scholarly journals An Improved Bayesian Structural Identification Using the First Two Derivatives of Log-Likelihood Measure

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jin Zhou ◽  
Akira Mita ◽  
Liu Mei
Keyword(s):  
Standard Deviation ◽  
Measurement Error ◽  
Differential Evolution ◽  
Structural Parameters ◽  
Structural Identification ◽  
Uncertainty Of Measurement ◽  
Posterior Density ◽  
Output Data ◽  
Log Likelihood ◽  
Derivatives Of

The posterior density of structural parameters conditioned by the measurement is obtained by a differential evolution adaptive Metropolis algorithm (DREAM). The surface of the formal log-likelihood measure is studied considering the uncertainty of measurement error to illustrate the problem of equifinality. To overcome the problem of equifinality, the first two derivatives of the log-likelihood measure are proposed to formulate a new informal likelihood measure for the sake of improving the accuracy of the estimator. Moreover, the proposed measure also reduces the standard deviation (uncertain range) of the posterior samples. The benefit of the proposed approach is demonstrated by simulations on identifying the structural parameters with limit output data and noise polluted measurements.

Toxicity of Para-Chloro Substituted Benzene Derivatives in the Microtox™ Test

1985 ◽  
Vol 20 (2) ◽  
pp. 36-43 ◽  
Author(s):  
Klaus L.E. Kaiser ◽  
Juan M. Ribo ◽  
Brian M. Zaruk
Keyword(s):  
General Formula ◽  
Functional Group ◽  
Structural Parameters ◽  
Systematic Investigation ◽  
Photobacterium Phosphoreum ◽  
Benzene Derivatives ◽  
Quantitative Structure ◽  
Chlorinated Benzenes ◽  
Chloro Derivatives ◽  
Derivatives Of

Abstract This paper gives the results of part of a systematic investigation into contaminant toxicity to Photobacterium phosphoreum in the Microtox™ test. Reported are the toxicity values for 39 para-chloro substituted benzene derivatives of the general formula l-Cl-C6h4-4-X=CH2CH(NH2)COOH, F, SO2NH2, OCH2COOH, CH2COOH, CONHNH2, NHCOCH3, CONH2, CH=CHCOOH, SeOOH, CH2NH2, CH2CH2NH2, NO2, H, CF3, CHO, CH2OH, OH, CH3, CCl3, COCH3, COOH, NH2, SO2C6H5, Cl, CH2COCH3, COCl, CN, OCH3, NCO, NHCH3, I, COC6H5, CH2Cl, SH, CH2SH, NCS, CH2CN and SO2C6H4Cl. Except for the last compound, whose solubility is below the required concentration, the toxicities increase in the presented order with a total range of more than three orders of magnitude. The data are discussed in terms of quantitative structure-toxicity correlations with compound-specific structural parameters. In combination with a previously developed submodel on chlorinated benzenes, phenols, nitrobenzenes and anilines, the observed relationships allow the prediction of the toxicity of some 780 possible chloro derivatives of the general formula C6H5-nClnX, where n=<5 and X is a functional group as listed above.

scholarly journals Application of Kalman Filtering Methods to Online Real-Time Structural Identification: A Comparison Study

2016 ◽  
Vol 16 (06) ◽  
pp. 1550016 ◽  
Author(s):  
Mohsen Askari ◽  
Jianchun Li ◽  
Bijan Samali
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Unscented Kalman Filter ◽  
Structural Parameters ◽  
Measurement Data ◽  
Linear Structure ◽  
Structural Identification ◽  
Input Output ◽  
Output Measurement ◽  
Highly Nonlinear

System identification refers to the process of building or improving mathematical models of dynamical systems from the observed experimental input–output data. In the area of civil engineering, the estimation of the integrity of a structure under dynamic loadings and during service condition has become a challenge for the engineering community. Therefore, there has been a great deal of attention paid to online and real-time structural identification, especially when input–output measurement data are contaminated by high-level noise. Among real-time identification methods, one of the most successful and widely used algorithms for estimation of system states and parameters is the Kalman filter and its various nonlinear extensions such as extended Kalman filter (EKF), Iterated EKF (IEKF), the recently developed unscented Kalman filter (UKF) and Iterated UKF (IUKF). In this paper, an investigation has been carried out on the aforementioned techniques for their effectiveness and efficiencies through a highly nonlinear single degree of freedom (SDOF) structure as well as a two-storey linear structure. Although IEKF is an improved version of EKF, results show that IUKF generally produces better results in terms of structural parameters and state estimation than UKF and IEKF. Also IUKF is more robust to noise levels compared to the other approaches.

S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

2020 ◽  
Vol 21 (6) ◽  
pp. 323-336
Author(s):  
N. N. Karabutov
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Structural Parameters ◽  
Linear Part ◽  
Structural Identification ◽  
Nonlinear Dynamic Systems ◽  
Necessary Condition ◽  
Structural Identifiability ◽  
Nonlinear Part

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

scholarly journals Modified data on geoeffective solar flares and seismic noise variations

2021 ◽  
Vol 929 (1) ◽  
pp. 012033
Author(s):  
N A Sycheva ◽  
L M Bogomolov
Keyword(s):  
Standard Deviation ◽  
Solar Flare ◽  
Solar Flares ◽  
Seismic Noise ◽  
Tien Shan ◽  
Output Data ◽  
Regional Seismicity ◽  
Eruptive Event ◽  
The Relationship ◽  
Northern Tien Shan

Abstract The problem of the relationship between strong magnetic swarms caused by solar flares and variations in seismicity is considered. The data on the temporal dependences of the parameters of seismic noise (average level, and standard deviation, RMS) recorded by the stations of the KNET seismic network have been used as the output data of monitoring the territory of the Bishkek geodynamic proving ground (Northern Tien Shan). The signatures of the influence of a magnetic swarm that occurred after an ultra-strong solar flare on September 6, 2017 have been established. The results obtained on the increase in seismic noise after this super-strong eruptive event are consistent with the results of studies on the influence of magnetic swarms on changes in regional seismicity.

scholarly journals Application of Characteristic Model-Based Principal Component Analysis in Optimization of Flowmeter Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Wenping Jiang ◽  
Zhencun Jiang ◽  
Lingyang Wang ◽  
Jun Min ◽  
Yi Zhu ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Measurement Error ◽  
Measurement Accuracy ◽  
Structural Parameters ◽  
Principal Component ◽  
Component Analysis ◽  
Characteristic Model ◽  
Industrial Systems ◽  
Model Based ◽  
High Level

In complex industrial processes, it is necessary to perform modeling analysis on some industrial systems and find and optimize the factors that have the greatest impact on the results, in order to achieve the optimization of the industrial systems. However, due to the high-level nature or complex working mechanism of complex industrial systems, traditional principal component analysis methods are difficult to apply. Therefore, this paper proposes a characteristic model-based principal component analysis (CMPCA) to perform principal component analysis on complex industrial systems. The differential pressure flowmeter is taken as an example to verify the effectiveness of the method. Flowmeter is an indispensable instrument in measurement, and its accuracy depends on its own structural parameters. However, the measurement accuracy of some flow meters is not high, and the measurement error is large, which affects the normal industrial production process. This method is used to analyze the influence of the structural parameters of the flowmeter on its measurement accuracy, and the four most important structural parameters are found and optimized. The measurement error of the Bitoba flowmeter is reduced from 1% to 0.2%, and the measurement repeatability is reduced from 0.3 to 0.06, which proves the effectiveness of the method.

The 2D Spring Splines Procedure Application With Prescribed Accuracy for Determination of the Global (Pipe Centerline) as Well as the Local (Dent) Curvatures

2012 ◽  
Author(s):  
I. V. Orynyak ◽  
A. V. Bohdan ◽  
I. V. Lokhman
Keyword(s):  
Standard Deviation ◽  
Wave Length ◽  
Elastic Beam ◽  
Local Geometry ◽  
Bending Stress ◽  
Position Measurement ◽  
Mean Square Errors ◽  
Local Dent ◽  
Derivatives Of

The problem of smoothing the spatial line based on position measurements of discrete points exists in cases where a) the positions of points are determined with some errors, b) the goal of smoothing is not a continuous position itself but the higher derivatives of it. It is a very common problem in many engineering applications. With respect to the pipeline industry this problem is very prominent at least in two cases but regretfully many researchers do not pay due attention to it at all. First, the Geopigs are widely used for the determination of spatial position of the pipe centerline points. This information inter alia may be (and in fact are widely) used for the calculation of the global centerline curvatures which are proportional to the global bending strains. Second, the maximum strain levels of the dents are calculated based on the local geometry of the dent as determined by radial sensor measurements from the in line inspection survey. Note, that in both cases mathematically the curvatures are the second derivatives of the function of global (pipeline) or local (dent) positions. The input information about the global X–Y–Z position of each consecutive point of axis line as well as the local radial position of the dent points are given with some error. This leads to a huge noise in predicted curvatures which can overrun the useful information. The amplitude of errors of calculation is inversely proportional to the squared distance between the points of measurement. The application of any smoothing procedure may lead to the loss of the useful information about real curvatures. Thus tradeoff between the smoothing of the noise and the loss of accuracy presents a big problem in the pipeline industry. Two quantitative parameters are introduced here to allow performing such a tradeoff. First parameter characterizes the standard deviation (also referred to as standard in the following) of the random value of the position measurement accuracy by the devices, ρ. Second parameter is the requested accuracy of the curvature determination and is defined in terms of the standard deviation of the bending stress, σ or strain, ε. The spatial beam on elastic foundation model is used to fit the measured point positions to the spatial curve. Its main characteristic is the specific compliance of the foundation α which is determined based on two above root-mean-square errors ρ and σ. The corresponding formulas and tables based on the solution for the elastic beam are obtained. The bigger the allowed error in bending stress σ the lesser is required compliance of the foundation, α. In turn this leads to the smaller value of characteristic wave length of solution and the possibility to retain more useful information about the actual short length stresses in the pipeline. Some practical examples of applications of the procedure are given.

Estimation of the integral of the square of derivatives of symmetric probability densities of one-dimensional random variables

Metrologiya ◽  
2020 ◽  
pp. 15-27
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Standard Deviation ◽  
Probability Density ◽  
Random Variables ◽  
Random Variable ◽  
Density Estimates ◽  
One Dimensional ◽  
Probability Densities ◽  
The One ◽  
Derivatives Of ◽  
Selection Of

When substantiating the method of fast selection of the bandwidth of kernel probability density estimates, a constant was found that is a functional of the second density derivative. In this paper, the obtained result is generalized to derivatives of symmetric probability densities of different orders. The functional dependences of the constants under study on the coeffi cient of antikurtosis of a random variable are established. The regularities peculiar to them are investigated. Based on the results obtained, a method for estimating functionals from derived probability densities has been developed, which involves the following actions. In the original sample estimated standard deviation of the one-dimensional random variables and the coeffi cient of antikurtosis. Using the reconstructed functional dependences on the antikurtosis coeffi cient, the constants are estimated, which are functionals of the derivatives of the probability density. With known estimates of the standard deviation of the investigated random variable and the considered constant, the values of the functional from the derivative of the probability density of the selected order are calculated. The obtained results are confi rmed by the analysis of the data of computational experiments. It is established that with increasing order of the derivative, the values of the estimates of the studied functionals increase. This fact is explained by the complication of the integrand function in the considered functionals. The proposed method provides objective results for the fi rst three derivatives of the probability density of a random variable. The obtained conclusions are confi rmed by the results of the confi dence estimation of the investigated functionals.

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