Search Results (1,484)

With the high penetration of renewable energy into power grids, grid-connected converters face severe challenges in adapting to wide-range variations of grid strength and suppressing fault overcurrents. A single grid-following (GFL) or grid-forming (GFM) control mode cannot ensure system stability across weak, moderately weak, and strong grid conditions, while the lack of current limiting measures may lead to damage to power electronic devices. To address these issues, an adaptive seamless switching strategy (ASSS) considering current limiting is proposed in this paper. The ASSS integrates three core modules: harmonic injection-based impedance identification for short-circuit ratio (SCR) calculation, a state variable reset method for seamless mode switching, and a hysteresis switching criterion to avoid frequent mode transitions. Besides ASSS, an adaptive virtual impedance is employed for fault current suppression. Based on MATLAB/Simulink, simulation verifications are conducted under typical working conditions including grid voltage sags and large-scale SCR variations. The results show that the proposed strategy can limit the maximum fault current efficiently, realize seamless switching between GFL and GFM modes with waveform distortion rate less than 5%, and ensure stable system operation across the entire range of grid strength variations. This strategy effectively improves the fault ride-through capability, grid adaptability, and switching dynamic stability of grid-connected converters, providing a reliable control solution for high-penetration renewable energy integration. Full article

We develop a design-conditional limit theory for kernel estimators of conditional U-functionals based on locally stationary functional random fields observed at irregular random locations and under incomplete response observation. The covariates take values in a separable Hilbert space, the responses are allowed to take values in a general Polish space, and the target is indexed by a class of symmetric kernels of a fixed order. Functional localization is induced by single-index semi-metrics, while spatial localization is performed on the rescaled observation domain. Missing responses are incorporated through a complete-case construction under a Missing At Random condition and a uniform-positivity assumption. The resulting estimator is a ratio of spatially weighted U-statistics with random tuplewise observation indicators. The asymptotic analysis must account simultaneously for four sources of complexity: dependence within the spatial field, nonstationarity across an expanding domain, concentration in an infinite-dimensional covariate space, and the random thinning generated by missing responses. Conditioning on the sampling locations removes the randomness of the spatial design weights but does not eliminate dependence among the observations. We therefore derive a design-conditional projection decomposition adapted to the triangular-array structure of the model. The leading component is represented by a spatially dependent complete-case empirical process, whereas the higher-order canonical terms are controlled uniformly over the response kernels, functional-target points, single-index directions, and rescaled spatial locations. The proofs combine stationary tangent-field approximations for locally stationary random fields, large-block–small-block decompositions, coupling arguments under spatial absolute regularity, small-ball probability estimates, and entropy bounds for the joint indexing class. These arguments yield a uniform stochastic expansion in which the empirical fluctuation, the spatial–functional smoothing bias, and the local-stationarity approximation error appear as distinct contributions. In particular, the local-stationarity remainder has no counterpart in the strictly stationary theory and quantifies the cost of replacing the observed nonstationary field with its stationary tangent approximation. Under the MAR and positivity conditions, complete-case sampling reduces the effective local information and modifies the covariance structure, but it does not change the formal order of the uniform-convergence rate. Under strengthened moment, mixing, entropy, and negligibility conditions, we establish weak convergence of the normalized conditional U-process in the corresponding supremum-norm function space to a tight centered Gaussian process. The limiting covariance is determined by the complete-case first-order projection and consequently retains the effect of the observation propensity and the spatial dependence structure. We also introduce a complete-case leave-tuple-out spatial prediction criterion for bandwidth selection and prove oracle optimality over admissible bandwidth families. The general theory applies to conditional rank association, discrimination probabilities, set-indexed conditional distribution functionals, and related pairwise statistical-learning criteria. Simulation experiments and applications to spatial environmental and epidemiological data illustrate the finite-sample implications of the theory and the stabilizing role of single-index localization. Viewed through the lens of data-driven science, the framework addresses a fundamental asymmetry between the information carried by irregular, locally heterogeneous functional covariates and the selectively observed response tuples. By combining design conditioning, complete-case normalization, tangent-field localization, and single-index dimension reduction, the proposed approach resolves this inferential asymmetry at the level of the model by matching estimation and uncertainty quantification to the information actually available locally, without imposing artificial stationarity or complete-data symmetry. Full article

This paper presents a systematic reward engineering methodology for training a Proximal Policy Optimization (PPO) quadrotor navigation policy in the Webots simulator, using a hierarchical architecture in which a PID controller handles low-level stabilization and a PPO policy issues velocity commands. We document the complete evolution of a composite ten-term reward function across seven versions (v5 through v11) and retrain the key versions with multiple independent training seeds. The multi-seed study revises the single-seed history: penalty-dominated configurations (v8, v10) fail across all seeds, while the strongest historical version proves seed-sensitive (v11: 32.2 +/− 15.8%). An ablation removing the continuous distance-shaping term from v11 yields 0% success across seven seeds, identifying that term as necessary for convergence. We further isolate a previously hidden co-factor: with the library-default exploration-noise initialization (sigma_0 = 1.0), sampled actions saturate the bounded action space, the exploration variance receives no learning gradient, and curriculum progression deadlocks regardless of reward design; initializing sigma_0 = 0.37 restores gradient flow. With this correction and a deterministic evaluation-gated curriculum, the final configuration is evaluated across the full curriculum rather than at a single operating point: across five independent training seeds under a deterministic protocol, it attains 95.0% ± 6.2% navigation success at Stage 0 conditions (2 m targets, no obstacles), 89.6% ± 6.9% at Stage 1 conditions (4 m, one obstacle), and 48.4% ± 10.8% at Stage 2 conditions (7 m, three obstacles). Reporting this difficulty curve, rather than a single headline value, exposes a substantial generalization gap whose dominant failure mode is obstacle collision (45–52% of episodes at Stage 2). Matched retraining of Soft Actor-Critic and TD3 baselines under identical reward and curriculum conditions yields one completed seed each both baselines show non-monotonic difficulty curves, and at Stage 2 conditions, TD3 (64.0%) exceeds PPO (48.4% ± 10.8%) while SAC (43.0%) falls just below it, whereas at Stage 0, PPO (95.0%) leads both, so the ranking is operating point-dependent on the current single-seed evidence. We conclude that a continuous shaping gradient and the exploration-noise initialization, interacting with the curriculum advancement criterion, determine convergence in continuous control deep reinforcement learning, and that reward polarity by itself does not. Full article

Passive tuned mass dampers (TMDs) can reduce chatter, but designing and fabricating an accurately tuned absorber remains challenging due to manufacturing constraints. This study proposes a Design of Experiments and Finite Element Analysis (DOE-FEA) based constrained design optimization framework for a passive two-degree-of-freedom (TDOF) TMD to suppress regenerative chatter in boring operations by considering practical and manufacturing constraints on absorber position, mass ratio, moment of inertia and fixed inter-spring distance. The proposed, additively manufactured TMD housing, made from polylactic acid (PLA), includes a mass block supported by two spring-damper elements that enable coupled translational and rotational interactions with the boring bar. A finite-element forced vibration analysis of the boring bar TMD system is developed to obtain the real and imaginary parts of the frequency response function (FRF), which are then used to construct the stability lobes. The minimum limiting depth of cut over the spindle speed range is used as the optimization criterion, and response surface methodology (RSM) is used to obtain optimum absorber parameters within realistic design constraints. The dynamic behaviour of the TDOF TMD is experimentally and numerically evaluated and compared with that of a single-degree-of-freedom (SDOF) TMD, attributing the relative improvement in performance primarily to the combined effects of independent absorber architecture, mass, stiffness and damping distribution and dynamic tuning. The results showed that the optimal TDOF TMD achieved a DOC of 11.054 mm, while the SDOF TMD achieved 4.335 mm. The experimental investigation of additively manufactured TDOF and SDOF TMDs demonstrated qualitatively similar dynamic phenomena to those of the corresponding numerically optimized absorbers. Time-domain acceleration response, spectrogram and power spectrum were used to compare these dynamic phenomena demonstrated by the SDOF and TDOF TMDs. A reduction in corresponding first and second amplitude peaks from −2.8 dB (670 Hz) and −22.7 dB (1360 Hz) in the case of the SDOF TMD to −17.6 dB (600 Hz) and −23.8 dB (1150 Hz) for the TDOF TMD verified the vibration attenuation and frequency redistribution phenomenon as exhibited by the FE-model. Full article

To address the slow response, low pointing accuracy, and degraded stability caused by the coexistence of fractional-order dynamics, dual-axis coupling, and system delay in liquid crystal optical phased array (LCOPA) beam control, a fractional-order composite control method is proposed. First, the LCOPA is modeled as a two-input two-output system, and a fractional-order time-delay dynamic model is established. A composite control architecture integrating a fractional-order controller, a diagonal decoupling compensator, and a Smith predictor is then designed to improve dynamic response, suppress cross-axis coupling, and mitigate delay-induced performance degradation. A multi-strategy improved sparrow search algorithm is used to optimize the dual-channel fractional-order controller parameters, and closed-loop stability is verified using characteristic roots and the Matignon criterion. Simulation results show that the settling times of both axes are 11.50 ms, reduced by 62.54%/62.30%, 57.09%/56.11%, and 51.68%/48.89% compared with the results for PID, FOPID, and ADRC, respectively. The maximum cross-axis deviations are reduced to 0.0036° and 0.0030°, respsectively. Experiments further show that the mean absolute pointing errors of the X- and Y-axes decrease from 0.0466° and 0.0362° to 0.0057° and 0.0045°, while the RMSEs under external disturbances are 0.0060° and 0.0044°, respectively. These results demonstrate improved response speed, pointing accuracy, decoupling performance, and disturbance rejection. Full article

This study investigates how coordinated wireless and fast charging services reshape electric vehicle departure time and path–charging choices when a trip-level charging requirement must be completed before arrival. A multi-class dynamic user equilibrium model is formulated for road networks containing wireless charging lanes and fast charging stations. An energy-aware dynamic network loading model propagates traffic and battery states, transfers upstream wireless energy into the residual station workload, and determines endogenous waiting. The equilibrium is expressed as a finite-dimensional variational inequality and solved by an energy-aware inertial fixed-point framework with safeguarded route swapping and independent verification. Experiments on the Nguyen–Dupuis and Sioux Falls networks show that low-state-of-charge users depart 6.91 min earlier on average, while exposure-informed wireless-charging placement can substantially reduce downstream station waiting and exhibits saturation once all behaviorally exposed links are active. Under compound demand and low-state-of-charge pressure, roadway queues activate more sharply than station waiting. In a common Sioux Falls algorithm benchmark, the inertial method reaches stable acceptance in 776.2 s compared with 1562.9 s for its non-inertial counterpart. The method of successive averages crosses the practical gap threshold earlier but does not satisfy the common flow-stability criterion within 3000 updates and 9018.1 s. Across 30 final Sioux Falls scenarios, all solutions satisfy the practical verified gap and physical feasibility gates, with 11 difficult cases requiring explicit route-swap continuation. The results clarify the complementary operational roles of corridor and station charging while delimiting the numerical and behavioral assumptions of the framework. Full article

Foliation-induced anisotropy in phyllite leads to complex deformation and failure responses, making excavation stability analysis and support design particularly challenging for geo-energy and geo-resource applications. To elucidate the influence of foliation angle (β) on mechanical behavior and fracture mechanisms, uniaxial compression tests were conducted and Particle Flow Code numerical simulations were performed on phyllite specimens with seven different foliation angles. The anisotropic mechanical behavior of phyllite under uniaxial compression was systematically analyzed across varying foliation angles. Furthermore, the interaction mechanism between matrix and foliation-induced cracks was investigated based on relevant theoretical frameworks. The foliation angle β has a significant effect on the stress–strain curve of phyllite. The elastic modulus generally increases with increasing β, whereas the peak strength displays an overall U-shaped distribution. As β increases, the macroscopic failure mode shifts from matrix-dominated fracturing to foliation plane-controlled slip/opening, and then trends back toward matrix-dominated fracturing at high β. In the simulations, microcrack type, initiation sequence, and the internal mechanism of instability vary markedly across β. Combined with the energy release rate criterion of fracture mechanics and the compression bar stability theory, the mutual induction mechanism between matrix cracks and foliation cracks is further clarified. The penetration or deflection behavior of matrix cracks near weak planes is jointly controlled by the crack propagation direction and foliation angle. When the foliation plane is parallel to the loading direction, the buckling instability of thin rock flakes resulting from tensile cracking along weak planes constitutes the primary factor contributing to the reduction in the strength of specimens where the foliation plane is normal to the loading direction. This finding clarifies the intrinsic cause of the prediction deviation of the conventional Jaeger weak plane theory and can provide a more accurate theoretical reference for the stability evaluation of layered rock mass engineering. Full article

This article presents a critical review of the development of window systems used in civil engineering, interpreting them not as discrete construction products, but as complex technical and material systems whose actual value emerges from the interdependence of structural configuration, material composition, thermal performance, durability, and manufacturing and implementation constraints. The review discusses the evolution of windows from simple envelope elements providing daylight, ventilation, and weather protection into advanced building-envelope systems associated with energy efficiency, occupant comfort, in-service durability, and environmental responsibility. Particular attention is given to the principal families of window systems, including PVC-U, aluminium, timber, steel, façade, hybrid, and composite-based solutions. The analysis shows that improving the thermal insulation of a single component is not, in itself, a sufficient criterion for evaluating system quality. Declared performance may be constrained by thermal bridges at the installation interface, ageing of sealing systems, imperfections in joining processes, material deformation, and difficulties related to repair, disassembly, and recycling. From the perspective of sustainable construction, window systems should therefore be assessed across their whole life cycle, taking into account energy effectiveness, in-service stability, technological feasibility, renovation potential, and the possibility of closing material loops. The review also identifies the need for further research into integrated assessment methods, the long-term durability of advanced frame systems, the role of the window-to-wall interface, and verifiable strategies for circularity. Full article

Hybrid marine energy systems that integrate wave and current technologies can improve resource complementarity and spatial utilization. However, the ranking stability of selected hybrid concepts under changes in criterion weights, score assumptions, and multi-criteria decision analysis (MCDA) methods requires further examination. This study extends an existing two-stage concept-selection procedure by evaluating four shortlisted wave energy converter–hydrokinetic turbine configurations using stochastic weight-space sampling, criterion-wise weight sensitivity, cross-method consistency, and bounded score-perturbation analyses. A fixed normalized decision matrix is first evaluated using the Simple Additive Weighting (SAW) method across three sets of 10,000 criterion-weight scenarios generated using normalized-uniform, Dirichlet α = 1, and Dirichlet α = 0.5 distributions. The same scenarios are then evaluated using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), with ranking consistency quantified using Spearman’s rank correlation and complete-ranking agreement. Score sensitivity is subsequently examined through bounded one-point perturbations of the Stage 2 criterion scores, with SAW and TOPSIS recalculated under equal criterion weights to identify dominance-breaking and rank-reversal conditions. The oscillating water column–Savonius configuration, W1H3, remains first-ranked under all three sampled weight distributions because its normalized criterion scores are equal to or higher than those of every competing configuration across all five criteria. Criterion-wise sensitivity analysis shows that W1H3 is not outranked over the investigated weight range, although it ties with the point absorber–Savonius configuration, W2H3, when the full weight is assigned to mooring synergy or control compatibility. A crossover between W2H3 and the oscillating water column–hybrid Savonius–Darrieus configuration, W1H4, occurs at a co-location-feasibility weight of 0.384615. Across the three weight-sampling distributions, SAW and TOPSIS achieve complete-ranking agreement of 65.91–87.08%, with mean Spearman rank correlations of 0.9318–0.9742; the remaining differences are confined to the ordering of W2H3 and W1H4. Bounded score perturbations show that single one-point score change is sufficient to break the dominance of W1H3 over W2H3, whereas four changes are required for W2H3 to attain a unique first rank under both methods. The results demonstrate that W1H3 is rank-stable under the investigated weight and method variations for the adopted decision matrix, while the score-perturbation analysis identifies the bounded score changes under which the preferred ranking may change. Full article

Public owners selecting design-build (DB) teams for sustainable buildings must justify how proposal evidence, long-term asset performance, and procurement accountability support a preferred contractor. Prior contractor-selection and hybrid MCDM studies provide criteria and ranking tools, but they rarely connect public-building requirements, mandatory floors, proposal evidence anchors, weighting, scoring, and auditability before mathematical ranking. The aim of this study is to develop and numerically demonstrate an evidence-traceable SWOT-AHP-TOPSIS framework for sustainable DB contractor selection in California courthouse procurement. Here, California courthouse procurement refers to public-owner procurement of judicial courthouse facilities in California, United States, under public-building procurement rules and publicly available RFQ/RFP-related records. The framework fixes source-linked criteria, SWOT role definitions, benefit directions, evidence anchors, and compliance floors before criteria weights are obtained using AHP and alternatives are ranked using the TOPSIS method. The proof of concept derives 16 criteria from procurement guidance, California courthouse records, and the literature; reports local and global criteria weights obtained using AHP; and compares synthetic proposal archetypes. Under baseline illustrative weights, A1 ranks first (C* = 0.6548), followed by A3 (0.5804) and A2 (0.3294). Robustness checks using the disclosed matrices show conditional stability: vector, min–max, and linear-sum TOPSIS, equal-criterion weights, weighted-sum comparison, grouped +20% scenarios, comparison-set checks, and 10,000-run Monte Carlo perturbation retain A1 most frequently. The Monte Carlo run selected A1 first in 79.80% of simulations, A3 in 20.19%, and A2 in 0.01%, with top-two practical ties in 7.10% of runs. The results demonstrate arithmetic consistency, reproducibility, and interpretable ranking behavior under stated synthetic assumptions; they do not establish actual evaluator preferences, real proposal quality, award outcomes, or generalizability beyond California courthouse settings. Full article

This paper presents a data-driven run-to-run (R2R) controller for manufacturing processes subject to process drift. The proposed approach combines the exponentially weighted moving average (EWMA) method with the K-nearest neighbors (KNN) algorithm to determine process recipe adjustments. Control actions are derived entirely from historical process output data. In the hybrid controller, the EWMA estimator recursively updates the accumulated process drift using historical process errors and generates the corresponding recipe compensation. The KNN-based controller, in turn, identifies the K nearest neighbors in the historical feature database based on the current process error and determines the compensation action from the associated error–compensation relationships. The proposed controller was evaluated through simulations of a chemical mechanical planarization (CMP) process, with removal rate as the control objective. Under linear process drift with random white-noise disturbances, the proposed controller maintained the removal rate close to the target value, with a maximum overshoot of 4.40%, and satisfied the settling criterion from the beginning of the control process. Its performance was superior to that of the conventional EWMA controller and the standalone KNN controller. The EWMA controller exhibited several oscillations during the initial runs, with a maximum overshoot of 15.17%. Although the KNN controller satisfied the settling criterion from the beginning of the control process and produced a relatively small maximum overshoot of 3.10%, it did not consistently maintain the removal rate near the target value. Under nonlinear process drift with random disturbances, the proposed controller also maintained the process output near the target value with satisfactory stability, provided that the process drift remained within a bounded range. The controller also has a simple and intuitive implementation, which may facilitate practical industrial application. Full article

Spontaneous combustion in fire-affected coal seams can degrade coal quality, alter rock mechanical parameters and reduce mining profitability. Traditional pit limit optimization methods ignore coal fire-induced quality degradation, ignore the coupling effect of economic fluctuation and slope stability, and lack quantitative optimization for fire-affected open-pit mines. Here, we optimize loss-reducing mining boundaries for the southern fire-affected highwall in the first mining district of the Dananhu No. 2 Mine, Hami, Xinjiang. The aim is to move beyond binary decisions that either sterilize or fully extract fire-affected reserves. We instead integrate economic return, slope stability and coal-price uncertainty into a single boundary-optimization framework. First, we established a three-dimensional Cartesian coordinate system for the study area. We then modeled and fitted the coal-seam roof and floor using MATLAB-based multiple integration, reducing edge errors in solid surfaces. Laboratory analyses of borehole coal samples defined how calorific value varied with advance distance. These data were used to derive the coal-quality curve. Net mining profit was then formulated as the objective function, replacing the conventional stripping-ratio criterion. Profit was calculated across advance distances to identify the economically optimal boundary. Mechanical parameters of thermally altered rocks were obtained from laboratory deformation tests. Rhino and FLAC3D 6.0 were then used to evaluate three-dimensional slope stability at critical locations. Coal-price perturbation scenarios were finally introduced to test the sensitivity of net profit and optimal advance distance. Under the baseline coal price, the slope remained stable at an advance distance of 193 m. At this boundary, net profit reached a maximum of RMB 676.608 million. The southern surface boundary contracted by 47 m relative to the initial boundary, reducing unnecessary land disturbance. Sensitivity analysis showed that lower coal prices sharply reduced both the optimal advance distance and maximum net profit. When coal price decreased by 30%, the optimal advance distance contracted to approximately 116.9 m. Maximum net profit fell to approximately RMB 248.239 million. Higher coal prices expanded the optimal boundary outward. Once coal price reached approximately 128.7 yuan/t, or 18.5% above baseline, the optimum reached the upper constraint of 240 m. Net profit then increased substantially with further price growth. These results provide a quantitative basis for dynamic boundary optimization and disturbance-reducing extraction in fire-affected open-pit coal mines. Full article

The development of hydrogel bioinks that combine structural stability with biological compatibility remains a major challenge in extrusion-based 3D printing for tissue engineering. In this proof-of-concept study, bacterial cellulose (BC) obtained from kombucha fermentation was explored as a sustainable nanofibrillar component for alginate/chondroitin sulfate (CS)/silicon-substituted hydroxyapatite (Si-HA) composite inks. Following alkaline purification, mechanical processing, and freeze-drying, BC was characterized by scanning electron microscopy (SEM), ATR-FTIR spectroscopy, and X-ray diffraction (XRD), revealing a highly entangled nanofibrillar architecture with high crystallinity (85.4%) and strong hydrogen-bonding potential. Four hydrogel formulations were developed as a comparative 2 × 2 matrix, contrasting BC-containing systems with methylcellulose (MC)-containing reference systems at two Si-HA loadings. Reduced-viscosity measurements of the uncrosslinked precursor formulations showed higher values at the lower Si-HA loading in both formulation series. All formulations could be extruded as acellular inks into grid-like constructs and retained identifiable macroporous architectures after ionic crosslinking. Swelling increased between 24 and 48 h, while mass loss remained limited after the initial 24 h incubation period. In direct-contact testing with L929 fibroblasts, cell viability remained above 84% after 48 h, meeting the ISO 10993-5 non-cytotoxicity criterion. These findings support the feasibility of incorporating physically processed kombucha-derived BC into alginate-based composite inks. Full article

Loss-of-excitation faults are a common fault form of pumped storage units that can threaten both unit safety and grid stability. However, the traditional loss-of-excitation protection based on the impedance principle may exhibit delayed operation or even fail to operate in the case of partial loss of excitation or loss of excitation under light-load conditions, and there is a risk of maloperation in the case of system oscillation. Therefore, this paper analyzes the differences in the characteristics of electrical quantities such as voltage, current, active power, reactive power and power angle during the loss of excitation and system oscillation of a pumped storage unit, and proposes a loss-of-excitation index criterion based on the magnitudes and polarities of variations in terminal voltage, reactive power, and power angle, which constitutes a new method of pumped storage unit loss of excitation fault protection. The simulation results show that compared with the traditional impedance principle loss-of-excitation protection, the proposed method reduces the operating time by 58.6–90.0%. It can reliably and quickly detect the loss-of-excitation fault of pumped storage units under various operating conditions, and shows good anti-maloperation ability for non-loss-of-excitation faults and system oscillation. In addition, the proposed protection method can still maintain reliable operation under the condition of noise interference with a signal-to-noise ratio of 20 dB or communication delay of 0.2 s, which verifies its strong engineering practicability and anti-interference ability. Full article

Mode veering is a modal-interaction phenomenon found in vibration systems. For inertially coupled structures, the combined influence of coupling delay, nonlinear restoring force, and stochastic coupling perturbation remain insufficiently understood. This work analyzes an inertially coupled two-coordinate prototype in which a discrete delay, a delayed cubic stiffness, and positive multiplicative stochastic modulation all enter through the same relative-coordinate coupling channel. We formulate the delayed linear spectrum through a quasi-polynomial characteristic equation. We also characterize the veering by the two positive-frequency characteristic-root branches descending from the mechanical modes. Coupling delay shifts the veering center, alters the minimum frequency gap, and moves the tracked rightmost roots toward the stability boundary. An analytical imaginary-axis-crossing criterion is derived to determine the delay-induced stability boundary of the deterministic linearized system, and the resulting boundary is independently validated by direct multi-start characteristic-root searches and Chebyshev-collocation approximation of the DDE generator. A fixed-reference modal-coordinate representation identifies the off-diagonal modal terms associated with branch exchange while retaining the full delayed characteristic equation. A first-harmonic treatment of the delayed cubic term can yield an amplitude-dependent nonlinear veering backbone. For the stochastic problem, frozen lognormal coupling samples and a time-dependent Ornstein–Uhlenbeck-driven multiplier are constructed from the same unit-mean positive lognormal marginal law. The former is used to quantify realization-wise spectral broadening, whereas the latter retains temporal correlation and is used to evaluate finite-time branch residence and pathwise delayed-work statistics. The pathwise energy balance reveals that the delayed relative-coordinate work rate is sign-indefinite. This provides a common energy-transfer mechanism through which delay, nonlinearity, and stochastic modulation reshape mode veering in the inertially coupled system. Full article