Academic literature on the topic 'Μ-Analyse probabiliste'
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Journal articles on the topic "Μ-Analyse probabiliste"
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Liu, Wen Feng, Xing Pan Fu, and Jie Ying Sui. "Probability Analyses of Response Spectra on Soft Soil Site." Advanced Materials Research 261-263 (May 2011): 1058–63. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.1058.
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The analyses on the statistical probability of the response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 369 records with a long characteristic period for SDOF systems were presented in statistical analyses. The empirical probability distributions of the spectral values were derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. And the spectra considering the probability guaranty were developed to investigate the characteristic of the response spectra. The formula for statistical average spectra of the ground motion ensemble were recommended, which were valuable for current research and code revisal. The results show:(1)the inelastic responses decrease with the increase of ductility demand μ when μ<4, and they decrease unclearly when μ≥4;(2) the inelastic spectra has a large value of Cov (coefficient of variance),the Cov range from 0.2 to 0.3 when T<1s,and it increases linearly when T≥1s;(3)the probabilistic distribution of the spectra value on acceleration is validated as the lognormal or the Gumbel type I distributions;(4) the probabilistic spectra may be a feasible way to determine earthquake load in the future.
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Aldous, David. "Hashing with Linear Probing under Nonuniform Probabilities." Probability in the Engineering and Informational Sciences 2, no. 1 (January 1988): 1–14. http://dx.doi.org/10.1017/s0269964800000577.
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Probabilistic analyses of hashing algorithms usually assume that hash values are uniformly distributed over addresses. We study how one of the simplest schemes, hashing with linear probing, behaves in the nonuniform case. A simple measure μ of nonuniformity is the probability two keys hash to the same address, divided by this probability in the uniform case. It turns out that the effect of nonuniformity is to multiply mean search lengths by μ. For high loads, the longest search is multiplied by approximately μ also. Our theoretical results are asymptotics: simulations show good fits with predictions for mean search lengths, but bad fits for longest search lengths.
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Field, R. V., P. G. Voulgaris, and L. A. Bergman. "Methods to Compute Probabilistic Measures of Robustness for Structural Systems." Journal of Vibration and Control 2, no. 4 (October 1996): 447–63. http://dx.doi.org/10.1177/107754639600200405.
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Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst- case analyses. These traditional methods include the use of the structured singular value (μ-analysis), as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. Because of this, an attempt to view controller robustness as a probability measure is presented. As a result, a much more intuitive insight into controller robustness can be obtained. In this context, the joint probability distribution is of dimension equal to the number of uncertain parameters, and the failure hypersurface is defined by the onset of instability of the closed-loop system in the eigenspace. A first-order reliability measure (FORM) of the system is computed and used to estimate controller robustness. It is demonstrated via an example that this FORM method can provide accurate results on the probability of failure despite the potential complexity of the closed-loop. In addition to the FORM method, a probabilistic measure of robustness is developed based on the fundamentals of μ-analysis. It is shown that the μ-analysis based method is inferior to the FORM method and can only have qualitative value when assessing control system robustness in a probabilistic framework.
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Liu, Wen Feng, Xue Zhong Chen, and Jie Ying Sui. "Statistical Analyses of Response Spectra on Medium-Stiff Soil Site." Applied Mechanics and Materials 90-93 (September 2011): 1549–54. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.1549.
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The analyses on the statistical response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 205 records on medium-stiff soil site for SDOF systems are presented in statistical analyses. The empirical probability distributions of the spectral values are derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. The formula for statistical average spectra of the ground motion ensemble are recommended, which are valuable for current research and code revisal. The results show that the statistical averaged elastic α spectra fits well to the design spectra prescribed in Chinese code when the period is smaller than 2s. The inelastic responses decrease with the increase of ductility demand μ when μ<4. The coefficients of variance of the elastic and inelastic spectra are still large and the dispersion cannot be ignored. The probabilistic distribution of the spectra value on acceleration is validated as the lognormal distributions. The proposed formulas give a good fit to the statistical average values.
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Brango, Hugo, Angie Guerrero, and Humberto Llinás. "Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW-μ): A Study of Its Properties and Correlation Structure." Mathematics 12, no. 14 (July 11, 2024): 2183. http://dx.doi.org/10.3390/math12142183.
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We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW-μ”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW-μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW-μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW-μ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines.
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AUSTIN, TIM. "On the norm convergence of non-conventional ergodic averages." Ergodic Theory and Dynamical Systems 30, no. 2 (June 23, 2009): 321–38. http://dx.doi.org/10.1017/s014338570900011x.
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AbstractWe offer a proof of the following non-conventional ergodic theorem: If Ti:ℤr↷(X,Σ,μ) for i=1,2,…,d are commuting probability-preserving ℤr-actions, (IN)N≥1 is a Følner sequence of subsets of ℤr, (aN)N≥1 is a base-point sequence in ℤr and f1,f2,…,fd∈L∞(μ) then the non-conventional ergodic averages converge to some limit in L2(μ) that does not depend on the choice of (aN)N≥1 or (IN)N≥1. The leading case of this result, with r=1 and the standard sequence of averaging sets, was first proved by Tao, following earlier analyses of various more special cases and related results by Conze and Lesigne, Furstenberg and Weiss, Zhang, Host and Kra, Frantzikinakis and Kra and Ziegler. While Tao’s proof rests on a conversion to a finitary problem, we invoke only techniques from classical ergodic theory, so giving a new proof of his result.
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DIETZFELBINGER, MARTIN, JONATHAN E. ROWE, INGO WEGENER, and PHILIPP WOELFEL. "Tight Bounds for Blind Search on the Integers and the Reals." Combinatorics, Probability and Computing 19, no. 5-6 (December 18, 2009): 711–28. http://dx.doi.org/10.1017/s0963548309990599.
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We analyse a simple random process in which a token is moved in the interval A = {0, . . ., n}. Fix a probability distribution μ over D = {1, . . ., n}. Initially, the token is placed in a random position in A. In round t, a random step sized is chosen according to μ. If the token is in position x ≥ d, then it is moved to position x − d. Otherwise it stays put. Let TX be the number of rounds until the token reaches position 0. We show tight bounds for the expectation Eμ(TX) of TX for varying distributions μ. More precisely, we show that $\min_\mu\{\E_\mu(T_X)\}=\Theta\bigl((\log n)^2\bigr)$. The same bounds are proved for the analogous continuous process, where step sizes and token positions are real values in [0, n + 1), and one measures the time until the token has reached a point in [0, 1). For the proofs, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over [0, 1] with a ‘blind’ optimization strategy.
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Hao, Yiqing, Hao Lu, Yehui Shi, Hao Geng, Xi J, and Shufang Feng. "Uncertainty Evaluation of Water Inrush in Karst Tunnels Based on Epistemic Uncertainty with Possibility Theory." Mathematical Problems in Engineering 2020 (August 6, 2020): 1–12. http://dx.doi.org/10.1155/2020/2819797.
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In the risk assessment of water inrush in karst tunnel, it is most important to provide an available theoretical model for qualifying the epistemic uncertainties due to a lack of knowledge and information. Firstly, a mechanical model dependent on geology is introduced associating with four parameters, i.e., the elastic modulus E, the Poisson ratio μ, the water differential pressure q, and the tunnel radius a. Then, a mathematical model representing epistemic uncertainty is represented with probability theory and possibility theory. The methodology was computerized to calculate the distribution of the margin and uncertainty and then to determine the ratio of “margin/uncertainty.” Analyses involving possibility theory and possibility theory are illustrated with the same engineering example used in the presentation indicated above to illustrate the use of probability to represent aleatory and epistemic uncertainty in QMU analyses. The comparison between the uses of possibility theory and probability theory for the representation of aleatory and epistemic uncertainty indicates that the possibility is not only has a better mathematical structure than probability theory but also has some challenges.
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Pinus, B. I., I. G. Korneeva, and V. D. Balheeva. "Fatigue life of bending reinforced concrete elements with fibre-reinforced matrices." Journal «Izvestiya vuzov. Investitsiyi. Stroyitelstvo. Nedvizhimost» 12, no. 3 (2022): 362–67. http://dx.doi.org/10.21285/2227-2917-2022-3-362-367.
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An experimental-probabilistic analysis of variations in the load-bearing capacity of bending reinforced concrete elements with matrices reinforced by polypropylene fibres was carried out. A numerical ex-periment was conducted using the normative methodology of multi-link and layerwise modelling of el-ement cross-sections and experimental "σ-ε" diagrams of fibrocomposites in initial and post-cyclic (50 cycles with η = 0.8 amplitude and zero asymmetry) states. Probabilistic changes in the load-bearing capacity of bending elements subjected to cyclic loads were estimated by the numerical strength modelling of rectangular beams (b × h = 100 × 200 mm) with the one-sided reinforcement (A400 class) of varying intensity. The observed high value of fatigue life of reinforced concrete ele-ments with fibre-reinforced matrices was found to be associated with the presence of mechanisms compensatory for structural changes, i.e., a decrease in the strength is accompanied by an increase in the ability to redistribute internal forces. A post-cyclic reduction in the strength of concrete causes practically no effect on the load-bearing capacity of bending elements with a large and economically preferable range of their structural reinforcement. The reliability kinetics of elements, estimated by the level of the realised concrete strength potential, was analysed. Moderate (μ ≤ μR) reinforcement was found to result in objective conditions for increasing the completeness of the stress diagram in the compressed cross-sectional part due to the redistribution of forces along the height. In this case, de-spite a significant decrease in the strength of concrete, the load-bearing capacity of elements at μ ≤ 2.5% reinforcement remains practically the same after cyclic effects.
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Lou, Yi, Ruofan Sun, Julian Cheng, Gang Qiao, and Jinlong Wang. "Physical-Layer Security for UAV-Assisted Air-to-Underwater Communication Systems with Fixed-Gain Amplify-and-Forward Relaying." Drones 6, no. 11 (November 3, 2022): 341. http://dx.doi.org/10.3390/drones6110341.
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We analyze a secure unmanned aerial vehicle-assisted two-hop mixed radio frequency (RF) and underwater wireless optical communication (UWOC) system using a fixed-gain amplify-and-forward (AF) relay. The UWOC channel was modeled using a mixture exponential-generalized Gamma distribution to consider the combined effects of air bubbles and temperature gradients on transmission characteristics. Both legitimate and eavesdropping RF channels were modeled using flexible α-μ distributions. Specifically, we first derived both the probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-noise ratio of the system. Based on the PDF and CDF expressions, we derived the closed-form expressions for the tight lower bound of the secrecy outage probability (SOP) and the probability of non-zero secrecy capacity (PNZ), which are both expressed in terms bivariate Fox’s H-function. To utilize these analytical expressions, we derived asymptotic expressions of SOP and PNZ using only well-known functions. We also used asymptotic expressions to determine the suboptimal transmitting power to maximize energy efficiency. Furthermore, we investigated the effect of levels of air bubbles and temperature gradients in the UWOC channel, and studied the nonlinear characteristics of the transmission medium and the number of multipath clusters of the RF channel on the secrecy performance. Finally, all analyses were validated using a simulation.
Dissertations / Theses on the topic "Μ-Analyse probabiliste"
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Somers, Franca Maria Emma. "Nouveaux outils probabilistes pour améliorer la vérification et la validation des systèmes de contrôle spatiaux." Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0054.
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Les activités actuelles de vérification et validation (V&V) dans l'industrie aérospatiale reposent principalement sur des outils de simulation qui prennent beaucoup de temps. Ces approches classiques de type Monte-Carlo sont largement utilisées depuis des décennies pour évaluer les performances des systèmes de guidage, de navigation et de contrôle (GNC) et des systèmes de contrôle d'attitude et d'orbite (SCAO) contenant de multiples paramètres incertains. Elles permettent de quantifier la probabilité d'occurrence de phénomènes suffisamment fréquents, mais peuvent échouer dans la détection de combinaisons rares, mais critiques, de paramètres. Au fur et à mesure que la complexité des systèmes spatiaux modernes augmente, cette limitation joue un rôle de plus en plus important. Ces dernières années, les méthodes d'analyse des pires cas basées sur des modèles ont atteint un bon niveau de maturité. Sans avoir recours à des simulations, ces outils peuvent explorer l'espace de toutes les combinaisons possibles de paramètres incertains et fournir des limites mathématiques garanties sur les marges de stabilité robustes et les niveaux de performance pire-cas. Les configurations problématiques, identifiées à l'aide de ces méthodes, peuvent être utilisées pour guider les campagnes Monte-Carlo finales, ce qui raccourcit considérablement le processus V&V standard. L'une des limites des méthodes classiques d'analyse pire-cas basées sur des modèles est qu'elles supposent que les paramètres incertains peuvent prendre n'importe quelle valeur dans un intervalle donné avec une probabilité égale. La probabilité d'occurrence d'une combinaison de paramètres pire-cas n'est donc pas mesurée et la conception d'un système peut ainsi être rejetée sur la base d'un scénario très rare et extrêmement improbable. Cette recherche se concentre sur μ-analyse probabiliste pour développer de nouveaux outils efficaces et fiables afin d'améliorer la caractérisation d'événements rares mais néanmoins possibles. Ceci permet de resserrer l'écart d'analyse V&V ci-dessus entre les méthodes basées sur la simulation et les approches pire-cas déterministes basées sur des modèlesCurrent verification and validation (V&V) activities in aerospace industry mostly rely on time-consuming simulation-based tools. These classical Monte Carlo approaches have been widely used for decades to assess performance of Guidance, Navigation and Control (GNC) algorithms and Attitude and Orbit Control Systems (AOCS) containing multiple uncertain parameters. They are able to quantify the probability of sufficiently frequent phenomena, but they may fail in detecting rare but critical combinations of parameters. As the complexity of modern space systems increases, this limitation plays an ever more important role. In recent years, model-based worst-case analysis methods have reached a good level of maturity. Without the need of simulations, these tools can fully explore the space of all possible combinations of uncertain parameters and provide guaranteed mathematical bounds on robust stability margins and worst-case performance levels. Problematic parameter configurations, identified using these methods, can be used to guide the final Monte Carlo campaigns, thereby drastically shortening the standard V&V process. A limitation of classical model-based worst-case analysis methods is that they assume the uncertain parameters can take any value within a given range with equal probability. The probability of occurrence of a worst-case parameter combination is thus not measured and a control architecture can be rejected based on a very rare and extremely unlikely scenario. This PhD research makes advances in probabilistic μ-analysis to develop new efficient and reliable tools to improve the characterization of rare but nonetheless possible events. This to tighten the aforementioned V&V analysis gap between simulation-based methods and deterministic model-based worst-case approaches
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Poreddy, Mahathi. "Outage Probability Analysis of CooperativeCognitive Radio Networks Over κ − μ Shadowed Fading Channels." Thesis, Blekinge Tekniska Högskola, Institutionen för tillämpad signalbehandling, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-13634.
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Over time, wireless technology advancements in the field of communications have been attracting every individual to turn into a wireless user. To accommodate the increasing number of users and to avoid the problem of spectrum scarcity, the concept of Cognitive Radio Network (CRN) has been developed. Cognitive Radio (CR) is an intelligent radio which efficiently detects and allocates the spectrums of primary licensed users (PUs) to the secondary unlicensed users (SUs). The SUs can utilize these spectrums as long as they do not cause harmful interfere to the PUs. Interference may occur because of the following reasons: misdetection of spectrum availability, the high transmission power of SU when both SU and PU are present in the same channel at the same time. In order to avoid interference, the radio has to have a very accurate spectrum sensing method, transmit power at SU should be constrained by the peak interference power of PU and the CR should continuously sense the presence of PUs. To increase the wireless coverage area and reliability of CRN, a new technology called Cooperative Cognitive Radio Network (CCRN), which is a combination of CRN and cooperative communications was developed. A CCRN not only increases the reliability and wireless coverage area of CR but also improves the overall performance of the system. In this context, the main objective of this research work is to evaluate the outage performance of a CCRN in an environment where fading and shadowing also come into the picture and to study the importance of relay networks in CRN. To fulfill the objectives of this research work, a two-hop decode-and-forward CCRN is considered. The recently introduced κ − µ shadowed fading channel is employed over the CCRN to generate a realistic environment. In order to implement such system as a whole, a deep literature study is performed beforehand. Analytical expressions for the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of the Signal-to-Noise Ratio (SNR) are obtained. The analytical expressions and simulation results for Outage Probability (OP) are obtained and compared under different fading parameters. The importance of a multiple-relay system in CRN is presented. From the results obtained in this research work, we can conclude that the OP decreases with increase in allowable peak interference power at the PU. The transmit power at SU should always be constrained by the peak interference power at the PU to avoid interference. The overall system performance increases with increasing number of relays.
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Kodide, Alekhya. "Performance Analysis of a Cooperative Communication Network Over κ - μ Shadowed Fading for Different Relaying Protocols." Thesis, Blekinge Tekniska Högskola, Institutionen för tillämpad signalbehandling, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-13603.
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With the fast development of today’s multimedia services, engineers face a huge hurdle that is, the overwhelming need of highly reliable communication over long distances. Cooperative communication is a novel concept which tackles this problem effectively. The direct link is assisted by nodes called relays, which also reduce shadowing and pathloss effects in wireless networks. An added advantage of such a cooperative communication network is that when combined with multiple-input multiple-output (MIMO) antenna systems and cognitive radio networks (CRN), the system performance in terms of spectral efficiency and reliability, can be extremely enhanced without any extra power and spectrum.The concept of cooperative communications in MIMO and CRN systems has gained immense interest in the literature. Most of the research works have assumed Rayleigh fading conditions. In this thesis, the performance of cooperative communications with practical constraints of shadowing is studied. Analytical expressions for the outage probability of cooperative networks under different relaying protocols with selection combining are presented under the assumption of κ − µ shadowing fading. Specifically, the relaying protocols that are investigated are incremental relaying, opportunistic relaying, adaptive amplify-and-forward and decode-and-forward. Furthermore, this system model is simulated and the simulation results are compared with the analytical results. Mathematica, a technical computing tool, is used for numerical estimations using stochastic processes and probability theory. Simulation is done in MATLAB.In this thesis, along with the analytical framework for evaluating outage probability for the system is presented. Simulations are performed for various fading parameters and the results closely match with analytical results which validate the derivations.
Book chapters on the topic "Μ-Analyse probabiliste"
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Mudoi, Rajkishur. "PERFORMANCE OF DF RELAY ASSISTED DUAL-HOP SYSTEM OVER GENERALIZED-K ALONG WITH κ-μ FADING ENVIRONMENTS." In Futuristic Trends in Computing Technologies and Data Sciences Volume 3 Book 2, 35–48. Iterative International Publisher, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bgct2p1ch4.
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The outage probability (OP), average bit-error probability (ABEP) as well as ergodic capacity of decode-and-forward (DF) relay-based dual-hop transmission are evaluated in this analysis. The mixed fading channel environments are considered to study the system performance. The channel connecting the source to relay experiences Generalized-K (KG) distribution, whereas the link joining the relay with the destination is assumed as κ-μ distribution. To analyse the system’s performance, the probability density function (PDF) based approach is used. The BPSK as well as QPSK modulation schemes are applied to analyse the ABEP of the system. The results are validated by computer simulations.
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Wise, Gary L., and Eric B. Hall. "Integration." In Counterexamples in Probability and Real Analysis, 103–19. Oxford University PressNew York, NY, 1993. http://dx.doi.org/10.1093/oso/9780195070682.003.0006.
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Abstract If (Ω, F) is a measurable space and ifμ. and v are measures on (Ω, F) such that v << μ., Radon-Nikodym theory is concerned with conditions under which there exists a function f in L1(Ω, F, μ.) such that v(A) = f A f dμ.. Such results comprise a fundamental part of analysis and also play a prominent role in probability theory. Indeed, for a given measure, results such as this permits us to represent other measures defined on F in terms of extended real-valued functions defined on Ω. Also, in probability theory, conditional expectations and condition probabilities are defined in tenns of Radon-Nikodym theory. Example 5.1. A nondecreasing sequence of functions mapping [0, 1] into [0, 1] may be such that each term in the sequence is Riemann integrable and such that the limit of the resulting sequence of Riemann integrals exists, but the limit of the sequence of functions is not Riemann integrable.
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Suhov, Yu M., and D. M. Rose. "The Poisson-independence hypothesis for infinitely-growing fully-connected packet-switching networks." In Stochastic Networks Theory and Applications, 323–38. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198523994.003.0019.
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Abstract We analyse a packet-switching network modelled by a complete graph with nodes 0, 1, ... , N. For each pair of nodes, (i,j), there is a rate- λ Poisson flow αi,j of messages generated at i and destined for j. The numbers of packets in the message (the message lengths) are IID variables with distribution μ. With probability p, a packet is directly transmitted from i to j on link (i,j), and with probability qN = (1 - p)/(N - 1), on any of the two-link paths joining i and j. The queueing discipline at each node is FCFS, and the end-to-end delay is the time of delivery of the last packet of a message. Under certain conditions on λ, μ and p, we prove that as N → ∞, the probability distribution of the end-to-end delay is deduced from the so-called Poisson-independence hypothesis, which is shown to be valid. The main requirement is that most packets should be routed directly to their destinations, i.e., the network is a small perturbation of the ‘ideal’ one in which the links act as independent entities.
Conference papers on the topic "Μ-Analyse probabiliste"
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Bhargav, Nidhi, David E. Simmons, Carlos Rafael Nogueira da Silva, Elvio Joao Leonardo, Simon L. Cotton, and Michel Daoud Yacoub. "Outage probability analysis for α-μ/κ-μ and κ-μ/α-μ fading scenarios." In 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2017. http://dx.doi.org/10.1109/pimrc.2017.8292529.
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Franca Somers, Miss, Clément Roos, Francesco Sanfedino, Samir Bennani, and Valentin Preda. "Probabilistic stability margins and their application to AOCS validation." In ESA 12th International Conference on Guidance Navigation and Control and 9th International Conference on Astrodynamics Tools and Techniques. ESA, 2023. http://dx.doi.org/10.5270/esa-gnc-icatt-2023-089.
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Current validation and verification (V&V) activities in aerospace industry mostly rely on time-consuming simulation-based tools. These tools can give a measure of probability for sufficiently frequent phenomena, but they may fail in detecting rare but critical combinations of parameters. As the complexity of modern space systems increases, this limitation plays an ever-increasing role. In recent years, model-based worst-case analysis methods have reached a good level of maturity. Without the need of simulations, these tools can fully explore the space of all possible combinations of uncertain parameters and provide guaranteed mathematical bounds on robust stability and worst-case performance levels. However, they give no measure of probability and can therefore be overly conservative. Introduced more recently probabilistic μ-analysis combines worst-case information with probability measure. As such, it tempts to bridge the analysis gap between Monte Carlo simulations and deterministic μ-analysis [4]. The STOchastic Worst-case Analysis Toolbox (STOWAT), is a toolbox dedicated to probabilistic μ-analysis, developed by ONERA, The French Aerospace Lab. The original version of the toolbox, released by [9] and [1], only allowed for probabilistic robust stability and H∞ performance analysis. However, for the STOWAT to be fully convincing for industry, it should be as efficient and versatile as possible. For this purpose, focus has been on efficiency improvement ever since [3]. Furthermore, the toolbox was recently equipped with four probabilistic stability margin algorithms, devoted to probabilistic gain, phase, disk and delay margin analysis [8], [2], [7]. All four can be classified as μ-analysis based Branch-and-Bound (B&B) algorithms. At each iteration sufficient μ-analysis based conditions are evaluated to ascertain if the considered margin is guaranteed to be below (violation test) or above (satisfaction test) a desired threshold on a given set of uncertainties. If no conclusions can be drawn, the uncertainty set is split into two subsets and the analysis is repeated on each of them. These tools are limited to Single-Input Single-Output (SISO) system analysis. But since most industrial problems involve Multiple-Input Multiple-Output (MIMO) systems, this contribution first focuses on extending the algorithms to MIMO system analysis. Only adjustments need to be made to the conditions used to determine whether the satisfaction test or violation test should be applied. For SISO systems these conditions mostly rely on grid-based methods. However, in [8] it was already shown that gridding is usually very efficient for SISO and loop-at-a-time margin analysis, but gets quickly slower as the number of input/output channels increases. An alternative approach for MIMO systems, using μ-based tools was already proposed for disk margin analysis in [8]. This approach is used again here for MIMO phase, gain and delay margin analysis. However, it should be noted that the μ-based algorithm used should be adapted to the type of uncertainties (real/complex) in the studied stability margin problem. The developed MIMO analysis algorithms are all implemented in the STOWAT. Besides MIMO analysis, there is also an increased interest in multivariable margin analysis. This is because most realistic systems are subject to multiple perturbations at the same time. Multivariable analysis can for instance be an alternative to disk margin analysis [6], [8] in the case of simultaneous analysis of gain and phase perturbations. A probabilistic multivariable margin analysis algorithm is proposed in this contribution and implemented in the STOWAT. It was developed to overcome the conservatism provided by the deterministic worst-case equivalent at the end of the distribution tail. The STOWAT implementation allows users to specify multiple desired stability margins and determine the probability of multivariable margin violation. Analysis can be performed for both SISO and MIMO systems, where for MIMO systems different margin requirements can be set for each input and/or output. The heart of the existing algorithms remains the same, but two main modifications are needed. First a few additional matrix operations to construct the perturbed system used by the B&B algorithm should be included. Then new μ-analysis based conditions involving multiple real and complex uncertainties should be defined to determine whether the satisfaction or violation test should be performed. To demonstrate the added value of the developed tools, they are applied to analyse two satellite models: an academic model and a realistic benchmark. The academic model represents the spinning satellite adapted from [10] and the realistic one concerns the satellite with two flexible solar panels, previously introduced in [5]. References [1] J.-M. Biannic, C. Roos, S. Bennani, F. Boquet, V. Preda, and B. Girouart, “Advanced probabilistic μ-analysis techniques for AOCS validation,” European Journal of Control, vol. 62, pp. 120–129, 2021. [2] F. Somers, C. Roos, F. Sanfedino, S. Bennani, and V. Preda, “Probabilistic delay margin analysis,” Submitted to the American Control Conference, 2023. [3] C. Roos, J.-M. Biannic, and H. Evain, “A new step towards the integration of probabilistic μ in the aerospace V&V process,” in Proceedings of the 6th CEAS Conference on Guidance, Navigation and Control, 2022. [4] C. Roos, F. Sanfedino, V. Preda, and S. Bennani, “Phd position in analysis of aerospace control systems: Enhanced probabilistic tools to improve verification and validation of space control systems,” 2021. [5] F. Sanfedino, D. Alazard, E. Kassarian, and F. Somers, “Satellite dynamics toolbox library: a tool to model multi body space systems for robust control synthesis and analysis,” Submitted to the IFAC World Congress, 2023. [6] P. Seiler, A. Packard, and P. Gahinet, “An introduction to disk margins [lecture notes],” IEEE Control Systems Magazine, vol. 40, no. 5, pp. 78–95, 2020. [7] F. Somers, C. Roos, F. Sanfedino, S. Bennani, and V. Preda, “Comparative study of new probabilistic delay margin analysis techniques,” Submitted to International Journal of Robust and Nonlinear Control, 2023. [8] F. Somers, S. Thai, C. Roos, J.-M. Biannic, S. Bennani, V. Preda, and F. Sanfedino, “Probabilistic gain, phase and disk margins with application to AOCS validation,” in Proceedings of the 10th IFAC Symposium on Robust Control Design, 2022. [9] S. Thai, C. Roos, and J.-M. Biannic, “Probabilistic μ-analysis for stability and H∞ performance verification,” in Proceedings of the American Control Conference, 2019. [10] K. Zhou, J. Doyle, and K. Glover, Robust and optimal control. Prentice-Hall, New Jersey, 1996.
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Somers, Franca, Clément Roos, Francesco Sanfedino, Samir Bennani, and Valentin Preda. "A μ-analysis based approach to probabilistic delay margin analysis of uncertain linear systems*." In 2023 IEEE Conference on Control Technology and Applications (CCTA). IEEE, 2023. http://dx.doi.org/10.1109/ccta54093.2023.10253108.
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Kocák, Tomáš, and Aurélien Garivier. "Epsilon Best Arm Identification in Spectral Bandits." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/363.
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We propose an analysis of Probably Approximately Correct (PAC) identification of an ϵ-best arm in graph bandit models with Gaussian distributions. We consider finite but potentially very large bandit models where the set of arms is endowed with a graph structure, and we assume that the arms' expectations μ are smooth with respect to this graph. Our goal is to identify an arm whose expectation is at most ϵ below the largest of all means. We focus on the fixed-confidence setting: given a risk parameter δ, we consider sequential strategies that yield an ϵ-optimal arm with probability at least 1-δ. All such strategies use at least T*(μ)log(1/δ) samples, where R is the smoothness parameter. We identify the complexity term T*(μ) as the solution of a min-max problem for which we give a game-theoretic analysis and an approximation procedure. This procedure is the key element required by the asymptotically optimal Track-and-Stop strategy.
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Mutlu, Ural, Mehmet Bilim, and Yasin Kabalci. "Approximate Error Probability Analysis of L-Branch MRC System over λ-μ Fading Environments." In 2024 6th Global Power, Energy and Communication Conference (GPECOM). IEEE, 2024. http://dx.doi.org/10.1109/gpecom61896.2024.10582555.
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Chen, Changfang, Minglei Shu, Yinglong Wang, and Chongqing Zhang. "Outage probability analysis for MRC in κ-μ shadowed fading channels with co-channel interference." In 2016 IEEE International Conference on Information and Automation (ICIA). IEEE, 2016. http://dx.doi.org/10.1109/icinfa.2016.7831834.
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Kumar, Sikandar, and Sonali Chouhan. "Outage probability analysis of cognitive decode-and-forward relay networks over k — μ Shadowed Channels." In 2015 21st Asia-Pacific Conference on Communications (APCC). IEEE, 2015. http://dx.doi.org/10.1109/apcc.2015.7412552.
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Evain, Hélène, Tommaso Casati, Clément Roos, and Jean-Marc Biannic. "Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws." In ESA 12th International Conference on Guidance Navigation and Control and 9th International Conference on Astrodynamics Tools and Techniques. ESA, 2023. http://dx.doi.org/10.5270/esa-gnc-icatt-2023-058.
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During the development of a new attitude control system for ambitious satellite missions, the validation & verification phase represents a large part of the process. One difficulty is to detect worst case configurations. In such cases, when applicable, µ-analysis [1] offers a nice additional tool to be used before launching the Monte Carlo simulation campaign, but does not provide any quantification of the probability of occurrence of the identified worst-cases. A control system can then be invalidated on the basis of unlikely events. Probabilistic µ-analysis was introduced in this context 20 years ago to bridge the gap between the two techniques. It has been used for the first time in [2] in the challenging context of validation of launcher thrust vector control systems. But it appeared to be computationally very expensive. At that time indeed, no practical tool offering both good reliability and reasonable computational time was available, making this technique hardly usable in an industrial context. After the preliminary work of [3,4], strong improvements have been achieved by ONERA supported by ESA and CNES to develop the STOchastic Worst-case Analysis Toolbox (STOWAT). With the help of this new Matlab toolbox, probabilistic µ-analysis may now be considered as a very good candidate for integration in the aerospace V&V process in a near future, finding its place between Monte Carlo simulations – useful for quantifying the probability of sufficiently frequent phenomena – and worst-case μ-analysis – relevant for detecting extremely rare events. Recently tested on a series of AOCS benchmarks of increasing complexity [5,6,7], the most recent version of the toolbox is now evaluated for the first time on a more challenging and realistic attitude control problem. The analysis focuses both on the normal mode (MNO) and on the orbit control mode (MCO) of the CNES MicroCarb mission [8,9]. The paper compares and discusses the results which have been obtained with different V&V techniques, critically assessing the advantages of the innovative method with respect to more classical procedures. [1] C. Roos. Systems Modeling, Analysis and Control (SMAC) toolbox: an insight into the robustness analysis library. Proceedings of the IEEE CACSD Conference, Hyderabad, India, 2013. [2] A. Marcos, S. Bennani, C. Roux. Stochastic µ-analysis for launcher thrust vector control systems. Proceedings of the EuroGNC Conference, Toulouse, France, 2015. [3] A. Falcoz, D. Alazard, C. Pittet. Probabilistic µ-analysis for system performances assessment. Proceedings of the 20th IFAC World Congress, Toulouse, France, 2017. [4] S. Thai, C. Roos, J.M. Biannic. Probabilistic µ-analysis for stability and H∞ performance verification. Proceedings of the ACC, Philadelphia, PA, USA, 2019. [5] J.M. Biannic, C. Roos, S. Bennani, F. Boquet, V. Preda, B. Girouart. Advanced probabilistic µ-analysis techniques for AOCS validation. European Journal of Control, 62 (2021), pp. 120-129. [6] C. Roos, J-M. Biannic, and H. Evain. A new step towards the integration of probabilistic µ in the aerospace V&V process. Proceedings of the EuroGNC Conference, Berlin, Germany, 2022. [7] F. Somers, S. Thai, C. Roos,[ J-M. Biannic, S. Bennani, V. Preda, and F. Sanfedino. Probabilistic gain, phase and disk margins with application to AOCS validation. Proceedings of the IFAC ROCOND Symposium, Kyoto, Japan, 2022. [8] Arnaud Varinois and al., “MICROCARB: A micro-satellite for atmospheric CO2 monitoring”, 4S 2016 [9] Genin, F. and Viaud, F. “An innovative control law for Microcarb microsatellite”, 32nd annual AAS Guidance and Control Conference, 2018
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Cao, KaiTian, and ChengYu Shen. "Analysis of Outage Probability for Intelligent Reflecting Surface Assisted Downlink NOMA Symbiotic Radio System in κ-μ Fading." In 2023 IEEE 15th International Conference on Advanced Infocomm Technology (ICAIT). IEEE, 2023. http://dx.doi.org/10.1109/icait59485.2023.10367414.
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Tian, Zhigang. "An Evaluation of Wave Impact Indicators." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79732.
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Wave impact on offshore structures has been the focus of several studies, due to its significant effect on offshore operations. We evaluate several parameters (wave impact indicators) which can be adopted to indicate the possibility of wave impact on offshore structures due to extreme waves. The indicators can be estimated quickly with given sea states, and thus may provide useful information to offshore structure designers at early design phases. Definitions of three wave impact indicators are presented and discussed. The first indicator, Ψ, is proposed by Stansberg (2008). The second one considered is a wave breaking parameter, μ, originally presented by Song and Banner (2002) in their construction of a wave breaking criterion. Finally, we propose a more generalized impact indicator, βn. The subscript n indicates its dependence on local wave steepness. Our study demonstrates that the three indicators are analytically related. To evaluate these indicators numerically, 2nd order random surface waves are generated with random phase method and Two-Dimensional Fast Fourier Transform (2D FFT). Hilbert analysis of the wave signal reveals that all indicators are able to identify steep and energetic waves that may potentially cause large wave impact loads. Further numerical study demonstrates that the quantitative correlation of wave impact loads to μ is less promising than that to Ψ and βn; while βn provides the best relationship to both local wave impact load and global wave load with its dependence on local wave steepness adjusted (i.e. adjusting n). The correlation is independent of sea states. Estimations and recommendations for thresholds of the two impact indicators (i.e. Ψ and βn with n = 1) are made based on model test results. With proper estimation of the thresholds, both indicators can be applied to predict wave impact and wave impact probability in given sea states.