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Modified parallel FFT energy detection using machine learning based spectrum sensing 利用基于机器学习的频谱传感技术进行改进型并行 FFT 能量检测
Pub Date : 2024-07-21 DOI: 10.1007/s00542-024-05702-2
M. Subbarao, N. Venkateswara Rao

The research presents an enhanced energy detector using windowing groups, machine learning, and parallel Fast Fourier Transforms to alleviate spectrum congestion in fifth-generation wireless services. Specifically designed for non-stationary signals with low signal-to-noise ratios, this technique addresses key challenges by improving Detection Probability (Pd) and augmenting FFT resolution. By applying specific weighting factors to samples within the sensing frame, the Probability of Detection (Pd) is increased. The Machine Learning algorithm dynamically adjusts the weighting factor multipliers based on the prevailing signal-to-noise conditions. Implementing parallel FFTs for sample groups further enhances resolution. Diverse windowing methods and grouping strategies significantly boost detection probability, especially for non-stationary signals under low SNRs. Compared to the conventional energy detector with 56% detection probability, the proposed method achieves 76–97% probability at − 15 dB SNR proving its efficiency in improving signal detection under challenging conditions.

该研究提出了一种使用窗口分组、机器学习和并行快速傅立叶变换的增强型能量检测器,以缓解第五代无线服务中的频谱拥塞问题。该技术专为低信噪比的非稳态信号而设计,通过提高检测概率(Pd)和增强快速傅立叶变换分辨率来应对主要挑战。通过对传感帧内的样本应用特定的加权因子,可提高检测概率 (Pd)。机器学习算法会根据当时的信噪比条件动态调整加权系数乘数。对样本组实施并行 FFT 可进一步提高分辨率。多样化的窗口方法和分组策略大大提高了检测概率,尤其是在低信噪比条件下的非稳态信号。与检测概率为 56% 的传统能量检测器相比,所提出的方法在 - 15 dB SNR 条件下的检测概率达到了 76-97%,这证明了它在具有挑战性的条件下提高信号检测效率的能力。
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引用次数: 0
Design and simulation of tunable bandstop filters by integrating RF MEMS shunt switch for K-band applications 为 K 波段应用设计和模拟集成射频 MEMS 分流开关的可调带阻滤波器
Pub Date : 2024-07-19 DOI: 10.1007/s00542-024-05720-0
Sk Shoukath Vali, G. Shanthi, Anish Yalavarthi, Sahithi Pingalakani, Dasari Chandrika, Chokkakula Ganesh, K. Girija Sravani

This paper represents the design and simulation of tunable bandstop filters by integrated with an RF MEMS shunt switch. The transformation of the bandpass filter to the bandstop filter is also done in this paper. The bandpass and bandstop filters are designed utilizing ECE-shaped DGS resonators within the coplanar waveguide (CPW) structure. Three different types of RF MEMS switches are proposed and investigated. The switch with low pull in voltage and better RF characteristics is considered for integration with filters The BPF exhibits an insertion loss of under 1.6 dB. It offers a relative 3-dB bandwidth of 60% and a 30-dB bandwidth of 77%. In the case of the BSF, it effectively achieves a 20 dB stop band at 20.5 GHz, maintaining a return loss of only 0.3 dB. The tunability of the filter is observed by integrating a MEMS capacitive shunt switch onto the transmission line. A pull in voltage of 4 V is achieved with a high capacitance ratio of 63.9.The simulation and parametric analysis of the RF MEMS switch is carried out by COMSOL and the RF performance of the switch, tunability of the filters are studied with the help of the HFSS FEM tools. The mechanical resonance frequency, other RF performance and tunability of the filters attained a frequency range (18–27 GHz). So the proposed switch and filters are suitable for K band applications, especially for satellite communications applications.

本文介绍了与射频微机电系统并联开关集成的可调带阻滤波器的设计和仿真。本文还完成了从带通滤波器到带阻滤波器的转换。带通和带阻滤波器是利用共面波导(CPW)结构中的 ECE 形 DGS 谐振器设计的。本文提出并研究了三种不同类型的射频 MEMS 开关。BPF 的插入损耗低于 1.6 dB。它的 3 分贝相对带宽为 60%,30 分贝带宽为 77%。就 BSF 而言,它在 20.5 GHz 频率上有效地实现了 20 dB 的阻带,回波损耗仅为 0.3 dB。通过在传输线上集成 MEMS 电容并联开关,可以观察到滤波器的可调谐性。COMSOL 对射频 MEMS 开关进行了仿真和参数分析,并借助 HFSS FEM 工具研究了开关的射频性能和滤波器的可调谐性。滤波器的机械共振频率、其他射频性能和可调谐性达到了(18-27 GHz)的频率范围。因此,建议的开关和滤波器适用于 K 波段应用,尤其是卫星通信应用。
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引用次数: 0
A Novel Four legged linear piezoelectric inchworm motor with high thrust force 具有高推力的新型四脚直线压电尺蠖电机
Pub Date : 2024-07-13 DOI: 10.1007/s00542-024-05722-y
Sandip Jana, Saikat Kumar Shome, Arup Kumar Nandi

A major limitation of most linear motors is limited travel range and low load capacity. In this research, a large motion range piezoelectric Inchworm Motor (IM) is realised which not only harnesses the prominent advantages of piezo-actuator but the four-legged design simultaneously offers reliable self-locking capability in a compact form-factor. The displacement deformation of each element of the motor (clamps, extender) is determined using finite element analysis (FEA) through force distribution analysis. Appropriate clamping force adjustment method on the rail/stator of the motor is adopted using load cell followed by multiple linear regression modelling to dynamically consider the clamping force and inherent non-linearities of piezo-actuators (PAs). The hardware prototype is fabricated and the experiment results verify the validity of the data driven model. Clamping error analysis, step length dependent stability profile and dynamic driving force has been carried out to characterize the IM. Performance evaluation of the motor has been researched at different voltages, frequencies and loads to assess its operating profile. Mechanical output suggests that the prototype achieves a maximum no load speed of 39.64 mm/sec under clamping force of 2 N at 100 V and frequency of 2000 Hz with 30% duty cycle. With load of 700 g, 0.46 mm/sec speed is obtained under a clamping force of 8 N. In addition, bidirectional control signal mechanism for the IM has been also developed, tested and implemented in real-time environment. The proposed large driving force prototype designed is highly suitable for industrial linear translation systems requiring high resolution, large strokes, and heavy loads capacities.

大多数直线电机的主要局限性在于行程范围有限和负载能力低。在这项研究中,我们实现了一种大运动范围压电英制电机(IM),它不仅利用了压电致动器的突出优势,而且四脚设计还同时提供了可靠的自锁能力,外形紧凑。通过力分布分析,利用有限元分析(FEA)确定了电机各元件(夹具、延伸器)的位移变形。使用称重传感器对电机的导轨/定子采用适当的夹紧力调整方法,然后建立多元线性回归模型,以动态考虑夹紧力和压电致动器(PA)的固有非线性。硬件原型已制作完成,实验结果验证了数据驱动模型的有效性。通过夹紧误差分析、与步长相关的稳定性曲线和动态驱动力,对 IM 进行了表征。在不同电压、频率和负载条件下对电机进行了性能评估研究,以评估其运行状况。机械输出结果表明,原型机在夹紧力为 2 N、电压为 100 V、频率为 2000 Hz、占空比为 30% 的情况下,空载最大速度为 39.64 mm/sec。此外,还开发了 IM 的双向控制信号机制,并在实时环境中进行了测试和实施。所设计的大驱动力原型非常适用于要求高分辨率、大行程和重负载能力的工业线性平移系统。
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引用次数: 0
Research on analytical models for reducing friction heat for flexible ultrasonic propagation using stranded wire 利用绞线减少柔性超声波传播摩擦热的分析模型研究
Pub Date : 2024-07-10 DOI: 10.1007/s00542-024-05655-6
Yukiko Kawasumi, Minoru Morita, Zhongwei Jiang

The flexible ultrasonic scalpels are currently required for surgical treatment of deep-seated areas of the living body. One of the surgical treatments for early-stage gastric cancer is surgery to remove the superficial layers of the stomach. Endoscopic surgery is used for early-stage gastric cancer. Polypectomy, one of the endoscopic surgical methods, involves hooking a snare over the affected area, squeezing, and applying a high-frequency electric current to burn it off. On the other hand, ultrasonic scalpels are effective at lower temperatures than conventionally used electrocautery scalpels, and have the advantage of having less thermal effect on tissues other than the affected area. However, due to the challenges associated with the propagation of ultrasonic waves, the use of flexible wires for this purpose in current research is limited. In this study, we attempted to observe the characteristics of ultrasonic wave propagation to the wire in the snare, which is a part of the electrocautery used in the polypectomy. The development of flexible ultrasonic scalpels will be advanced when ultrasonic propagation with less energy loss to the strand wire can be realized. In addition, Finite Element Method analysis was performed to identify the heat sources generated when ultrasonic vibration is applied to a stranded wire and to investigate a solution. Additionally, to find conditions where ultrasonic energy propagation is strong and heat generation is minimal, the partial single lines model was examined. The analysis confirmed that heat was generated by friction between strands of stranded wire.

目前,活体深层部位的手术治疗需要使用柔性超声波手术刀。早期胃癌的外科治疗方法之一是手术切除胃的表层。内窥镜手术用于早期胃癌。息肉切除术是内窥镜手术方法之一,它是将一个套管钩住患处,进行挤压,然后用高频电流将其烧掉。另一方面,与传统的电烧手术刀相比,超声波手术刀在较低的温度下也能发挥作用,其优点是对患处以外的组织产生的热影响较小。然而,由于超声波的传播具有一定的挑战性,在目前的研究中,将柔性导线用于这一目的受到了限制。在本研究中,我们尝试观察超声波传播到套管中导线的特性,套管是息肉切除术中使用的电烧的一部分。如果能实现能量损失较小的超声波在绞线上的传播,将推动柔性超声刀的发展。此外,还进行了有限元法分析,以确定在对绞线施加超声波振动时产生的热源,并研究解决方案。此外,为了找到超声波能量传播强而发热量最小的条件,研究了部分单线模型。分析证实,热量是由绞合导线股间的摩擦产生的。
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引用次数: 0
Design and analysis of dual working area micro-hotplate based on thermal crosstalk 基于热串扰的双工作区微型加热板的设计与分析
Pub Date : 2024-07-09 DOI: 10.1007/s00542-024-05721-z
Youpeng Yang, Guangfen Wei, Shasha Jiao, Aixiang He, and Zhonghai Lin

Micro-hotplates have provided the possibilities of miniaturization, low power consumption, and high integration for widespread application in MEMS sensors, such as the MEMS-based metal oxide gas sensors. However, thermal crosstalk among micro-heating areas has greatly restricted the design of a micro-hotplate. Although the issue of thermal crosstalk is annoying between independent working areas, it can reduce power consumption to a certain extent. This paper proposed a dual working area micro-hotplate based on thermal crosstalk through the foundation of an electro-thermal analysis model. It especially proposes a strategy of introducing optimized parameters from a single working area to a dual working area. Besides, evaluation for thermal crosstalk was achieved by setting the temperature of one working area as constant and monitoring the power of the other working area when it reaches a certain temperature. The results indicated that the designed dual working area micro-hotplate can save at least a quarter of the heating power compared with the single working area micro-hotplate at the same working temperature of 300 (^circ textrm{C}) and other same parameter settings. Within the acceptable limits of mechanical deformation, the heating efficiency of the micro-hotplate is improved from 4.10 mW/(mm(^2).(^circ textrm{C})) to 2.99 mW/(mm(^2) (^circ textrm{C})). It was demonstrated that the introduction of thermal crosstalk can significantly reduce the power consumption of the micro-hotplate, providing a viable solution for enhancing the properties of MOX gas sensor array.

微型加热板具有微型化、低功耗和高集成度的特点,可广泛应用于 MEMS 传感器,如基于 MEMS 的金属氧化物气体传感器。然而,微加热区域之间的热串扰极大地限制了微加热板的设计。虽然独立工作区之间的热串扰问题令人烦恼,但它能在一定程度上降低功耗。本文在电热分析模型的基础上,提出了一种基于热串扰的双工作区微型加热板。它特别提出了将单工作区的优化参数引入双工作区的策略。此外,还通过设定一个工作区的温度为恒定值,并监测另一个工作区达到一定温度时的功率,实现了对热串扰的评估。结果表明,在工作温度为 300 (^circ textrm{C})和其他参数设置相同的情况下,所设计的双工作区微热板比单工作区微热板至少能节省四分之一的加热功率。在机械变形可接受的范围内,微热板的加热效率从 4.10 mW/(mm(^2).(^circ textrm{C}))提高到 2.99 mW/(mm(^2)(^circ textrm{C}))。研究表明,热串扰的引入可以显著降低微热板的功耗,为增强 MOX 气体传感器阵列的性能提供了可行的解决方案。
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引用次数: 0
3D printed kenics static micromixer 三维打印的 kenics 静态微搅拌器
Pub Date : 2024-07-09 DOI: 10.1007/s00542-024-05718-8
Yanfei Liao, Shihuang Liu, Xiao Li, Guang Feng, Wei Xue, Fengping Li, Kunpeng Zhang

Kenics static mixer (KSM), which comprises helical blades twisted 180° in left and right-hand directions alternatively and connected 90° to each other, has been widely used in macroscale because of its excellent mixing performance. Despite the high mixing efficiency, it is hard to apply in microscale conditions since it is difficult to fabricate the helical blades with conventional manufacturing methods and still mainly stays in the simulation stage. In this study, the Inkjet 3D printing method, which provides a rapid and cost-effective manufacturing method in one step without considering the complex three-dimensional structures for microfluidics, was adopted to build the Kenics static mixer and the Fibonacci’s golden ratio theory that caused a small pressure loss in spiral motion was introduced into the helical blade design. Both simulations and experiments were conducted to characterize the mixing performance of the 3D printed KSM and compared with the slanted groove micromixer (SGM) and Y-shaped micromixer. The results demonstrated the superiority (mixing efficiency > 90%) of the 3D printed KSM proposed in this study.

肯尼克斯静态混合器(KSM)由左右方向交替扭转 180° 并相互连接 90° 的螺旋叶片组成,因其出色的混合性能而在宏观领域得到广泛应用。尽管螺旋叶片具有很高的混合效率,但在微观条件下却很难应用,因为传统的制造方法很难制造出螺旋叶片,而且仍主要停留在模拟阶段。本研究采用喷墨 3D 打印方法制造 Kenics 静态混合器,该方法无需考虑微流控复杂的三维结构,可提供一步到位的快速、低成本制造方法,并在螺旋叶片设计中引入了导致螺旋运动压力损失较小的斐波纳契黄金比例理论。研究人员通过模拟和实验鉴定了三维打印 KSM 的混合性能,并将其与斜槽式微混合器(SGM)和 Y 型微混合器进行了比较。结果表明,本研究中提出的三维打印 KSM 具有优越性(混合效率达 90%)。
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引用次数: 0
Instantaneous power theory-fuzzy intelligent controller (IPT-FIC) based improved low voltage ride-through strategy for grid connected photovoltaic system 基于瞬时功率理论-模糊智能控制器 (IPT-FIC) 的并网光伏系统改进型低电压穿越策略
Pub Date : 2024-07-06 DOI: 10.1007/s00542-024-05715-x
Soubhik Bagchi, Raj Chakraborty, Pritam Bhowmik, Priyanath Das

The installation of Renewable Energy Sources (RESs) has increased tremendously over the past few decades. Due to the large-scale grid integration of RESs, many countries have had to modify their grid codes. For smooth operation during contingencies, the grid code mandates Low Voltage Ride-Through (LVRT) operation of the inverter, requiring it to remain connected for a stipulated duration and provide necessary support to the grid. In this article, an Instantaneous Power Theory-Fuzzy Intelligent Controller (IPT-FIC) based improved LVRT strategy is implemented to control a grid-connected Photovoltaic (PV) inverter. This enhanced strategy efficiently provides the necessary active and reactive power support to the grid during faults or voltage sags. The IPT-FIC is proposed to make the controller intelligent, accurate, and faster. Simulations were performed in a MATLAB/SIMULINK 2021 environment, and the feasibility of the proposed technique was verified through the dSPACE DS1103 driven Hardware-in-the-Loop (HIL) platform, achieving an accuracy level of 96.67%. The proposed technique improves system response time during transient scenarios by 19.88%. The technique ensures the active power loss is limited to 7.91% during LVRT operation while maintaining a very low ride-through time.

过去几十年来,可再生能源(RES)的安装量大幅增加。由于可再生能源的大规模并网,许多国家不得不修改其电网规范。为了在紧急情况下平稳运行,电网规范规定逆变器必须进行低电压穿越(LVRT)操作,要求逆变器在规定的时间内保持连接,并为电网提供必要的支持。本文采用基于瞬时功率理论-模糊智能控制器(IPT-FIC)的改进型低电压穿越策略来控制并网光伏(PV)逆变器。这种增强型策略能在故障或电压骤降时为电网提供必要的有功和无功功率支持。为了使控制器更加智能、精确和快速,提出了 IPT-FIC。仿真在 MATLAB/SIMULINK 2021 环境中进行,并通过 dSPACE DS1103 驱动的硬件在环(HIL)平台验证了所提技术的可行性,准确度达到 96.67%。所提出的技术将瞬态情况下的系统响应时间缩短了 19.88%。该技术确保在 LVRT 运行期间将有功功率损耗限制在 7.91%,同时保持极短的穿越时间。
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引用次数: 0
Investigation and analysis of silver interdigitated electrodes with natural rubber infused graphene for capacitive-based flexible pressure sensor 用于电容式柔性压力传感器的银插接电极与注入天然橡胶的石墨烯的研究与分析
Pub Date : 2024-07-06 DOI: 10.1007/s00542-024-05717-9
R. Vishnukumar, A. A. Saifizul, Ab Rahman Marlinda, Azim Danial Azam, Md. Shalauddin

The development of flexible capacitive pressure sensors has recently drawn significant interest among researchers for emerging wearable electronic devices, monitoring applications, and smart systems. However, it still poses enormous difficulty to design capacitive sensors with excellent sensitivity. Few studies have reported the use of interdigitated electrodes (IDE) designs to improve the sensitivity of sensors. In our study, we selected graphene-infused natural rubber (NRG) as the sensing dielectric layer owing to its excellent cyclic pressure loading response as well as its high flexibility and conductivity. Here, we reported the impedance response of different graphene contents in natural rubber (NR) with the optimization of different geometrical parameters of IDEs. The electrical properties of silver IDEs are simulated using COMSOL Multiphysics. The impedance characteristics of NRG and its capability for detecting a wide variety of pressures and bending angles are analyzed using a Digilent Analog Discovery impedance analyzer. Understanding these properties and how they can be affected is vital in designing highly sensitive capacitive pressure sensors. Simulations were used to show the voltage potential, electrical field, and capacitance developed between the individual digits of the electrodes. The impedance analysis was helpful in computing the electrical conductivity of the NRG. The impedance analysis showed that the NRG sensing material improved in conductivity (≈0.006 S/m) and capacitance (≈0.30 pF) with a graphene loading of 5 wt.%. In this novel work, a capacitive-based pressure sensor incorporating unvulcanized NR and 5 wt.% graphene nanoplatelet as the sensing material was successfully fabricated with a sensor sensitivity of 0.004 kPa−1 for the low-force detection region of 40 kPa.

最近,柔性电容式压力传感器的开发引起了研究人员对新兴可穿戴电子设备、监控应用和智能系统的极大兴趣。然而,要设计出灵敏度极高的电容式传感器仍然存在巨大困难。很少有研究报道使用电极间插设计(IDE)来提高传感器的灵敏度。在我们的研究中,我们选择了注入石墨烯的天然橡胶(NRG)作为传感介电层,因为它具有出色的循环压力加载响应以及高柔韧性和导电性。在此,我们报告了天然橡胶(NR)中不同石墨烯含量与 IDE 不同几何参数优化的阻抗响应。我们使用 COMSOL Multiphysics 模拟了银 IDE 的电特性。使用 Digilent Analog Discovery 阻抗分析仪分析了 NRG 的阻抗特性及其检测各种压力和弯曲角度的能力。了解这些特性及其如何受到影响对于设计高灵敏度电容式压力传感器至关重要。模拟显示了电压电位、电场和电极各数位之间形成的电容。阻抗分析有助于计算 NRG 的导电率。阻抗分析表明,当石墨烯含量为 5 wt.% 时,NRG 传感材料的电导率(≈0.006 S/m)和电容(≈0.30 pF)均有所提高。在这项新颖的工作中,成功地制造出了一种基于电容的压力传感器,该传感器采用了未硫化的 NR 和 5 wt.% 的石墨烯纳米板作为传感材料,在 40 kPa 的低力检测区域,传感器的灵敏度为 0.004 kPa-1。
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引用次数: 0
Glucose concentration evaluation in blood samples using novel microwave antenna sensor 利用新型微波天线传感器评估血液样本中的葡萄糖浓度
Pub Date : 2024-07-05 DOI: 10.1007/s00542-024-05716-w
Jagadeesh Babu Kamili, Kiran Kumar Bandi

A highly sensitive and novel antenna sensor is designed for evaluating concentration of glucose in the human blood. The proposed sensor is constructed on an FR4 substrate layer of dimensions 20 mm × 30 mm × 1.6 mm with dielectric constant value of 4.3 resonance at 5 GHz with a quality factor of 471. In order to predict the amount of glucose, a human finger phantom model is developed in the electromagnetic simulator. The glucose levels are varied in various degrees from 0 to 1000 mg/dL and the resulting frequency shifts are measured by placing the phantom at various locations at different angles on the developed antenna sensor. When the phantom is located at 00 on the proposed sensor, a total frequency shift of 24 MHz, FDR of 24 kHz/(mg/dL) and sensitivity of 0.48x({10}^{-3}{(mg/dL)}^{-1}) are observed enabling the proposed sensor to detect diabetic conditions in the patients with high precision. The performance of the proposed sensor is analyzed for different real human finger positions and the resulting resonant frequencies are measured to verify the sensor’s performance in real-time scenario. The proposed sensor shows the average measurement error of about 1.9875% to detect glucose concentration levels.

设计了一种高灵敏度的新型天线传感器,用于评估人体血液中的葡萄糖浓度。拟议的传感器是在尺寸为 20 mm × 30 mm × 1.6 mm、介电常数为 4.3、谐振频率为 5 GHz、品质因数为 471 的 FR4 基板层上构建的。为了预测葡萄糖量,在电磁模拟器中开发了一个人体手指模型。葡萄糖水平在 0 至 1000 mg/dL 之间有不同程度的变化,通过将人体模型以不同角度放置在开发的天线传感器上的不同位置,测量由此产生的频率偏移。当人体模型位于拟议传感器上的 00 位置时,观察到的总频移为 24 MHz,FDR 为 24 kHz/(mg/dL),灵敏度为 0.48x({10}^{-3}{(mg/dL)}^{-1}/),使拟议传感器能够高精度地检测患者的糖尿病状况。针对不同的真实人体手指位置分析了拟议传感器的性能,并测量了由此产生的共振频率,以验证传感器在实时场景中的性能。拟议的传感器在检测葡萄糖浓度水平时的平均测量误差约为 1.9875%。
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引用次数: 0
On the stability of Markov feedback loops of a microsystem 论微观系统马尔可夫反馈回路的稳定性
Pub Date : 2024-07-02 DOI: 10.1007/s00542-024-05710-2
Feng-Rung Hu, Jia-Sheng Hu

In the field of control engineering, there has been a growing emphasis on systems with feedback loops that involve stochastic factors. Simultaneously, with the advancements in probability theory, feedback loops with stochastic processes have gained practicality due to their customizability and the potential for practical applications. Essentially, the effect of adding additive random signals in linear feedback systems can be viewed as the introduction of filtered stochastic noise. However, when random signals enter the feedback loop multiplicatively, a richer set of state behaviors emerges. This study utilizes multiplicative feedback loops to construct Markov chains and provides a probabilistic modeling approach to investigate the stability and asymptotic behavior of Markov feedback loops, offering insights for microsystems. This paper derives properties of such stochastic processes and provides corresponding theoretical proofs. The theoretical foundation of this probabilistic modeling can be applied in economics, biological variation processes, epidemic control predictions, and linear perturbation models, offering a theoretical perspective for feedback systems with uncertain triggers.

在控制工程领域,人们越来越重视涉及随机因素的反馈回路系统。与此同时,随着概率论的进步,带有随机过程的反馈回路因其可定制性和实际应用的潜力而变得越来越实用。从本质上讲,在线性反馈系统中添加添加性随机信号的效果可视为引入了滤波随机噪声。然而,当随机信号以乘法方式进入反馈回路时,就会出现更丰富的状态行为。本研究利用乘法反馈回路来构建马尔可夫链,并提供一种概率建模方法来研究马尔可夫反馈回路的稳定性和渐近行为,从而为微系统提供启示。本文推导了此类随机过程的特性,并提供了相应的理论证明。这种概率建模的理论基础可应用于经济学、生物变异过程、流行病控制预测和线性扰动模型,为具有不确定触发因素的反馈系统提供了理论视角。
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引用次数: 0
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Microsystem Technologies
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