Identification Of Mechanical Systems Research Articles

Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress

Abstract This paper contains a review of the theory and applications of nonlinear normal modes, which have been developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers by the same authors. The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal form theory for nonlinear modes construction; nonlinear modes in finite degrees-of-freedom systems; resonances and bifurcations; reduced-order modeling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.

An Uncertainty Model for Strain Gages Using Monte Carlo Methodology.

For the purpose of validation and identification of mechanical systems, measurements are indispensable. However, they require knowledge of the inherent uncertainty to provide valid information. This paper describes a method on how to evaluate uncertainties in strain measurement using electric strain gages for practical engineering applications. Therefore, a basic model of the measurement is deduced that comprises the main influence factors and their uncertainties. This is performed using the example of a project dealing with strain measurement on the concrete surface of a large-span road bridge under static loading. Special attention is given to the statistical modeling of the inputs, the underlying physical relationship, and the incorporation and the impact of nonlinearities for different environmental conditions and strain levels. In this regard, also experiments were conducted to quantify the influence of misalignment of the gages. The methodological approach used is Monte Carlo simulation. A subsequent variance-based sensitivity analysis reveals the degree of nonlinearity in the relationship and the importance of the different factors to the resulting probability distribution. The developed scheme requires a minimum of expert knowledge of the analytical derivation of measurement uncertainties and can easily be modified for differing requirements and purposes.

Online Identification of Mechanical Systems Using the Simplified Output Error Model

Online Identification of Mechanical Systems Using the Simplified Output Error Model

The Accuracy and Computational Efficiency of the Loewner Framework for the System Identification of Mechanical Systems

The Loewner framework has recently been proposed for the system identification of mechanical systems, mitigating the limitations of current frequency domain fitting processes for the extraction of modal parameters. In this work, the Loewner framework computational performance, in terms of the elapsed time till identification, is assessed. This is investigated on a hybrid, numerical and experimental dataset against two well-established system identification methods (least-squares complex exponential, LSCE, and subspace state space system identification, N4SID). Good results are achieved, in terms of better accuracy than LSCE and better computational performance than N4SID.

A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

Abstract An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

Optimal excitation trajectories for mechanical systems identification

System identification for multibody mechanical systems such as robots and vehicles is typically formulated as a parameter optimization problem, in which the model parameters are chosen to minimize the difference between measured and predicted trajectories of the system. The problem is made difficult by the large number of parameters of different scales and physical units, and also noisy and incomplete measurements. Even more critically, the choice of reference trajectory has a decisive impact on the accuracy and robustness of the identification procedure. In this paper we propose a set of geometric optimal excitation criteria that can be optimized to generate high-quality reference trajectories. The resulting optimal trajectories are coordinate- and frame-invariant, and can be obtained efficiently and robustly using recursive analytic gradients of the criteria. For high-dimensional systems that can execute only a limited range of feasible trajectories, we also show how our geometrical framework can be used to optimally identify a reduced set of parameters for the given set of trajectories. The improved robustness and accuracy of our geometric approach vis-á-vis existing methods is demonstrated through both numerical and hardware experiments involving robot manipulators and a high-dimensional humanoid robot.

A New Health Condition Detection Method for Planetary Gears Based on Modified Distributed Compressed Sensing and Multiscale Symbol Dynamic Entropy

Planetary gear transmission system is an important transmission part of large machinery and is prone to failure. Aiming at the problem of how to extract fault information from vibration signals of nonlinear and nonstationary planetary gearboxes, a performance degradation evaluation index of planetary gearboxes based on improved distributed compressed sensing and modified multiscale symbolic dynamic entropy (DCSMDE) is proposed. DCSMDE combines distributed compression sensing with modified multiscale symbol dynamic entropy and solves the problem of strong nonlinearity and strong vibration signal coupling of the planetary transmission system from the homologous signals of multiple sensors. A distributed compression sensing parameter optimization algorithm based on Rényi entropy is proposed, which uses improved distributed compression sensing technology to simultaneously sample, compress, and denoise the multisource vibration data of rotating machinery. DCSMDE is used to calculate the reconstructed signal, extract the features with higher recognition characteristics, and use the change trend of the DCSMDE value to judge the working status of the planetary gearbox. Experimental results show that DCSMDE can be applied to dynamic evolution and fault identification of mechanical systems and accurately classify actual fault signals. It provides a new idea for the classification of planetary gear faults and the recognition of performance degradation.

Significance of Frequency Domain Features of PCG Records for Murmur Detection - An Investigation

Introduction The feature extraction is one of the important steps in any artificial intelligence framework. Signal processing techniques employed for separating the features assume a vital role in schemes implied for automated study like fault identification of mechanical systems from the vibrati

Direct identification of nonlinear damping: application to a magnetic damped system

In the identification of mechanical systems through inverse receptance methods, a linear model is usually assumed, at least on a first approximation. However, most of the systems have a degree of nonlinearity in their elastic or dissipative properties. Usually, stiffness nonlinearities are identified, while damping nonlinearities are neglected or even not detected. Indeed, an equivalent linear damping model, correctly representing the nonlinear dissipation of the system under testing condition, can always be found, but it is test-specific and not generally valid.This paper addresses the identification of dissipative models for multi degrees of freedom mechanical systems with a single damping nonlinearity. Based on the direct damping matrix identification through inverse receptance methods, this research proposes an extension of the Stabilised Layers Method, valid for linear systems, to damping nonlinearities, resulting in the identification of the test-independent linear and nonlinear damping matrices of the system. The proposed method is theoretically derived for the identification of nonlinear damping forces depending on powers of displacement and velocity. The sinusoidal input describing function approximation of the nonlinear damping is exploited to identify the coefficients of the nonlinear damping force from the system receptances, measured under sinusoidal sweeps at constant amplitudes of oscillation across the nonlinearity.The presented method is applied to identify the linear and nonlinear damping matrices of a multi degrees of freedom system with a localised nonlinear magnetic damper. The coefficients of the nonlinear magnetic damping force are identified for two configurations of the magnetic damper.The proposed approach is a parametric method to identify the nonlinear damping models of mechanical systems using standard experimental techniques usually adopted for linear systems. The identified model is valid under general excitation forces, predicting the system behaviour in a broader range of operation than the test-specific linear equivalent model.

Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. Additionally, purely data-based models often require large amounts of data and are often difficult to interpret. In this paper, we present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. This new approach directly incorporates the equations of motion originating from the Lagrange Mechanics into a deep neural network structure. Thus, we can integrate prior physics knowledge where it is available and use function approximation--e. g., neural networks--where it is not. The method is tested with a forward model of a real-world physical system with large uncertainties. The resulting model is accurate and data-efficient while ensuring physical plausibility. With this, we demonstrate a method that beneficially merges physical insight with real data. Our findings are of interest for model-based control and system identification of mechanical systems.

Information Theoretic Causality Measures for System Identification of Mechanical Systems

Parameter estimation and model order reduction (MOR) are important system identification techniques used in the development of models for mechanical systems. A variety of classical parameter estimation and MOR methods are available for nonlinear systems but performance generally suffers when little is known about the system model a priori. Recent advancements in information theory have yielded a quantity called causation entropy (CSE), which is a measure of influence between elements in a multivariate time series. In parameter estimation problems involving dynamic systems, CSE can be used to identify which state transition functions in a discrete-time model are important in driving the system dynamics, leading to reductions in the dimensionality of the parameter space. This method can likewise be used in black box system identification problems to reduce model order and limit issues with overfitting. Building on the previous work, this paper illustrates the use of CSE-enabled parameter estimation for nonlinear mechanical systems of varying complexity. Furthermore, an extension to black-box system identification is proposed wherein CSE is used to identify the proper model order of parameterized black-box models. This technique is illustrated using nonlinear differential equation (NDE) models of physical devices, including a nonlinear spring–mass–damper, a pendulum, and a nonlinear model of a car suspension. Overall, the results show that CSE is a promising new tool for both gray-box and black-box system identification that can speed convergence toward a parameter solution and mitigate problems with model overfitting.

An iterated cubature unscented Kalman filter for large-DoF systems identification with noisy data

Structural and mechanical system identification under dynamic loading has been an important research topic over the last three or four decades. Many Kalman-filtering-based approaches have been developed for linear and nonlinear systems. For example, to predict nonlinear systems, an unscented Kalman filter was applied. However, from extensive literature reviews, the unscented Kalman filter still showed weak performance on systems with large degrees of freedom. In this research, a modified unscented Kalman filter is proposed by integration of a cubature Kalman filter to improve the system identification performance of systems with large degrees of freedom. The novelty of this work lies on conjugating the unscented transform with the cubature integration concept to find a more accurate output from the transformation of the state vector and its related covariance matrix. To evaluate the proposed method, three different numerical models (i.e., the single degree-of-freedom Bouc–Wen model, the linear 3-degrees-of-freedom system, and the 10-degrees-of-freedom system) are investigated. To evaluate the robustness of the proposed method, high levels of noise in the measured response data are considered. The results show that the proposed method is significantly superior to the traditional UKF for noisy measured data in systems with large degrees of freedom.

Time Series Prediction Based on Adaptive Weight Online Sequential Extreme Learning Machine

A novel adaptive weight online sequential extreme learning machine (AWOS-ELM) is proposed for predicting time series problems based on an online sequential extreme learning machine (OS-ELM) in this paper. In real-world online applications, the sequentially coming data chunk usually possesses varying confidence coefficients, and the data chunk with a low confidence coefficient tends to mislead the subsequent training process. The proposed AWOS-ELM can improve the training process by accessing the confidence coefficient adaptively and determining the training weight accordingly. Experiments on six time series prediction data sets have verified that the AWOS-ELM algorithm performs better in generalization performance, stability, and prediction ability than the OS-ELM algorithm. In addition, a real-world mechanical system identification problem is considered to test the feasibility and efficacy of the AWOS-ELM algorithm.

Modified Levenberg–Marquardt Algorithm for Backpropagation Neural Network Training in Dynamic Model Identification of Mechanical Systems

For modeling a dynamic system in practice, it often faces the difficulty in improving the accuracy of the constructed analytical model, since some components of the dynamic model are often ignored deliberately due to the difficulty of identification. It is also unwise to apply the neural network to approximate the entire dynamic system as a black box, when the comprehensive knowledge of most components of the dynamics of a large system are available. This paper proposes a method that utilizes the backpropagation (BP) neural network to identify the unknown components of the dynamic system based on the experimental front-end inputs–outputs data of the entire system. It can avoid the difficulty in getting the direct training data for the unknown components, and brings great benefits in the practical application, since to get the front-end inputs–outputs data of the entire dynamic system is easier and cost-effective. In order to train such neural network for the unknown components of dynamics, a modified Levenberg–Marquardt algorithm, which can utilize the front-end inputs–outputs data of the entire dynamic system, has been developed in the paper. Three examples from different application points of view are presented in the paper, and the results show that the proposed modified Levenberg–Marquardt algorithm is efficient to train the neural network for the unknown components of the system based on the data of entire system. The constructed dynamics model, in which the unknown components are substituted by the neural network, can satisfy the requisite accuracy successfully in the computation.

Nonlinear factor analysis and its application to acoustical source separation and identification

Acoustical signals of mechanical systems can provide original information of operating conditions, and thus benefit for machinery condition monitoring and fault diagnosis. However, acoustical signals measured by sensors are mixed signals of all the sources, and normally it is impossible to be directly used for acoustical source identification or feature extraction. Therefore, this paper presents nonlinear factor analysis (NLFA) and applies it to acoustical source separation and identification of mechanical systems. The effects by numbers of hidden neurons and mixed signals on separation performances of NLFA are comparatively studied. Furthermore, acoustical signals from a test bed with shell structures are separated and identified by NLFA and correlation analysis, and the effectiveness of NLFA on acoustical signals is validated by both numerical case studies and an experimental case study. This work can benefit for machinery noise monitoring, reduction and control, and also provide pure source information for machinery condition monitoring or fault diagnosis.

Spectrum-based modal parameters identification with Particle Swarm Optimization

The paper presents the new method of the natural frequencies and damping identification based on the Artificial Intelligence (AI) Particle Swarm Optimization (PSO) algorithm. The identification is performed in the frequency domain. The algorithm performs two PSO-based steps and introduces some modifications in order to achieve quick convergence and low estimation error of the identified parameters’ values for multi-mode systems. The first stage of the algorithm concentrates on the natural frequencies estimation. Using the information about the natural frequencies, measurement data are filtered and corrected dampings as well as amplitudes are calculated for each preliminary identified mode. This allows regrouping particles to the area around proper parameters values. Particle regrouping is based on the physical properties of modally tested structures. This differs the algorithm from other PSO based algorithms with particles regrouping. In the second stage of the algorithm parameters of all modes are tuned together in order to adjust estimates. The procedure of identification, as well as the appropriate algorithm, is presented and some SISO examples are provided. Results are compared with the results obtained for the selected, already developed modal identification methods. The paper presents practical application of AI method for mechanical systems identification.

Construction of hierarchical diagnosis network based on deep learning and its application in the fault pattern recognition of rolling element bearings

A novel hierarchical diagnosis network (HDN) is proposed by collecting deep belief networks (DBNs) by layer for the hierarchical identification of mechanical system. The deeper layer in HDN presents a more detailed classification of the result generated from the last layer to provide representative features for different tasks. A two-layer HDN is designed for a two-stage diagnosis with the wavelet packet energy feature. The first layer is intended to identify fault types, while the second layer is developed to further recognize fault severity ranking from the result of the first layer. To confirm the effectiveness of HDN, two similar networks constructed by support vector machine and back propagation neuron networks (BPNN) are employed to present a comprehensive comparison. The experimental results show that HDN is highly reliable for precise multi-stage diagnosis and can overcome the overlapping problem caused by noise and other disturbances.

Nonsmooth identification of mechanical systems with backlash-like hysteresis

Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlashlike hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.

A Method for Parameter Identification of Mechanical System Based on Differential Motion Equations

Correct identification of system parameters contributes to construct more precise model of the system and therefore improves the performance of controller. The current identification algorithms have some disadvantages, such as the complication of algorithms and the high requirement on hardware. In this paper, we propose a new system identification method which only utilizes the data from serve motor encoder. Based on the differential equations of motion and the theory of undetermined coefficients, mechanical parameters of the system can be solved using the least square method with the equations constructed based on kinematic parameters obtained by experimental tests. The identified mechanical parameters are then used to construct the system transfer function and a SIMULINK model. The method is validated by comparing the results between simulation and experiment. This method has advantages of low requirement on hardware and simple algorithm. It is proper to be applied in mechanical parameter identification of servo system.

A Mechanical System Identification Method for Non-Invasive Ultrasound Theragnostic System

Abstract: In this paper, we propose a mechanical system identification method for the Non-Invasive Ultrasound Theragnostic System (NIUTS). NIUTS tracks and follows the movement in an affected area (kidney stones, in the present study) by irradiating the area with high-intensity focused ultrasound (HIFU). Blur noise caused by oscillation of the mechanical systems deteriorates the servoing performance. To enhance the servoing performance, it should be required to identify the mechanical system with mechanical oscillation part.