arXiv subjects

Chunlei Xu

Publications and source records attributed to Chunlei Xu.

18 recordsLinked to original sources

arXiv2026

Structural Properties and Applications of the Augmented Sombor Index

Topological indices are key quantitative descriptors in mathematical chemistry, unchanged under symmetry operations and retaining graph connectivity; they capture molecular structural features to provide insights into molecular stability and chemical properties, becoming indispensable in cheminformatics and theoretical chemistry. Among degree-based indices, the \textbf{Sombor index} is widely concerned for capturing structural information, and motivated by enhanced structural discrimination, the \textbf{augmented Sombor index} ($ASO$) is defined for a connected graph $\Omega$ with $|V(\Omega)|\geq 3$ as $$ASO(\Omega) = \sum_{v_iv_j\in E(\Omega)} \sqrt{\frac{{d_i^2 + d_j^2}}{d_i + d_j - 2}},$$ where $d_i$ and $d_j$ are the degrees of vertices $v_i$ and $v_j$, respectively. Within the scope of this study, we first establish several sharp bounds for the augmented Sombor index and characterize the extremal graphs attaining these bounds. In particular, we determine the minimum value of the $ASO$ index for unicyclic graphs with a prescribed girth and characterize all graphs achieving this minimum. We also identify the second maximum $ASO$ value among trees and characterize the corresponding extremal tree structures. Furthermore, the minimum and maximum values of the $ASO$ index for bipartite graphs and chemical graphs are obtained, together with a complete characterization of the associated extremal graphs. In addition, we characterize the chemical trees that maximize the $ASO$ index. The chemical applicability of the $ASO$ index is investigated through quantitative structure-property relationship (QSPR) analysis, supported by a comparative assessment of several variants of the Sombor index. Finally, we present concluding remarks and outline potential directions for future research on the augmented Sombor index of graphs.

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arXiv2025

Soil analysis with machine-learning-based processing of stepped-frequency GPR field measurements: Preliminary study

Ground Penetrating Radar (GPR) has been widely studied as a tool for extracting soil parameters relevant to agriculture and horticulture. When combined with Machine Learning (ML) methods, air-coupled Stepped Frequency Continuous Wave Ground Penetrating Radar (SFCW GPR) measurements could offer a cost-effective way to obtain depth-resolved soil data. As a first step of our study in this direction, we conducted an extensive field survey using a tractor-mounted air-coupled SFCW GPR instrument. Leveraging ML-based data processing, we evaluate the GPR instrument's ability by predicting the apparent electrical conductivity (ECaR) measured by a co-recorded Electromagnetic Induction (EMI) instrument. The large-scale field measurement campaign with 3472 co-registered and geo-located GPR and EMI data samples distributed over approximately 6600 square meters was performed on a golf course. This terrain offers high surface homogeneity but also presents the challenge of subtle soil parameter variations. Based on the results, we discuss challenges in this multi-sensor regression setting and propose the use of the nugget-to-sill ratio as a performance metric for evaluating ML models in agricultural field survey applications.

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arXiv2023

On Sombor Index of Graphs

Recently, Gutman defined a new vertex-degree-based graph invariant, named the Sombor index $SO$ of a graph $G$, and is defined by $$SO(G)=\sum_{uv\in E(G)}\sqrt{d_G(u)^2+d_G(v)^2},$$ where $d_G(v)$ is the degree of the vertex $v$ of $G$. In this paper, we obtain the sharp lower and upper bounds on $SO(G)$ of a connected graph, and characterize graphs for which these bounds are attained.

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arXiv2021

Temporal Alignment Prediction for Few-Shot Video Classification

The goal of few-shot video classification is to learn a classification model with good generalization ability when trained with only a few labeled videos. However, it is difficult to learn discriminative feature representations for videos in such a setting. In this paper, we propose Temporal Alignment Prediction (TAP) based on sequence similarity learning for few-shot video classification. In order to obtain the similarity of a pair of videos, we predict the alignment scores between all pairs of temporal positions in the two videos with the temporal alignment prediction function. Besides, the inputs to this function are also equipped with the context information in the temporal domain. We evaluate TAP on two video classification benchmarks including Kinetics and Something-Something V2. The experimental results verify the effectiveness of TAP and show its superiority over state-of-the-art methods.

cs.CV↗

arXiv2021

A Transductive Maximum Margin Classifier for Few-Shot Learning

Few-shot learning aims to train a classifier that can generalize well when just a small number of labeled examples per class are given. We introduce a transductive maximum margin classifier for few-shot learning (FS-TMMC). The basic idea of the classical maximum margin classifier is to solve an optimal prediction function so that the training data can be correctly classified by the resulting classifer with the largest geometric margin. In few-shot learning, it is challenging to find such classifiers with good generalization ability due to the insufficiency of training data in the support set. FS-TMMC leverages the unlabeled query examples to adjust the separating hyperplane of the maximum margin classifier such that the prediction function is optimal on both the support and query sets. Furthermore, we use an efficient and effective quasi-Newton algorithm, the L-BFGS method for optimization. Experimental results on three standard few-shot learning benchmarks including miniImagenet, tieredImagenet and CUB show that our method achieves state-of-the-art performance.

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arXiv2020

On Training Effective Reinforcement Learning Agents for Real-time Power Grid Operation and Control

Deriving fast and effectively coordinated control actions remains a grand challenge affecting the secure and economic operation of today's large-scale power grid. This paper presents a novel artificial intelligence (AI) based methodology to achieve multi-objective real-time power grid control for real-world implementation. State-of-the-art off-policy reinforcement learning (RL) algorithm, soft actor-critic (SAC) is adopted to train AI agents with multi-thread offline training and periodic online training for regulating voltages and transmission losses without violating thermal constraints of lines. A software prototype was developed and deployed in the control center of SGCC Jiangsu Electric Power Company that interacts with their Energy Management System (EMS) every 5 minutes. Massive numerical studies using actual power grid snapshots in the real-time environment verify the effectiveness of the proposed approach. Well-trained SAC agents can learn to provide effective and subsecond control actions in regulating voltage profiles and reducing transmission losses.

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arXiv2020

Deriving AC OPF Solutions via Proximal Policy Optimization for Secure and Economic Grid Operation

Optimal power flow (OPF) is a very fundamental but vital optimization problem in the power system, which aims at solving a specific objective function (ex.: generator costs) while maintaining the system in the stable and safe operations. In this paper, we adopted the start-of-the-art artificial intelligence (AI) techniques to train an agent aiming at solving the AC OPF problem, where the nonlinear power balance equations are considered. The modified IEEE-14 bus system were utilized to validate the proposed approach. The testing results showed a great potential of adopting AI techniques in the power system operations.

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arXiv2020

Distributed Frequency Emergency Control with Coordinated Edge Intelligence

Developing effective strategies to rapidly support grid frequency while minimizing loss in case of severe contingencies is an important requirement in power systems. While distributed responsive load demands are commonly adopted for frequency regulation, it is difficult to achieve both rapid response and global accuracy in a practical and cost-effective manner. In this paper, the cyber-physical design of an Internet-of-Things (IoT) enabled system, called Grid Sense, is presented. Grid Sense utilizes a large number of distributed appliances for frequency emergency support. It features a local power loss $ΔP$ estimation approach for frequency emergency control based on coordinated edge intelligence. The specifically designed smart outlets of Grid Sense detect the frequency disturbance event locally using the parameters sent from the control center to estimate active power loss in the system and to make rapid and accurate switching decisions soon after a severe contingency. Based on a modified IEEE 24-bus system, numerical simulations and hardware experiments are conducted to demonstrate the frequency support performance of Grid Sense in the aspects of accuracy and speed. It is shown that Grid Sense equipped with its local $ΔP$-estimation frequency control approach can accurately and rapidly prevent the drop of frequency after a major power loss.

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arXiv2019

Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering

Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model. While the resolution of this quantization clearly impacts the quality of signal reconstruction, there actually exist incompatible combinations of quantization functions and sensing matrices that proscribe arbitrarily low reconstruction error when the number of measurements increases. This work shows that a large class of random matrix constructions known to respect the restricted isometry property (RIP) is "compatible" with a simple scalar and uniform quantization if a uniform random vector, or a random dither, is added to the compressive signal measurements before quantization. In the context of estimating low-complexity signals (e.g., sparse or compressible signals, low-rank matrices) from their quantized observations, this compatibility is demonstrated by the existence of (at least) one signal reconstruction method, the projected back projection (PBP), whose reconstruction error decays when the number of measurements increases. Interestingly, given one RIP matrix and a single realization of the dither, a small reconstruction error can be proved to hold uniformly for all signals in the considered low-complexity set. We confirm these observations numerically in several scenarios involving sparse signals, low-rank matrices, and compressible signals, with various RIP matrix constructions such as sub-Gaussian random matrices and random partial discrete cosine transform (DCT) matrices.

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arXiv2018

Quantity over Quality: Dithered Quantization for Compressive Radar Systems

In this paper, we investigate a trade-off between the number of radar observations (or measurements) and their resolution in the context of radar range estimation. To this end, we introduce a novel estimation scheme that can deal with strongly quantized received signals, going as low as 1-bit per signal sample. We leverage for this a dithered quantized compressive sensing framework that can be applied to classic radar processing and hardware. This allows us to remove ambiguous scenarios prohibiting correct range estimation from (undithered) quantized base-band radar signal. Two range estimation algorithms are studied: Projected Back Projection (PBP) and Quantized Iterative Hard Thresholding (QIHT). The effectiveness of the reconstruction methods combined with the dithering strategy is shown through Monte Carlo simulations. Furthermore we show that: (i), in dithered quantization, the accuracy of target range estimation improves when the bit-rate (i.e., the total number of measured bits) increases, whereas the accuracy of other undithered schemes saturate in this case; and (ii), for fixed, low bit-rate scenarios, severely quantized dithered schemes exhibit better performances than their full resolution counterparts. These observations are confirmed using real measurements obtained in a controlled environment, demonstrating the feasibility of the method in real ranging applications.

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arXiv2018

1-bit Localization Scheme for Radar using Dithered Quantized Compressed Sensing

We present a novel scheme allowing for 2D target localization using highly quantized 1-bit measurements from a Frequency Modulated Continuous Wave (FMCW) radar with two receiving antennas. Quantization of radar signals introduces localization artifacts, we remove this limitation by inserting a dithering on the unquantized observations. We then adapt the projected back projection algorithm to estimate both the range and angle of targets from the dithered quantized radar observations, with provably decaying reconstruction error when the number of observations increases. Simulations are performed to highlight the accuracy of the dithered scheme in noiseless conditions when compared to the non-dithered and full 32-bit resolution under severe bit-rate reduction. Finally, measurements are performed using a radar sensor to demonstrate the effectiveness and performances of the proposed quantized dithered scheme in real conditions.

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arXiv2018

Taking the edge off quantization: projected back projection in dithered compressive sensing

Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal reconstruction quality in this framework, most of the existing theoretical analyses lie heavily on the quantization of sub-Gaussian random projections (e.g., Gaussian or Bernoulli). We show here that a simple uniform scalar quantizer is compatible with a large class of random sensing matrices known to respect, with high probability, the restricted isometry property (RIP). Critically, this compatibility arises from the addition of a uniform random vector, or "dithering", to the linear signal observations before quantization. In this setting, we prove the existence of (at least) one signal reconstruction method, i.e., the projected back projection (PBP), whose reconstruction error decays when the number of quantized measurements increases. This holds with high probability in the estimation of sparse signals and low-rank matrices. We validate numerically the predicted error decay as the number of measurements increases.

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arXiv2017

The Allocation of a Variable Series Reactor Considering AC Constraints and Contingencies

The Variable Series Reactors (VSRs) can efficiently control the power flow through the adjustment of the line reactance. When they are appropriately allocated in the power network, the transmission congestion and generation cost can be reduced. This paper proposes a planning model to optimally allocate VSRs considering AC constraints and multi-scenarios including base case and contingencies. The planning model is originally a non-convex large scale mixed integer nonlinear program (MINLP), which is generally intractable. The proposed Benders approach decomposes the MINLP model into a mixed integer linear program (MILP) master problem and a number of nonlinear subproblems. Numerical case studies based on IEEE 118-bus demonstrate the high performance of the proposed approach.

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arXiv2017

Online Coherence Identification Using Dynamic Time Warping for Controlled Islanding

Controlled islanding is considered to be the last countermeasure to prevent system-wide blackouts in case of cascading failures. It splits the system into self-sustained islands to maintain transient stability at the expense of possible loss of load. Generator coherence identification is critical to controlled islanding scheme as it helps identify the optimal cut-set to maintain system transient stability. This paper presents a novel approach for online generator coherency identification using phasor measurement unit (PMU) data and dynamic time warping (DTW). Results from the coherence identification are used to further cluster non-generator buses using spectral clustering with the objective of minimizing power flow disruption. The proposed approach is validated and compared to existing methods on the IEEE 39-bus system, through which its advantages are demonstrated.

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arXiv2017

PMU Assisted Power System Parameter Calibration at Jiangsu Electric Power Company

An online PMU-assisted Power System Parameter Calibration System (PSPCS) was recently developed and implemented at State Grid Jiangsu Electric Power Company (JEPC). PSPCS leverages high-resolution PMU data and data mining techniques to perform online screening of the EMS and Production Management System (PMS) databases for data cleaning, model validation, and parameter calibration. PSPCS calculates transmission line and generator parameters on a regular real-time basis and compares the results with databases to identify record(s) with significant discrepancy, if any. Once consistent discrepancy is observed, the system will raise a flag and further investigation will be initiated, including a novel density-based spatial clustering procedure for parameter/data calibration. A novel metric is proposed to quantify the credibility of PMU-based parameter identification. This paper discusses the proposed methodologies, challenges, as well as implementation issues identified during the development and deployment of PSPCS.

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arXiv2017

Online Calibration of Phasor Measurement Unit Using Density-Based Spatial Clustering

Data quality of Phasor Measurement Unit (PMU) is receiving increasing attention as it has been identified as one of the limiting factors that affect many wide-area measurement system (WAMS) based applications. In general, existing PMU calibration methods include offline testing and model based approaches. However, in practice, the effectiveness of both is limited due to the very strong assumptions employed. This paper presents a novel framework for online bias error detection and calibration of PMU measurement using density-based spatial clustering of applications with noise (DBSCAN) based on much relaxed assumptions. With a new problem formulation, the proposed data mining based methodology is applicable across a wide spectrum of practical conditions and one side-product of it is more accurate transmission line parameters for EMS database and protective relay settings. Case studies demonstrate the effectiveness of the proposed approach.

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arXiv2017

The Rare Eclipse Problem on Tiles: Quantised Embeddings of Disjoint Convex Sets

Quantised random embeddings are an efficient dimensionality reduction technique which preserves the distances of low-complexity signals up to some controllable additive and multiplicative distortions. In this work, we instead focus on verifying when this technique preserves the separability of two disjoint closed convex sets, i.e., in a quantised view of the "rare eclipse problem" introduced by Bandeira et al. in 2014. This separability would ensure exact classification of signals in such sets from the signatures output by this non-linear dimensionality reduction. We here present a result relating the embedding's dimension, its quantiser resolution and the sets' separation, as well as some numerically testable conditions to illustrate it. Experimental evidence is then provided in the special case of two $\ell_2$-balls, tracing the phase transition curves that ensure these sets' separability in the embedded domain.

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arXiv2013

Uniqueness Conditions for A Class of l0-Minimization Problems

We consider a class of l0-minimization problems, which is to search for the partial sparsest solution to an underdetermined linear system with additional constraints. We introduce several concepts, including lp-induced norm (0 < p < 1), maximal scaled spark and scaled mutual coherence, to develop several new uniqueness conditions for the partial sparsest solution to this class of l0-minimization problems. A further improvement of some of these uniqueness criteria have been also achieved through the so-called concepts such as maximal scaled (sub)coherence rank.

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