Substructural damage identification using autoregressive moving average with exogenous inputs model and sparse regularization

Substructural damage detection in shear structures via ARMAX model and optimal subpattern assignment distance

Structural damage identification is essentially an inverse problem. Ill-posedness is a common obstacle encountered in solving such an inverse problem, especially in the context of a sensitivity-based model updating for damage identification. Tikhonov regularization, also termed as ℓ2-norm regularization, is a common approach to handle the ill-posedness problem and yields an acceptable and smooth solution. Tikhonov regularization enjoys a more popular application as its explicit solution, computational efficiency, and convenience for implementation. However, as the ℓ2-norm term promotes smoothness, the solution is sometimes over smoothed, especially in the case that the sensor number is limited. On the other side, the solution of the inverse problem bears sparse properties because typically, only a small number of components of the structure are damaged in comparison with the whole structure. In this regard, this paper proposes an alternative way, sparse regularization, or specifically ℓ1-norm regularization, to handle the ill-posedness problem in response sensitivity-based damage identification. The motivation and implementation of sparse regularization are firstly introduced, and the differences with Tikhonov regularization are highlighted. Reweighting sparse regularization is adopted to enhance the sparsity in the solution. Simulation studies on a planar frame and a simply supported overhanging beam show that the sparse regularization exhibits certain superiority over Tikhonov regularization as less false-positive errors exist in damage identification results. The experimental result of the overhanging beam further demonstrates the effectiveness and superiorities of the sparse regularization in response sensitivity-based damage identification. Copyright © 2015 John Wiley & Sons, Ltd.

Recently, many structural damage detection (SDD) methods have been proposed to monitor the safety of structures. As an important modal parameter, mode shape has been widely used in SDD, and the difference of vectors was adopted based on sensitivity analysis and mode shapes in the existing studies. However, amplitudes of mode shapes in different measured points are relative values. Therefore, the difference of mode shapes will be influenced by their amplitudes, and the SDD results may be inaccurate. Focus on this deficiency, a multi-strategy SDD method is proposed based on the included angle of vectors and sparse regularization in this study. Firstly, inspired by modal assurance criterion (MAC), a relationship between mode shapes and changes in damage coefficients is established based on the included angle of vectors. Then, frequencies are introduced for multi-strategy SDD by a weighted coefficient. Meanwhile, sparse regularization is applied to improve the ill-posedness of the SDD problem. As a result, a novel convex optimization problem is proposed for effective SDD. To evaluate the effectiveness of the proposed method, numerical simulations in a planar truss and experimental studies in a six-story aluminum alloy frame in laboratory are conducted. The identified results indicate that the proposed method can effectively reduce the influence of noises, and it has good ability in locating structural damages and quantifying damage degrees.

Two-stage structural damage detection using fuzzy neural networks and data fusion techniques

The present work addresses the problem of structural damage identification built on the statistical inversion approach. Here, the damage state of the structure is continuously described by a cohesion parameter, which is spatially discretized by the finite element method. The inverse problem of damage identification is then posed as the determination of the posterior probability densities of the nodal cohesion parameters. The Markov Chain Monte Carlo method, implemented with the Metropolis–Hastings algorithm, is considered in order to approximate the posterior probabilities by drawing samples from the desired joint posterior probability density function. With this approach, prior information on the sought parameters can be used and the uncertainty concerning the known values of the material properties can be quantified in the estimation of the cohesion parameters. The assessment of the proposed approach has been performed by means of numerical simulations on a simply supported Euler–Bernoulli beam. The damage identification and assessment are performed considering time domain response data. Different damage scenarios and noise levels were addressed, demonstrating the feasibility of the proposed approach.

Chemical industries are characterized often by nonlinear processes. Therefore, it is often difficult to obtain nonlinear models that accurately describe a plant in all regimes. The main contribution of this work is to establish a reliable model of a process behavior. The use of this model should reflect the normal behavior of the process and allow distinguishing it from an abnormal one. Consequently, the black‐box identification based on the neural network (NN) approach by means of a nonlinear autoregressive with exogenous input (NARX) model has been chosen in this study. A comparison with an autoregressive with exogenous input (ARX) model based on the least squares criterion is carried out. This study also shows the choice and the performance of ARX and NARX models in the training and test phases. Statistical criteria are used for the validation of the experimental data of these approaches. The identified neural model is implemented by training a multilayer perceptron artificial neural network (MLP‐ANN) with input–output experimental data. An analysis of the inputs number, hidden neurons and their influence on the behavior of the neural predictor is carried out. In order to illustrate the proposed ideas, a reactor‐exchanger is used. Satisfactory agreement between identified and experimental data is found and results show that the neural model predicts the evolution of the process dynamics in a better way. Copyright © 2008 Curtin University of Technology and John Wiley & Sons, Ltd.

The neural control of the human cardiovascular system has been modeled using a NARMAX (non-linear autoregressive moving-average model with exogenous inputs) model, and compared with MA (moving-average) model and an ARMAX (autoregressive moving-average model with exogenous inputs) model. In these approaches, models are sought in the form of difference equations with unknown parameters to be estimated on the basis of input-output data. The input variable considered has been the carotid-sinus blood pressure and five output variables have been analyzed: heart rate control, peripheral resistance control, myocardial contractility control, venous tone control, and coronary resistance control. Results obtained show that NARMAX models present a better fit than the ARMAX models. >

A comparison between neural network and traditional approaches to nonlinear system identification is investigated with respect to aspects of model performance. Two neural network models, the state space and input-output model structures, are considered. A global recurrent RMLP and a teacher forcing RMLP are categorized as the state space models, and a global feedback FMLP and a teacher forcing FMLP are considered as the input-output models. In the traditional methods an AutoRegressive eXogeneous (ARX) Input model and a Nonlinear AutoRegressive eXogeneous (NARX) Input model are considered. Basic algorithms of models are described, and simulation results are also presented through the system output response. Performance of models is compared based on the Mean-Square-Errors (MSE). Noise-added sinusoidal, pulse and step signals are chosen as the test inputs for the validation of the obtained models. Two different noise levels are augmented to the chosen input signals.

Experimental investigation on use of regularization techniques and pre-post measurement changes for structural damage identification

A novel damage identification procedure is presented that is ideally suited for long-term structural health monitoring of large civil structures. The procedure is based on the redistribution of dead load stress that occurs in a structure when damage takes place. The damaged structure is modeled using finite elements, in which the damage is represented by a section of reduced flexural rigidity. Forward analyses are first presented to show how the dead load is redistributed for different damage scenarios. The inverse damage identification problem is set up as a constrained optimization problem and solved using a real coded genetic algorithm. The proposed method correctly identified damage for a wide range of locations and damage severities. Results show that damage is difficult to identify when it is close to the inflection points of the structure, where the dead load strain is zero, and when the damage is not located between two sensors. The effect of measurement error is investigated.

In order to meet the fine demand of different travelers, a multi-dimensional prediction method of travel time is proposed combining the toll collection data and meteorological data of highway. First, a logical model of multi-dimensional database is designed including vehicles’ dimension, meteorological dimension, and time dimension. Second, aiming at integration of the toll collection data and meteorological data, a matching method is presented within the space and time scale. Then, the multi-dimensional database is constructed. Next, an autoregressive moving average with exogenous input model is constructed using the travel time series and traffic flow series. The maximum likelihood estimation method is used to solve the parameters of the autoregressive moving average with exogenous input model. Considering the complexity and solving difficulty of the maximum likelihood equation, the particle swarm optimization algorithm is used to optimize the solution process. Finally, the toll collection data of two road links on Shenyang–Haikou expressway (G15) and the corresponding meteorological monitoring data are used to validate the algorithm. The results show that the prediction accuracy of the particle swarm optimization–autoregressive moving average with exogenous input model under normal and special conditions can be accepted and the absolute percentage error of road section between two neighboring toll stations is reduced by almost 5% after optimization.

The problem of structural damage identification based on vibration measurements (eigenfrequencies and incomplete mode shapes) is generally formulated as an inverse problem aiming to identify changes encountered on the global stiffness matrix. In most cases, the measured quantities are less than the damage parameters to be identified; thus, an infinite number of possible damage configurations are expected to satisfy the measurements. Therefore, damage identification problems are often proven to be ill-conditioned. The problem becomes more complex when measurements' noise and model uncertainties are considered. Therefore, depending on the structural system, damage scenario and available vibration measurements, additional eigenmode data may need to be considered in order to increase the robustness of the damage identification procedure. In this work, a new two-loop trajectory method is presented, that relies on an iterative nonlinear sensitivity analysis procedure. The main advantage of the proposed method is its ability to identify damage scenarios that match the measured data with high accuracy as well as to explore effectively the solution space. This feature can be exploited in order to assess the adequacy of the measurements in noisy and/or uncertain environment. Copyright © 2016 John Wiley & Sons, Ltd.

The representation of structural dynamics in the absence of physics-based models, is often accomplished through the identification of parametric models, such as the autoregressive with exogenous inputs, e.g. ARX models. When the structure is amenable to environmental variations, parameter-varying extensions of the original ARX model can be implemented, allowing for tracking of the operational variability. Yet, the latter occurs in sufficiently longer time-scales (days, weeks, months), as compared to system dynamics. For inferring a “global”, long time-scale varying ARX model, data from a full operational cycle has to typically become available. In addition, when the sensor network comprises multiple nodes, the identification of long time-scale varying, vector ARX models grow in complexity. We address these issues by proposing a distributed framework for structural identification, damage detection and localization. Its main features are: (i) the individual estimation of local, single-input-single-output ARX models at every operational point; (ii) the long time-scale representation of each individual ARX coefficient via a Gaussian process regression, which captures dependency on varying Environmental and Operational Conditions (EOCs); (iii) the establishment of a distributed residual generation algorithm for damage detection, which produces time-series of well-defined stationary statistics, with detected discrepancies used for damage diagnosis; and, (iv) exploitation of ARX-inferred mode shape curvatures, obtained via ARX-inferred global state-space models, of the healthy and damaged states, for damage localization. The method is assessed via application on two numerical case studies of different complexity, with the results confirming its efficacy for diagnostics under varying EOCs.

Structural nonlinear damage identification based on Bayesian optimization GNAR/GARCH model and its experimental study

Vibration-based damage detection and localization are often performed aiming to relate modal analysis’ results with appropriate metrics that express structural damages. The problem of structural damage identification is generally formulated as an inverse problem aiming to detect changes encountered on the global stiffness matrix of the structure’s model. In most cases, the measured quantities are less than the damage parameters to be identified, thus an infinite number of possible damage configurations is expected to satisfy the measurements. Therefore, damage identification problems are often proven to be ill-conditioned. In addition, as in situ measurements are interpreted by a computer model, a number of uncertainties play an important role in the success of the identification procedure. The class of uncertainties consist of model, discretization, material and measurement errors. Furthermore, a large number of parameters need to be identified in order to assess arbitrary damage scenario and time consuming structure monitoring need to be implemented. In the majority of the developed methods the tendency is to use measurements from sensors while the vibrations are caused either by random (e.g. wind, earthquake etc.) causes or from force actuators in one or more points of the structure. In this work the implementation of actuator connections that divide a structure in several substructures is proposed. These connections can be installed on the structure during construction or retrofit. As it will be demonstrated, these connections can be controlled and excite each substructure separately and record its fundamental frequencies. In this way, each substructure can be monitored in arbitrary time while the complexity and often ill-conditioning of damage localization for large structures can be drastically reduced.