Structural Identification and Damage Detection from Noisy Modal Data

In this paper we present a simple, yet powerful, method for the identification of stiffness matrices of structural and mechanical systems from information about some of their measured natural frequencies and corresponding mode shapes of vibration. The method is computationally efficient and is shown to perform remarkably well in the presence of measurement errors in the mode shapes of vibration. It is applied to the identification of the stiffness distribution along the height of a simple vibrating structure. An example illustrating the method’s ability to detect structural damage that could be highly localized in a building structure is also given. The efficiency and accuracy with which the method yields estimates of the system’s stiffness from noisy modal measurement data makes it useful for rapid, on-line damage detection of structures.     

System Identification through Model Composition and Stochastic Search

System identification methodologies are useful for identifying characteristics of structural systems using measurement data. However, incorrect systems might be identified when many combinations of system characteristics result in the same predicted responses at measured locations. The reliability of identification is affected by a number of factors that most previous work has overlooked. This paper presents a system identification methodology that explicitly treats factors that affect the success of identification. Rather than simply determining parametric values, this methodology also involves identification of model characteristics including boundary conditions. Due to inevitable modeling errors, models that provide absolute minimum differences between predictions and measurements are rarely correct models. In such situations, the challenge is to define a population of candidate models that result in such differences being below threshold values that are determined by the magnitude of modeling errors. The methodology is illustrated using a case study in civil engineering. This work contributes to providing engineers with general strategies to meet interpretation challenges associated with sensor data.     

Modal Perturbation Method and its Applications in Structural Systems

A new perturbation method is developed to solve any eigenvalue equation of the form (A0+ΔA)X? = (B0+ΔB)X?Λ? based on the solution of an original system described by A0X = B0XΛ. The eigenvectors of the modified system are expanded in a subspace spanned with a small number of vibration modes of the original system. In doing so, the former eigenvalue equation of the modified system is transformed into a set of algebraic equations, which require a significantly less computational effort to solve for the eigensolutions of complex structural systems. Four numerical examples show that the developed technique gives rise to the eigensolution of high accuracy and it is an effective approach for dynamic reanalysis of the structures with numerous degrees of freedom. In comparison with the conventional small parameter perturbation, the developed technique is applicable to a wider range of problems, and only m mode shapes are used based on the Ritz expansion so that the final solution can be derived efficiently. The technique also extends laboratory model tests for complex structures with the concept of dynamic hybrid tests numerically and experimentally.     

Model Correction via Compatible Element Method

The theoretical derivation proposed in this paper uses a specific pseudoinverse technique baesd on an incomplete set of measured modes to satisfy the orthogonality condition. Unlike others, this method demonstrates that the updated model derived from the special pseudoinverse technique does exist in the complete modal space and satisfy the eigenequation. There are three basic, compatible, model characteristics in the updated model: (1) Both low‐order and high‐order modes of the updated model correspond to the measured modes and the analytical high‐order modes of the original finite element model, respectively; (2) the distortion (such as negative eigenvalues) of eigenpairs obtained from the modified model can be eliminated by controlling the high‐order modes of the updated model; and (3) the updated matrices retain the properties of the original finite element matrices, including the banded‐state matrix using the element approach. The derivation of modification formulas in this paper is only based on the orthogonality conditions; therefore, the formulas are much simpler than other procedures.     

OCR Prediction Using Support Vector Machine Based on Piezocone Data

The determination of the overconsolidation ratio (OCR) of clay deposits is an important task in geotechnical engineering practice. This paper examines the potential of a support vector machine (SVM) for predicting the OCR of clays from piezocone penetration test data. SVM is a statistical learning theory based on a structural risk minimization principle that minimizes both error and weight terms. The five input variables used for the SVM model for prediction of OCR are the corrected cone resistance (qt), vertical total stress (σv), hydrostatic pore pressure (u0), pore pressure at the cone tip (u1), and the pore pressure just above the cone base (u2). Sensitivity analysis has been performed to investigate the relative importance of each of the input parameters. From the sensitivity analysis, it is clear that qt=primary in situ data influenced by OCR followed by σv, u0, u2, and u1. Comparison between SVM and some of the traditional interpretation methods is also presented. The results of this study have shown that the SVM approach has the potential to be a practical tool for determination of OCR.     

Modal Identification Algorithm with Unmeasured Input

This paper investigates the possibility of generating a time‐domain modal identification algorithm that does not need measurements of the input signals. Such a technique is useful when complete input data acquisition cannot be performed. The approach is based on the Yule‐Walker equations, extended to the case where the input signal is not white noise. The algorithm is written recursively both to minimize data acquisition and to be flexible enough when time‐varying modal parameters are tracked. Natural frequencies and damping ratios are extracted with an error magnitude inferior to impulse response techniques but superior to methods using the input time history. From a computational aspect, the algorithm only introduces scalar inversions, which presents an important gain of time and stability. Examples and comparisons with other techniques are presented. The case where a change in the modal parameter values occur is also highlighted. A normalized error, taking into account the quality and the swiftness of the new estimation, is introduced.     

Revised Multilinear Regression Equations for Prediction of Lateral Spread Displacement

In 1992 and 1995, Bartlett and Youd introduced empirical equations for the prediction of lateral spread displacement; these equations have gained wide use in engineering practice. The equations were developed from the multilinear regression (MLR) of a large case history database. This study corrects and updates the original analysis. Corrections and modifications include: (1) Bartlett and Youd erroneously overestimated measured displacements for lateral spreads generated by the 1983 Nihonkai-Chubu, Japan earthquake; those errors are corrected herein. (2) Several sites were deleted where boundary shear impeded free lateral displacement. (3) Data were added from three additional earthquakes. (4) The functional form of the mean-grain-size term was modified from (D5015) to log(D5015+0.1?mm) to produce improved prediction of displacements for coarse-grained granular sites. (5) The functional form of the model was changed from log(R) to log(R?), where R? is a function of the magnitude of the earthquake, to prevent unrealistic overprediction of displacements when R becomes small. The revised data were re-regressed to generate new MLR equations. The new equations are recommended for engineering practice.     

Sensitivity of Shallow Foundation Response to Model Input Parameters

From a predictive point of view, it is desirable to characterize the effect of varying model input parameters on the seismic response of soil-foundation systems. In this paper, this issue is studied for shallow foundation systems in dry dense sand with varying vertical factors of safety, embedment depths, demand levels, and moment to shear ratios. Response parameters considered are the moment, shear, sliding, settlement, and rotation demands of the foundation. First-order sensitivity analyses indicate that among the soil input parameters, the friction angle has the most significant effect on capturing the foundation force and displacement demands. Furthermore, the uncertainty in friction angle contributes 80% of the variance of the settlement demand and 40% of the variance of the moment demand. It is also found that the uncertainty in Poisson’s ratio has a marginal effect in predicting the studied foundation response. Although the findings of this study are limited to the parameter space considered herein and care should be taken for broader applicability, it does shed light on which parameters uncertainty should be minimized.     

Laboratory Rainfall-Induced Slope Failure with Moisture Content Measurement

The development of a physically based warning system for rainfall-induced slope failures requires a comprehensive understanding of the failure process. A set of laboratory-scale soil slopes was subjected to instability, through three different modes of raising water level, to clarify the process of failure initiation. Hydrologic responses of the model slopes to the saturation process were recorded by volumetric soil moisture content sensors. The results of model tests show that failures of the model slopes were essentially initiated by the development of an unstable area near the slope toe, upon the formation of the seepage area, with shallow noncircular sliding being the dominant failure mode. The volumetric moisture content of the slope region where localized failures initiated was noted to reach a nearly saturated value. However, the major portion of soil slopes involved in overall instability was still in an unsaturated condition. Based on the observed moisture content response of the model slopes, a concept for prediction methodology of rainfall-induced slope failures is introduced.     

Generalization of ETo ANN Models through Data Supplanting

This paper describes the application of artificial neural networks (ANNs) for estimating reference evapotranspiration (ETo) as a function of local maximum and minimum air temperatures as well as exogenous relative humidity and reference evapotranspiration in different continental contexts of the autonomous Valencia region, on the Spanish Mediterranean coast. The development of new and more precise models for ETo prediction from minimum climatic data is required, since the application of existing methods that provide acceptable results is limited to those places where large amounts of reliable climatic data are available. The Penman-Monteith model for ETo prediction, proposed by the FAO as the sole standard method for ETo estimation, was used to provide the ANN targets for the training and testing processes. Concerning models which demand scant climatic inputs, the proposed model provides performances with lower associated errors than the currently existing temperature-based models, which only consider local data.     

Method for Measurement of Canopy Interception under Sprinkler Irrigation

A procedure called water wiping is developed to measure the amount of water intercepted by the canopy of winter wheat under sprinkler irrigation. Macromolecule bibulous materials with high water absorption is used to collect sprinkler water intercepted by winter wheat canopy by wiping water from leaves, sheathes, heads, and stems. A procedure is developed for application and verified using field experiments. The results show that this method is rational and applicable. This method could be used to measure canopy interception of other crops with small leaves and short heights.     

Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes

Previously a Bayesian theory for modal identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the modal identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to modal identification of two field buildings. Using the proposed algorithm, Bayesian modal identification can now be performed in a few seconds even for a moderate to large number of measurement channels.     

Substructural Identification Method without Interface Measurement

Substructural identification provides a novel means by which to reduce a large problem to smaller problems of manageable size, thereby improving numerical convergence and accuracy. Various methods proposed by several researchers thus far require interface response measurements, which are then treated as input to the substructures of concern. In practice, however, it is not always possible to obtain interface measurements, particularly if rotational response is required for beam/frame structures. In this paper, a method for parameter identification of substructures without the need of interface measurements is proposed. On the basis of receptance theory, an inverse problem is formulated in the frequency domain. Interface forces are eliminated by using different sets of measurements in the substructure concerned under the same dynamic excitation. The genetic algorithms approach is employed to determine the unknown parameters, and the fitness function is defined to minimize the difference between the estimates of interface forces obtained using different sets of response measurements. Three numerical examples are presented to illustrate the proposed method, and account for effects of measurement noise.     

Reasoning Mechanism for Construction Nonconformance Root-Cause Analysis

This paper describes how problem patterns can be identified and analyzed for diagnosing and/or predicting nonconformance of constructed facilities. This will enable appropriate actions to be taken for eradicating the causes of nonconformance and preventing their recurrence and/or their occurrence. A structure has been defined for representing construction projects information and organizing knowledge extracted from past experience to facilitate the analyses. Pattern analyses have been directed at deriving root cause classes of problems including (1) design, which relates to the assigned specifications, methods, and/or procedures; (2) execution, which involves errors or the inability to execute tasks; and (3) external, which includes unforeseen events or accidents. Highway pavement construction has been selected as an application and illustrative domain. Expert knowledge related to low density and roughness of constructed pavements has been assembled and organized to support the analyses. The approach provides a generic mechanism to carry out integrated root cause analyses with design/planning, construction, and quality management information. Its application has been demonstrated and validated using case studies from different construction domains.     

Soft Bedrock Erosion Modeling with a Two-Dimensional Depth-Averaged Model

Many rivers in Taiwan have steep slopes, are subject to typhoon-induced flood flows, and contain soft bedrock that is exposed at many locations and easily erodible. The occurrence of extensive bedrock erosion has been a major threat to river infrastructure at many locations. Soft bedrock erosion, therefore, is an important process to consider for river projects in Taiwan. In this study, bedrock erosion models are reviewed. A specific model is proposed by combining two existing models incorporating both the hydraulic and abrasive scour mechanisms. The proposed bedrock erosion model is incorporated into a two-dimensional mobile-bed model, and the integrated model is tested by simulating bedrock erosion downstream of the Chi-Chi weir on the Choshui River in Taiwan. A calibration study is performed to determine appropriate values of the model parameters based on two and a half years of measured data. The model is then assessed based on a verification study that compares model predictions of bedrock erosion of the same reach to two additional years of measured data. The bedrock erosion model is found to be suitable for the river reach studied. Further improvement, however, is still necessary, which points to potential future research.     

Model Selection Using Response Measurements: Bayesian Probabilistic Approach

A Bayesian probabilistic approach is presented for selecting the most plausible class of models for a structural or mechanical system within some specified set of model classes, based on system response data. The crux of the approach is to rank the classes of models based on their probabilities conditional on the response data which can be calculated based on Bayes’ theorem and an asymptotic expansion for the evidence for each model class. The approach provides a quantitative expression of a principle of model parsimony or of Ockham’s razor which in this context can be stated as “simpler models are to be preferred over unnecessarily complicated ones.” Examples are presented to illustrate the method using a single-degree-of-freedom bilinear hysteretic system, a linear two-story frame, and a ten-story shear building, all of which are subjected to seismic excitation.     

Prediction/Verification of Particle Motion in One Dimension with the Discrete-Element Method

Although the availability of discrete-element method (DEM) codes has improved, the need still exists to solve simple verification problems to obtain an understanding of these codes. Different DEM codes may have subtle differences in the manner in which the method is implemented, and the significance of these differences may be problem dependent. This paper investigates a series of simple, one and two-particle contact problems. These problems, which employ various types of damping, are shown to be equivalent to classical one-dimensional vibration problems. The solutions are discussed in the context of the DEM, and results from the DEM are shown to compare very well with the classical solutions. It is demonstrated that results from a well-known commercial two-dimensional code (PFC2D) and the open source three-dimensional code (YADE) yield identical solutions to these problems provided the problem solution process is manipulated properly. A discussion of the differences in how gravity and damping are implemented may be of interest to users of PFC2D.     

Study of Time-Domain Techniques for Modal Parameter Identification of a Long Suspension Bridge with Dense Sensor Arrays

While numerous studies have been published concerning the application of a variety of system identification techniques in conjunction with vibration measurements from civil infrastructure systems, there is a paucity of publications addressing the influence of algorithm-specific control parameters that impact the correct and efficient application of the selected identification scheme. Furthermore, as dense sensor arrays become widely accessible in civil infrastructure applications, voluminous amounts of multichannel data streams are becoming available for processing, thus imposing new demands on identification procedures regarding high-dimensionality (in both the spatial as well as the temporal domains) requirements that may render some methods inapplicable if careful attention is not paid to practical implementation issues. This paper provides a comprehensive study of three time-domain identification algorithms applied in conjunction with the Natural Excitation Technique in order to extract the modal parameters of a newly constructed long-span bridge that was monitored, in its virgin state, over a relatively long period of time with a state-of-the-art dense sensor array. The three methods used are: the eigensystem realization algorithm (ERA), the ERA with data correlations, and the least squares algorithm. One of the critical issues in the mentioned algorithms, is selection of the reference degree-of-freedom (DOF). Previous experiences have shown that one cannot rely on a single reference DOF for identification of all modes. Consequently, the aforementioned identification formulations were modified to include multiple reference DOF, simultaneously, or one at a time. An autonomous algorithm was presented to distinguish the genuine structural modes from spurious noise or computational modes. Based on some parameter studies, some useful guidelines for the selection of critical user-selectable parameters are presented.     

Simulation of Airfoil Icing with a Novel Morphogenetic Model

In this paper, we describe a new modeling approach to tackle the challenging problem of in-flight icing prediction. In this approach, termed morphogenetic modeling, we predict the structural details of aircraft ice accretion by emulating the behavior of individual fluid elements. A two-dimensional morphogenetic model is used here to predict the ice accretion shape forming on a National Advisory Committee For Aeronautics 0012 airfoil under various atmospheric conditions. The influence of the surface heat transfer formulation on the ice accretion shape is examined. We complement the numerical simulation with an analytical model for airfoil icing that is based on a simple form of the mass and heat conservation equations. This analytical investigation allows us to identify a significant new dimensionless ratio, the runback factor, defined as the ratio of the impinging water mass flux to the freezing mass flux at the stagnation line. An increasing runback factor leads to a quantifiable downstream displacement of the accretion mass. We also use the analytical model to verify the morphogenetic model during the early stages of icing, and find that there is reasonable agreement between the two models in terms of ice accretion shape. A comparison with experimental data and other models shows that even simple morphogenetic modeling is competitive with existing models. Further improvements will take advantage of the model’s unique ability to simulate discontinuous ice accretions in complex geometries, leading to a considerable advancement in the simulation of in-flight icing.     

平方振型加权模态参数整体识别法

提出了整体频响函数的新概念(GFRF).以振型平方和的形式对全部频响函数进行加权组合,建立了多输入多输出模态参数的识别模型.仿真验算的分析结果表明,该方法具有精度高,一致性好,能分离密集模态和消除随机噪声等优点,可以应用于大型复杂结构的试验模态分析.