Adaptive Tikhonov Regularization for Simultaneous Identification of Structural Parameters and Input

A structural parametric identification strategy based on neural networks algorithms using dynamic macro-strain measurements in time domain from a long-gage strain sensor by fiber optic sensing technique such as Fiber Bragg Grating (FBG) sensor is developed. An array of long-gage sensors is bounded on the structure to measure reliably and accurately macro-strains. By the proposed methodology, the structural parameter of stiffness can be identified. A beam model with known mass distribution is considered as an object structure. Without any eigenvalue analysis or optimization computation, the structural parameter of stiffness can be identified. First an emulator neural network is presented to identify the beam structure in current state. Free vibration macro-strain responses of the beam structure are used to train the emulator neural network. The trained emulator neural network can be used to forecast the free vibration macro-strain response of the beam structure with enough precision and decide the difference between the free vibration macro-strain responses of other assumed structure with different structural parameters and those of the original beam structure. The root mean square (RMS) error vector is presented to evaluate the difference. Subsequently, corresponding to each assumed structure with different structural parameters, the RMS error vector can be calculated. By using the training data set composed of the structural parameters and RMS error vector, a parametric evaluation neural network is trained. A beam structure is considered as an existing structure, based on the trained parametric evaluation neural network, the stiffness of the beam structure can be forecast. It is shown that the parametric identification strategy using macro-strain measurement from long-gage sensors has the potential of being a practical tool for a health monitoring methodology applied to civil engineering structures.

Simultaneous identification of structural damage and nonlinear hysteresis parameters by an evolutionary algorithm-based artificial neural network

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.

Identification of structural vibration parameters by using a frequency domain filter

Sufficient statistics for unobserved heterogeneity in structural dynamic logit models

The extended minimum variance unbiased estimation approach can be used for joint state/parameter/input estimation based on the measured structural responses. However, it is necessary to measure the structural displacement and acceleration responses at each story for the simultaneous identification of structural parameters and unknown wind load. A novel method of identifying structural state, parameters, and unknown wind load from incomplete measurements is proposed. The estimation is performed in a modal extended minimum variance unbiased manner, based on incomplete measurements of wind‐induced structural displacement and acceleration responses. The feasibility and accuracy of the proposed method are numerically validated by identifying the wind load and structural parameters on a ten‐story shear building structure with incomplete measurements. The effects of crucial factors, including sampling duration and the number of measurements, are discussed. Furthermore, the practical application of the developed inverse method is evaluated based on wind tunnel testing results of a 234 m tall building structure. The results indicate that the structural state, parameters, and unknown wind load can be identified accurately using the proposed approach.

A new method based on dynamic response sensitivity is proposed for the identification of local nonlinear system. The unknown local nonlinear hysteresis parameters are identified together with linear structural parameters. The sensitivities of structural dynamic response with respect to unknown parameters are derived. The identification equation is set up based on Taylor’s first order approximation, and is solved with the damped least-squares method. A four-story shearing system with rubber isolation bearing of nonlinear hysteresis model is studied to validate the proposed method. Numerical simulation with noisy measured accelerations shows that the proposed method can accurately identify both linear and nonlinear parameters of the system. This method provides a new approach for detecting local nonlinear structures with incomplete measured output information.

The detection of structural damages, either on-line or almost on-line, based on vibration data measured from sensors, is essential for the structural health monitoring system. The problem is quite challenging, in particular when the external excitations are not completely measured and when the structural system is complex. In practical applications, external excitations (inputs), such as seismic excitations, wind loads, traffic loads, etc., may not be measured or may not be measurable, and the structure may not always be shear-beam type which can be easily represented as spring-mass system. In this paper, a newly proposed damage detection method, referred to as the adaptive quadratic sum-squares error with unknown inputs (AQSSE-UI), is used for the detection of structural damages of a plane steel truss with finite element model. In this approach, external excitations and some structural responses may not be measured. Analytical recursive solution for the proposed AQSSE-UI method will be presented. The accuracy and effectiveness of the proposed approach will be demonstrated by numerical simulations where the structure is excited by different external loads. The simulation results indicate that the proposed approach is a viable damage detection technique capable of: (i) identifying structural parameters, (ii) tracking the changes of parameters leading to the detection of structural damages, and (iii) identifying the unknown external excitations.

Structural parameters and dynamic loading identification from incomplete measurements: Approach and validation

In this paper, a theoretical and numerical study on bridge simultaneous damage detection procedure for identifying both the system parameters and input excitation mass, are presented. This method is called \'Adjoint Variable Method\' which is an iterative gradient-based model updating method based on the dynamic response sensitivity. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. Moving mass is a model which takes into account the inertia effects of the vehicle. This interaction model is a time varying system and proposed method is capable of detecting damage in this variable system. Robustness of proposed method is illustrated by correctly detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparison study of common sensitivity and proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. Various sources of errors including the effects of measurement noise and initial assumption error in stability of method are also discussed.

The Time-Varying First Order Plus Dead Time (TV-FOPDT) model is an extension of the conventional FOPDT by allowing the system parameters, which are primarily defined on the transfer function description, i.e., the DC-gain, time constant and time delay, to be time dependent. The TV-FOPDT identification problem turns to estimate these time-varying parameters based on measured control input and system output. This work considers a TV-FOPDT identification problem in the presence of an unknown disturbance input. By regarding the unknown input as one extra system parameter, the considered identification problem is formulated as a Stochastic Mixed Integral Programming (SMIP) problem after discretizing the original problem. The sliding window technique with forgetting factor is employed to cope with time resolution issue, and the Least Mean Square (LMS) method is used to obtain the optimal solution of each individual optimization problem based on different time delay assumptions. The proposed method is firstly tested through a number of numerical examples, and then it is applied to estimate a TV-FOPDT model of the superheat dynamic of a supermarket refrigeration system.

Fuzzy neural networks have both the interpretability of fuzzy systems and the self-learning ability of neural networks, but they will face the challenge of “rule explosion” when dealing with high-dimensional data. Moreover, the structure and parameter identifications of models are generally performed in two stages, and this always attends to one thing and loses another in terms of interpretability and predictive performance. In this paper, a fuzzy neural network regression method (FNNR) that coordinates structure identification and parameter identification is proposed. To alleviate the problem of rule explosion, the structure identification and parameter identification are coordinated in the training process, and the numbers of fuzzy rules and fuzzy partitions are effectively limited, while the parameters of fuzzy rules are optimized. The symmetrical architecture of the FNNR is designed for automatic structure identification. An alternate training strategy is adopted by treating discrete and continuous parameters differently, and thus the convergence efficiency of the algorithm is improved. To enhance interpretability, regularized terms are designed from fuzzy rule level and fuzzy partition level to guide the model to learn fuzzy rules with simple structures and clear semantics. The experimental results show that the proposed method has both a compact structure and high precision.

The structural size parameters (SSP) of the beam pumping unit (BPU) are crucial for kinematic analysis and other related technologies. However, early equipment often lacked data, and measuring a large number of SSPs for the BPU is costly and inefficient. To enable the automatic recognition of SSPs and reduce labor and resource investments, this paper proposes a method for recognizing the SSPs of the BPU. A kinematic model for calculating the crank angle based on beam tilt angle and SSPs is established, along with an SSP recognition model. Based on the traditional particle swarm optimization (PSO) algorithm, a comprehensive enhanced particle swarm optimization (CEPSO) algorithm is designed to solve the model. Latin hypercube sampling (LHS) is used to obtain the initial values of the SSPs, which are then substituted into the kinematic model using the measured beam tilt angle. The algorithm aims to minimize the average absolute error between the measured and calculated crank angles. The CEPSO algorithm iteratively updates the SSP values, and when the error converges to a minimum, the SSPs are obtained. Experimental results demonstrate the effectiveness of the model and the algorithm. The parameter recognition error of the CEPSO algorithm is within 5%, significantly outperforming traditional PSO. This method provides a new technological approach for measuring SSPs.

A novel constrained UKF method for both updating structural parameters and identifying excitations for nonlinear structures

The synthesis of structural health monitoring and vibration control is important in order to provide facilities for constructing smart structures. In recent years, some techniques have been developed to integrate structural identification and optimal vibration control. However, it is still challenging to integrate the identification and vibration control of time-varying structures subject to unknown earthquake excitation. The main difficulties are that structural dynamic responses collected by a simple harmonic motion system are absolute responses under unknown earthquake ground motion while previous identification approaches for unknown external excitation are not applicable for this situation and the need of an efficient algorithm to accurately track the various scenarios of time-varying structures with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, a novel algorithm is presented, in which structural time-varying parameters are treated as ‘virtual unknown inputs’ to the underlying time-invariant structure, a generalized Kalman filter with unknown inputs is proposed for joint identification of joint structural state, unknown earthquake excitation and ‘virtual unknown inputs’ with only partially measured structural absolute responses, and the identification results are integrated in real-time with the instantaneous optimal control scheme to reach the goal of optimal semi-active control provided by magneto-rheological dampers. Some numerical examples of integrated identification and vibration control of various time-varying structures subject to unknown earthquake excitation are used to demonstrate the performances of the proposed algorithm.