Effective management and monitoring of the operating temperature of a polymer electrolyte membrane fuel cell (PEMFC) are critical to maintaining the temperature within an optimal range, thereby preventing thermal extremes that can degrade both performance and lifespan of the cell. Nevertheless, monitoring the internal temperature of PEMFC remains challenging owing to their complex multilayered structure, non-uniform heat distribution, and limited accessibility for sensor placement, which complicate accurate measurement of internal temperature and heat generation sources. To address these challenges, this study proposes an inverse heat conduction framework based on temperature measurements acquired at the surrounding surface of the bipolar plates to estimate both equivalent heat sources and internal temperature distributions of PEMFC. The proposed methodology integrates a one-way coupled computational fluid dynamics model to provide physically realistic convective boundary conditions for the inverse solver. A whole-time domain solution combined with Tikhonov regularization is implemented under a receding-horizon framework, providing a robust and comprehensive methodology for estimating the complex heat-generation behavior occurring during PEMFC operation. To enable real-time application, a reduced-order model based on Krylov subspace projection is employed to enhance computational efficiency. The proposed approach was experimentally validated under various operating conditions (0.4 V and 0.6 V with 0% and 100% relative humidity). The results demonstrate that the estimated equivalent heat source successfully captures complex thermophysical phenomena. The reconstructed internal temperature fields exhibit excellent agreement with the embedded thermocouple measurement, confirming the high accuracy and reliability of the proposed approach. With a processing time per time step significantly shorter than the data acquisition interval, this work validates the proposed inverse framework as a powerful and computationally efficient tool for advanced thermal diagnostics and management of PEMFC systems.

Electronic components inside integrated module is designed to endure harsh thermal condition. Information about interior temperature and heat sources is then crucial for the optimal design of the electronic components. However, because of the compact design and internal position within the housing, it is difficult to experimentally measure the heat sources and internal temperature. To handle this issue, this study presents a method for estimating the heat source and internal temperature distribution via an inverse heat conduction problem. A sequential time domain approach with Tikhonov regularization is employed to predict equivalent heat sources of motor and MOSFET from a few and noisy measured temperature data. Krylov subspace-based finite element model reduction is also utilized to increase computational efficiency of the proposed framework. As a result, the suggested IHCP framework can be synchronized with sensor systems, including thermocouples and can provide the essential information such as unmeasured heat sources and temperature contour. A 200 W BLDC motor drive module for a collaborative robot is taken into consideration to validate the suggested approach with a practical application. Well-designed experimental tests using the BLDC motor drive module are used to assess the accuracy and efficiency of the suggested approach. A heat dissipation design of the BLDC motor drive is also carried out to show off a good application of the suggested method.

This study presents a novel filtering approach for the accurate estimation of unknown heat sources in inverse heat conduction problems, which have been widely utilized for identifying boundary conditions from measured temperature data. The inverse heat conduction problem can be categorized into sequential and whole-domain approaches, depending on the temporal formulation of the estimation process. The sequential method can encounter difficulties arising from inherent trade-offs between stability and accuracy, as the regularization term acts as a penalty. In contrast, Tikhonov regularization formulated in the whole-time domain can be interpreted from a Bayesian perspective, in which the regularization term inherently acts as an effective filter rather than as a penalty. This paper presents an inverse heat conduction problem formulated in a receding-horizon time domain, employing a Tikhonov digital filter. The proposed method is developed to integrate the complementary strengths of sequential and whole-domain approaches. In the receding-horizon estimation strategy, a sliding window of temporal measurement data is employed to obtain a sequential inverse solution through localized filtering, thereby stabilizing and regularizing the inherently ill-posed nature of inverse heat conduction problems. The proposed method mitigates error accumulation by utilizing only the first estimated value within a receding-horizon domain and advancing the prediction in a step-wise sliding manner. This strategy prevents the propagation of estimation errors. In conclusion, the proposed method is expected to exhibit reliable performance even in problems characterized by low thermal diffusivity and requiring small time-step sizes, and also demonstrating potential applicability to systems requiring real-time thermal monitoring. This paper demonstrated the performance of the proposed method using several numerical examples, which range from one-and two-dimensional models to a real-world three-dimensional fuel cell finite element model.

Substructure coupling and model order reduction using Component Mode Synthesis (CMS) have, over recent years, gained considerable attention in the vibroacoustic analysis of complex structures. In the CMS methodology, the interior dynamics of each subcomponent in a substructured system are represented by a truncated set of normal modes within the lower frequency range, while all physical degrees of freedom (DOFs) at the interface are retained. In cases where there are many interconnected subcomponents within a system, in particular when these components are finely discretised in the Finite Element (FE) domain, the reduced system matrices may still involve a significant number of equations. This, in turn, leads to a considerable computational workload. To address this issue, further reduction of the system matrices concerning the interface DOFs by using a set of truncated interface modes can be considered. However, the accuracy of the reduced matrices depends on the representation of the truncated dynamics in the reduction process. In this work, two interface reduction techniques are presented to truncate the interface dynamics of the Enhanced Craig-Bampton (ECB) equations of motion. The first technique is a classical interface reduction approach that assumes decoupled internal and interface dynamics. The second approach is an extension of the first one by incorporating an additional coupling term that accounts for interactions between the truncated internal and interface dynamics. The performance of each interface reduction technique is evaluated by applying them to three practical engineering examples. In these instances, resonance frequencies, associated errors, transfer functions, and normal modes are compared to those obtained using both the classical CB method and the full model.

To deal with the ill-posed nature of the inverse heat conduction problem (IHCP), the regularization parameter alpha can be incorporated into a minimization problem, which is known as Tikhonov regularization method, a popular technique to obtain stable sequential solutions. Because alpha is a penalty term, its excessive use may cause large bias errors. Ridge regression was developed as an estimator of the optimal alpha to minimize the magnitude of a gain coefficient matrix appropriately. However, the sensitivity coefficient matrix included in the gain coefficient matrix depends on the time integrator; thus, certain parameters of the time integrators should be carefully considered with alpha to handle instability. Based on this motivation, we propose an effective iterative hybrid parameter selection algorithm to obtain stable inverse solutions.

A monitoring system is essential for controlling temperatures under safe levels of operation. It is often challenging to attach temperature sensors directly to drive chips owing to the operating environment or geometric challenges. Based on this motivation, we present a model-based virtual thermal sensing technique for the real-time temperature monitoring of the electronics package. A few real sensors located far from the target position are utilized in this virtual sensing system. These are then connected to a well-tuned finite element model for data augmentation utilizing an inverse heat conduction framework. Therefore, the virtual sensor allows us to estimate the temperature without the aid of a sensor installed inside. However, this technique has a stability issue because it is classified into an inverse problem (i.e., an ill-posed problem). We propose a Tikhonov regularization method to address this challenge, including an efficient ridge estimator. The ridge estimator is used to select an optimal regularization parameter so that we can obtain the stable and reliable inverse solution. Since conventional ridge estimators rely on total transient errors, they require a significant computation. The proposed estimator is based on the bias and variance errors, not the total errors, which allow us to efficiently find the optimal parameter. In this paper, the thermal model is modeled using the finite element method, and the Krylov subspace-based model order reduction is employed to reduce the computational burden. Finally, the proposed virtual thermal sensor was experimentally validated utilizing a sealed cylindrical structure in which the commercial servo drive operated.

The Craig–Bampton component mode synthesis uses interface constraint modes and deformed substructural modes for model reduction. In some instances, it may be of interest to realize additional reductions after reducing the substructural degrees of freedom, and this is generally done by the reduction of the interface degrees of freedom. The characteristic constraint modes were developed to achieve the interface reduction of the Craig–Bampton method. However, the interface reduction process can compromise accuracy because using a small number of characteristic constraint modes, focusing on low-frequency range, may interrupt vibration energy transmission between substructures in relatively mid and/or high-frequency ranges. Based on this motivation, an improved reduction technique of the interface regions is introduced for refining characteristic constraint modes. Considering a residual modal effect is the main point of refinement of the characteristic constraint modes. The modified characteristic constraint modes and fixed-interface normal modes computed by a newly derived formulation with residual modal flexibility can represent the characteristics of interface motion better than the conventional constraint modes. Consequently, the improved transformation matrix may facilitate vibration energy transmission between substructures. Numerical experiments indicate that the proposed refinement method can complement the conventional method in terms of accuracy, and the refined constraint and fixed interface normal modes are better representations of the original mode shapes than conventional approaches are.

A partitioned symmetric formulation and its attendant solution method of coupled thermoelastic problems are presented, which lead to improved computational efficiency and more importantly achieves improved accuracy. A key feature of the present formulation is to treat the energy flux between the elastic and the thermal conduction fields as a constraint, through which the coupling of the two partitioned field equations are effected. Exploiting the symmetric feature of the present formulation for solution efficiency, the implicit–implicit time integration is adopted, avoiding a staggered solution procedure that inherently involves predictor-correction steps. The proposed partitioned formulation is implemented and applied to some benchmark thermoelastic problems and as well as new problems, which indicate the proposed method indeed achieves both computational efficiency and improved accuracy.

The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement of reduced matrices without an increasing number of eigenbasis. However, it also needs additional computational requirements to treat the residual flexibility. In this paper, an efficient parallelization of the ECB method is presented to handle this issue and accelerate the applicability for large-scale structural vibration problems. A new ECB formulation within a substructuring strategy is derived to achieve better scalability. The parallel implementation is based on OpenMP parallel architecture. METIS graph partitioning and Linear Algebra Package (LAPACK) are used to automated algebraic partitioning and computational linear algebra, respectively. Numerical examples are presented to evaluate the accuracy, scalability, and capability of the proposed parallel ECB method. Consequently, based on this work, one can expect effective computation of the ECB method as well as accuracy improvement.