IEEE Transactions on Instrumentation and Measurement最新文献_第5页

Adaptive Periodic Impulse Extraction Method and Its Application in Rolling Bearing Fault Diagnosis

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545547

Jian Cheng;Tong Chen;Haiyang Pan;Jinde Zheng;Jinyu Tong

{"title":"Adaptive Periodic Impulse Extraction Method and Its Application in Rolling Bearing Fault Diagnosis","authors":"Jian Cheng;Tong Chen;Haiyang Pan;Jinde Zheng;Jinyu Tong","doi":"10.1109/TIM.2025.3545547","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545547","url":null,"abstract":"Considering that weak periodic impulse components are difficult to be separated and extracted from strong noise interference, the accuracy of fault diagnosis is greatly affected. A new adaptive periodic impulse extraction (APIE) method is proposed. First, the APIE method introduces the correlation Renyi entropy (CRE) index, which is based on the cyclo-stationarity of the signal and can accurately quantify the periodicity and impulsivity of the signal. Then, the APIE takes CRE as the objective function and realizes the accurate locking of fault feature information by iteratively updating filter parameters, and then, the redundant modes and mixed modes are eliminated by correlation coefficient (CC) index. Finally, the optimal mode number is adaptively determined by CRE index again, which improves the stability of the decomposition effect of APIE. The analysis results of rolling bearing composite simulation signal and experimental signals show that APIE method can not only effectively separate different characteristic information components but also accurately extract periodic impulse components and has outstanding noise robustness.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-9"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143570821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A 4H–SiC Vibration Sensor With the Working Temperature up to 600 ∘C

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545532

Yu Yang;You Zhao;Lukang Wang;Yabing Wang;Yulong Zhao

{"title":"A 4H–SiC Vibration Sensor With the Working Temperature up to 600 ∘C","authors":"Yu Yang;You Zhao;Lukang Wang;Yabing Wang;Yulong Zhao","doi":"10.1109/TIM.2025.3545532","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545532","url":null,"abstract":"High-temperature vibration sensors are critical in extreme environments such as aerospace, automotive, power generation, where common sensors fail due to excessive heat. This study introduces a vibration sensor that can withstand high temperatures up to <inline-formula> <tex-math>$600~^{circ }$ </tex-math></inline-formula>C based on the piezoresistive effect of N-type 4H-SiC. The sensor chip was designed by theoretical modeling and multiphysics simulation, and fabricated by combining micro-electronmechanical systems (MEMSs) technology and femtosecond laser etching. The sensor performance was extensively verified from <inline-formula> <tex-math>$25~^{circ }$ </tex-math></inline-formula>C to <inline-formula> <tex-math>$600~^{circ }$ </tex-math></inline-formula>C. The sensitivity of the sensor decreases from 0.153 mV/g at <inline-formula> <tex-math>$25~^{circ }$ </tex-math></inline-formula>C to 0.105 mV/g at <inline-formula> <tex-math>$600~^{circ }$ </tex-math></inline-formula>C with a temperature coefficient of −0.054% FS/°C at <inline-formula> <tex-math>$600~^{circ }$ </tex-math></inline-formula>C. The sensor’s sensitivity decreases essentially linearly with increasing temperature. Dynamic tests showed the sensor’s usable frequency is 0–590 Hz and the resonant frequency is 1179.85 Hz at <inline-formula> <tex-math>$25~^{circ }$ </tex-math></inline-formula>C while decreasing to 1156.76 Hz at <inline-formula> <tex-math>$600~^{circ }$ </tex-math></inline-formula>C. The designed sensor showed the reliability of high impact resistance up to 225% overload and random vibration. These findings suggest that the designed vibration sensor can be a promising alternative for high-temperature vibration monitoring.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-10"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

LoRa Mesh Network With Time-Efficient Medium Utilization for IoT Building Monitoring System

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545712

Man Ho Tsoi;Yuen Wing Lo;Yat Sze Choy;Cheuk-Fai Chow;Steve W. Y. Mung

{"title":"LoRa Mesh Network With Time-Efficient Medium Utilization for IoT Building Monitoring System","authors":"Man Ho Tsoi;Yuen Wing Lo;Yat Sze Choy;Cheuk-Fai Chow;Steve W. Y. Mung","doi":"10.1109/TIM.2025.3545712","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545712","url":null,"abstract":"Flexibility, reliability, large coverage, and low cost are critical traits for low-power wide-area networks (LPWANs). The network infrastructure is the prerequisite for implementing the Internet of Things (IoT) end device (ED) in building monitoring systems. Long range (LoRa) is one of the best candidates for LPWAN, but the lack of a mesh network limits its potential, especially on the cost. Multiple medium access control (MAC) protocols with various features were proposed to handle the collision problem in LoRa mesh networks. New evaluation methods were established to verify the MAC protocols in the highly contentious period in which network extenders (NEs) compete for idle medium in a mesh network. The experiments consisted of 30 NEs with overlapping coverage, whereas in real-life applications, usually, coverage overlap of only two to three NEs occurs. The performance of the proposed MAC protocols was evaluated by comparing their packet delivery ratios (PDRs) and data throughput values (bps). The best MAC protocol, namely, carrier-sense multiple access (CSMA)/collision avoidance (CA) with assigned distributed interframe spacing (DIFS), achieved a PDR of approximately 100% and data throughput of approximately 2500 bps. The proposed LoRa mesh network can serve as the basis of low-latency, low-collision, wide-coverage IoT monitoring, and control systems. A real commercial large-scale building was deployed by this proposed network with 205 devices located across 23 continuous floors with single gateway as a deployment test. The test period spans over six months and an overall PDR of 92% is obtained, which outperforms previous research in terms of duration, scales, and PDR.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-14"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fault Detection for Ex-Core Neutron Detectors in Nuclear Power Plants Using Global-Fused Dynamic Detection Model

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545728

Weiqing Lin;Xiren Miao;Jing Chen;Pengbin Duan;Mingxin Ye;Yong Xu;Xinyu Liu;Hao Jiang;Yanzhen Lu

{"title":"Fault Detection for Ex-Core Neutron Detectors in Nuclear Power Plants Using Global-Fused Dynamic Detection Model","authors":"Weiqing Lin;Xiren Miao;Jing Chen;Pengbin Duan;Mingxin Ye;Yong Xu;Xinyu Liu;Hao Jiang;Yanzhen Lu","doi":"10.1109/TIM.2025.3545728","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545728","url":null,"abstract":"In nuclear power plants (NPPs), ex-core neutron detectors are deployed around reactor cores and are essential for reactor stability, but their deterioration and malfunction can cause misperceptions and misdiagnoses. Existing fault detection seldom accounts for global spatial-temporal coupling relationships implied among overall detectors and uncertainty under transient operations. Thus, we propose a novel detector-oriented fault detection scheme called the global-fused dynamic detection (GFDD) model, established by the global spatial-temporal graph (GSTG), moving-global graph convolution (MGGC), and uncertainty-quantified dynamic detection (UQDD). To enrich informational sources and disperse faulty propagation, we specifically design the GSTG for characterizing the spatial-temporal relationships among overall detectors and the MGGC for efficiently capturing global high-level features, further generating multidetector reconstructed signals and residuals. Through calculating dynamic statistics and quantifying uncertainty under varying operating conditions, the UQDD identifies faulty detectors and corrects erroneous signals. Experiments on steady and transient states from a real-world NPP with simulated faults validate that the GFDD model outperforms various state-of-the-art methods with regard to signal reconstruction and fault detection.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-15"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143570819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hybrid DCNN–Transfer Learning Model Coupled With Background Clutter Mitigation for FMCW Radar-Based People Counting Improvement

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545718

Massala Mboyi Gilles Yowel;Dong-Hyun Oh;Jung-Hoon Han

{"title":"Hybrid DCNN–Transfer Learning Model Coupled With Background Clutter Mitigation for FMCW Radar-Based People Counting Improvement","authors":"Massala Mboyi Gilles Yowel;Dong-Hyun Oh;Jung-Hoon Han","doi":"10.1109/TIM.2025.3545718","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545718","url":null,"abstract":"Automatic people counting has garnered significant attention due to its broad civilian and military applications. In civilian settings, it helps detect unusual occupancy patterns or manage crowding in public transportation. In military contexts, it serves to count and track enemy movements, providing real-time data on troop numbers and positions on the battlefield, which is critical for tactical decision-making. Radar systems are often used for such tasks due to their ability to function in all weather conditions, day or night. However, the signal collected by the radar is hindered by unwanted signals reflected by clutter. Also, the direct coupling between transmit and receive antennas can mask targets with a weak signal. All these artifacts can decay the performance of deep learning models for automatic people counting. This work proposes a background mitigation algorithm based on the multiresolution analysis of the maximal overlap discrete wavelet transform (MRA-MODWT) to enhance the accuracy of deep learning models for automatic people counting. Subsequently, the Daubechies least asymmetric wavelet with four vanishing moments (sym4) is used to isolate and cancel background signals, and a fusion layer combining a transfer learning block with a customized deep convolutional neural network (DCNN) is introduced to improve the accuracy. The hybrid DCNN-InceptionV3 model achieved a peak accuracy of 98.31%, an average precision of 0.9827, an average recall of 0.9827, and an average <inline-formula> <tex-math>$F1$ </tex-math></inline-formula> score of 0.9836 on realistic radar data.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-14"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143583160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Attitude Measurement and Zero Offset Calibration for a Novel Spherical Actuator With Tiltable Stator

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545497

Xinghua He;Pengjie Xiang;Liang Yan;Xiaoshuai Liu;Xuxu Yang

{"title":"Attitude Measurement and Zero Offset Calibration for a Novel Spherical Actuator With Tiltable Stator","authors":"Xinghua He;Pengjie Xiang;Liang Yan;Xiaoshuai Liu;Xuxu Yang","doi":"10.1109/TIM.2025.3545497","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545497","url":null,"abstract":"Spherical actuators serve as active joints capable of rotation in three directions and are more compact than traditional joints with multiple single-axis motors embedded in series. Accurate attitude measurement is essential for real-time and precise control. However, existing noncontact attitude measurement methods for spherical actuators suffer from low accuracy and poor integration, limiting their practical application. This article introduces a novel stator-tiltable spherical actuator that incorporates a high-precision encoder in a frame structure, achieving enhanced precision and integration in attitude measurement. Zero-offset self-calibration is achieved by comparing the encoder readings with open-loop controlled angles, eliminating the need for external sensors or structures. The design of the proposed spherical actuator, along with the principles of attitude measurement and calibration, is explained in detail. An open-loop control method supports the calibration process. Experimental tests assess the accuracies of open-loop control and repeat orientation. Additionally, closed-loop control is employed on the spherical actuator to verify the measurement results. This detection method achieves a repeat orientation accuracy of less than 0.03° while increasing the spherical actuator’s mass by less than 0.5%.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-9"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Large-Area Low-Temperature Vacuum Blackbody System of High Emissivity and Temperature Uniformity

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545489

Jian Song;Xuheng Cao;Gang Wang;Jingjing Zhou;Ruiheng Sima;Chunyuan Xu;Xiaopeng Hao

{"title":"Large-Area Low-Temperature Vacuum Blackbody System of High Emissivity and Temperature Uniformity","authors":"Jian Song;Xuheng Cao;Gang Wang;Jingjing Zhou;Ruiheng Sima;Chunyuan Xu;Xiaopeng Hao","doi":"10.1109/TIM.2025.3545489","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545489","url":null,"abstract":"Large-area blackbodies are essential for the accurate radiometric calibration of large-aperture infrared optical instruments. However, current blackbody systems face limitations in emissivity and temperature uniformity, particularly at low temperatures. This deficiency is principally attributed to insufficient light absorption and uncontrolled thermal convection on the radiation surface of the blackbody. Here, by regulating optical reflection characteristics and implementing a cooling compensation-based temperature control mechanism, a low-temperature blackbody with high emissivity and temperature uniformity is developed. Simulations indicate that the designed blackbody efficiently improves the emissivity from 0.985 to 0.991 and enhances the temperature uniformity by 75% compared to traditional design. A vacuum blackbody system with dimensions of <inline-formula> <tex-math>$500times 500$ </tex-math></inline-formula> mm, operating at 150–360 K, was constructed. Measurements made in the vacuum radiation-temperature calibration facility confirmed that the experimental results were in good agreement with the simulations, achieving an emissivity of 0.992 and a temperature uniformity of 0.1 K under cryo-vacuum conditions. With its radiation performance, the developed large-area blackbody source can significantly improve calibration accuracy for large-aperture infrared optical instruments, contributing to more precise measurements in applications.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-11"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Incremental Double Q-Learning-Enhanced MPC for Trajectory Tracking of Mobile Robots

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545523

Xiaoliang Fan;Chunguang Bu;Xingang Zhao;Jin Sui;Hongwei Mo

引用次数: 0

Circular Dichroism Analysis and Ellipticity Measurement in SERF Atom Ensemble

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545202

Haoran Lv;Bozheng Xing;Xiujie Fang;Danyue Ma;Hongtao Lu

{"title":"Circular Dichroism Analysis and Ellipticity Measurement in SERF Atom Ensemble","authors":"Haoran Lv;Bozheng Xing;Xiujie Fang;Danyue Ma;Hongtao Lu","doi":"10.1109/TIM.2025.3545202","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545202","url":null,"abstract":"In the research of the interaction between light and atoms, ellipticity is an important characterization of the pump and absorption rates. In previous researches, it was generally believed that ellipticity only originated from the interaction between magnetic fields and polarized alkali metal atomic ensembles. In this article, we derive and analyze the circular dichroism based on density matrix and Maxwell equations during the interaction between magnetic fields, probe light, and alkali metal atomic ensembles in spin-exchange relaxation-free (SERF) regime. We construct an optical path for measuring ellipticity based on photo elastic modulator (PEM) to measure ellipticity. Under different experimental conditions, we compare the measurement results of ellipticity from circular dichroism effect and rotation angle from circular birefringence effect. The results indicates that the interaction between magnetic field and alkali metal atomic ensemble which is polarized by probe light is a new source of ellipticity. Then, we research the ratio of rotation angle to ellipticity, and the results indicates that ellipticity generated by the interaction between the magnetic field and the alkali metal atomic ensemble is an intrinsic characteristic, which is independent of external conditions. The confidence level of the fitting between the experimental results and the theoretical equation is 99.7%. This research can be applied to SERF magnetometers and co-magnetometers.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-7"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143570663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multiteacher Multifeature Knowledge Distillation Based on Dynamic Mutual Selection

IF 5.6 2区工程技术

IEEE Transactions on Instrumentation and Measurement Pub Date : 2025-02-25 DOI: 10.1109/TIM.2025.3545724

Guangjie Han;Yumeng Zhang;Li Liu;Zhen Wang;Yuanyang Zhu;Dan Xia

{"title":"Multiteacher Multifeature Knowledge Distillation Based on Dynamic Mutual Selection","authors":"Guangjie Han;Yumeng Zhang;Li Liu;Zhen Wang;Yuanyang Zhu;Dan Xia","doi":"10.1109/TIM.2025.3545724","DOIUrl":"https://doi.org/10.1109/TIM.2025.3545724","url":null,"abstract":"Multiteacher knowledge distillation methods exhibit superior adaptability and flexibility over single-teacher models when handling diverse datasets. However, these methods encounter significant challenges when dealing with varying feature types and different numbers of teacher models. The first challenge lies in selecting the optimal distillation samples for the student model, and the second involves choosing the most appropriate teacher model for specific feature types. To address these challenges, we propose a multiteacher multifeature knowledge distillation learning framework based on dynamic mutual selection (DMS-MTMF). DMS-MTMF employs a dynamic mutual selection module search for the optimal combination of teacher models and features, ensuring a harmonious collaboration that yields superior training outcomes. During this process, selection mismatches may arise between teacher models and features. To address this, we adopt the multiagent depth determination policy gradient algorithm for collaborative optimization within the mutual selection module. Finally, a dynamic sample selection module is proposed to model the sample selection cost. DMS-MTMF eliminates the distortion caused by static distillation sample selection. Experimental results on the HHU and PU datasets not only highlight the importance of dynamic mutual selection and sample selection but also achieve higher accuracy than other comparative methods.","PeriodicalId":13341,"journal":{"name":"IEEE Transactions on Instrumentation and Measurement","volume":"74 ","pages":"1-15"},"PeriodicalIF":5.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143583173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0