Search Results (82)

This study proposes a parallel model reduction method for two-dimensional discrete-time systems, utilizing Krawtchouk moments and equivalent transformation. This work makes two significant contributions. First, we introduce a projection subspace that is independent of the input as well as of the Krawtchouk parameters, thus ensuring robustness. Second, we propose an efficient parallel algorithm for computing the basis of the projection subspace. With the difference relation of Krawtchouk polynomials and the analytic identity theorem, we obtain the explicit formula for the Krawtchouk moments of the state, which is input-dependent and Krawtchouk-parameter-dependent. We derive a projection subspace that is independent of both input and Krawtchouk parameter, such that it is equivalent to the subspace spanned by the Krawtchouk moments. Further, we propose a parallel strategy based on the equivalent transformation of the block bi-diagonal Toeplitz matrices with bi-diagonal blocks to compute the basis of the projection subspace, facilitating acceleration of the model reduction process on high-performance computers. Moreover, we analyze the Krawtchouk moment invariants of the proposed parallel method. Finally, the effectiveness of the proposed method is illustrated by two numerical examples. Full article

Remaining useful life (RUL) prediction of rolling bearings is of significance for improving the reliability and durability of rotating machinery. Aiming at the problem of suboptimal RUL prediction precision under cross-working conditions due to distribution discrepancies between training and testing data, enhanced cross-working condition RUL prediction for rolling bearings via an initial degradation detection-enabled joint transfer metric network is proposed. Specifically, the health indicator, called reconstruction along projection pathway (RAPP), is calculated for initial degradation detection (IDD), in which RAPP is obtained from a novel deep adversarial convolution autoencoder network (DACAEN) and compares discrepancies between the input and the reconstruction by DACAEN, not only in the input space, but also in the hidden spaces, and then RUL prediction is triggered after IDD via RAPP. After that, a joint transfer metric network is proposed for cross-working condition RUL prediction. Joint domain adaptation loss, which combines representation subspace distance and variance discrepancy representation, is designed to act on the final layer of the mapping regression network to decrease data distribution discrepancies and ultimately obtain cross-domain invariant features. The experimental results from the PHM2012 dataset show that the proposed method has higher prediction accuracy and better generalization ability than typical and advanced transfer RUL prediction methods under cross-working conditions, with improvements of 0.047, 0.053, and 0.058 in the MSE, RMSE, and Score. Full article

Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science. Full article

The thermal runaway propagation (TRP) model of energy storage batteries can provide solutions for the safety protection of energy storage systems. Traditional TRP models are solved using the finite element method, which can significantly consume computational resources and time due to the large number of elements and nodes involved. To ensure solution accuracy and improve computational efficiency, this paper transforms the heat transfer problem in finite element calculations into a state-space equation form based on the reduced-order theory of linear time-invariant (LTI) systems; a simplified method is proposed to solve the heat flow changes in the battery TRP process, which is simple, stable, and computationally efficient. This study focuses on a four-cell 100 Ah lithium iron phosphate battery module, and module experiments are conducted to analyze the TRP characteristics of the battery. A reduced-order model (ROM) of module TRP is established based on the Arnoldi method for Krylov subspace, and a comparison of simulation efficiency is conducted with the finite element model (FEM). Finally, energy flow calculations are performed based on experimental and simulation data to obtain the energy flow rule during TRP process. The results show that the ROM achieves good accuracy with critical feature errors within 10%. Compared to the FEM, the simulation duration is reduced by 40%. The model can greatly improve the calculation efficiency while predicting the three-dimensional temperature distribution of the battery. This work facilitates the efficient computation of TRP simulations for energy storage batteries and the design of safety protection for energy storage battery systems. Full article

We investigate the synchronization dynamics of two non-identical, mutually coupled Rulkov neurons, emphasizing the effects of coupling strength and parameter mismatch on the system’s behavior. At low coupling strengths, the system exhibits multistability, characterized by the coexistence of three distinct 3-cycles. As the coupling strength is increased, the system becomes monostable with a single 3-cycle remaining as the sole attractor. A further increase in the coupling strength leads to chaos, which we identify as arising through a novel type of intermittency. This intermittency is characterized by alternating dynamics between two low-dimensional invariant subspaces: one corresponding to synchronization and the other to asynchronous behavior. We show that the system’s phase-space trajectory spends variable durations near one subspace before being repelled into the other, revealing non-trivial statistical properties near the onset of intermittency. Specifically, we find two key power-law scalings: (i) the mean duration of the synchronization interval scales with the coupling parameter, exhibiting a critical exponent of $-0.5$ near the onset of intermittency, and (ii) the probability distribution of synchronization interval durations follows a power law with an exponent of $-1.7$ for short synchronization intervals. Intriguingly, for each fixed coupling strength and parameter mismatch, there exists a most probable super-long synchronization interval, which decreases as either parameter is increased. We term this phenomenon “dragon intermittency” due to the distinctive dragon-like shape of the probability distribution of synchronization interval durations. Full article

This study concerns Riemannian manifolds with two types of tangent vectors. Let it be given that there are two subspaces of a tangent space with the property that each tangent vector has a unique decomposition as the sum of a vector in one subspace and a vector in the other subspace. Then, these tangent spaces can be complexified in such a way that the theory of the modular operator applies and that the complexified subspaces are invariant for the modular automorphism group. Notions coming from Kubo–Mori theory are introduced. In particular, the admittance function and the inner product of the Kubo–Mori theory can be generalized to the present context. The parallel transport operators are complexified as well. Suitable basis vectors are introduced. The real and imaginary contributions to the connection coefficients are identified. A version of the fluctuation–dissipation theorem links the admittance function to the path dependence of the eigenvalues and eigenvectors of the Hamiltonian generator of the modular automorphism group. Full article

In orthodontics, the manual tracing of cephalometric radiographs is a common practice, where the Sella Turcica (ST) serves as a reference point. The radiologist often manually traces the outline of the sella using manual tools (e.g., calipers on radiographs). Perhaps the inherent complexity and variability in the shapes of sella and the lack of advanced assessment tools make the classification of sella challenging, as it requires extensive training, skills, time, and manpower to detect subtle changes that often may not be apparent. Moreover, existing semi-supervised learning (SSL) methods face key limitations such as shift invariance, inadequate feature representation, overfitting on small datasets, and a lack of generalization to unseen variations in ST morphology. Medical imaging data are often unlabeled, limiting the training of automated classification systems for ST morphology. To address these limitations, a novel semi-supervised deep subspace embedding (SSLDSE) framework is proposed. This approach integrates real-time stochastic augmentation to significantly expand the training dataset and introduce natural variability in the ST morphology, overcoming the constraints of small and non-representative datasets. Non-linear features are extracted and mapped to a non-linear subspace using Kullback–Leibler divergence, which ensures that the model remains consistent despite image transformations, thus resolving issues related to shift invariance. Additionally, fine-tuning the Inception-ResNet-v2 network on these enriched features reduces retraining costs when new unlabeled data becomes available. t-distributed stochastic neighbor embedding (t-SNE) is employed for effective feature representation through manifold learning, capturing complex patterns that previous methods might miss. Finally, a zero-shot classifier is utilized to accurately categorize the ST, addressing the challenge of classifying new or unseen variations. Further, the proposed SSLDSE framework is evaluated through comparative analysis with the existing methods (Active SSL, GAN SSL, Contrastive SSL, Modified Inception-ResNet-v2) for ST classification using various evaluation metrics. The SSLDSE and the existing methods are trained on our dataset (sourced from PGI Chandigarh, India), and a blind test is conducted on the benchmark dataset (IEEE ISBI 2015). The proposed method improves classification accuracy by 15% compared to state-of-the-art models and reduces retraining costs. Full article

Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects. Full article

This paper presents a novel step in the extension of subspace identification toward the direct identification of harmonic decomposition linear time-invariant models from nonlinear time-periodic system responses. The proposed methodology is demonstrated through examples involving the nonlinear time-periodic dynamics of a flapping-wing micro aerial vehicle. These examples focus on the identification of the vertical dynamics from various types of input–output data, including linear time-invariant, linear time-periodic, and nonlinear time-periodic input–output data. A harmonic analyzer is used to decompose the linear time-periodic and nonlinear time-periodic responses into harmonic components and introduce spurious dynamics into the identification, which make the identified model order selection challenging. A similar effect is introduced by measurement noise. The use of model order reduction and model-matching methods in the identification process is studied to recover the harmonic decomposition structure of the known system. The identified models are validated in the frequency and time domains. Full article

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with N observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower-dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of N. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles. Full article

In this paper, we derive new probabilistic bounds on the sensitivity of invariant subspaces, deflation subspaces and singular subspaces of matrices. The analysis exploits a unified method for deriving asymptotic perturbation bounds of the subspaces under interest and utilizes probabilistic approximations of the entries of random perturbation matrices implementing the Markoff inequality. As a result of the analysis, we determine with a prescribed probability asymptotic perturbation bounds on the angles between the corresponding perturbed and unperturbed subspaces. It is shown that the probabilistic asymptotic bounds proposed are significantly less conservative than the corresponding deterministic perturbation bounds. The results obtained are illustrated by examples comparing the known deterministic perturbation bounds with the new probabilistic bounds. Full article

Multisource domain adaptation (MDA) is committed to mining and extracting data concerning target tasks from several source domains. Many recent studies have focused on extracting domain-invariant features to eliminate domain distribution differences. However, there are three aspects that require further consideration. (1) Efforts should be made to ensure the maximum correlation in the potential subspace between the source and target domains. (2) While aligning the marginal distribution, the conditional distribution must also be considered. (3) Merely aligning the source distribution and target distribution cannot guarantee sufficient differentiation for classification tasks. To address these problems, we propose a novel approach named towards discriminability with distribution discrepancy constrains for multisource domain adaptation (TD-DDC). Specifically, TD-DDC first mines features of maximal relations learned from all domains while constructing domain data distribution mean distance metrics for interdomain distribution adaptation. Simultaneously, we integrate discriminability into domain alignment, which means increasing the distance among labels that are distinct from one another while reducing the distance among labels that are the same. Our proposed method not only reduces the interdomain distributional differences but also takes into account the preservation of interdomain correlation and inter-category discrimination. Numerous experiments have shown that TD-DDC performs much better than its competitors on three visual benchmark test databases. Full article

In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations as invariant subspaces that nonlinear operators admit. Some concrete examples and corresponding reduced systems are presented to illustrate this method. Full article

This paper introduces a novel wavelet-based methodology for identifying the modal parameters of a structure in the aftermath of an earthquake. Our proposed approach seamlessly combines a subspace method with a stationary wavelet packet transform. By relocating the subspace method into the wavelet domain and introducing a weighting function, complemented by a moving window technique, the efficiency of our approach is significantly augmented. This enhancement ensures the precise identification of the time-varying modal parameters of a structure. The capacity of the stationary wavelet packet transform for rich signal decomposition and exceptional time-frequency localization is harnessed in our approach. Different subspaces within the stationary wavelet packet transform encapsulate signals with distinct frequency sub-bands, leveraging the fine filtering property to not only discern modes with pronounced modal interference, but also identify numerous modes from the responses of a limited number of measured degrees of freedom. To validate our methodology, we processed numerically simulated responses of both time-invariant and time-varying six-floor shear buildings, accounting for noise and incomplete measurements. Additionally, our approach was applied to the seismic responses of a cable-stayed bridge and the nonlinear responses of a five-story steel frame during a shaking table test. The identified modal parameters were meticulously compared with published results, underscoring the applicability and reliability of our approach for processing real measured data. Full article