Data driven model identification methods have grown increasingly popular due to enhancements in measuring devices and data mining. They provide a useful approach for comparing the performance of a device to the simplified model that was used in the design phase. One of the modern, popular methods for model identification is Sparse Identification of Nonlinear Dynamics (SINDy). Although this approach has been widely investigated in the literature using mostly numerical models, its applicability and performance with physical systems is still a topic of current research. In this paper we extend SINDy to identify the mathematical model of a complicated physical experiment of a chaotic pendulum with a varying potential interaction. We also test the approach using a simulated model of a nonlinear, simple pendulum. The input to the approach is a time series, and estimates of its derivatives. While the standard approach in SINDy is to use the Total Variation Regularization (TVR) for derivative estimates, we show some caveats for using this route, and we benchmark the performance of TVR against other methods for derivative estimation. Our results show that the estimated model coefficients and their resulting fit are sensitive to the selection of the TVR parameters, and that most of the available derivative estimation methods are easier to tune than TVR. We also highlight other guidelines for utilizing SINDy to avoid overfitting, and we point out that the fitted model may not yield accurate results over long time scales. We test the performance of each method for noisy data sets and provide both experimental and simulation results. We also post the files needed to build and reproduce our experiment in a public repository.
{"title":"Data Driven Model Identification for a Chaotic Pendulum With Variable Interaction Potential","authors":"Melih C. Yesilli, Firas A. Khasawneh","doi":"10.1115/detc2020-22597","DOIUrl":"https://doi.org/10.1115/detc2020-22597","url":null,"abstract":"\u0000 Data driven model identification methods have grown increasingly popular due to enhancements in measuring devices and data mining. They provide a useful approach for comparing the performance of a device to the simplified model that was used in the design phase. One of the modern, popular methods for model identification is Sparse Identification of Nonlinear Dynamics (SINDy). Although this approach has been widely investigated in the literature using mostly numerical models, its applicability and performance with physical systems is still a topic of current research. In this paper we extend SINDy to identify the mathematical model of a complicated physical experiment of a chaotic pendulum with a varying potential interaction. We also test the approach using a simulated model of a nonlinear, simple pendulum. The input to the approach is a time series, and estimates of its derivatives. While the standard approach in SINDy is to use the Total Variation Regularization (TVR) for derivative estimates, we show some caveats for using this route, and we benchmark the performance of TVR against other methods for derivative estimation. Our results show that the estimated model coefficients and their resulting fit are sensitive to the selection of the TVR parameters, and that most of the available derivative estimation methods are easier to tune than TVR. We also highlight other guidelines for utilizing SINDy to avoid overfitting, and we point out that the fitted model may not yield accurate results over long time scales. We test the performance of each method for noisy data sets and provide both experimental and simulation results. We also post the files needed to build and reproduce our experiment in a public repository.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125831020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Model predictive control (MPC) has become more attractive in control engineering for the last decades because of its efficiency and robustness. In this paper, an effective control strategy is proposed for vibration reduction of mechanical flexible systems in which establishment of a global dynamic model of the controlled system is not necessary. A modified model-free adaptive predictive controller is designed by combination of MPC and model-free control theory. The novel idea of this contribution is that by using the compact-form dynamic linearization technique, the upcoming system outputs within a specified prediction horizon can be predicted in sequence. The data-based prediction model of the system only requires input/output information, and therefore the future control input increments as well as the unknown system parameters called pseudo-jacobian matrix can be estimated. To improve parameter estimation accuracy, another online estimation method namely recursive least-squares algorithm is applied instead of using the conventional projection algorithm. The control performance is verified nummerically for vibration control of a flexible ship-mounted crane represented as a multi-input multi-output (MIMO) system. Simulation results indicate that significant reduction of the crane oscillations and better control performance are observed when using the proposed controller in comparison with other traditional methods.
{"title":"Modified Model-Free Adaptive Predictive Control Applied to Vibration Reduction of Mechanical Flexible Systems","authors":"H. Pham, D. Söffker","doi":"10.1115/detc2020-22033","DOIUrl":"https://doi.org/10.1115/detc2020-22033","url":null,"abstract":"\u0000 Model predictive control (MPC) has become more attractive in control engineering for the last decades because of its efficiency and robustness. In this paper, an effective control strategy is proposed for vibration reduction of mechanical flexible systems in which establishment of a global dynamic model of the controlled system is not necessary. A modified model-free adaptive predictive controller is designed by combination of MPC and model-free control theory. The novel idea of this contribution is that by using the compact-form dynamic linearization technique, the upcoming system outputs within a specified prediction horizon can be predicted in sequence. The data-based prediction model of the system only requires input/output information, and therefore the future control input increments as well as the unknown system parameters called pseudo-jacobian matrix can be estimated. To improve parameter estimation accuracy, another online estimation method namely recursive least-squares algorithm is applied instead of using the conventional projection algorithm. The control performance is verified nummerically for vibration control of a flexible ship-mounted crane represented as a multi-input multi-output (MIMO) system. Simulation results indicate that significant reduction of the crane oscillations and better control performance are observed when using the proposed controller in comparison with other traditional methods.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"21 41","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132742593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, recursive Newton-Euler sensitivity equations are derived for robot manipulator motion planning problems. The dynamics and sensitivity equations depend on the 3 × 3 rotation matrices based on the moving coordinates. Compared to recursive Lagrangian formulation, which depends on 4 × 4 Denavit-Hartenberg (DH) transformation matrices, the moving coordinate formulation increases computational efficiency significantly as the number of matrix multiplications required for each optimization iteration is greatly reduced. A two-link manipulator time-optimal trajectory planning problem is solved using the proposed recursive Newton-Euler dynamics formulation. Only revolute joint is considered in the formulation. The predicted joint torque and trajectory are verified with the data in the literature. In addition, the optimal joint forces are retrieved from the optimization using recursive Newton-Euler dynamics.
{"title":"Recursive Newton-Euler Dynamics and Sensitivity Analysis for Robot Manipulator With Revolute Joints","authors":"Shuvrodeb Barman, Y. Xiang","doi":"10.1115/detc2020-22646","DOIUrl":"https://doi.org/10.1115/detc2020-22646","url":null,"abstract":"\u0000 In this study, recursive Newton-Euler sensitivity equations are derived for robot manipulator motion planning problems. The dynamics and sensitivity equations depend on the 3 × 3 rotation matrices based on the moving coordinates. Compared to recursive Lagrangian formulation, which depends on 4 × 4 Denavit-Hartenberg (DH) transformation matrices, the moving coordinate formulation increases computational efficiency significantly as the number of matrix multiplications required for each optimization iteration is greatly reduced. A two-link manipulator time-optimal trajectory planning problem is solved using the proposed recursive Newton-Euler dynamics formulation. Only revolute joint is considered in the formulation. The predicted joint torque and trajectory are verified with the data in the literature. In addition, the optimal joint forces are retrieved from the optimization using recursive Newton-Euler dynamics.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124892607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Human balancing on rolling balance board in the sagittal plane is analyzed such that the geometry of the balance board can be adjusted: the radius R of the wheels and the elevation h between the top of the wheels and the board can be changed. These two parameters have a significant influence on the stability of standing on the board as shown by preliminary experiments. The human body was modeled by a single inverted pendulum, while the balance board was considered by the geometry of the mechanical model. Based on literature, it was assumed that the central nervous system (CNS) controls by signals proportional to the angle and angular velocity of the human body and the balance board and is able to tune the feedback gains with 40% accuracy during the balancing process. To take the reaction time into consideration, operation of the CNS was modeled as a delayed proportional-derivative feedback. The critical time delay for the stabilization process is defined such that if the delay is larger than the critical one then no control gains could stabilize the system. Four balance board configurations were chosen with different wheel radius and the corresponding critical time delays were computed based on the mechanical model. Eight young healthy individuals participated in the experiments. Their task was to perform 60 s long balancing trials on each balance board. The reaction time of the participants was estimated by comparing the numerical results obtained for the critical time delay and their successful and unsuccessful balancing trials. The reaction times were found to be in the range of 0.10–0.15 s which are in good agreement with the literature.
{"title":"Estimation of Reaction Time During Human Balancing on Rolling Balance Board Based on Mechanical Models","authors":"Csenge A. Molnar, T. Insperger","doi":"10.1115/detc2020-22407","DOIUrl":"https://doi.org/10.1115/detc2020-22407","url":null,"abstract":"\u0000 Human balancing on rolling balance board in the sagittal plane is analyzed such that the geometry of the balance board can be adjusted: the radius R of the wheels and the elevation h between the top of the wheels and the board can be changed. These two parameters have a significant influence on the stability of standing on the board as shown by preliminary experiments. The human body was modeled by a single inverted pendulum, while the balance board was considered by the geometry of the mechanical model. Based on literature, it was assumed that the central nervous system (CNS) controls by signals proportional to the angle and angular velocity of the human body and the balance board and is able to tune the feedback gains with 40% accuracy during the balancing process. To take the reaction time into consideration, operation of the CNS was modeled as a delayed proportional-derivative feedback. The critical time delay for the stabilization process is defined such that if the delay is larger than the critical one then no control gains could stabilize the system. Four balance board configurations were chosen with different wheel radius and the corresponding critical time delays were computed based on the mechanical model. Eight young healthy individuals participated in the experiments. Their task was to perform 60 s long balancing trials on each balance board. The reaction time of the participants was estimated by comparing the numerical results obtained for the critical time delay and their successful and unsuccessful balancing trials. The reaction times were found to be in the range of 0.10–0.15 s which are in good agreement with the literature.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133282813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We subjected rubber coupons to cyclical uniaxial tension to investigate the softening effect, where the primary loading at its initial position was followed by additional unloading and reloading. Less stress was required upon reloading than that required in the previous loading for the same degree of stretch, reached on the first loading. This stress softening is significant when reloading follows virgin loading. The magnitude of stress softening is related to the maximum stretch elastomers can achieve in each cycle. To investigate this phenomenon, rubber coupons were subjected to four cycles of simple tension until the desired stretch was reached. We expected that several tests under the same conditions would provide almost identical results. However, we observed different stress requirements for different degrees of stretch when multiple cycles of the same stretch were performed. For three different experimental tests of the same amount of stretch, we saw huge differences in each cycle of loading-relaxation-reloading, a phenomenon that was more obvious during stress relaxation.
{"title":"Experimental Study of Mullins Effect in Natural Rubber for Different Stretch Conditions","authors":"E. Gkouti, B. Yenigun, K. Jankowski, A. Czekanski","doi":"10.1115/detc2020-22565","DOIUrl":"https://doi.org/10.1115/detc2020-22565","url":null,"abstract":"\u0000 We subjected rubber coupons to cyclical uniaxial tension to investigate the softening effect, where the primary loading at its initial position was followed by additional unloading and reloading. Less stress was required upon reloading than that required in the previous loading for the same degree of stretch, reached on the first loading. This stress softening is significant when reloading follows virgin loading. The magnitude of stress softening is related to the maximum stretch elastomers can achieve in each cycle. To investigate this phenomenon, rubber coupons were subjected to four cycles of simple tension until the desired stretch was reached. We expected that several tests under the same conditions would provide almost identical results. However, we observed different stress requirements for different degrees of stretch when multiple cycles of the same stretch were performed. For three different experimental tests of the same amount of stretch, we saw huge differences in each cycle of loading-relaxation-reloading, a phenomenon that was more obvious during stress relaxation.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115153136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the dynamics of pathological tremors (e.g., Parkinson’s Disease, Essential Tremor) is crucial to developing effective treatments for these neurological disorders. This paper studies the data-driven modeling of periodic and quasiperiodic tremors. A general neuromusculoskeletal model is proposed to serve as the theoretical basis of this study. The Parkinsonian tremor data is first observed in terms of periodicity, frequency composition, and chaotic characteristics, which confirm tremor is a nonlinear dynamics problem. Two data-driven models are then proposed to predict the nonlinear dynamics of tremor: (1) a model-free approach via long short-term memory recurrent neural network, and (2) a model-based approach via extended dynamical mode decomposition. These models are compared to existing models and the results show that the proposed models outperform existing models for long term prediction of tremor.
{"title":"Towards Data-Driven Modeling of Pathological Tremors","authors":"Jiamin Wang, S. K. Gupta, O. Barry","doi":"10.1115/detc2020-22147","DOIUrl":"https://doi.org/10.1115/detc2020-22147","url":null,"abstract":"\u0000 Understanding the dynamics of pathological tremors (e.g., Parkinson’s Disease, Essential Tremor) is crucial to developing effective treatments for these neurological disorders. This paper studies the data-driven modeling of periodic and quasiperiodic tremors. A general neuromusculoskeletal model is proposed to serve as the theoretical basis of this study. The Parkinsonian tremor data is first observed in terms of periodicity, frequency composition, and chaotic characteristics, which confirm tremor is a nonlinear dynamics problem. Two data-driven models are then proposed to predict the nonlinear dynamics of tremor: (1) a model-free approach via long short-term memory recurrent neural network, and (2) a model-based approach via extended dynamical mode decomposition. These models are compared to existing models and the results show that the proposed models outperform existing models for long term prediction of tremor.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115374421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mechanical systems are typically described through multi-body models with redundant coordinates, related by imposed constraints, where the dynamics is expressed with Differential Algebraic Equations. Alternatively, for rigid models, it may be preferable to employ minimal coordinates that do not require additional constraints, thus leading to Ordinary Differential Equations. However, to reduce a general multibody model to minimal coordinates and perform the simulation in the reduced space, the mapping between the minimal coordinates and the full coordinates is required. In this work, it is proposed to approximate such mapping using a neural network. In order to avoid overfitting and guarantee a continuous description of the solution manifold, the multibody dynamics information are included in the neural network training. The particular case where periodic minimal coordinates are required is treated and validated. In general, the methodology can be used when the mapping is unknown such as for spatial mechanisms with closed loops.
{"title":"Deep Learning of (Periodic) Minimal Coordinates for Multibody Simulations","authors":"A. Angeli, F. Naets, W. Desmet","doi":"10.1115/detc2020-22529","DOIUrl":"https://doi.org/10.1115/detc2020-22529","url":null,"abstract":"\u0000 Mechanical systems are typically described through multi-body models with redundant coordinates, related by imposed constraints, where the dynamics is expressed with Differential Algebraic Equations. Alternatively, for rigid models, it may be preferable to employ minimal coordinates that do not require additional constraints, thus leading to Ordinary Differential Equations. However, to reduce a general multibody model to minimal coordinates and perform the simulation in the reduced space, the mapping between the minimal coordinates and the full coordinates is required. In this work, it is proposed to approximate such mapping using a neural network. In order to avoid overfitting and guarantee a continuous description of the solution manifold, the multibody dynamics information are included in the neural network training. The particular case where periodic minimal coordinates are required is treated and validated. In general, the methodology can be used when the mapping is unknown such as for spatial mechanisms with closed loops.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115474255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the design of the suspension system for Heavy Goods Vehicles (HGV) is proposed, which deals with two performance criteria simultaneously. A semi-tractor trailer is used in present work and modeled with half vehicle model. Four types of linear, as well as non-linear, passive and semi-active suspension systems, are presented in this work. The control law is proposed for the semi-active suspension system using a PID controller to remove the need for passive damper along with active damper. Two objective optimization is performed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Road Damage (RD) is taken as the first objective along with Goods Damage (GD) as the second objective. All problems are minimization problems. It is concluded based on Pareto front comparison of different suspension systems that the semi-active suspension system with the proposed control law performs well for HGV.
{"title":"Controller Design and Road-Friendly Suspension Optimization: Half Vehicle Model","authors":"V. Prasad, P. Seshu, D. N. Pawaskar","doi":"10.1115/detc2020-22051","DOIUrl":"https://doi.org/10.1115/detc2020-22051","url":null,"abstract":"\u0000 In this paper, the design of the suspension system for Heavy Goods Vehicles (HGV) is proposed, which deals with two performance criteria simultaneously. A semi-tractor trailer is used in present work and modeled with half vehicle model. Four types of linear, as well as non-linear, passive and semi-active suspension systems, are presented in this work. The control law is proposed for the semi-active suspension system using a PID controller to remove the need for passive damper along with active damper. Two objective optimization is performed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Road Damage (RD) is taken as the first objective along with Goods Damage (GD) as the second objective. All problems are minimization problems. It is concluded based on Pareto front comparison of different suspension systems that the semi-active suspension system with the proposed control law performs well for HGV.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130144912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lautaro Cilenti, A. Chijioke, N. Vlajic, B. Balachandran
Characterization and quantification of dynamic measurements is an ongoing area of research in the metrological community, as new calibration methods are being developed to address dynamic measurement applications. In the development undertaken to date, one largely assumes that nominally linear transducers can be used with linear assumptions in deconvolution of the input from the response and in system identification. To quantify the errors that arise from these assumptions, in this article, the effects of weak nonlinearities in transducers that are assumed to behave linearly during dynamic excitations are studied. Specifically, a set of first-order and second-order systems, which can model many transducers with weak nonlinearities, are used to numerically quantify the systemic errors due to the linear assumptions underlying the deconvolution. We show through the presented results the evolution of different error metrics over a large parameter space of possible transducers. Additionally, an example of quantification of the errors due to linear assumptions in system identification is demonstrated by using a time-series sparse regression system identification strategy. It is shown that the errors generated from linear identification of a nonlinear transducer can counteract the systemic errors that arise in linear deconvolution when the linear system identification is performed in similar loading conditions. In general, the methodology and results presented here can be useful for understanding the effect of nonlinearity in single degree of freedom transient dynamics deconvolution and specifically in specifying certain metrics of errors in transducers with known weak nonlinearities.
{"title":"Error Quantification in Dynamic Applications of Weakly Nonlinear Transducers","authors":"Lautaro Cilenti, A. Chijioke, N. Vlajic, B. Balachandran","doi":"10.1115/detc2020-22137","DOIUrl":"https://doi.org/10.1115/detc2020-22137","url":null,"abstract":"\u0000 Characterization and quantification of dynamic measurements is an ongoing area of research in the metrological community, as new calibration methods are being developed to address dynamic measurement applications. In the development undertaken to date, one largely assumes that nominally linear transducers can be used with linear assumptions in deconvolution of the input from the response and in system identification. To quantify the errors that arise from these assumptions, in this article, the effects of weak nonlinearities in transducers that are assumed to behave linearly during dynamic excitations are studied. Specifically, a set of first-order and second-order systems, which can model many transducers with weak nonlinearities, are used to numerically quantify the systemic errors due to the linear assumptions underlying the deconvolution. We show through the presented results the evolution of different error metrics over a large parameter space of possible transducers. Additionally, an example of quantification of the errors due to linear assumptions in system identification is demonstrated by using a time-series sparse regression system identification strategy. It is shown that the errors generated from linear identification of a nonlinear transducer can counteract the systemic errors that arise in linear deconvolution when the linear system identification is performed in similar loading conditions. In general, the methodology and results presented here can be useful for understanding the effect of nonlinearity in single degree of freedom transient dynamics deconvolution and specifically in specifying certain metrics of errors in transducers with known weak nonlinearities.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127277272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the performance of a nonlinear vibration absorber with different nonlinearity is studied. The analytical solutions of periodic motions are obtained using the general harmonic balance method. As the nonlinear strength is weak, the effectiveness of the absorber is discussed. For strong nonlinearities, unstable parodic motions can be obtained and stabilities of the periodic motions are determined through the eigenvalue analysis. The Hopf and saddle bifurcations are observed. Numerical simulations are illustrated for both masses at the resonance peaks. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions.
{"title":"Vibration Suppression of a Harmonically Forced Oscillator Using a Passive Nonlinear Vibration Absorber","authors":"B. Yu","doi":"10.1115/detc2020-22715","DOIUrl":"https://doi.org/10.1115/detc2020-22715","url":null,"abstract":"\u0000 In this paper, the performance of a nonlinear vibration absorber with different nonlinearity is studied. The analytical solutions of periodic motions are obtained using the general harmonic balance method. As the nonlinear strength is weak, the effectiveness of the absorber is discussed. For strong nonlinearities, unstable parodic motions can be obtained and stabilities of the periodic motions are determined through the eigenvalue analysis. The Hopf and saddle bifurcations are observed. Numerical simulations are illustrated for both masses at the resonance peaks. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions.","PeriodicalId":236538,"journal":{"name":"Volume 2: 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129015939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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