Improving Identifiability in Model Calibration Using Multiple Responses

Author(s):  
Paul D. Arendt ◽  
Wei Chen ◽  
Daniel W. Apley

The use of complex computer simulations to design, improve, optimize, or simply to better understand complex systems in many fields of science and engineering is now ubiquitous. However, simulation models are never a perfect representation of physical reality. Two general sources of uncertainty that account for the differences between simulations and experiments are parameter uncertainty and model uncertainty. The former derives from unknown model parameters, while the latter is caused by underlying missing physics, numerical approximations, and other inaccuracies of the computer simulation that exist even if all of the parameters are known. To obtain knowledge of these two sources of uncertainty, data from computer simulations (usually abundant) and data from physical experiments (typically more limited) are often combined using statistical methods. Statistical adjustment of the computer simulation model to account for the two sources of uncertainty is referred to as calibration. We argue that calibration as it is typically implemented, using only a single response variable, is challenging in that it is often extremely difficult to distinguish between the effects of parameter and model uncertainty. However, many different responses (distinct responses and/or the same response measured at different spatial and temporal locations) are automatically calculated in simulations. As multiple responses generally share a mutual dependence on the unknown parameters, they provide valuable information that can improve identifiability of parameter and model uncertainty in calibration, if they are also measured experimentally. In this paper, we explore the use of multiple responses for calibration.

Author(s):  
Matthew J. Hillegass ◽  
James G. Faller ◽  
Mark S. Bounds ◽  
Moustafa El-Gindy ◽  
Abhishek S. Joshi

The dynamic performance of a multi-wheeled combat vehicle model specially developed in multi-body dynamics code was validated against measured data obtained on the U.S. Army Aberdeen Test Center’s (ATC) test courses. The multi-wheeled combat vehicle variant that was tested was developed in the modeling software TruckSim from Mechanical Simulation Corporation. Prior to validating the model, the vehicle weights, dimensions, tires and suspension characteristics were measured and referenced in the specially developed computer simulation model. Non-linear measured tire and suspension look-up tables were used in the simulation. The predictions of the vehicle handling characteristics and transient response during lane change at different vehicle speeds were compared with field tests results. Measured and predicted results are compared on the basis of vehicle steering, yaw rates, accelerations and handling diagrams. Statistical methods such as power spectral density, root mean square, skewness, and kurtosis are applied to validate the model. Validation tolerances are defined for each set of statistical results based on ATC’s experience.


Author(s):  
Yi-Ping Chen ◽  
Kuei-Yuan Chan

Abstract Validation in vehicle engineering identifies and quantifies the differences between simulation models and experiment data. In this work we consider these differencesthe lack of ability to model uncertainties and to identify unknown parameters values, especially for coupled complex systems such as vehicles. Effects of unknown model parameters vary under different maneuvers and the ability to excite a source of uncertainty is the focus of this study. We propose an optimization method to generate a proper maneuver that maximize the sensitivity of uncertain parameters based on global sensitivity analysis (GSA). Sensitivities with respect to individual uncertain parameters and those that consider coupled effects are all included. We utilize Kriging-based metamodels to improve the efficiency of the GSA problems with computationally expensive simulations. The optimal design of excitation maneuvers to create the most sensitive performances can then be obtained. The applicability and the accuracy of the proposed method are assessed via a math model and a practical application on a x-by-wire autonomous tricycle. Results show that our proposed method can assist in providing a suitable maneuver as an alternative validation to uncertain parameters in a vehicle system.


2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Anton v. Beek ◽  
Mian Li ◽  
Chao Ren

Simulation models are widely used to describe processes that would otherwise be arduous to analyze. However, many of these models merely provide an estimated response of the real systems, as their input parameters are exposed to uncertainty, or partially excluded from the model due to the complexity, or lack of understanding of the problem's physics. Accordingly, the prediction accuracy can be improved by integrating physical observations into low fidelity models, a process known as model calibration or model fusion. Typical model fusion techniques are essentially concerned with how to allocate information-rich data points to improve the model accuracy. However, methods on subtracting more information from already available data points have been starving attention. Subsequently, in this paper we acknowledge the dependence between the prior estimation of input parameters and the actual input parameters. Accordingly, the proposed framework subtracts the information contained in this relation to update the estimated input parameters and utilizes it in a model updating scheme to accurately approximate the real system outputs that are affected by all real input parameters (RIPs) of the problem. The proposed approach can effectively use limited experimental samples while maintaining prediction accuracy. It basically tweaks model parameters to update the computer simulation model so that it can match a specific set of experimental results. The significance and applicability of the proposed method is illustrated through comparison with a conventional model calibration scheme using two engineering examples.


Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6324
Author(s):  
Tudur Wyn David ◽  
Noel Bristow ◽  
Vasil Stoichkov ◽  
Han Huang ◽  
Grazia Todeschini ◽  
...  

The outdoor performance of large area Organic Photovoltaics (OPVs) is investigated in this work. Initially, the diurnal performance of the three modules is determined and found to be similar. Subsequently module degradation is monitored, and it is found that the larger area module displays a significantly greater stability as compared to the smallest area module; in fact the larger module displays a T50% (time to fall to 50% of its original value) of 191 days whilst the smallest module displays a T50% of 57 days. This is attributed to an increased level of water infiltration due to a larger perimeter-to-area ratio. These findings are then used to verify a computer simulation model which allows the model parameters, series and shunt resistances, to be calculated. It is determined that the series resistance is not an obvious obstruction at these module sizes. The findings of this work provide great promise for the application of OPV technology on a larger scale.


Author(s):  
Zenon Zwierzewicz

This chapter covers the concerns with a problem of adaptive ship control synthesis in the case of substantially limited knowledge of the plant model. In fact we have at our disposal only its highly general structure in the form of Norrbin’s-like representation with unknown nonlinearities. Two tasks of ship control are considered. The first task is concerning the ship course-keeping system design while the second refers to the path-following system. Two different approaches to the control synthesis problem are considered. One is based on an adaptive feedback linearization technique, while the second refers to the backstepping method where the tuning of unknown parameters is also taken into account. It has been demonstrated that the controllers thereby obtained enable on-line learning of unknown model characteristics, having at the same time the performance comparable to the case of fully known model parameters. The system’s performance assessment for the each case has been tested via Matlab/Simulink simulations.


Author(s):  
Matthew J. Hillegass ◽  
James G. Faller ◽  
Mark S. Bounds ◽  
Moustafa El-Gindy ◽  
Seokyong Chae

Performance testing is an important step in the development of any vehicle model. Generally, full-scale field tests are conducted to collect the dynamic response characteristics for evaluating the vehicle performance. However, with increases in computational power and the accuracy of simulation models, virtual testing can be extensively used as an alternative to the time consuming and costly full-scale tests, especially for severe maneuvers. Validation of the simulation results is critical for the acceptance of such simulation models. In this paper, a methodology for validating the vertical dynamic performance of a virtual vehicle has been discussed. The dynamic performance of a multi-wheeled combat vehicle model specially developed using a multi-body dynamics code was validated against the measured data obtained on the U.S. Army Aberdeen Test Center’s (ATC) test courses. The multi-wheeled combat vehicle variant computer simulation model was developed in TruckSim, a vehicle dynamic simulation software developed by the Mechanical Simulation Corporation. Prior to validating the model, the vehicle weights, dimensions, tires and suspension characteristics were measured and referenced in the specially developed computer simulation model. The data for the tire and suspension characteristics were acquired from the respective leading manufacturers in the form of look-up tables. The predictions of the vehicle vertical dynamics on different road profiles at various vehicle speeds were compared with the field test results. The time domain data for the vertical acceleration at the vehicle center of gravity, pitching, vehicle speed and the suspension/damper displacement were compared to analyze the feasibility of using the computer simulation models to predict the vertical dynamic performance of the vehicle. Based on the results it was found that the particular combat vehicle computer simulation model is capable of predicting the vertical dynamic performance characteristics.


2007 ◽  
Vol 23 (4) ◽  
pp. 300-308 ◽  
Author(s):  
Michael J. Hiley ◽  
Maurice R. Yeadon

The release window for a given dismount from the asymmetric bars is the period of time within which release results in a successful dismount. Larger release windows are likely to be associated with more consistent performance because they allow a greater margin for error in timing the release. A computer simulation model was used to investigate optimum technique for maximizing release windows in asymmetric bars dismounts. The model comprised four rigid segments with the elastic properties of the gymnast and bar modeled using damped linear springs. Model parameters were optimized to obtain a close match between simulated and actual performances of three gymnasts in terms of rotation angle (1.5°), bar displacement (0.014 m), and release velocities (<1%). Three optimizations to maximize the release window were carried out for each gymnast involving no perturbations, 10-ms perturbations, and 20-ms perturbations in the timing of the shoulder and hip joint movements preceding release. It was found that the optimizations robust to 20-ms perturbations produced release windows similar to those of the actual performances whereas the windows for the unperturbed optimizations were up to twice as large. It is concluded that robustness considerations must be included in optimization studies in order to obtain realistic results and that elite performances are likely to be robust to timing perturbations of the order of 20 ms.


1991 ◽  
Vol 113 (1) ◽  
pp. 17-24 ◽  
Author(s):  
S. J. You ◽  
K. F. Ehmann

The synthesis and generation of milled surfaces under tertiary cutter motion of the spindle with ball nose end mills was investigated and shown that a multitude of surface topographies can be generated. A basis for theoretical investigation was established by the derivation of the tooth path equations and the development of computer simulation models for ball nose end milling processes. The accuracy of the developed computer model and the feasibility of the tertiary cutter motion concept were subsequently authenticated and verified by the agreement between the experiments and the computer simulations.


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