Determination of extreme values in autonomous driving based on multifractals and dynamic scaling

Author(s):  
Jozsef Z. Szabo ◽  
Peter Bakucz
2021 ◽  
Vol 1 (2) ◽  
pp. 58-64
Author(s):  
Peter Bakucz ◽  
Gabor Kiss

In this paper, we approximate the probable maximum (very rare, extremal) values of highly autonomous driving sensor signals by reviewing two methods based on dynamic time series scaling and multifractal statistics.The article is a significantly revised and modified version of the conference material ("Determination of extreme values ​​in autonomous driving based on multifractals and dynamic scaling") presented at the conference "2021 IEEE 15th International Symposium on Applied Computational Intelligence and Informatics, SACI". The method of dynamic scaling is originally derived from statistical physics and approximates the critical interface phenomena. The time series of the vibration signal of the corner radar can be considered as a fractal surface and grow appropriately for a given scale-inverse dynamic equation. In the second method we initiate, that multifractal statistics can be useful in searching for statistical analog time series that have a similar multifractal spectrum as the original sensor time series.


Author(s):  
Ali Cetin ◽  
Trond Pytte ◽  
Sveinung Eriksrud

Operation limits for temporary riser system are determined according to some probability of exceedance of a relevant variable. Accordingly, consistent statistical analysis and probability modelling of the data is required. The common industry approach is to rely on the classical narrow-banded Gaussian process assumption when considering time series of variables of interest. Thus, the time series peaks are characterized by means of the Rayleigh distribution and the relevant extreme values are estimated based on this. However, non-linearities present in riser systems may yield non-Gaussian (wide-banded) processes, rendering the classical approach inappropriate. In the present work, an approximate and practical method is presented to address above issue. It is demonstrated that the approximate method is capable of consistently estimating the relevant extreme values, even where the classical method comes short.


2007 ◽  
Vol 24 (5) ◽  
pp. 835-846 ◽  
Author(s):  
Yvonne B. L. Hinssen ◽  
Wouter H. Knap

Abstract Two pyranometric methods for the determination of sunshine duration (SD) from global irradiance measurements are evaluated by means of summated sunshine seconds derived from pyrheliometric measurements in combination with the WMO threshold of 120 W m−2 for the direct solar irradiance. The evaluation is performed using direct and global radiation measurements made at the Cabauw Baseline Surface Radiation Network (BSRN) site in the Netherlands for the period March 2005–February 2006. The “Slob algorithm” uses 10-min mean and extreme values of the measured global irradiance and parameterized estimates of the direct and diffuse irradiance. The “correlation algorithm” directly relates SD to 10-min mean measurements of global irradiance. The cumulative pyrheliometric SD for the mentioned period is 1429 h. Relative to this value, the Slob algorithm and correlation algorithm give −72 h (−5%) and +8 h (+0.6%). On a daily mean basis, the values are −0.22 ± 0.05 h day−1 and 0.03 ± 0.03 h day−1, respectively. By means of tuning the irradiance parameterizations of the Slob algorithm, the yearly cumulative and daily mean differences can be reduced to +7 h (+0.5%) and 0.02 ± 0.04 h day−1, respectively. It is concluded that, by use of either algorithm, it is possible to estimate daily sums of SD from 10-min mean measurements of global irradiance with a typical uncertainty of 0.5–0.7 h day−1. For yearly sums, the uncertainty typically amounts to 0.5%.


Author(s):  
Y. A. Nozhnitski ◽  
E. A. Lokshtanov ◽  
I. N. Dolgopolov ◽  
G. V. Shashurin ◽  
M. E. Volkov ◽  
...  

Lifetime of disks and other aviation engine parts critical for safe operation is currently probabilistically predicted using mainly two methods. One method to predict lifetime is to confirm lifetime to low-cycle fatigue (LCF) cracking of a part without initial defects. The other method to predict lifetime is to confirm lifetime for safe propagation of a crack from initial defects available in a part. Combination of the above stated methods along with usage of margins on cyclic durability that ensure the required nonfracture probability presents another more conservative approach. Confirmation of lifetime to LCF cracking of a part without initial defects is usually performed based on results of cyclic tests of parts. The safe life determination algorithms were developed in Central Institute of Aviation Motors (CIAM) that take into account a difference in test outcome (“failure”–“no failure”). The developed software makes possible to consider the admissible failure probability, use the actual cyclic durability spread characteristics of the parts involving both lognormal and Weibull durability distributions. This paper discusses the examples of application of the elaborated methods and software. To confirm lifetime for safe propagation of a crack from defects available in a part, a program of statistical determination of durability of powder alloy disks with random fields of ceramic inclusions was developed in CIAM. This program allows performing the partition of disks into typical elements, the generation of realizations of initial defects for each typical disk element and calculation of life realizations corresponding to them, the statistical processing of the obtained data made with usage of asymptotic theory of extreme values, and the determination of technical risk functions for a disk as a whole. While developing the software, the problems of crack initiation and its stable propagation from ceramic inclusions were sequentially decided. Example of the calculation made according to the developed program is given in this paper. The probabilistically-justified approaches to determine the safe life shall be supplemented with the methods of economical and ecological risk analysis. In this case these approaches may become a good support for arranging the engine service to Reliability Centered Maintenance.


1969 ◽  
Vol 60 (2) ◽  
pp. 327-351 ◽  
Author(s):  
Kai R. Jørgensen

ABSTRACT The use of the double antibody method for radio-immunological determination of insulin in plasma was evaluated on the basis of dilution and recovery experiments, as well as by the investigation of the reproducibility and accuracy of the method. Given the optimum conditions for the precipitation reaction, the method appears from the present investigations to be well suited for plasma insulin determinations. With the technique used for the separation of free and antibody bound insulin, the results of the insulin determination were found to be independent of the radioactive degradation products present in the tracer insulin. It was not possible to demonstrate any increased degradation of the tracer insulin by incubation in plasma or urine as compared with incubation in 0.5 % human albumin buffer. The absolute insulin values were found to be independent of the length of the incubation period. No difference was found between the fasting insulin concentrations in a group of new-born infants of non-diabetic mothers and a group of adult normal subjects. Similarly, the fasting insulin values were found to be independent of the sex of the subject investigated. After oral administration of glucose a considerable variation was found in the insulin response in a group of normal subjects. This variation, within the weight limits used, was found to be independent of the sex, age and weight of the subject investigated. A corresponding condition was found to be valid for the insulin excretion in the urine of normal subjects. It was concluded that the large variation in the insulin response in a group of normal subjects did not allow conclusions about the clinical significance of the extreme values, but that the variation alone must be taken as an expression for a pronounced biological variation.


Author(s):  
Miroslav Rusko ◽  
Dana Procházková

Size and Return Periods of Extreme Disasters Extreme disasters occur rarely and altogether occasionally, and therefore, the determination of maximum possible size or maximum expected size of natural and other disasters is important for the safety management and for the insurance domain, and considerable attention is paid to it. Systematic methodology development has been supported by professional papers since 70s of the last century or so. At present, the extreme value methods based on the great numbers of law, fuzzy sets etc. are used. The example shows the high differences in the extreme values existing in the application of old concepts and new methods. By use of the extreme value methods, it is also possible to calculate the return period of extreme disasters. The example showing return periods for different disaster sizes is given.


Author(s):  
Peidong Liang ◽  
Habte Tadesse Likassa ◽  
Chentao Zhang ◽  
Jielong Guo

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ∗ , w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.


Author(s):  
David Barreto ◽  
Madjid Karimirad ◽  
Arturo Ortega

Abstract In the field of stochastic dynamics of marine structures, the determination of long-term extreme responses is a crucial aspect to ensure the desired level of structural reliability. The calculation of these responses requires precise knowledge of the environmental conditions and reliable methods to predict the values associated with a reliability target level. While there is a very precise method to determine the value of these extreme values, e. g. the full long-term analysis (FLTA), this approach is computationally expensive. Then, approximated methods are needed. One practical approach for the determination of the most relevant environmental conditions for extreme calculation is the environmental contour method (ECM). However, some limitations have been detected when this method is used for offshore structures that consider survival strategies e. g. offshore wind turbines (OWT). Lastly, a modified ECM procedure (MECM) has been developed with the purpose to bypass the limitations of the traditional ECM. This method is based on short-term simulations and through an iterative process by testing many environmental contours in the operational range allows finding an important wind speed with its corresponding return period and thus, the problem that traditional ECM has, is avoided. The environmental conditions, which are represented by a large number of parameters, are also an important aspect of extreme calculation. Whereas some of them are treated as stochastic values, some are considered deterministic and, therefore the existence of uncertainties in their measured/estimated values is inevitable. These uncertainties are addressed by adopting values recommended by standards and guidelines and, in practice, it is often necessary to be conservative when there is a lack of information about the specific site studied. Therefore, the understanding of the impact that these uncertainties can have on the loads/responses that govern the design of offshore structures, especially wind turbines, is of great relevance. In this work, the influence of uncertainty in the wind shear coefficient (WSC) is studied. This parameter is directly related to one critical environmental condition i. e. wind speed at hub height, and its influence in power production and fatigue loads has been documented in the literature, but, few cases have addressed their influence in bottom fixed OWT responses. This work seeks to highlight the relevance of an accurate selection of shear coefficient and, its influence on the probabilistic analysis of a bottom fixed OWT taking into account that considerable variations from recommended values may occur. Through the use of coupled simulations in FAST, the NREL 5MW wind turbine will be subjected to varying wind shear conditions, and the corresponding 50-yr long-term responses will be calculated considering the MECM to take into account the influence of the wind turbine survival mode. The extreme values are fitted from a Global Maxima Method (GMM). Finally, it is sought to relate the uncertainty in a relevant input parameter (i. e. WSC) with the uncertainties propagated to the output parameters (i. e. extrapolated long-term extreme responses).


1991 ◽  
Vol 18 (2) ◽  
pp. 225-236 ◽  
Author(s):  
Daniel Caissie ◽  
Nassir El-Jabi

Peak stream discharge is a hydrologic parameter that is very important for the determination of flood risk, design of engineering works, and management of water resources. In this study, some 237 stream records across Canada were analyzed using the theory of stochastic processes applied to extreme values. This model, based on partial duration series analysis, was applied to each stream record, considering the time of occurrence of floods to be a Poisson process. In addition, exceedances (values above a given discharge level or truncation level) were considered to be independent random variables identically distributed over a one-year time interval. After this frequency analysis of each stream record, a regionalization of the flood frequency characteristics in Canada was performed using two different approaches: multiple regression analysis and index-flood method. A comparison of the two approaches was carried out by examining mean relative error and root-mean-square error. It was determined that the level of difficulty in applying the stochastic flood model was not the same across Canada. Moreover, error associated with the index-flood method is mainly due to error in estimating low return floods. Key words: flood, partial duration series, regional hydrology, index-flood method, low return flood.


Nativa ◽  
2018 ◽  
Vol 6 (6) ◽  
pp. 675
Author(s):  
Rafael Alvarenga Almeida ◽  
Gilberto Coelho ◽  
Isabela Alvarenga Almeida ◽  
Jéfferson De Oliveira Costa

O objetivo desse trabalho foi determinar os parâmetros α e β espacializados e, assim, possibilitar a estimativa de chuvas intensas em todo o estado de Minas Gerais com uma determinada probabilidade, e também para tempos de retorno diferentes dos tradicionais. A área de estudo considerada foi o Estado de Minas Gerais, foram utilizados dados de 96 estações pluviométricas presentes na região e aplicados testes de aderência da distribuição generalizada de valores extremos (GEV) e de tendência. Os resultados da avaliação da dependência espacial dos parâmetros α e β e seus respectivos intervalos de confiança, demonstram que o modelo de semivariograma exponencial foi o mais adequado para descrever a dependência espacial dos parâmetros da distribuição GEV, podendo ser aplicados os valores de precipitação máxima diária no Estado de Minas Gerais. Concluiu-se que os mapas gerados podem ser utilizados para determinação dos parâmetros α e β em qualquer localidade de Minas Gerais e, assim, a precipitação máxima diária pode ser obtida para quaisquer tempos de retorno desde que os intervalos de confiança de α e β sejam respeitados.Palavras-chave: eventos extremos, precipitação máxima, probabilidade. GEOSTATISTICS APPLIED IN THE ESTIMATION OF DAILY MAXIMUM RAINS IN THE STATE OF MINAS GERAIS ABSTRACT:The objective of this work is to determine the parameters α and β estimates of rainfall in the entire state of Minas Gerais with a certain probability, as well as our traditional return times. A study area of the State of Minas Gerais, with rainfall data of 96 rainfall stations present in the region and tested for generalized distribution of extreme values (GEV)adherence and trend. The results of the spatial dependence evaluation of the parameters and their confidence parameters demonstrate that the exponential semivariogram model was the most adequate to describe a spatial dependence of the parameters of the GEV distribution, being able to be applied to values of daily maximum non-state precipitation Minas Gerais. It was concluded that the generated maps can be used for the determination of the parameters and in any locality of Minas Gerais and, thus, a maximum daily precipitation, can be obtained by times of return since the confidence intervals of α and β are respected.Keywords: extreme events, maximum precipitation, probability.


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