Nonlinear Structural Identification Research Articles

Reduced-order model-inspired experimental identification of damped nonlinear structures

In this work, we address Nonlinear System Identification (NSI) of geometrically nonlinear structures using experimental response data. Specifically we consider nonlinear structures with large inertia effects. A laboratory scale cantilever-type beam structure is considered, which is chosen for its large inertial effects. Free decay data is gathered from the experimental cantilever-type beam system using an image-based measurement technique. A general mathematical model is derived for nonlinear systems with large inertia, by taking inspiration from model reduction methods. Specifically, a reduced-order modelling method, which accounts for the kinetic energy of the modes not included in the reduction basis, is utilised for experimental NSI. Experimental system identification using the ROM-inspired model shows superior accuracy compared to standard stiffness nonlinear models typically used for modelling such systems. We also identify the damping of the structure by projecting the effect of unmodelled modes onto non-conservative dissipative forces in the ROM-inspired model. We show that this addresses issues of poor fit associated with using a linear damping model. This results in a nonlinear damping force in the ROM-inspired model which accounts for the damping effect of the unmodelled modes. These nonconservative effects of unmodelled modes are often neglected, which results in an incorrect damping estimation. A crude Finite-Element (FE) model of the cantilever-type beam is used to generate the nonlinear mapping of nonlinear damping force. The free decay response of the identified nonconservative ROM-inspired model closely matches the measurement decay response. This further validates the accuracy of the ROM-inspired model in NSI.

Predicting the Maximum Displacements of Structures during an Earthquake based on Chaos Theory

The maximum displacements are an important index for the structural health monitoring (SHM) after an earthquake. However, the measurement of displacements is not easy compared to that of accelerations, and nonlinear structural identification is problematic. This study estimates displacements using input and output accelerations with a small database without assuming any physical models. A nonlinear-dynamics prediction algorithm based on chaos theory is proposed combining Takens’s embedding theorem and nearest-neighbor method. Using 12 ground motions in simulation and three motions in experimental cases, the maximum displacements are predicted with 8 % to 25 % mean absolute errors (MAEs). A practical method is developed for robustly and accurately evaluating displacements.

A subspace parameter identification method for nonlinear structures under oversampling conditions

In engineering practice, sampling frequencies much higher than the Nyquist frequency are often used to obtain accurate measurements of the dynamic characteristics of nonlinear systems. However, it may lead to oversampling when using the nonlinear subspace identification method (NSIM). This study proposes a subspace parameter identification method to address the identification of nonlinear structures under oversampling conditions. The proposed method first employs the prediction error method (PEM) to estimate the linear part of the state space model. In noisy environments, the PEM can achieve more accurate results than the NSIM by minimizing an error criterion function. The initial values fed into the PEM are obtained by the stochastic subspace identification method. The nonlinear part of the state space model is estimated by solving a linear regression equation. The proposed method effectively reduces the impact of high sampling frequencies on identification accuracy by combining data with different sampling frequencies to construct the linear regression equation. Among them, the low sampling frequency data is obtained by downsampling the high sampling frequency measurement data. The proposed method effectively reduces the effect of high sampling frequencies and environmental noise on identification accuracy by accurately estimating both the linear and nonlinear parts of the state space model. The identification accuracy of the proposed method is numerically verified by a chain-type structure with five degrees of freedom and a cantilever beam structure. Additionally, experimental verification is carried out on a two degrees of freedom floor structure with local nonlinearities. The results show that the proposed method achieves high identification accuracy in oversampling conditions and noisy environments.

Synchronous identification of nonlinear structural parameters and unknown external excitation based on improved UKF

The traditional Unscented Kalman Filter (UKF) approach for nonlinear structural identification usually requires knowledge of external excitation. However, in real application, obtaining the input excitation of nonlinear structures can be challenging due to measurement error or difficulty in acquiring the accurate information. Consequently, the real-time application of the UKF method will be constrained. To address this issue, this paper develops an improved UKF-based synchronous identification method of nonlinear structural parameters and unknown external excitation. The proposed method starts with a preliminary estimate of the unknown excitation using the current predicted values of structural dynamic responses and parameters. Subsequently, the external excitation is further identified based on the updated state vector. In addition, to reduce the effect of measurement noise on the nonlinear structural identification and ensure the accuracy of the identified results, a Kalman Filter (KF) process is embedded in the UKF to optimize measurement noise covariance matrix in real time. The practicability and accuracy of the improved UKF method are confirmed by conducting numerical simulations on a single degree-of-freedom (S-DOF) and a six degree-of-freedom (six-DOF) nonlinear structural systems due to unknown seismic excitation. Moreover, a shake table test of a five-storey steel frame subjected to seismic excitation is employed to attest the feasibility of the proposed method. Both numerical and experimental results demonstrate that the improved UKF method can effectively achieve synchronous identification for nonlinear structural parameters and unknown excitation.

Identification of multiple nonlinear lap joints using instantaneous power flow balance

PurposeThe purpose of this paper is to apply the novel instantaneous power flow balance (IPFB)-based identification strategy to a specific practical situation like nonlinear lap joints having single and double bolts. The paper also investigates the identification performance of the proposed power flow method over conventional acceleration-matching (AM) methods and other methods in the literature for nonlinear identification.Design/methodology/approachA parametric model of the joint assembly formulated using generic beam element is used for numerically simulating the experimental response under sinusoidal excitations. The proposed method uses the concept of substructure IPFB criteria, whereby the algebraic sum of power flow components within a substructure is equal to zero, for the formulation of an objective function. The joint parameter identification problem was treated as an inverse formulation by minimizing the objective function using the Particle Swarm Optimization (PSO) algorithm, with the unknown parameters as the optimization variables.FindingsThe errors associated with identified numerical results through the instantaneous power flow approach have been compared with the conventional AM method using the same model and are found to be more accurate. The outcome of the proposed method is also compared with other nonlinear time-domain structural identification (SI) methods from the literature to show the acceptability of the results.Originality/valueIn this paper, the concept of IPFB-based identification method was extended to a more specific practical application of nonlinear joints which is not reported in the literature. Identification studies were carried out for both single-bolted and double-bolted lap joints with noise-free and noise-contamination cases. In the current study, only the zone of interest (substructure) needs to be modelled, thus reducing computational complexity, and only interface sensors are required in this method. If the force application point is outside the substructure, there is no need to measure the forcing response also.

Static load identification of nonlinear structure based on internal force estimation exemplified by underground straight-wall arch structure

Due to the complexity of the interaction between surrounding rock and support structure, underground structures have complex and time-varying boundary conditions that is difficult to determine in advance. It is necessary to perform damage/load identification of underground structures in real time, but there is a lack of relevant studies. Therefore, a load inversion method of nonlinear structure based on internal force estimation is proposed in this paper. First, a static damage experiment of straight-wall arch model was conducted to analyze its crack development pattern and damage mode. Then, interpolation and integration method (IIM) was used to calculate the internal force of the section through numerous strain data, and its estimation accuracy was verified by experiment and simulation. Finally, a new method of load identification, IVW-LAD (Incremental Variable Weighted - Least Absolute Deviation), using internal forces as optimization variables was proposed and validated. In summary, the findings of this paper can provide a reference for health diagnosis and load identification of nonlinear underground structures.

Design and Development of Structural Parameter Identification Software for Nonlinear Vibration Isolators

This paper developed an object-oriented software to facilitate parameter calibration of the quasi-zero stiffness (QZS) vibration isolator for engineering applications. Considering its advantages of convenient programming and high noise resistance, we employ the harmonic balance method to construct the identification core algorithm. The developed software consists of data pre-processing, parameter identification, and post-processing modules. The data pre-processing module imports and classifies all the required data. Then, the parameter identification module conducts preliminary nonlinearity analysis so that nonlinear structural parameter identification can be successfully carried out. After parameter identification, the data post-processing module displays and stores the identified results. The performance of the software is tested by a numerical example of a two-degree-of-freedom QZS vibration isolator, proving the software can give accurate identification results within a few user-friendly graphical interfaces. Based on this software, we hope that the application and promotion of nonlinear system parameter identification become more convenient.

Data-driven nonlinear system identification of blood glucose behaviour in Type I diabetics

Data-driven nonlinear system identification with sparse regression is a promising method to represent nonlinear dynamics in the form of a rigorous model description. Therefore, nonlinear functional structure identification and parameter estimation are performed simultaneously. Classical identification methods require functional structures that are manually derived using process knowledge either from first principles or practical experience. However, the effort required to provide these structures is time-consuming, labour-intensive, and in connection with operational trials in production plants, also associated with high costs. In addition, the latest sparse regression solution for nonlinear system identification does not offer an analytical solution due to the properties of the L1 norm. For this reason, sparse regression with smoothed L1 regularisation is proposed for nonlinear system identification. For this purpose, a nonlinear library function is first constructed based on the extended dynamic mode decomposition theory (eDMD), which contains all possible nonlinear bijective function candidates. For the process description, the most suitable functions with the related weighting parameters are selected using the regularisation properties. The performance of the method is demonstrated using the blood glucose behaviour from Type I Diabetes. The validation of the method is performed for a simulation study with and without noise influence and applied to experimental data of two patients in a Python simulation. It can be shown that the identification is successful for both studies with a performance limit for a signal-to-noise ratio (SNR) of 0.45 (3.46 dB).

Sensitivity-based constitutive parameter identification of nonlinear structures with unknown input earthquake excitation

System identification methods are widely developed in structural health monitoring, in which the force or structural damage is identified from a linearised structure. However, the real-world civil infrastructures are generically nonlinear and subject to extreme loading conditions, such as earthquake. This study proposes a system identification method for material constitutive nonlinear structures subject to earthquake, where sensitivity analysis is developed to accelerate the complicated nonlinear system identification. First, the nonlinear structural model based on the material constitutional law is constructed by fiber beam-column elements. The earthquake input is parameterized by Chebyshev orthogonal polynomials in a recognizable form. Afterwards, the dynamic response sensitivities with respect to the constitutive parameters and the orthogonal factors of earthquake excitation are derived to accelerate the system identification from a complex material constitutive model. Finally, the constitutive parameters and the earthquake input are simultaneously identified by an optimization process. Numerical structures subjected to earthquake excitation are employed to verify the accuracy of the proposed method, by which the influence of parameter's order, input intensity and measurement noise is discussed. The proposed method develops Chebyshev parameterization to recognize the earthquake input and sensitivity analysis to accelerate the optimization, which leads to an accurate nonlinear system identification of civil structures.

Parallel Substructure Identification of Linear and Nonlinear Structures Using Only Partial Output Measurements

Parallel Substructure Identification of Linear and Nonlinear Structures Using Only Partial Output Measurements

Parameter identification of nonlinear bistable piezoelectric structures by two-stage subspace method

Parameter identification of nonlinear bistable piezoelectric structures by two-stage subspace method

A novel strategy for force identification of nonlinear structures

Dynamic force is the key indicator for monitoring the condition of a mechanical product. These mechanical structures always encompass some nonlinear factors. Most previous studies focused on obtaining the dynamic force of linear structures. Consequently, this study focuses on the nonlinear mechanical structure, and a novel identification strategy is proposed to indirectly identify the excitation force. For the identification strategy, based on a nonlinear state-space model, a force identification equation for the nonlinear structure is built, wherein the transfer matrix consists of coefficient matrices of the nonlinear state-space model, and these coefficient matrices are calculated by a nonlinear subspace identification algorithm. Then, under the generalized cross-validation criterion, the truncated total least squares method is introduced to solve the ill-posed equation to eventually obtain the excitation force of the nonlinear structure. The identification results from two numerical simulation cases and one experimental case illustrate that the proposed identification strategy can stably and accurately identify the excitation force of nonlinear structures.

Displacement measurement and nonlinear structural system identification: A vision‐based approach with camera motion correction using planar structures

Displacement measurement and nonlinear structural system identification: A vision‐based approach with camera motion correction using planar structures

Real-time structural health monitoring of nonlinear hysteretic structures using a fast and slow dynamics separation method

Structural health monitoring (SHM) is the process of identification, localisation, and quantification of structural damage due to external loads, such as an earthquake. SHM results simplify and automate typical visual or localised experimental approaches and enable more informed structural safety assessment and post-event retrofit. On-line SHM is of particular interest for rapid safety assessment by owners and civil defence authorities, and can also inform active control systems to further avoid or mitigate damage during an event. This significant advantage over off-line SHM has drawn many researchers to on-line or real-time methods. This paper presents an on-line SHM algorithm for model-based identification and monitoring of non-linear hysteretic structures. It separates fast and slow dynamics and uses robust piecewise least squares fitting over different time intervals to identify key structural parameters over time, including stiffness, damping, and the well-accepted Bouc–Wen hysteretic model parameters, which are directly related to well-recognised damage metrics. Proof-of-method simulations of a realistic nonlinear case study structure, subjected to a suite of 20 different ground motions, show the algorithm accurately identifies structural parameters to within 2.7% and 4.3% of the actual as-modelled values for stiffness and damping, respectively. Results for a range of major changes (damage) in structural parameters show the algorithm performs well in tracking these changes in real-time. Overall, the results present an accurate, real-time, model-based SHM method for highly nonlinear structures.

Damage Detection in Initially Nonlinear Structures Based on Variational Mode Decomposition

Nonlinear characteristics in the dynamic behaviors of civil structures degrade the performance of damage detection of the linear theory based traditional time- and frequency-domain methods. To overcome this challenge, this paper proposes a damage detection approach for nonlinear structures based on Variational Mode Decomposition (VMD). In this approach, the measured dynamic responses from nonlinear structures under earthquake excitations are adaptively decomposed into a finite number of monocomponents by using VMD. Each decomposed mono-component represents an amplitude modulated and frequency modulated (AMFM) signal with a limited frequency bandwidth. Hilbert transform is then employed to identify the instantaneous modal parameters of the decomposed monomodes, including instantaneous frequencies and mode shapes. Based on the identified modal parameters from the decomposed structural dynamic responses, two damage indices are defined to identify the location and severity of structural damage, respectively. To validate the effectiveness and accuracy of the proposed approach, a nonlinear seven-storey shear building model with four different damage cases under earthquake excitations is used in the numerical studies. In experimental verifications, data from shake table tests on a 12-storey scaled reinforced concrete frame structure with different earthquake excitations are analyzed with the proposed approach. The results in both numerical studies and experimental validations demonstrate that the proposed approach can be successfully applied for nonlinear structural damage identification.

Existence of a Bilinear Differential Realization in the Constructions of Tensor Product of Hilbert Spaces

The paper describes the results of a functional-geometric study of the necessary and sufficient conditions for the existence of a differential realization in the terms of the tensor product of real Hilbert spaces. There are considered continuous infinite-dimensional dynamical system in the class of controlled bilinear nonstationary ordinary differential equations of the second order (including quasi-linear hyperbolic models) in a separable Hilbert space. Therefore the topological and metric conditions for the continuity of the RayleighRitz operator with the calculation of the fundamental group of its image are analytically substantiated. The results of paper give incentives for generalizations in the qualitative theory of nonlinear structural identification of higher order multi-linear differential models.

Identifying the pulsed neuron networks\u2019 structures by a nonlinear Granger causality method

BackgroundIt is a crucial task of brain science researches to explore functional connective maps of Biological Neural Networks (BNN). The maps help to deeply study the dominant relationship between the structures of the BNNs and their network functions.ResultsIn this study, the ideas of linear Granger causality modeling and causality identification are extended to those of nonlinear Granger causality modeling and network structure identification. We employed Radial Basis Functions to fit the nonlinear multivariate dynamical responses of BNNs with neuronal pulse firing. By introducing the contributions from presynaptic neurons and detecting whether the predictions for postsynaptic neurons’ pulse firing signals are improved or not, we can reveal the information flows distribution of BNNs. Thus, the functional connections from presynaptic neurons can be identified from the obtained network information flows. To verify the effectiveness of the proposed method, the Nonlinear Granger Causality Identification Method (NGCIM) is applied to the network structure discovery processes of Spiking Neural Networks (SNN). SNN is a simulation model based on an Integrate-and-Fire mechanism. By network simulations, the multi-channel neuronal pulse sequence data of the SNNs can be used to reversely identify the synaptic connections and strengths of the SNNs.ConclusionsThe identification results show: for 2–6 nodes small-scale neural networks, 20 nodes medium-scale neural networks, and 100 nodes large-scale neural networks, the identification accuracy of NGCIM with the Gaussian kernel function was 100%, 99.64%, 98.64%, 98.37%, 98.31%, 84.87% and 80.56%, respectively. The identification accuracies were significantly higher than those of a traditional Linear Granger Causality Identification Method with the same network sizes. Thus, with an accumulation of the data obtained by the existing measurement methods, such as Electroencephalography, functional Magnetic Resonance Imaging, and Multi-Electrode Array, the NGCIM can be a promising network modeling method to infer the functional connective maps of BNNs.

К тензорному анализу решения задачи реализации билинейной системы второго порядка с опозданием

Определены аналитические условия (необходимые/достаточные) решения задачи дифференциальной реализации континуального пучка управляемых траекторных кривых в классе билинейных неавтономных обычных дифференциальных уравнений (с опозданием и без) второго порядка в материальном сепарабельном гильбертовом пространстве. Эта задача относится к типу обратных задач для аддитивной комбинации нестационарных линейных и билинейных операторов эволюционных уравнений в бесконечномерном гильбертовом пространстве. Метамовой данной теории служат конструкции тензорных произведений гильбертовых пространств, структуры решеток с ортодополнением и функциональный аппарат нелинейного оператора Релея-Ритца. При этом показано, что при конечном пучке траекторий наличие свойств типа сублинейности данного оператора позволяет получить достаточные условия для существования таких реализаций. Попутно обосновываются тополого-метрические условия непрерывности проектизации нелинейного функционального опера-тора Релея–Ритца с вычислением фундаментальной группы его образа. Полученные результаты побуждают к развитию теории нелинейной структурной идентификации полилинейных дифференциальных моделей высших порядков (например, для моделирования многоканальных нейроимплантов типа Neuralink).

Structural damage identification based on short-time temporal coherence using free-vibration response signals

This paper proposes a short-time temporal coherence (STC)-based approach for linear and nonlinear structural damage identification. Two novel damage indices (damage detection index, DDI and damage localization index, DLI) are constructed based on the peak coherence function of the STC, which aims at detecting and localizing the damage using the measured free-vibration responses. Detailed numerical investigation was performed on a spring-damping-mass system. The results show that the two indices are sensitive to linear and nonlinear structural damage, and they can accurately identify the damage even with severely noise-polluted signals. An experimental study was conducted on a steel cantilever column to further validate the proposed approach. A typical nonlinear structural damage was simulated by loosening the bolts in the flange connection, which was successfully identified by the two indices. The results demonstrate that the proposed STC-based damage identification approach is effective to identify the bolt-loosening of structure with free-vibration response signals.

Impact load identification of nonlinear structures using deep Recurrent Neural Network

Abstract In this paper, a novel impact load identification method of nonlinear structures by using deep Recurrent Neural Network (RNN) is proposed. The deep RNN model, mainly consisting of two Long Short-Term Memory (LSTM) layers and one bidirectional LSTM (BLSTM) layer, is trained through a large number of dynamic responses and impact loads to learn the complex inverse mapping between structural inputs and outputs. The effectiveness and practicability of the proposed method are verified by three nonlinear cases: damped Duffing oscillator, nonlinear three-degree-of-freedom system and nonlinear composite plate. The results show that the proposed method has the capability for identifying the complex impact load even when the impact location is unknown. Meanwhile, hyperparameters of the deep RNN model and placement scheme of sensors are not highly sensitive to the identification accuracy.