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Although the battery surface temperature is commonly measured, the core temperature of a cell may be much higher hence more critical than the surface temperature. The core temperature of a battery, though usually unmeasured in commercial applications, can be estimated by an observer, based on a lumped-parameter battery thermal model and the measurement of the current and the surface temperature. Even with a closed loop observer based on the measured surface temperature, the accuracy of the core temperature estimation depends on the model parameters. For such purpose, an online parameterization methodology and an adaptive observer are designed for a cylindrical battery. The single cell thermal model is then scaled up to create a battery cluster model to investigate the temperature pattern of the cluster. The modeled thermal interconnections between cells include cell to cell heat conduction and convection to the surrounding coolant flow. An observability analysis is performed on the cluster before designing a closed loop observer for the pack. Based on the analysis, guidelines for determining the minimum number of required sensors and their exact locations are derived that guarantee the observability of all temperature states. Bien que la température de surface d’une batterie soit généralement mesurée, la température interne d’une cellule peut être beaucoup plus élevée donc plus critique que la température de surface. La température interne d’une batterie, pourtant normalement non mesurée dans les applications commerciales, peut être évaluée par un observateur, sur la base d’un modèle thermique de batterie à constantes localisées et à partir de la mesure du courant et de la température de surface. Même avec un observateur en boucle fermée basé sur la température de surface mesurée, la précision de l’estimation de la température interne dépend des constantes du modèle. Dans cette optique, une méthodologie de paramétrage en ligne et un observateur adaptatif sont conçus pour une batterie cylindrique. Le modèle thermique à une seule cellule est ensuite agrandi afin de créer un modèle de cluster de batteries dans le but d’étudier le schéma de température du cluster. Les interconnexions thermiques modélisées entre les cellules incluent la conduction de chaleur de cellule à cellule et la convection au flux du liquide de refroidissement environnant. Une analyse d’observabilité est effectuée sur le cluster avant la conception, pour le pack, d’un observateur en boucle fermée. Sur la base de l’analyse, les lignes directrices permettant la détermination du nombre minimal de sondes requises et leurs positionnements exacts sont déduites permettant d’assurer l’observabilité de tous les états thermiques.

In this paper, a node sampling methodology for nonlinear vibration problems of elastic structures involving intermittent contact is proposed. Of particular interest is a vibration problem of platelike elastic structures with a crack, with a large number of degrees of freedom involved on the crack surfaces. Because of the localized nature of such nonlinearity, the number of degrees of freedom on the surfaces greatly affects the computational time of the analysis. Therefore, reducing the number of degrees of freedom on the crack surfaces without significantly sacrificing the accuracy of the results is a critical issue for conducting vibration analysis of such structures in a reasonable amount of time. The focus is placed on the development of an efficient algorithm to select a set of nodes on the crack surfaces, where nonlinear boundary conditions are imposed. The method is developed, based on a procedure for selecting master degrees of freedom for Guyan reduction. The accuracy, efficiency, and optimality of the method are discussed in detail and compared with those aspects of previous methods. The advantages of the new method are demonstrated in terms of the accuracy of the frequency response and the resonant frequencies. DOI: 10.2514/1.J050061

In this work, an integrated testing and calibration procedure is presented for performing mistuning identification (ID) and traveling wave excitation (TWE) of one-piece bladed disks (blisks). The procedure yields accurate results while also being highly efficient and is comprised of three basic phases. First, selected modes from a tuned blisk finite element model are used to determine a minimal set of measurement degrees of freedom (and locations) that will work well for mistuning ID. Second, a testing procedure is presented that allows the mistuning to be identified from relatively few vibration response measurements. A numerical validation is used to investigate the convergence of the mistuning ID results to a prescribed mistuning pattern using the proposed approach and alternative testing strategies. Third, a method is derived to iteratively calibrate the excitation applied to each blade so that differences among the blade excitation magnitudes can be minimized for a single blade excitation, and also the excitation phases can be accurately set to achieve the desired traveling wave excitation. The calibration algorithm uses the principle of reciprocity and involves solving a least-squares problem to reduce the effects of measurement noise and uncertainty. Because the TWE calibration procedure re-uses the data collected during the mistuning ID, the overall procedure is integrated and efficient. [DOI: 10.1115/1.3204656]

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The influence of small random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of component mode synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response of an example rotor are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack and the vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared with those obtained with linear ROMs, as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar to those of mistuning, the effects of mistuning and damage can be distinguished by observing and comparing the response across multiple families of system modes. [DOI: 10.111511.4000458]

The reduced-order modeling of integrally bladed disks for predicting the mistuned vibration response has been well studied and understood. For solving a direct vibration problem, adding modes to the modeling basis improves the accuracy of the reduced-order model with respect to the parent finite element model. In contrast, when solving an inverse problem for system identification, adding modes to the reduced-order model while using the same measurements may actually reduce its accuracy. This is especially true for solving inverse problems related to the identification of blade mistuning parameters, because the characteristics of the selected system modes for the reduced-order model may not match the assumptions used in the mistuning modeling approach. In this work, a procedure is introduced for constructing a reduced-order model referred to as the inverse reduced-order model that is well suited for solving the mistuning identification inverse problem. First, a quantitative metric is defined to characterize and rank the tuned-system modes with respect to their suitability for constructing inverse reducedorder models. Then, the direct problem is solved using a larger direct reduced-order model with prescribed mistuning to interrogate and validate the performance of various inverse reduced-order models as modes are added. This enables the automated construction of suitable inverse reduced-order models and improves the overall accuracy and robustness of mistuning identification. DOI: 10.2514/1.37314

New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.

The forced vibration response of bladed disks can increase dramatically due to blade mistuning, which can cause major durability and reliability problems in turbine engines. To predict the mistuned forced response efficiently, several reduced-order modeling techniques have been developed. However, for mistuned bladed disks, increases in blade amplitude levels do not always correlate well with increases in blade stress levels. The stress levels may be computed by postprocessing the reduced-order model results with finite element analysis, but this is cumbersome and expensive. In this work, three indicators that can be calculated directly from reduced-order models are proposed as a way to estimate blade stress levels in a straightforward, systematic, and inexpensive manner. It is shown that these indicators can be used to predict stress values with good accuracy relative to finite element results, even for a case in which the displacement and stress levels show different frequency response trends.

Component mode synthesis (CMS) is used as a basis for predicting power flow in complex structures. The power flow formulation is cast in a general framework of multilevel CMS, in which a hierarchy of substructures can be recursively partitioned from a very large finite element model. Additional computational efficiency is achieved by finding characteristic constraint (CC) modes. The CC modes are computed by performing an eigenanalysis on the partitions of the CMS mass and stiffness matrices that correspond to the constraint-mode degrees of freedom. The CC modes describe the vibration, and the exchange of vibration energy, at the interface between connected substructures. Therefore, a relatively small number of CC modes that capture the primary interface motion can be selected to yield a reduced-order model for computing the power flow. The performance and accuracy of the method are illustrated by examples of a two-span beam, a cantilever plate, and the body structure of a military vehicle. For the vehicle structure, multiple levels of substructures are used to map the power flow in the system. It is seen that this multilevel, characteristic-mode-based approach provides a general framework for the efficient calculation of power flow in the low- to midfrequency range.

The maximum blade forced response amplitudes for mistuned turbomachinery rotors are generally much greater than those of their tuned counterparts. However, it is known that the ratio of mistuned to tuned maximum vibration amplitudes, the amplitude magnification, is often largest at a relatively small level of mistuning. Increasing the level of mistuning beyond this critical value actually leads to a decrease in the amplitude magnification. This suggests that it might be beneficial to introduce some level of mistuning into the nominal design of the system intentionally. In this study, the effectiveness of this intentional mistuning strategy is investigated. Intentional mistuning is introduced into the rotor design by varying the nominal blade stiffnesses in harmonic and square-wave patterns. In addition, the unavoidable, random mistuning of the blades is included in the model as usual. The statistics of the forced response are examined for lumped parameter models, as well as for a finite element based reduced-order model of an industrial rotor. For the cases considered, it is found that intentional mistuning can greatly reduce a rotor's sensitivity to random mistuning.

In this work, an investigation is performed into developing a genera/framework for predicting the power flow between coupled component structures with uncertain system parameters. A specific example of two coupled beams is considered, in which a torsional spring is attached at the coupling point to adjust the coupling strength. The power flow in the nominal system is formulated using component mode synthesis (CMS). First, the parameter-based statistical energy method, which employs free-interface component modes, is applied to obtain approximations for the ensemble-averaged power flow with each beam length having a uniformly-distributed random perturbation. Then, using fixed-interface component modes and constraint modes, the Craig-Bampton method of CMS is employed to formulate the nominal power flow equation in terms of the constraint-mode degrees of freedom. This fixed-interface CMS method is seen to provide a systematic and efficient platform for power flow analysis. Using this CMS basis, a general approximation for the ensemble-averaged power flow is formulated regardless of the probability distribution of the random parameters or the coupling strengths between the substructures. This approximation is derived using Galerkin's method, in which each modal response is expanded in locally linear interpolation functions in the random system parameters. The proposed general framework is numerically validated by comparisons with wave approximation from the literature for this two-coupled-beam system. [DOI: 10.1115/1.1399051]

Motivated by military applications, this work considers connected platoons of ground vehicles of potentially different sizes and presents a model-free approach for optimizing the speed of the platoon to adjust the tradeoff between fuel economy and mobility as measured by travel speed. The motivation to seek a model-free solution is twofold: (1) vehicle models that are typically assumed to be available in model-based methods are not available on-board for military vehicles; (2) a model-free solution can offer robustness to modeling errors. Therefore, in this paper, the problem of optimizing the tradeoff between fuel economy and mobility of a mixed platoon is formulated as an optimization problem and solved using the model-free Nelder-Mead approach. To explore the performance characteristics of this approach, a case study is performed with two different size vehicles that are representative of military trucks, both in simulation and in a novel networked engine-in-the-loop setup. The results show that the proposed approach can achieve the desired balance between fuel economy and mobility in a model-free manner despite the nonlinearity caused by gear shift deadzones, albeit at the expense of relatively slow convergence time. In addition, a design guideline for the parameters in the Nelder-Mead approach is also discussed. [ABSTRACT FROM AUTHOR]

A technique is presented for reducing the size of a model generated by the Craig-Bampton method (Craig, R. R., and Bampton, M. C. C., 'Coupling of Substructures for Dynamic Analyses,' AIAA Journal, Vol. 6, No. 7, 1968, pp. 1313-1319) of component mode synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as characteristic constraint modes because they represent the characteristic motion of the interface between the component structures. When the characteristic constraint modes are truncated, a CMS model with a highly reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. Furthermore, this method yields physical insight into the mechanisms of vibration transmission in complex structures, and it provides an excellent framework for the efficient calculation of power flow.

Battery packs used in electrified vehicles exhibit high modal density due to their repeated cell substructures. If the excitation contains frequencies in the region of high modal density, small commonly occurring structural variations can lead to drastic changes in the vibration response. The battery pack fatigue life depends strongly on their vibration response; thus, a statistical analysis of the vibration response with structural variations is important from a design point of view. In this work, parametric reduced-order models (PROMs) are created to efficiently and accurately predict the vibration response in Monte Carlo calculations, which account for stochastic structural variations. Additionally, an efficient iterative approach to handle material nonlinearities used in battery packs is proposed to augment the PROMs. The nonlinear structural behavior is explored, and numerical results are provided to validate the proposed models against full-order finite element approaches. [ABSTRACT FROM AUTHOR]