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Keywords = black-box identification

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21 pages, 9390 KB  
Article
Closed-Loop Black-Box Identification of Active Magnetic Bearing System Under Decentralized Control
by Penghui Zhang, Peng Wen, Yuexin Feng, Yuancheng Zhang, Jingchun Xu and Zigang Deng
Actuators 2026, 15(7), 372; https://doi.org/10.3390/act15070372 (registering DOI) - 4 Jul 2026
Abstract
Active magnetic bearings (AMBs) require accurate dynamic models for controller design and performance analysis, but their inherent open-loop instability makes modeling difficult under practical operating conditions. This study presents a closed-loop black-box identification method for an AMB system under decentralized control. A pseudo-random [...] Read more.
Active magnetic bearings (AMBs) require accurate dynamic models for controller design and performance analysis, but their inherent open-loop instability makes modeling difficult under practical operating conditions. This study presents a closed-loop black-box identification method for an AMB system under decentralized control. A pseudo-random binary sequence (PRBS) excitation was injected into the closed-loop system, and the measured input–output data were used to estimate a nonparametric frequency-response model. The effects of excitation amplitude were first examined, and an excitation level of about 10–12% of the saturation current was found to provide a suitable balance among coherence, signal-to-noise ratio, and frequency-response variance. Based on the obtained frequency-domain data, ARX, output-error (OE), and state-space (SS) models were identified and compared. An initial model order range was estimated using the ARX structure and quantitative criteria, including the loss function and Bayesian information criterion. Within this candidate range, different model structures and orders were further evaluated. The 7th-order SS model showed the best overall agreement with the nonparametric frequency response and captured the dominant dynamic features more accurately. Independent time-domain validation and closed-loop reconstruction further confirmed that the selected SS model can represent the practical AMB dynamics with acceptable accuracy. Full article
(This article belongs to the Section Control Systems)
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24 pages, 9508 KB  
Article
A Fractional-Derivative Multi-Kernel Adaptive Learning Approach for Remaining Useful Life Prediction of Rotating Machinery
by Long Pan, Juan Xu, Libiao Peng, Dongjie Bi and Yongle Xie
Sensors 2026, 26(13), 4137; https://doi.org/10.3390/s26134137 - 1 Jul 2026
Viewed by 177
Abstract
Robust Remaining Useful Life (RUL) forecasting is indispensable for condition-based maintenance in rotating machinery. Nevertheless, realizing high predictive precision constitutes an arduous endeavor, primarily complicated by the highly nonlinear and nonstationary nature of degradation processes. Existing prognostic approaches typically face critical bottlenecks: physical [...] Read more.
Robust Remaining Useful Life (RUL) forecasting is indispensable for condition-based maintenance in rotating machinery. Nevertheless, realizing high predictive precision constitutes an arduous endeavor, primarily complicated by the highly nonlinear and nonstationary nature of degradation processes. Existing prognostic approaches typically face critical bottlenecks: physical models require arduous parameter calibration, while data-driven deep learning methods suffer from “black-box” limitations and rely heavily on massive run-to-failure datasets. To overcome these challenges, this paper proposes a novel fractional-derivative multi-kernel adaptive learning approach for robust RUL prediction of rotating machinery. By integrating kernel adaptive learning with a multi-kernel mixture measure, the method provides a mathematically transparent “white-box” architecture that operates effectively in practical small-sample scenarios. Innovatively, the Hadamard fractional derivative is incorporated into the algorithm’s weight-updating mechanism, mathematically encoding the “memory capacity” and “hereditary properties” of physical degradation to capture complex long-range temporal dependencies. Additionally, an adaptive 3σ confidence interval scheme featuring sequential delayed-triggering logic is designed for First Prediction Time (FPT) identification, effectively eliminating noise-induced false alarms. Extensive evaluations through multi-point sequential tracking on two practical datasets confirm that the proposed method surpasses established baselines. Notably, it achieves superior predictive accuracy and lower estimation errors while obtaining the lowest asymmetric penalty scores. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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24 pages, 4958 KB  
Review
Interpreting the Black Box: Interpretable Machine Learning and Systems Pharmacology in Small-Molecule Therapeutics
by Huan Zhang, Yangyang Wang, Jihan Wang and Hui Li
Pharmaceutics 2026, 18(6), 743; https://doi.org/10.3390/pharmaceutics18060743 (registering DOI) - 16 Jun 2026
Viewed by 466
Abstract
Small-molecule drug development faces high attrition rates driven by complex pharmacokinetics and unforeseen toxicities. While deep learning offers high predictive accuracy, its opaque “black-box” nature hinders mechanistic transparency, clinical trust, and regulatory approval. This review synthesizes how Interpretable Machine Learning, synergized with systems [...] Read more.
Small-molecule drug development faces high attrition rates driven by complex pharmacokinetics and unforeseen toxicities. While deep learning offers high predictive accuracy, its opaque “black-box” nature hinders mechanistic transparency, clinical trust, and regulatory approval. This review synthesizes how Interpretable Machine Learning, synergized with systems pharmacology, advances this paradigm by enhancing mechanistic transparency in drug development. By providing insights into algorithmic decisions, Interpretable Machine Learning helps researchers identify molecular features that are statistically associated with absorption, distribution, metabolism, and excretion optimization and preemptively mitigate toxicophores, while noting that these associations require experimental validation to establish genuine causality. Furthermore, integrating multi-omics data via Interpretable Machine Learning guides rational polypharmacology, bridging in silico target identification with “dry-wet loop” validations. Crucially, Interpretable Machine Learning accelerates clinical translation by discovering causal biomarkers, refining patient stratification, and generating transparent “Model Cards” to satisfy U.S. Food and Drug Administration/European Medicines Agency regulations. We also discuss future challenges: data heterogeneity, out-of-distribution generalizability, and the evolution toward Causal Artificial Intelligence. Ultimately, the integration of Interpretable Machine Learning provides a framework for more transparent and evidence-based drug design, realizing the promise of precision medicine. Full article
(This article belongs to the Special Issue Advanced Algorithms for Small-Molecule Therapeutics Development)
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30 pages, 1436 KB  
Article
Computationally Efficient Predictive Control Using SINDy Models
by Maciej Ławryńczuk and Aleksander Samek
Electronics 2026, 15(12), 2530; https://doi.org/10.3390/electronics15122530 - 8 Jun 2026
Viewed by 314
Abstract
The Sparse Identification of Nonlinear Dynamics (SINDy) method yields compact and interpretable models that preserve physical system properties, offering a superior alternative to black-box models. This work proposes a computationally efficient Model Predictive Control (MPC) algorithm for SINDy models. The algorithm employs a [...] Read more.
The Sparse Identification of Nonlinear Dynamics (SINDy) method yields compact and interpretable models that preserve physical system properties, offering a superior alternative to black-box models. This work proposes a computationally efficient Model Predictive Control (MPC) algorithm for SINDy models. The algorithm employs a successively obtained online linear Taylor approximation of the model for future prediction, while the full SINDy model captures past dynamics. As a result, the nonlinear MPC problem is reformulated as a tractable quadratic program. The implementation covers three discretization schemes: the first-order Euler and the simplified and full fourth-order Runge–Kutta. Simulation benchmarks for population dynamics and aircraft models show that the algorithm achieves performance comparable to nonlinear MPC with significantly lower complexity, enabling real-time use. Full article
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13 pages, 8645 KB  
Article
Stochastic Mask Causal Graph Network for Industrial System Fault Diagnosis
by Jiajia Zhang and Weijun Zhang
Machines 2026, 14(6), 644; https://doi.org/10.3390/machines14060644 - 2 Jun 2026
Viewed by 254
Abstract
Despite their demonstrated effectiveness in modeling sensor interaction networks for industrial fault diagnosis, graph neural networks (GNNs) still encounter two key limitations: black-box operation that lacks transparency in fault identification and propagation analysis, and unreliable attention mechanisms whose weights fail to faithfully reflect [...] Read more.
Despite their demonstrated effectiveness in modeling sensor interaction networks for industrial fault diagnosis, graph neural networks (GNNs) still encounter two key limitations: black-box operation that lacks transparency in fault identification and propagation analysis, and unreliable attention mechanisms whose weights fail to faithfully reflect the genuine relevance of sensors or their interactions. To tackle these challenges, we put forward the Stochastic Mask Causal Graph Network, a novel framework that integrates a learnable stochastic masking mechanism guided by the information bottleneck principle. Unlike conventional attention-based or post-hoc approaches, our method automatically suppresses label-irrelevant graph components while preserving causally relevant structures, thereby providing faithful inherent interpretability without biased assumptions and effectively removing spurious correlations to enhance generalization. Comprehensive experiments on realistic complex industrial system datasets demonstrate that the proposed method achieves superior diagnostic accuracy and enhanced interpretability compared with existing advanced approaches. Full article
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38 pages, 25380 KB  
Systematic Review
Mapping the Landscape of Machine Learning in Bridge Engineering: A Scientometric and Technical Synthesis
by Zhanhui Liu, Muhammad Shahid Khan, Yongle Li, Chao Wang and Hongzhu Chen
Buildings 2026, 16(11), 2241; https://doi.org/10.3390/buildings16112241 - 2 Jun 2026
Viewed by 581
Abstract
As bridge infrastructure globally transitions from theoretical monitoring toward intelligent digital management, Machine Learning (ML) has emerged as a transformative tool for data-driven lifecycle decision-making. This study presents a systematic and critical review of ML applications across the entire bridge lifecycle, integrating a [...] Read more.
As bridge infrastructure globally transitions from theoretical monitoring toward intelligent digital management, Machine Learning (ML) has emerged as a transformative tool for data-driven lifecycle decision-making. This study presents a systematic and critical review of ML applications across the entire bridge lifecycle, integrating a PRISMA-based scientometric analysis (2020–2025) with a rigorous technical synthesis of 3 major domains. The research reveals a clear hierarchy in deployment readiness; while Design & Optimization and Seismic Fragility Assessment have achieved “High” readiness by leveraging deep learning surrogates to achieve up to a 50-fold computational speedup over traditional simulations, Vibration-Based Damage Identification remains at a “Low–Medium” level due to environmental noise sensitivity and low Signal-to-Noise Ratios (SNR). Technical findings indicate that vision-based models (e.g., ViT, YOLOv8) show strong and promising performance for surface defect detection in controlled or semi-controlled settings, though broader field deployment remains constrained by lighting variability, dataset diversity, and validation at scale. In deterioration modeling and Remaining Useful Life (RUL) prediction, temporal architectures (e.g., LSTM) effectively capture non-linear trends, though operational risks such as “model drift” and “domain shift” in simulation-dependent models necessitate periodic retraining. This review identifies critical bottlenecks, including the “small data” paradox and the “black-box” dilemma. The work concludes by outlining a strategic roadmap centered on Physics-Informed Neural Networks (PINNs), Federated Learning for cross-agency collaboration, and Explainable AI (XAI) to foster professional trust in safety-critical infrastructure management. Full article
(This article belongs to the Special Issue Advanced Study on Urban Environment by Big Data Analytics)
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33 pages, 4302 KB  
Article
Development of a Low-Cost Open-Architecture 2-DOF Shake Table: Design, Modeling, and Control
by Diego Armando Ramírez-Zúñiga, Antonio Concha-Sánchez, Suresh Kumar Gadi, Suresh Thenozhi, Juan Luis Mata-Machuca and Yajaira Concha-Sánchez
Mathematics 2026, 14(11), 1918; https://doi.org/10.3390/math14111918 - 1 Jun 2026
Viewed by 391
Abstract
This paper presents the mechatronic design, mathematical modeling, parameter identification, and nonlinear position control of an open-architecture biaxial shake table capable of generating base acceleration along two orthogonal horizontal directions. The shake table is tailored for engineering research and education. Addressing the limitations [...] Read more.
This paper presents the mechatronic design, mathematical modeling, parameter identification, and nonlinear position control of an open-architecture biaxial shake table capable of generating base acceleration along two orthogonal horizontal directions. The shake table is tailored for engineering research and education. Addressing the limitations of proprietary “black-box” systems, the platform is constructed using standard industrial components (HLTNC-CNC modules and NEMA 23 BLDC motors) to ensure reproducibility. A core contribution is the characterization of the system’s nonlinear dynamics to enhance tracking fidelity. The mathematical model, derived via the Euler–Lagrange formulation, incorporates viscous and Coulomb friction phenomena, which are critical for accurately reproducing zero-velocity crossings in seismic signals. System parameters are identified using the Recursive Least Squares (RLS) algorithm combined with State Variable Filters (SVFs) to process the regression vector. To enable precise closed-loop performance, a nonlinear state observer incorporating the identified friction dynamics is designed for velocity estimation. Furthermore, a Computed Torque Control (CTC) strategy is synthesized and compared against a conventional Proportional-Velocity (PV) controller. Experimental validations using historical ground motions, including the 1986 Colima earthquake, confirm that the CTC strategy reduces the maximum absolute tracking error by more than 75% compared to the PV approach, bounding the peak error to 0.36mm across both axes. Furthermore, in high-amplitude scenarios, the proposed model-based approach achieved an RMS tracking error reduction of more than 83%. These results validate the proposed platform as a reliable and accessible tool for structural dynamics testing. Full article
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24 pages, 1916 KB  
Article
Weak Node Identification for Small-Signal Stability in Renewable Energy-Dominated Power System Based on Residue-Centered Participation Analysis
by Yige Li and Qianying Mou
Sustainability 2026, 18(11), 5507; https://doi.org/10.3390/su18115507 - 1 Jun 2026
Viewed by 210
Abstract
With high renewable penetration, power system oscillations become more complex. Since internal control details of renewable stations are often inaccessible, classic participation analysis relying on detailed models is difficult to apply, making weak node identification urgently needed. To address this problem, this paper [...] Read more.
With high renewable penetration, power system oscillations become more complex. Since internal control details of renewable stations are often inaccessible, classic participation analysis relying on detailed models is difficult to apply, making weak node identification urgently needed. To address this problem, this paper proposes a residue-centered impedance-based method for small-signal stability in renewable energy-dominated power systems. First, an equivalent state-space model is built from station impedance models, linking the black-box impedance and white-box state-space participation analysis. Then, the physical essence of weak node identification is analyzed, and a residue-centered participation factor is introduced as the indicator. Subsequently, the effect of the station impedances at weak nodes on system stability is quantified. Finally, the method is validated on a four-station testing system and a real-life renewable energy-dominated power system. The rank correlation between the proposed method and the traditional state-space method is close to 1, demonstrating its effectiveness for system-level weak node identification. The proposed method provides engineering guidance for parameter tuning and damping control in practical power systems, which can help improve renewable energy accommodation and support low-carbon, secure, and sustainable power system operation. Full article
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28 pages, 8452 KB  
Article
Causal Graph-Enhanced Large Language Models for Automated Fault Diagnosis and Intelligent Operation and Maintenance in Distributed Computing Systems
by Yu Gu, Jian Zhang and Yugen Du
Electronics 2026, 15(11), 2359; https://doi.org/10.3390/electronics15112359 - 29 May 2026
Viewed by 439
Abstract
Modern distributed computing systems face increasingly complex architectural evolution and potentially costly failures, calling for efficient and robust automated diagnosis to ensure the stability of large-scale data processing. Existing data-driven approaches are constrained by scarce labeled data and black-box behaviors, while expert-based knowledge-driven [...] Read more.
Modern distributed computing systems face increasingly complex architectural evolution and potentially costly failures, calling for efficient and robust automated diagnosis to ensure the stability of large-scale data processing. Existing data-driven approaches are constrained by scarce labeled data and black-box behaviors, while expert-based knowledge-driven solutions suffer from high construction costs and insufficient coverage of dynamic scenarios, especially when domain expertise is limited. This work proposes a fault diagnosis framework that integrates a unified causal graph (UCG) with large language models (LLMs), leveraging a dual knowledge-driven and data-driven mechanism to construct causal graph representations and dynamically generate structured diagnostic reasoning chains-of-thought based on system state awareness. Here, “causal” is used in a restricted sense, combining knowledge-driven dependencies with data-driven statistical regularities. Experimental results indicate that, using GPT-4o as an example, this study achieves accurate fault identification across the eight evaluated fault scenarios within the controlled evaluation scope of this study. Labeled instances are partitioned using stratified sampling into 80% for training and 20% for held-out evaluation; the procedure is repeated five times with independent train–test partitions, and reported matching rates are averaged across these runs. Compared with baselines that rely solely on fault information or on symptom information, the fault matching rate improves by 41.4% and 33.5%, respectively. By tightly coupling structured causal logic with generative artificial intelligence, the approach significantly enhances the interpretability and reliability of the diagnostic process and provides high-value, expert-level support for intelligent operations and maintenance (O&M) in distributed computing systems. Full article
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29 pages, 14588 KB  
Article
Using the LSTM Network for Gray-Box Dynamic Identification of Aircraft at Post-Stall Maneuvers
by Seyed Amin Bagherzadeh
Math. Comput. Appl. 2026, 31(3), 85; https://doi.org/10.3390/mca31030085 - 18 May 2026
Viewed by 218
Abstract
Accurate aerodynamic modeling of aircraft during post-stall maneuvers remains challenging due to massive flow separation, vortex breakdown, and unsteady hysteresis. This paper presents a gray-box system identification framework that integrates a Long Short-Term Memory (LSTM) network into the physical equations of aircraft motion. [...] Read more.
Accurate aerodynamic modeling of aircraft during post-stall maneuvers remains challenging due to massive flow separation, vortex breakdown, and unsteady hysteresis. This paper presents a gray-box system identification framework that integrates a Long Short-Term Memory (LSTM) network into the physical equations of aircraft motion. Unlike black-box methods that sacrifice interpretability, the proposed architecture preserves the rigid-body Newton-Euler equations while replacing empirical aerodynamic coefficient models with an LSTM network. The LSTM directly predicts the aerodynamic coefficients, which are transformed into forces and moments via exact physical laws, ensuring hard constraint satisfaction. Validation using real flight test data from a large-scale (3/8) fighter aircraft at angles of attack up to 80° demonstrates that the method achieves regression coefficients exceeding 0.96 for all coefficients on unseen data, with near-zero mean errors. Quantitative comparisons show that the proposed method reduces prediction error by 50–70% compared to black-box LSTM and PINN baselines. The framework offers a practical balance of accuracy, interpretability, and extrapolation reliability for post-stall aerodynamic identification. Full article
(This article belongs to the Section Engineering)
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25 pages, 1655 KB  
Review
From Data to Physics: Physics-Informed Machine Learning Frameworks in Interdisciplinary Applications
by Carlos A. Valentim and Sergio A. David
Dynamics 2026, 6(2), 16; https://doi.org/10.3390/dynamics6020016 - 14 May 2026
Viewed by 831
Abstract
Computational modeling and machine learning have impacted several different areas of science and accelerated advancements in multiple venues. Yet traditional machine learning models have many well-known drawbacks: besides demanding a significant amount of data, they may fail to generalize beyond training data, are [...] Read more.
Computational modeling and machine learning have impacted several different areas of science and accelerated advancements in multiple venues. Yet traditional machine learning models have many well-known drawbacks: besides demanding a significant amount of data, they may fail to generalize beyond training data, are often treated as “black boxes”, and may predict physically inconsistent results. In response to these limitations, Physics-Informed Machine Learning (PIML) has emerged as a new area that integrates domain knowledge, such as energy or mass conservation, directly into data-driven algorithms. This review paper examines the foundations and main strategies of PIML, organizing the approaches into three categories: automated discovery and system identification, continuous-time modeling, and operator learning. In addition, Physics-Informed Neural Networks are analyzed in a dedicated section that covers architecture fundamentals, forward and inverse problem formulations, loss function design and implementation challenges. The paper also presents a survey of interdisciplinary applications of PIML in materials science, biomedical engineering, and fractional calculus. In this context, the review also analyzes open challenges and outlines future directions in the field. Full article
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38 pages, 7190 KB  
Article
A Trust-Aware Explainable AI Framework for Mental Health Classification Using SHAP and Permissioned Blockchain
by Esra’a Alkafaween, Mahmoud Moshref and Mamoun Dmour
Electronics 2026, 15(9), 1965; https://doi.org/10.3390/electronics15091965 - 6 May 2026
Viewed by 691
Abstract
Artificial intelligence applications in mental health diagnosis face persistent challenges related to interpretability, trust, and the integrity of results. This study presents a trust-aware explainable deep learning framework that combines systematic benchmarking, SHAP-based interpretability, and permissioned blockchain verification to achieve secure mental health [...] Read more.
Artificial intelligence applications in mental health diagnosis face persistent challenges related to interpretability, trust, and the integrity of results. This study presents a trust-aware explainable deep learning framework that combines systematic benchmarking, SHAP-based interpretability, and permissioned blockchain verification to achieve secure mental health classification. The Depression & Mental Health Classification Dataset was used, which contains 1999 records, 21 features, and 12 classes. Data preprocessing included categorical encoding and Z-score normalization for continuous variables. To ensure robust evaluation, a stratified train–test split was applied, and class imbalance was addressed using the Synthetic Minority Over-sampling Technique (SMOTE). Eight machine learning and deep learning models were assessed under identical preprocessing and validation settings. In addition, two models were proposed: Feature Attention XGBoost (FA-XGBoost) and Feature Attention Feedforward Neural Network (FA-FNN). The FA-FNN model achieved the best performance, attaining an accuracy of 96.00%, precision of 98.31%, recall of 97.31%, and F1-score of 98.04%. To address deep learning’s black-box limitation, SHapley Additive ExPlanations (SHAPs) were used to provide both global feature importance and instance-level explanations, enabling transparent identification of the most influential mental health markers. Beyond interpretability, a permissioned blockchain layer was added to provide tamper-proof logging and traceable verification of AI results. The framework securely stores cryptographic hashes of model versions, prediction results, and generated SHAP artifacts, including visualization images, without exposing sensitive medical data. By integrating explainable decision-making, high-performance classification, and blockchain-based trust enforcement, the proposed framework creates a transparent and secure pipeline suitable for real-world mental healthcare systems. Controlled experiments on a permissioned Ethereum-InterPlanetary File System (IPFS) network demonstrated predictable latency, stable throughput (≈28–30 transactions/s), and lower operational costs, proving the framework’s suitability for enterprise and healthcare deployments. Full article
(This article belongs to the Section Artificial Intelligence)
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20 pages, 765 KB  
Article
Does Green Productivity Drive ESG? Associational Evidence from Instrumental Variable and Panel Analyses
by Meina Liu, Shuke Fu, Jiachao Peng and Jiali Tian
Sustainability 2026, 18(9), 4342; https://doi.org/10.3390/su18094342 - 28 Apr 2026
Viewed by 480
Abstract
Green Total Factor Productivity (GTFP) serves as a pivotal indicator for balancing high-quality economic growth with increasingly stringent environmental regulations. However, empirical evidence regarding whether and how firm-level GTFP is associated with enhanced Environmental, Social, and Governance (ESG) performance in emerging markets remains [...] Read more.
Green Total Factor Productivity (GTFP) serves as a pivotal indicator for balancing high-quality economic growth with increasingly stringent environmental regulations. However, empirical evidence regarding whether and how firm-level GTFP is associated with enhanced Environmental, Social, and Governance (ESG) performance in emerging markets remains limited. This study addresses this gap by examining the GTFP–ESG nexus within the macro-context of China’s “Dual-Carbon” goals (aiming for peak carbon emissions by 2030 and carbon neutrality by 2060). Utilizing an unbalanced panel dataset of Chinese A-share listed companies strictly covering the period from 2011 to 2022 (with 2010 data exclusively used for one-period lagged variables), we construct firm-level GTFP metrics using a non-radial SBM-DDF global Malmquist–Luenberger index—incorporating both desirable economic outputs and undesirable environmental emissions—and link them with Huazheng ESG ratings. To ensure robust empirical identification, we employ two-way fixed-effects models with lagged variables, propensity score matching (PSM), and an instrumental variable two-stage least squares (IV-2SLS) approach utilizing the leave-one-out provincial average GTFP as an instrument. The results indicate a significant positive association between GTFP and overall ESG performance, as well as its three sub-pillars. Specifically, a one-standard-deviation increase in GTFP corresponds to a 0.15-standard-deviation increase in the ESG score, a marginal effect of profound economic significance, providing robust associational insights via the IV estimates. Mechanism analyses reframe traditional mediation as descriptive associational pathways, revealing that digital transformation, green innovation, and information transparency serve as significant channels, theoretically demonstrating how resource efficiency translates into social legitimacy. Heterogeneity tests show that this association is more pronounced for non-state-owned enterprises, firms in eastern China, and those with lower financing constraints. These findings unpack the “black box” between technical efficiency and sustainability, providing empirical support for policymakers to align corporate productivity with international disclosure standards (such as the EU’s CSRD). Full article
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25 pages, 4545 KB  
Article
Symmetry-Guided Analysis of Market Characteristics and Electricity Prices Anomaly: A Comparative Framework of Influencing Factors
by Siting Dai, Wenyang Deng and Mengke Zhang
Symmetry 2026, 18(2), 390; https://doi.org/10.3390/sym18020390 - 23 Feb 2026
Viewed by 604
Abstract
Electricity spot prices jointly encode network physics and strategic bidding outcomes. In a well-functioning market, nodal and temporal price patterns tend to remain approximately invariant under mild perturbations-exhibiting symmetry-preserving regularities in distribution shape, spatial gradients, and temporal variation. Conversely, congestion binding, net-load stress, [...] Read more.
Electricity spot prices jointly encode network physics and strategic bidding outcomes. In a well-functioning market, nodal and temporal price patterns tend to remain approximately invariant under mild perturbations-exhibiting symmetry-preserving regularities in distribution shape, spatial gradients, and temporal variation. Conversely, congestion binding, net-load stress, and abnormal bidding can induce symmetry breaking, manifested as heavy tails, mean shifts, and localized price discontinuities. This study develops a symmetry-guided and explainable diagnostic framework to identify price anomalies and attribute their dominant drivers. First, representative anomaly types (spike and mean shift) are defined using statistically and operationally motivated criteria, together with robustness checks across alternative thresholds. Second, principal component analysis is applied to construct compact, anomaly-specific feature sets, filtering weakly related variables while retaining system stress, congestion proxies, and renewable-induced variability indicators. Third, leveraging the optimization structure of market clearing and the associated KKT conditions, we characterize the price–feature linkage as a piecewise mapping and quantify each feature’s contribution via a sampling-based influence scoring procedure, yielding a ranked causal attribution. Case studies on a regional day-ahead spot market dataset demonstrate that the proposed framework achieves high consistency with expert assessments, with traceability accuracy exceeding 85% overall and particularly strong performance for spike-type anomalies. The method reduces reliance on purely manual diagnosis and black-box learning, and provides symmetry-oriented, actionable evidence for market surveillance and renewable-friendly flexibility and congestion management design. The proposed framework enables transparent identification of dominant structural drivers underlying different types of electricity price anomalies, linking observed price signals to market-clearing mechanisms. The results provide actionable diagnostic insights for market monitoring and regulatory assessment in electricity markets with high renewable penetration. Full article
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25 pages, 769 KB  
Article
Can Digital–Intelligent Integration Enhance Urban Green Economic Efficiency? An Empirical Analysis Based on National Big Data Comprehensive Pilot Zones and Smart-City Dual-Pilot Programs
by Feng He and Yue Zhang
Sustainability 2026, 18(4), 1710; https://doi.org/10.3390/su18041710 - 7 Feb 2026
Cited by 1 | Viewed by 614
Abstract
Digital–intelligent integration (DII) has emerged as a pivotal driver for high-quality urban development, offering a pathway to overcome pressing resource and environmental constraints. By harnessing data as a core production factor and integrating advanced intelligent technologies, DII can substantially elevate urban green economic [...] Read more.
Digital–intelligent integration (DII) has emerged as a pivotal driver for high-quality urban development, offering a pathway to overcome pressing resource and environmental constraints. By harnessing data as a core production factor and integrating advanced intelligent technologies, DII can substantially elevate urban green economic efficiency (GEE). This study constructs a quasi-natural experiment using the staggered rollout of national big data comprehensive pilot zones (initiated in 2012) and smart-city pilot programs (from 2016 onward). Employing a rigorous staggered difference-in-differences (DID) estimator on panel data from 279 Chinese prefecture-level cities over 2010–2021, we find that DII causally increases GEE by 5.03 percentage points (p < 0.01). This benchmark result remains robust across a comprehensive set of checks, including parallel-trend validation, placebo tests, double/debiased machine learning, two-stage least squares with historical IT-sector instruments, and controls for overlapping policies (e.g., ETS, low-carbon pilots, green finance zones). Mechanism analysis, conducted via a sequential 2SLS control-function approach with lagged mediators and Sobel–Goodman mediation tests, reveals three theoretically grounded channels: (i) enhanced urban ecological resilience (mediates 62%, z = 4.68), (ii) accelerated green technological innovation (55%, z = 4.12, measured by IPC/Y02 patent share), and (iii) heightened entrepreneurial vitality (58%, z = 4.39, new firms per 10,000 residents). Heterogeneity tests show pronounced effects in growing and mature resource-based cities (+1.21% and +11.21%), high-fintech cities (+11.35%), and high-river-density areas (+10.29%) but insignificant impacts in declining resource-exhausted cities (joint F p = 0.08). This study makes four key contributions: (1) it innovatively constructs a continuous DII policy variable by exploiting the synergistic timing of dual pilots, thereby overcoming the limitation of analyzing policies in isolation; (2) it opens the “theoretical black box” by integrating institutional theory and information economics into a unified conceptual framework that explicitly links DII to GEE through reduced transaction costs and alleviated information asymmetry; (3) it enriches the mediation identification strategy in staggered settings using 2SLS control functions and sequential G-estimation, addressing endogeneity in intermediary variables more rigorously than traditional three-step approaches; and (4) it delivers nuanced evidence on the contextual conditions (when and where) under which DII yields the strongest green dividends, providing actionable guidance for China’s “dual-carbon” goals and the global green transition. Full article
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