Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yousheng Chen ◽  
Andreas Linderholt ◽  
Thomas J. S. Abrahamsson
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Test Data ◽  
Nonlinear Model ◽  
Model Calibration ◽  
Experimental Validation ◽  
Calibration Method ◽  
Model Parameters ◽  
Response Data ◽  
Starting Point

Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the École Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated model's output corresponds well with the measured responses.

Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multiharmonic Frequency Responses

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Yousheng Chen ◽  
Vahid Yaghoubi ◽  
Andreas Linderholt ◽  
Thomas J. S. Abrahamsson
Keyword(s):  
Steady State ◽  
Test Data ◽  
Model Calibration ◽  
Cross Validation ◽  
Nonlinear Frequency ◽  
Nonlinear Characteristics ◽  
Physical Test ◽  
True Parameter ◽  
Starting Point ◽  
Fold Cross Validation

In industry, linear finite element (FE) models commonly serve as baseline models to represent the global structural dynamics behavior. However, available test data may show evidence of significant nonlinear characteristics. In such a case, the baseline linear model may be insufficient to represent the dynamics of the structure. The causes of the nonlinear characteristics may be local in nature and the remaining parts of the structure may be satisfactorily represented by linear descriptions. Although the baseline model can then serve as a good foundation, the physical phenomena needed to substantially increase the model's capability of representing the real structure are most likely not modeled in it. Therefore, a set of candidate parameters to control the nonlinear effects have to be added and subjected to calibration to form a credible model. An overparameterized model for calibration may results in parameter value estimates that do not survive a validation test. The parameterization is coupled to the test data and should be chosen so that the expected covariance matrix of the parameter estimates is made small. Accurate test data, suitable for calibration, is often obtained from sinusoidal testing. Because a pure monosinusoidal excitation is difficult to achieve during a physical test of a nonlinear structure, a multisinusoidal excitation is here designed. In this paper, synthetic test data from a model of a nonlinear benchmark structure are used for illustration. The steady-state solutions of the nonlinear system are found using the multiharmonic balance (MHB) method. The steady-state responses at the side frequencies are shown to contain valuable information for the calibration process that can improve the accuracy of the parameters' estimates. The model calibration made and the associated κ-fold cross-validation used is based on the Levenberg–Marquardt and the undamped Gauss–Newton algorithm, respectively. Starting seed candidates for calibration are found by the Latin hypercube sampling method. The candidate that gives the smallest deviation to test data is selected as a starting point for the iterative search for a calibration solution. The calibration result shows good agreement with the true parameter setting and the κ-fold cross validation result shows that the variances of the estimated parameters shrink when multiharmonics nonlinear frequency response functions (FRFs) are included in the data used for calibration.

scholarly journals Steady-State Steering Characteristics of Mathematical Model for Semitrailer Based on Variations in Camber Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yi Wei ◽  
Shuilong He ◽  
Enyong Xu ◽  
Genge Zhang ◽  
Rongjiang Tang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Test Data ◽  
Dynamic State ◽  
Model Parameters ◽  
Stability Factor ◽  
Camber Angle ◽  
Body Roll ◽  
Vehicle Test ◽  
Real Vehicle

To master the basic characteristics of steady-state cornering for a semitrailer, this paper summarises the current modelling methods for handling and stability and discusses their limitations. The classical linear mathematical model for a two-degree-of-freedom (DOF) handling and stability system is used to develop a new model. Analysis methods are proposed to introduce the influence of the camber angle and body roll into the model parameters. Thus, a mathematical model for the lateral stability of semitrailer with five DOFs is established. At the same time, a modified formula to calculate the stability factor of the semitrailer is developed with a MATLAB model to solve the dynamic state equation. The mathematical model, which considers the body roll and the changes in the camber angle caused by roll, compares the turning radius ratio and yaw rate as the evaluation index with the classical linear mathematical model of a two-DOF system. The vehicle parameters for three different types of semi-tractor trailers are used to calculate and compare two mathematical models for handling and stability using real vehicle test data. The results show that the new modelling and analysis method proposed in this paper has a high calculation accuracy and fast calculation speed, is clear and concise, and is consistent with the real vehicle test data. In addition, the accuracy of the new mathematical model for handling and stability and the improved stability factor are verified.

scholarly journals Calibration of a simple and a complex model of global marine biogeochemistry

2017 ◽  
Author(s):  
Iris Kriest
Keyword(s):  
Steady State ◽  
Model Calibration ◽  
Organic Phosphorus ◽  
Model Performance ◽  
Parametric Uncertainty ◽  
Complex Model ◽  
Component Model ◽  
Model Parameters ◽  
Model Assessment ◽  
High Level

Abstract. The assessment of the ocean biota's role in climate climate change is often carried out with global biogeochemical ocean models that contain many components, and involve a high level of parametric uncertainty. Examination the models' fit to climatologies of inorganic tracers, after the models have been spun up to steady state, is a common, but computationally expensive procedure to assess model performance and reliability. Using new tools that have become available for global model assessment and calibration in steady state, this paper examines two different model types – a complex seven-component model (MOPS), and a very simple two-component model (RetroMOPS) – for their fit to dissolved quantities. Before comparing the models, a subset of their biogeochemical parameters has been optimised against annual mean nutrients and oxygen. Both model types fit the observations almost equally well. The simple model, which contains only nutrients and dissolved organic phosphorus (DOP), is sensitive to the parameterisation of DOP production and decay. The spatio-temporal decoupling of nitrogen and oxygen, and processes involved in their uptake and release, renders oxygen and nitrate valuable tracers for model calibration. In addition, the non-conservative nature of these tracers (with respect to their upper boundary condition) introduces the global bias as a useful additional constraint on model parameters. Dissolved organic phosphorous at the surface behaves antagonistically to phosphate, and suggests that observations of this tracer – although difficult to measure – may be an important asset for model calibration.

scholarly journals Influence of rainfall observation network on model calibration and application

2006 ◽  
Vol 3 (6) ◽  
pp. 3691-3726 ◽  
Author(s):  
A. Bárdossy ◽  
T. Das
Keyword(s):  
Model Calibration ◽  
Goodness Of Fit ◽  
Missing Values ◽  
Calibration Method ◽  
Model Parameters ◽  
Missing Measurements ◽  
Observation Network ◽  
Complete Set ◽  
Fit Indexes ◽  
Hbv Model

Abstract. The objective in this study is to investigate the influence of the spatial resolution of the rainfall input on the model calibration and application. The analysis is carried out by varying the distribution of the raingauge network. The semi-distributed HBV model is calibrated with the precipitation interpolated from the available observed rainfall of the different raingauge networks. An automatic calibration method based on the combinatorial optimization algorithm simulated annealing is applied. Aggregated Nash-Sutcliffe coefficients at different temporal scales are adopted as objective function to estimate the model parameters. The performance of the hydrological model is analyzed as a function of the raingauge density. The calibrated model is validated using the same precipitation used for the calibration as well as interpolated precipitation based on networks of reduced and increased raingauge density. The effect of missing rainfall data is investigated by using a multiple linear regression approach for filling the missing values. The model, calibrated with the complete set of observed data, is then run in the validation period using the above described precipitation field. The simulated hydrographs obtained in the three sets of experiments are analyzed through the comparisons of the computed Nash-Sutcliffe coefficient and several goodness-of-fit indexes. The results show that the model using different raingauge networks might need recalibration of the model parameters: model calibrated on sparse information might perform well on dense information while model calibrated on dense information fails on sparse information. Also, the model calibrated with complete set of observed precipitation and run with incomplete observed data associated with the data estimated using multiple linear regressions, at the locations treated as missing measurements, performs well. A meso-scale catchment located in the south-west of Germany has been selected for this study.

scholarly journals Calibration of a simple and a complex model of global marine biogeochemistry

2017 ◽  
Vol 14 (21) ◽  
pp. 4965-4984 ◽  
Author(s):  
Iris Kriest
Keyword(s):  
Steady State ◽  
Model Calibration ◽  
Large Scale ◽  
Organic Phosphorus ◽  
Model Performance ◽  
Complex Model ◽  
Component Model ◽  
Model Parameters ◽  
Model Assessment ◽  
Dissolved Organic Phosphorus

Abstract. The assessment of the ocean biota's role in climate change is often carried out with global biogeochemical ocean models that contain many components and involve a high level of parametric uncertainty. Because many data that relate to tracers included in a model are only sparsely observed, assessment of model skill is often restricted to tracers that can be easily measured and assembled. Examination of the models' fit to climatologies of inorganic tracers, after the models have been spun up to steady state, is a common but computationally expensive procedure to assess model performance and reliability. Using new tools that have become available for global model assessment and calibration in steady state, this paper examines two different model types – a complex seven-component model (MOPS) and a very simple four-component model (RetroMOPS) – for their fit to dissolved quantities. Before comparing the models, a subset of their biogeochemical parameters has been optimised against annual-mean nutrients and oxygen. Both model types fit the observations almost equally well. The simple model contains only two nutrients: oxygen and dissolved organic phosphorus (DOP). Its misfit and large-scale tracer distributions are sensitive to the parameterisation of DOP production and decay. The spatio-temporal decoupling of nitrogen and oxygen, and processes involved in their uptake and release, renders oxygen and nitrate valuable tracers for model calibration. In addition, the non-conservative nature of these tracers (with respect to their upper boundary condition) introduces the global bias (fixed nitrogen and oxygen inventory) as a useful additional constraint on model parameters. Dissolved organic phosphorus at the surface behaves antagonistically to phosphate, and suggests that observations of this tracer – although difficult to measure – may be an important asset for model calibration.

scholarly journals A new Bayesian methodology for nonlinear model calibration in Computational Systems Biology

2019 ◽  
Author(s):  
Fortunato Bianconi ◽  
Lorenzo Tomassoni ◽  
Chiara Antonini ◽  
Paolo Valigi
Keyword(s):  
Systems Biology ◽  
Nonlinear Model ◽  
Model Calibration ◽  
Sequential Monte Carlo ◽  
Profile Likelihood ◽  
Computational Cost ◽  
Robustness Analysis ◽  
Model Parameters ◽  
Computational Systems Biology ◽  
Proposal Distribution

AbstractComputational modeling is a common tool to quantitatively describe biological processes. However, most model parameters are usually unknown because they cannot be directly measured. Therefore, a key issue in Systems Biology is model calibration, i.e. estimate parameters from experimental data. Existing methodologies for parameter estimation are divided in two classes: frequentist and Bayesian methods. The first ones optimize a cost function while the second ones estimate the parameter posterior distribution through different sampling techniques. Here, we present an innovative Bayesian method, called Conditional Robust Calibration (CRC), for nonlinear model calibration and robustness analysis using omics data. CRC is an iterative algorithm based on the sampling of a proposal distribution and on the definition of multiple objective functions, one for each observable. CRC estimates the probability density function (pdf) of parameters conditioned to the experimental measures and it performs a robustness analysis, quantifying how much each parameter influences the observables behavior. We apply CRC to three Ordinary Differential Equations (ODE) models to test its performances compared to the other state of the art approaches, namely Profile Likelihood (PL), Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) and Delayed Rejection Adaptive Metropolis (DRAM). Compared with these methods, CRC finds a robust solution with a reduced computational cost. CRC is developed as a set of Matlab functions (version R2018), whose fundamental source code is freely available at https://github.com/fortunatobianconi/CRC.

System identification of civil engineering structures

1987 ◽  
Vol 14 (1) ◽  
pp. 7-18 ◽  
Author(s):  
J.-G. Béliveau
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Frequency Response ◽  
Civil Engineering ◽  
Time Response ◽  
Scale Model ◽  
Engineering Structures ◽  
Modal Data ◽  
Response Data ◽  
Civil Engineering Structures

The comparison of measured dynamic characteristics or response of large structures with that of an appropriate finite element model with all its underlying assumptions often reveals discrepancies. This may be due to improperly determined parameters, such as interstory stiffness, mass of different stories, and the modulus of elasticity of the concrete, as well as the inadequacies of the model.The measured dynamic response generally occurs in one of three forms: time response, frequency response, and modal data. For time response data, either in free vibration or for a known input, parameters are estimated by proper adjustments to match more closely the measured motion. For steady-state frequency response, a sinusoidal load (or synchronized loads) is input mechanically and the response, both in amplitude and in phase, is measured for different frequencies of excitation. Damped resonant frequencies, the associated modal damping ratios, and the corresponding mode shapes are the measured quantities for modal data.The finite element models used for civil engineering structures often incorporate a large number of degrees of freedom. Measured response is sparse and usually limited to the lower frequency range. A procedure for estimating these parameters must be able to allow for the small amount of data and must utilize efficient numerical algorithms to determine the best parameters. Nonlinear least squares, within a Bayesian framework, is such a method. It can be applied to time-history data, steady-state response, and modal characteristics. This method is used to determine aerodynamic coefficients of a scale model of a suspension bridge deck from free response data in a wind tunnel, stiffness parameters from frequency measurements of a 5-story steel building frame loaded by mechanical exciters on the roof, and stiffness parameters from modal data of a 12-story reinforced concrete frame, as obtained from transient wind observation of lateral accelerations.

scholarly journals Influence of rainfall observation network on model calibration and application

2008 ◽  
Vol 12 (1) ◽  
pp. 77-89 ◽  
Author(s):  
A. Bárdossy ◽  
T. Das
Keyword(s):  
Model Calibration ◽  
Goodness Of Fit ◽  
Calibration Method ◽  
Model Parameters ◽  
Missing Measurements ◽  
Observation Network ◽  
Complete Set ◽  
Fit Indexes ◽  
Hbv Model ◽  
Linear Regressions

Abstract. The objective in this study is to investigate the influence of the spatial resolution of the rainfall input on the model calibration and application. The analysis is carried out by varying the distribution of the raingauge network. A meso-scale catchment located in southwest Germany has been selected for this study. First, the semi-distributed HBV model is calibrated with the precipitation interpolated from the available observed rainfall of the different raingauge networks. An automatic calibration method based on the combinatorial optimization algorithm simulated annealing is applied. The performance of the hydrological model is analyzed as a function of the raingauge density. Secondly, the calibrated model is validated using interpolated precipitation from the same raingauge density used for the calibration as well as interpolated precipitation based on networks of reduced and increased raingauge density. Lastly, the effect of missing rainfall data is investigated by using a multiple linear regression approach for filling in the missing measurements. The model, calibrated with the complete set of observed data, is then run in the validation period using the above described precipitation field. The simulated hydrographs obtained in the above described three sets of experiments are analyzed through the comparisons of the computed Nash-Sutcliffe coefficient and several goodness-of-fit indexes. The results show that the model using different raingauge networks might need re-calibration of the model parameters, specifically model calibrated on relatively sparse precipitation information might perform well on dense precipitation information while model calibrated on dense precipitation information fails on sparse precipitation information. Also, the model calibrated with the complete set of observed precipitation and run with incomplete observed data associated with the data estimated using multiple linear regressions, at the locations treated as missing measurements, performs well.

scholarly journals A Multivariable Adaptive Control Approach for Stabilization of a Cart-Type Double Inverted Pendulum

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
I. Hassanzadeh ◽  
A. Nejadfard ◽  
M. Zadi
Keyword(s):  
Steady State ◽  
Nonlinear Model ◽  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Feedback Gain ◽  
Practical Implementation ◽  
Model Parameters ◽  
Lagrange Equations ◽  
Control Approach ◽  
Input Structure

This paper considers the design and practical implementation of linear-based controllers for a cart-type double inverted pendulum (DIPC). A constitution of two linked pendulums placed on a sliding cart, presenting a three Degrees of Freedom and single controlling input structure. The controller objective is to keep both pendulums in an up-up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted nonlinear model is linearized around up-up position. First, the LQR method is used to stabilize DIPC by a feedback gain matrix in order to minimize a quadratic cost function. Without using an observer to estimate the unmeasured states, in the next step we make use of LQG controller which combines the Kalman-Bucy filter estimation and LQR feedback control to obtain a better steady-state performance, but poor robustness. Eventually, to overcome the unknown nonlinear model parameters, an adaptive controller is designed. This controller is based on Model Reference Adaptive System (MRAS) method, which uses the Lyapunov function to eliminate the defined state error. This controller improves both the steady-state and disturbance responses.

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