation for electrical resistance tomography

Electrical resistance tomography (ERT) is a promising measurement technique in industrial process imaging. However, image reconstruction in ERT is an ill-posed inverse problem. Regularization methods have been developed to solve the ill-posed inverse problem. Since the penalty term is a form of L2-norm, Tikhonov regularization method guarantees the stability of the solution, but it always makes the image edge oversmoothed. Total variation (TV) regularization method has good ability of preserving image edges. A hybrid regularization method, which combines Tikhonov with TV regularization method, is proposed to get better reconstructed images. The choice of the adaptive weighted parameter between TV and Tikhonov penalty term has been discussed in detail. In the proposed hybrid regularization method, the function of conductivity gradients is used as the adaptive weighted parameter to control automatically the weighting between the penalty terms from TV and Tikhonov regularization. For the model with sharp edges, the proportion of the penalty term from TV regularization is increased to preserve the edges, while for the model with smooth edges, the proportion of penalty term from Tikhonov regularization is increased to make the solution stable and robust to noise. Both simulation and experimental results of Tikhonov, TV and hybrid regularization method are shown respectively, which indicates that the hybrid regularization method can improve the reconstruction quality with sharp edges and is more robust to noise, and it is applicable for models with different edge characteristic.     

考虑模型偏差的结构动力学模型修正

针对结构有限元模型修正后仍可能存在模型偏差的问题,提出用待修正参数的不确定性来表征模型偏差的有限元模型修正方法。首先,基于响应面方法识别得到待修正参数的最优值,并通过计算结果与试验结果比较获得模型偏差;然后,基于响应面模型并结合灵敏度分析计算得到模型偏差对待修正参数的影响,从而得到考虑模型偏差后待修正参数的区间;最后,通过一个悬臂梁工程实例的模型修正,验证了笔者所提出方法的可行性。结果表明,考虑模型偏差的修正可以提高模型可靠性。     

建立斜拉桥基准有限元模型的新方法与实现

在进行斜拉桥监测与检测研究时,为了建立准确而可靠的基准有限元模型,使其索力、位移等趋于监测或检测结果,需进行模型修正工作,但各种模型修正方法多数需要进行迭代运算,不仅计算工作量巨大,而且有时难以实现预期目标。针对这一问题,提出了一种使用Ansys与Matlab软件,利用影响矩阵和优化算法相结合进行模型修正的新方法。该方法不需要迭代,可获得索力、位移等参数,且与实测值相吻合。通过实例对该方法进行了验证,证明了该方法可行并易于实现。     

A non-convex regularization method combined with Landweber method for image reconstruction in electrical resistance tomography

Electrical resistance tomography (ERT) is a promising technique with which the conductivity distribution in the detected region can be visualized. Mathematically, the reconstruction of conductivity distribution is a seriously ill-posed inverse problem which poses a great challenge for the ERT sensing technique. The regularization method has been found to be an effective approach in coping with the inverse problem. In this work, a novel reconstruction strategy which combines the non-convex regularization method with Landweber method is proposed for the image reconstruction in ERT. At each iteration, the non-convex regularization is used to constrain the conductivity calculated with the Landweber method. A simple and efficient generalized iterated shrinkage algorithm is developed to solve the proposed method. To validate the performance of the proposed method, a series of numerical simulation is conducted and comparative analysis with other methods is performed. From the results, it can be observed that images with high quality are obtained when reconstructing with the proposed method. The impact of noise on the reconstruction is also investigated which shows that the images reconstructed by the proposed method are the least sensitive to the noise. The performance of the proposed method in the image reconstruction is also verified by experimental data. The results demonstrate that the inclusion is accurately reconstructed and the background is clear when the proposed method is adopted for the image reconstruction.     

Finite element model updating based on eigenvalue and strain energy residuals using multiobjective optimisation technique

The numerical results from a finite element (FE) model often differ from the experimental results of real structures. FE model updating is often required to identify and correct the uncertain parameters of FE model and is usually posed as an optimisation problem. Setting up of an objective function, selecting updating parameters and using robust optimisation algorithm are three crucial steps in FE model updating. In this paper, a multiobjective optimisation technique is used to extremise two objective functions simultaneously which overcomes the difficulty of weighing the individual objective function of more objectives in conventional FE model updating procedure. Eigenfrequency residual and modal strain energy residual are used as two objective functions of the multiobjective optimisation. Only few updating parameters are selected on the basis of the prior knowledge of the dynamic behaviours of the structure and eigenfrequency sensitivity study. The proposed FE model updating procedure is first applied to the simulated simply supported beam. This case study shows that the methodology is robust with an effective detection of assumed damaged elements. The procedure is then successfully applied to the updating of a precast continuous box girder bridge that was tested on field under operational conditions.     

A novel strategy for response and force reconstruction under impact excitation

Force and response amplitude are vital to mechanical product life-time. However, these data are always difficult, even impossible, to measure directly. Therefore, we propose a reconstruction strategy based on the subspace identification (SI) algorithm and fast iterative shrinkage-thresholding (FIST) algorithm to reconstruct impact-force and response at desired location. For the reconstruction strategy, reconstruction equations are built by a state-space model, and SI algorithm is utilized to estimate coefficient matrices of the state-space model to form transfer matrices. And then, considering ill-condition of transfer matrix and sparsity of impact-force, FIST algorithm is employed to solve sparse regularization model by minimizing the l₁-norm. Numerical and experimental studies indicate that the proposed reconstruction strategy can be used to accurately reconstruct force and response under impact excitation, and compared with typical l₂-norm regularization methods, FIST algorithm is more efficient and accurate in both single-time impact and consecutive impact cases.