Efficient Stability and Robustness Analysis of Uncertain Nonlinear Systems using a New Response-based Method

2017 ◽  
Vol 24 (02) ◽  
pp. 1750010
Author(s):  
Young Kap Son ◽  
Gordon J. Savage
Keyword(s):  
Robustness Analysis ◽  
Life Time ◽  
Engineering System ◽  
Time Dynamics ◽  
Singular Vectors ◽  
Uncertain Dynamic Systems ◽  
Design Variables ◽  
The Stability ◽  
The Right ◽  
Value Decomposition

A stable dynamic system implies safety, reliability, and satisfactory performance. However, the determination of stability is very difficult when the system is nonlinear and when the ever present uncertainties in the components must be considered. Herein a response-based approach that uses both system and time information obtained through singular value decomposition is presented to determine the stability space of nonlinear, uncertain dynamic systems: any approximating linearization of the nonlinearities has been obviated. The approach extends previous work for linear systems that invoked only the variability of the left singular vectors to predict stability. In the new approach, the variability of the right singular vectors is augmented to that of the left singular vectors and it is shown that a simulation time span, as short as two or three periods, is sufficient to predict stability over the entire life-time dynamics rendering the method very efficient. The stability space is a subset of the design space and its robustness is proportional to the tolerances assigned to the random design variables. Errors due to sampling size, time increments, and number of singular vectors used are controllable. The method can be implemented with readily available software. A study of a practical engineering system with different tolerances and different time spans shows the efficacy of the proposed approach.

Stability and Robustness Analysis of Uncertain Nonlinear Systems Using Entropy Properties of Left and Right Singular Vectors

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Young Kap Son ◽  
Gordon J. Savage
Keyword(s):  
Initial Conditions ◽  
Mechanistic Model ◽  
Robustness Analysis ◽  
Life Time ◽  
Small Time ◽  
Time Span ◽  
Singular Vectors ◽  
Design Variables ◽  
Left And Right ◽  
The Stability

This paper presents a novel approach to determine the stability space of nonlinear, uncertain dynamic systems that obviates the traditional eigenvalue approach and the accompanying linearizing approximations. In the new method, any long-term dynamic uncertainty is used in an extremely simple and economical way. First, the variability of the design variables about a particular design point is captured through the design of experiments (DOE). Then, corresponding computer simulations of the mechanistic model, over only a small time span, provide a matrix of discrete time responses. Finally, singular value decomposition (SVD) separates out parameter and time information and the expected uncertainty of the first few left and right singular vectors predicts any instability that might occur over the entire life-time of the dynamics. The singular vectors are viewed as random variables and their entropy leads to a simple metric that accurately predicts stability. The stable/unstable spaces are found by investigating the overall design space using an array of grid points of suitable spacing. The length of the time span needed to capture the nature of the dynamics can be as short as two or three periods. The robustness of the stability space is related to the tolerances assigned to the design variables. Errors due to sampling size, time increments, and number of significant singular vectors are controllable. The method can be implemented with readily available software. A study of two practical engineering systems with different distributions and tolerances, various initial conditions, and different time spans shows the efficacy of the proposed approach.

Stability Analysis of Uncertain Systems Using a Singular Value Decomposition-Based Metric

2015 ◽  
Vol 22 (05) ◽  
pp. 1550021 ◽  
Author(s):  
Young Kap Son ◽  
Gordon J. Savage
Keyword(s):  
Singular Value Decomposition ◽  
Dynamic Systems ◽  
Life Time ◽  
Singular Value ◽  
New Approach ◽  
Safety And Reliability ◽  
The Stability ◽  
Value Decomposition ◽  
Time Information ◽  
Domain Information

The stability of dynamic systems is important for satisfactory performance, safety and reliability. The study becomes more difficult when the system is nonlinear and when the ever present uncertainties in the components are considered. Herein a new approach is presented that uses time-domain information: It invokes design of experiments based on the uncertainty within the system, computer simulation of the dynamics to generate a matrix of discrete time responses that presents the variability of the response, and finally, singular value decomposition to separate out parameter information from time information. The variability in the elements in the first few left singular vectors predicts any instability that might occur over the complete life-time of the system. The key to the approach is the introduction of random variables and subsequent co-variance operations. A real-world example and comparison to established methods show the efficacy of the approach.

scholarly journals НАСЛЕДОВАНИЕ СИНГУЛЯРНЫХ ВЕКТОРОВ ПРИ ПОПОЛНЕНИИ МАТРИЦЫ СТОЛБЦОМ

2021 ◽  
Vol 6 (12(81)) ◽  
pp. 36-40
Author(s):  
В. Кутрунов ◽  
Т. Латфуллин
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Symmetric Matrices ◽  
Singular Vectors ◽  
The Matrix ◽  
Singular Value Decompositions ◽  
Singular Numbers ◽  
The Right ◽  
Value Decomposition

Let the matrix A1 be obtained from the matrix A by adding a column to it on the right. The possibility of inheritance of singular numbers and the corresponding singular vectors when passing from matrix A to matrix A1 is investigated. The singular value decompositions of the matrix A are based on the scalar and vector properties of the square symmetric matrices ATA and AAT. The article deals with the singular value decomposition of the matrix A, which has more rows than columns, and the decomposition is based on the analysis of the ATA matrix.

Time-Series Data Analysis Using Sliding Window Based SVD for Motion Evaluation

2017 ◽  
Vol 21 (7) ◽  
pp. 1240-1250
Author(s):  
Yinlai Jiang ◽  
Isao Hayashi ◽  
Shuoyu Wang ◽  
Kenji Ishida ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Sliding Window ◽  
Singular Values ◽  
Singular Value ◽  
Series Data ◽  
Singular Vectors ◽  
Walking Difficulty ◽  
The Right ◽  
Value Decomposition

A method based on singular value decomposition (SVD) is proposed for extracting features from motion time-series data observed with various sensing systems. Matrices consisting of the sliding window (SW) subsets of time-series data are decomposed, yielding singular vectors as the patterns of the motion, and the singular values as a scalar, by which the corresponding singular vectors describe the matrices.The sliding window based singular value decomposition was applied to analyze acceleration during walking. Three levels of walking difficulty were simulated by restricting the right knee joint in the measurement. The accelerations of the middles of the shanks and the back of the waist were measured and normalized before the SW-SVD was performed.The results showed that the first singular values inferred from the acceleration data of the restricted side (the right shank) significantly related to the increase of the restriction among all the subjects while there were no common trends in the singular values of the left shank and the waist. The SW-SVD was suggested to be a reliable method to evaluate walking disability. Furthermore, a 2D visualization tool is proposed to provide intuitive information about walking difficulty which can be used in walking rehabilitation to monitor recovery.

scholarly journals Cycle-Based Robot Drive Train Optimization Utilizing SVD Analysis

2007 ◽  
Author(s):  
Xiaolong Feng ◽  
Shiva Sander-Tavallaey ◽  
Johan O¨lvander
Keyword(s):  
Cycle Time ◽  
Industrial Robot ◽  
Life Time ◽  
Drive Train ◽  
Original Design ◽  
Svd Analysis ◽  
Design Variables ◽  
Duty Cycles ◽  
Wide Range ◽  
Value Decomposition

Designing a drive train for an industrial robot is a demanding task where a set of design variables need to be determined so that optimal performance is obtained for a wide range of different duty cycles. The paper presents a method where singular value decomposition (SVD) is used to reduce the design variable set. The application is a six degree of freedom serial manipulator, with nine drive train parameters for each axis and the objective is to minimize the cycle time on 122 representative design cycles without decreasing the expected lifetime of the robot. The optimization is based on a simulation model of the robot and conducted on a reduced set of the initial duty cycles and with the design variables suggested by the SVD analysis. The obtained design reduces the cycle time with 1.6% on the original design cycles without decreasing the life time of the robot.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Pemanfaatan Metil Ester Sulfonat pada Pembuatan Deterjen Cair

2016 ◽  
Vol 7 (14) ◽  
pp. 143-155
Author(s):  
Eldha Sampepana ◽  
Suroto Hadi Saputra
Keyword(s):  
Fatty Acids ◽  
Methyl Ester ◽  
Linear Alkylbenzene Sulfonate ◽  
Emulsion Stability ◽  
Alcohol Sulfate ◽  
Stable Emulsion ◽  
Linear Alkylbenzene ◽  
Alkylbenzene Sulfonate ◽  
The Stability ◽  
The Right

In the manufacture of detergents still using surfactants (which serves as an emulsifier) of crude oil in the form of the AS. (alcohol sulfate) and LAS (linear alkylbenzene sulfonate), where this type of surfactant cannot be degraded by microorganisms when discharged into the environment, causing environmental pollution. Methyl ester sulfonate surfactant is an anionic surfactant which has a composition of C16 - C18 fatty acids are capable of acting against nature deterjensinya, while the C12 - C14 fatty acids contribute to the foaming effect. The purpose of this study was to look for the formulation of methyl ester sulfonate (MES) the right to produce a good detergent by using materials such as methyl ester sulfonate surfactant self-made, methyl ester sulfonate and sodium lauryl market Ester Sulfate (SLS) with a concentration of 15 %, 20 % and 25 %. Detergent results of the study have high detergency ( net ) compared with the detergency of detergent commercial, have a stable emulsion stability, the stability of the foam/foam detergent power made from methyl ester sulfonate surfactant produces less foam, compared with a detergent made from SLS and surfactant SNI 06-4075-1996 standards.

scholarly journals A Machine Learning-Based Seismic Data Compression and Interpretation Using a Novel Shifted-Matrix Decomposition Algorithm

2021 ◽  
Vol 11 (11) ◽  
pp. 4874
Author(s):  
Milan Brankovic ◽  
Eduardo Gildin ◽  
Richard L. Gibson ◽  
Mark E. Everett
Keyword(s):  
Real Time ◽  
Seismic Data ◽  
Matrix Decomposition ◽  
Original Data ◽  
Velocity Estimation ◽  
Singular Vectors ◽  
Well Stimulation ◽  
Marine Seismic ◽  
Value Decomposition ◽  
Seismic Data Compression

Seismic data provides integral information in geophysical exploration, for locating hydrocarbon rich areas as well as for fracture monitoring during well stimulation. Because of its high frequency acquisition rate and dense spatial sampling, distributed acoustic sensing (DAS) has seen increasing application in microseimic monitoring. Given large volumes of data to be analyzed in real-time and impractical memory and storage requirements, fast compression and accurate interpretation methods are necessary for real-time monitoring campaigns using DAS. In response to the developments in data acquisition, we have created shifted-matrix decomposition (SMD) to compress seismic data by storing it into pairs of singular vectors coupled with shift vectors. This is achieved by shifting the columns of a matrix of seismic data before applying singular value decomposition (SVD) to it to extract a pair of singular vectors. The purpose of SMD is data denoising as well as compression, as reconstructing seismic data from its compressed form creates a denoised version of the original data. By analyzing the data in its compressed form, we can also run signal detection and velocity estimation analysis. Therefore, the developed algorithm can simultaneously compress and denoise seismic data while also analyzing compressed data to estimate signal presence and wave velocities. To show its efficiency, we compare SMD to local SVD and structure-oriented SVD, which are similar SVD-based methods used only for denoising seismic data. While the development of SMD is motivated by the increasing use of DAS, SMD can be applied to any seismic data obtained from a large number of receivers. For example, here we present initial applications of SMD to readily available marine seismic data.

Film Elasticity and Film Stabilization in Firefighting Foam Stabilized by Solid Particles

2017 ◽  
Vol 744 ◽  
pp. 346-349
Author(s):  
Xiu Juan Li ◽  
Rui Song Guo ◽  
Min Zhao
Keyword(s):  
Life Time ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Solid Particles ◽  
High Concentration ◽  
Hydration Effect ◽  
Fixed Area ◽  
The Stability ◽  
Hydration Layers ◽  
Hydration Forces

The structure of the thin liquid films determines the stability of foams and emulsions. In this work the bubbles stretched length with different hollow SiO2 particles concentration is measured when the foam has been stilled for different time. The results show that the bubbles stretched length is longer than that of bubbles when the foam is free of hollow SiO2 particles even when the foam has been stilled for 500mins. The bubbles stretched length increases with increasing the concentration of hollow SiO2 particles. A strong hydration effect leaves a large volume of hydration layers on the solid particles surfaces in aqueous solutions. The water in hydration layers can help the film keep a certain thickness. The existence of hydration forces leads that two particles cannot be too close each other. The high concentration surfactant limited in the fixed area helps the film keep good elasticity. Therefore the film has a long life time with compatible thickness and elasticity and the three-phrase foam is upper stable.

scholarly journals The training schedule affects the stability, not the magnitude, of the interlimb transfer of learned dynamics

2013 ◽  
Vol 110 (4) ◽  
pp. 984-998 ◽  
Author(s):  
Wilsaan M. Joiner ◽  
Jordan B. Brayanov ◽  
Maurice A. Smith
Keyword(s):  
Short Duration ◽  
Dynamic Environment ◽  
Internal Representation ◽  
Motor Adaptation ◽  
Training Period ◽  
Visually Guided ◽  
Brief Training ◽  
Long Duration ◽  
The Stability ◽  
The Right

The way that a motor adaptation is trained, for example, the manner in which it is introduced or the duration of the training period, can influence its internal representation. However, recent studies examining the gradual versus abrupt introduction of a novel environment have produced conflicting results. Here we examined how these effects determine the effector specificity of motor adaptation during visually guided reaching. After adaptation to velocity-dependent dynamics in the right arm, we estimated the amount of adaptation transferred to the left arm, using error-clamp measurement trials to directly measure changes in learned dynamics. We found that a small but significant amount of generalization to the untrained arm occurs under three different training schedules: a short-duration (15 trials) abrupt presentation, a long-duration (160 trials) abrupt presentation, and a long-duration gradual presentation of the novel dynamic environment. Remarkably, we found essentially no difference between the amount of interlimb generalization when comparing these schedules, with 9–12% transfer of the trained adaptation for all three. However, the duration of training had a pronounced effect on the stability of the interlimb transfer: The transfer elicited from short-duration training decayed rapidly, whereas the transfer from both long-duration training schedules was considerably more persistent (<50% vs. >90% retention over the first 20 trials). These results indicate that the amount of interlimb transfer is similar for gradual versus abrupt training and that interlimb transfer of learned dynamics can occur after even a brief training period but longer training is required for an enduring effect.

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