In biaxial micromirror imaging, distortion directly affects image quality and may further cause information errors. From a dynamic perspective, the study explores how the mechanical motion performance of a biaxial micromirror affects optical imaging performance. The relative torsional motion of the internal components of the micromirror is considered, and a rotation matrix is applied to describe the attitude changes in spatial orientation. Based on this, nonlinear dynamic equations and optical vector equations are established for the electrostatic comb-driven biaxial micromirror. The system performances of torsional microbeams are compared under traditional and metamaterial structural design. The effect of microbeam structure on the natural frequency and static torsion angles is analyzed. The dynamic characteristics are then discussed under primary and subharmonic resonance conditions. The variation of the maximum scanning angle range and imaging distortion is examined under different microbeam structure parameters and various working conditions. In addition, the influence of mechanical motion states on imaging feature points is studied under different periodic motion conditions. The results indicate that the key parameters affecting the static torsion angle differ between structures. The metamaterial structure design has lower distortion rate range. The multi-period imaging phenomenon was discovered. The performance advantages of the two microbeam structures under different application requirements are systematically explained, providing theoretical support for the optimal design of high-precision micromirror systems.
B-cell receptor (BCR) signalling is a key regulator of cytosolic calcium (Ca2+) dynamics in B cells and plays a pivotal role in determining cell fate, including survival and apoptosis. Dysregulation of BCR signalling and Ca2+ homeostasis is a hallmark of B-cell lymphoma. Despite its importance, the mechanistic link between BCR-mediated Ca2+ dynamics and cell fate regulation in B-cell lymphoma remains poorly understood. In this study, we developed a minimal mathematical model of the BCR signalling pathway to elucidate how BCR activity shapes pro- and anti-apoptotic Ca2+ dynamics under lymphoma conditions. The model reproduces Ca2+ oscillations observed in B cells and enables systematic investigation of the effects of key signalling parameters on Ca2+ behaviour. We propose restoration strategies to induce apoptosis through sustained elevation of cytosolic Ca2+ levels in B-cell lymphoma. We hypothesise that increased expression of PLC-γ2, a critical mediator of BCR signalling, together with enhanced Ca2+ release from the endoplasmic reticulum (ER) and reduced Ca2+ flux from the cytosol into the ER, can shift Ca2+ dynamics toward sustained high levels that promote apoptosis. A two-dimensional parameter analysis identifies the most influential regulatory parameters governing this transition. Overall, this mathematical modelling approach provides mechanistic insight into BCR-driven Ca2+ regulation and offers a rational basis for developing potential therapeutic strategies for B-cell lymphoma.
In this work, we propose a conditional combined incentive scheme to promote cooperation, in which rewards and punishments are applied only when interacting individuals adopt different strategies, and investigate the associated evolutionary dynamics in the presence of mutation. Considering that the institutional incentives are typically subject to limited resources and implemented periodically, we formulate an optimal control problem to maximize the level of cooperation under inecntive resource constraints in a periodic environment. By applying Pontryagin’s Maximum Principle, we derive the optimal incentive protocols, which are characterized by Bang-Bang control behavior. Numerical results indicate that under weak mutation, the resulting optimal protocols achieve the highest cooperation level in both single-period and multi-period scenarios. Finally, we further perform Monte Carlo simulations to verify the theoretical predictions and numerical results, and to examine their robustness on different network topologies.
Image denoising is a typical ill-posed inverse problem, where reliable recovery heavily depends on integrating intrinsic image priors. Among various priors, global low-rankness and local smoothness have been widely used to capture image structures. In this paper, we focus on addressing sparse noise removal from images. We first propose a two-layer nonconvex tensor model with low-rankness and smoothness fusion (TNLS), where a class of commonly adopted nonconvex functions are embedded to more accurately characterize images’ structure. Then, we establish a general framework to analyze the model’s error bound. To our knowledge, these results should be the first theoretical analysis specifically targeting nonconvex models that integrate low-rankness and smoothness priors. Furthermore, we design an alternating direction method of multipliers algorithm and conduct convergence analysis to ensure its stable performance. Finally, extensive experiments on various datasets demonstrate that TNLS outperforms several state-of-the-art methods in both numerical metrics and visual quality.
Finite element analysis of porous materials typically requires highly refined meshes to accurately resolve stress distributions around small pores, which leads to substantial computational costs. Homogenization methods, by contrast, can significantly reduce computational expense. However, most existing approaches compromise accuracy in predicting local stress fields. In this work, we propose a hybrid finite element-deep learning method that enables efficient and simultaneous simulation of deformation at both the global and pore scales. Within this framework, implicit interpolation functions are predicted using a novel deep learning model and subsequently employed to construct stiffness matrices for macroscopic computations. The macroscopic results are then coupled with these functions to evaluate local stress fields around pores. The deep learning model for prediction utilizes 3D multiple parallel DeepONets to infer implicit interpolation functions in the form of scalar fields, assigning function values to each point within the porous structure. Besides, ResNets are employed to ensure the accuracy of the first-order derivatives of the interpolation functions, enabling reliable stress evaluation. Validation results show that our method maintains excellent agreement with finely meshed FEM solutions. For the analysis of an ultra-large porous structure in which the ratio of structure and pore dimensions exceeds 102, the proposed method only requires about 10 s, whereas the FEM simulation cannot be completed since it exceeds the available computational memory. These findings demonstrate that the proposed method offers a powerful tool for multiscale mechanical analysis and the design of porous materials.
Cancer subtype classification plays a crucial role in precision medicine and individualized therapy. With the continuous advancement of multi-omics profiling technologies, multi-view clustering has emerged as an effective framework for cancer subtype identification. However, practical multi-omics data are frequently challenged by missing views, noise in high-dimensional settings, and complex redundancy across views. In the context of these problems, we propose a tensorized incomplete multi-view subspace clustering framework for cancer subtyping. Specifically, the Hilbert–Schmidt Independence Criterion (HSIC) captures potential nonlinear statistical dependence among representation matrices from different views in a reproducing kernel Hilbert space, thereby strengthening cross-view consistency and complementary information exchange. In addition, the latent shared high-order low-rank structure in multi-view observations can be effectively characterized by an exponential nonconvex tensor nuclear norm. Meanwhile, an ℓ2,log-based group-sparse regularization term is employed to flexibly and robustly model structured outliers and noise. The resulting optimization problem is solved by an ADMM-based procedure equipped with iterative reweighting. Results obtained from several cancer multi-omics cohorts indicate that the proposed method achieves strong effectiveness and robustness in incomplete multi-view cancer subtyping.
This study presents a novel multi-material topology optimization framework for geometrically nonlinear continuum structures exhibiting elasto-plastic behavior. The main contribution lies in the integration of the Bi-directional Evolutionary Structural Optimization (BESO) method with geometrically nonlinear elasto-plastic finite element analysis through a MATLAB–ABAQUS coupling, enabling simultaneous consideration of material yielding, large deformations, and optimal multi-material distribution within a unified optimization framework. The formulation is governed by the plastic-limit ultimate load multiplier, enabling direct control of structural collapse resistance during the optimization process. The nonlinear structural response is evaluated through incremental finite element analysis accounting for large deformations. An extended BESO strategy is adopted to distribute multiple material phases with distinct mechanical characteristics under prescribed volume constraints. A consistent interpolation scheme is incorporated to facilitate smooth transitions between candidate materials and ensure stable convergence. By integrating nonlinear analysis with evolutionary material redistribution, the proposed methodology generates stiffness-efficient topologies while enforcing plastic-limit admissibility, thereby ensuring that the optimized layouts satisfy the required collapse resistance under geometrically nonlinear elasto-plastic behavior. The effectiveness of the proposed framework is demonstrated through four benchmark problems, including one elastic case and three geometrically nonlinear elasto-plastic examples. Additional comparative studies with linear elastic and single-material formulations further verify the advantages of the proposed methodology, confirming its robustness, effectiveness, and capability to identify mechanically meaningful optimal layouts under realistic nonlinear loading conditions.
This paper proposes an intelligent adaptive algorithm for enhancing the reliability of a tri-stable piezoelectric energy harvesting system under fractional-order proportional-integral-derivative control and Gaussian white-noise excitation. The controlled electromechanical system is reduced using an equivalent decoupling procedure and an improved stochastic averaging method. The conditional reliability function is obtained from the backward Kolmogorov equation, while the mean first-passage time is evaluated using the generalized Pontryagin equation. An adaptive particle swarm optimization method combined with a Logistic basis function neural network is then developed to solve the reliability equation and simultaneously optimize the two fractional orders. For the considered parameter set, the optimized controller increases the time-averaged reliability by 6.3% and extends the mean first-passage time by 29.2% relative to the uncontrolled case. The network solution achieves a mean error of 0.0044 compared with Monte Carlo simulations. Finally, a sensitivity analysis is discussed to assess the effects of the main algorithm parameters. The proposed algorithm provides an efficient reliability-oriented tool for the optimal fractional-order control of strongly nonlinear energy harvesting systems under random excitation.
Folding wings of a flight vehicle may experience progressive surface-stress accumulation under normal tensile loading, leading to failure once a critical threshold is exceeded. To characterize this stochastic degradation and support safety assessment, this study proposes a displacement-based degradation modeling and reliability framework based on the Tweedie exponential dispersion (TED) process. Finite element analysis in ANSYS Workbench predicts the surface-stress response and guide strain-gauge placement. Normal tensile tests are conducted on deployed folding wings to obtain surface-stress degradation data, which are modeled using the TED process. Since the TED increment density has no closed form, a saddle point approximation with a dual-branch reparameterization strategy is introduced to enable robust maximum likelihood estimation. Reliability is evaluated using a hybrid scheme that combines fine displacement-grid Monte Carlo simulation with a Birnbaum–Saunders (BS) representation to estimate the first-hitting displacement distribution and reliability. Results show that the TED model achieves higher fitting accuracy than the Gamma-process benchmark, while the MC–BS method provides more conservative reliability predictions. The proposed framework offers a practical and physically interpretable tool for reliability assessment of folding wings and related deployable aerospace structures under tensile loading.
This paper proposes a reaction-diffusion-based level set topology optimization framework for unimorph cantilevered piezoelectric energy harvesters that is formulated for consistency with a planar thin-film microfabrication route. The piezoelectric thin film is kept continuous, and only the electrode layout is patterned. The electrode pattern is represented by an internal interface that partitions the film into electrode-covered and uncovered piezoelectric subdomains, while the substrate topology is optimized simultaneously using an extended level set formulation. Cross-sectional uniformity and substrate-support conditions are incorporated into the level-set evolution as process-consistent formulation constraints that define the admissible design space. Numerical examples targeting multiple eigenfrequencies demonstrate accurate tuning of the fundamental eigenfrequency and higher RMS output voltage than a first-mode-matched rectangular baseline under higher-mode excitations.
Analytical solutions are developed for stresses and displacements of supported tunnels constructed in elastic saturated ground, fully taking into account the influence of seepage flow on the mechanical phase, the no-slip interactions between surrounding rocks and support structure for twin tunnels. In order to determine the analytical solutions, all governing equations as well as boundary and compatibility conditions are fully taken into account, including the compatibility conditions of pore pressure and hydraulic flow at rock-support interfaces of twin tunnels. Analytical solutions are finally obtained by applying the complex variable method and the Schwarz alternating method. As verification and validation steps, comparisons are performed between the current analytical solutions and numerical predictions, and in-situ monitoring data. Finally, a comprehensive parametric analysis is performed to investigate the influence of key factors on hydro-mechanical behaviours of twin supported tunnels, such as net spacings of twin tunnels, thickness and permeabilities of supports. Interestingly, it is observed that lower permeability of supports leads to higher pore pressure buildup at the rock-support interfaces, therefore subjecting the tunnel to dangerous conditions. The proposed theoretical framework for mechanical solutions of twin supported tunnels with seepage flow provides an alternative approach for the preliminary design of twin supported tunnels.
Constitutive models facilitate numerical simulations that support the design and optimization of soft-material-based components, reducing reliance on costly, time-consuming trial-and-error experiments. Commonly used constitutive models often balance between simplicity and predictive accuracy: simple models have limited predictive power, while complex models face challenges in parameter identification and numerical stability. This study introduces a simple two-parameter phenomenological model, formulated in terms of the principal stretches, for incompressible, isotropic soft materials undergoing large deformations. The model’s admissibility is established analytically via the Baker-Ericksen inequality and polyconvexity; its recovery of the classical linear-elastic limit at infinitesimal strain is demonstrated; and an extension to the nearly incompressible case is presented. Material parameters were identified using a hybrid differential evolution and trust-region reflective optimization strategy under two calibration scenarios: uniaxial tension (UT) data only, and simultaneous fitting to uniaxial tension, equibiaxial (EB), and pure shear (PS) data. The predictive performance of the proposed model was benchmarked against the one-term Ogden and Mooney-Rivlin models using experimental data for three soft materials from the literature: vulcanized rubber, silicon rubber, and polymer hydrogel. Model accuracy was quantified using the normalized mean absolute deviation (NMAD) and the coefficient of determination (R2) across all three loading modes, regardless of the calibration strategy. The proposed model consistently achieved lower or comparable NMAD relative to the comparison models and retained accurate multiaxial predictions even when calibrated from uniaxial tension data alone, demonstrating a favorable balance between mathematical simplicity, calibration efficiency, and predictive accuracy.
Geometrical stiffness provides a contribution to the load‑bearing stiffness of tensegrities comparable to that of elastic stiffness under loading. However, relying too much on geometrical stiffness to sustain loads requires a high level of prestress, and is therefore costlier and far less efficient than utilizing elastic stiffness. By strategically adjusting the structural configuration, the contribution of geometrical stiffness can be partially replaced by elastic stiffness without compromising the load-bearing stiffness. A sensitivity matrix is established to characterize the relationship between load‑induced displacements and member rest lengths. It is shown that member length actuation constructed from the null‑space of this sensitivity matrix does not alter the load‑bearing stiffness and can modify the prestress state, thereby enhancing the structural efficiency. Accordingly, an active deformation strategy is proposed to progressively redistribute the load‑bearing contribution from geometrical stiffness to elastic stiffness. A tensegrity manipulator is presented as an illustrative example, demonstrating that the proposed strategy effectively reduces elastic strain energy and prestress while maintaining the load‑bearing stiffness. These results highlight an important adaptive capability of tensegrities as morphing structures, offering promising potential for applications in robotics, civil engineering, and deployable systems.
Additive NARMAX models have been widely used in industrial process modeling and biomedical signal analysis. By introducing RBF networks into the nonlinear part, stronger nonlinear approximation capability and greater modeling flexibility can be achieved. However, parameter estimation of RBF-network-based NARMAX systems remains challenging due to the coupling between dynamic parameters and hyperparameters. In this paper, a hierarchical optimization framework is proposed to decouple the estimation of dynamic parameters from that of hyperparameters. Specifically, an adaptive step-size matrix based gradient iterative algorithm is developed for dynamic parameter estimation using the auxiliary model identification method, while a particle swarm optimization assisted gradient iterative algorithm is proposed for hyperparameter optimization. Simulation results show that the proposed algorithm achieves faster convergence and more accurate parameter estimation than the conventional gradient iterative algorithm. The mean parameter estimation error is reduced by more than 90%, and the median estimation error remains below 5% under low noise and below 15% under high noise. In the electroencephalography cortical response modeling example, the model identified by the proposed algorithm achieves a variance accounted for of 91.70% and 84.67% under one-step-ahead and three-step-ahead prediction, respectively, demonstrating improved recursive prediction performance.
