Stochastic methods in engineering
著者
書誌事項
Stochastic methods in engineering
WIT Press, c2012
- : hbk.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The increasing industrial demand for reliable quantification and management of uncertainty in product performance forces engineers to employ probabilistic models in analysis and design, a fact that has occasioned considerable research and development activities in the field. Notes on Stochastics eventually address the topic of computational stochastic mechanics. The single volume uniquely presents tutorials on essential probabilistics and statistics, recent finite element methods for stochastic analysis by Taylor series expansion as well as Monte Carlo simulation techniques. Design improvement and robust optimisation represent key issues as does reliability assessment. The subject is developed for solids and structures of elastic and elasto-plastic material, large displacements and material deformation processes; principles are transferable to various disciplines. A chapter is devoted to the statistical comparison of systems exhibiting random scatter. Where appropriate examples illustrate the theory, problems to solve appear instructive; applications are presented with relevance to engineering practice.The book, emanating from a university course, includes research and development in the field of computational stochastic analysis and optimization.
It is intended for advanced students in engineering and for professionals who wish to extend their knowledge and skills in computational mechanics to the domain of stochastics. Contents: Introduction, Randomness, Structural analysis by Taylor series expansion, Design optimization, Robustness, Monte Carlo techniques for system response and design improvement, Reliability, Time variant phenomena, Material deformation processes, Analysis and comparison of data sets, Probability distribution of test functions.
目次
- Contents Introduction Uncertainty
- Structural analysis and design improvement
- Reliability
- Evolutionary processes
- Statistical comparison Randomness Random variables
- Uni- and bivariate case
- Multivariate systems, random vectors: Transformed vector variables
- Standardization
- Principal components: Probability
- Relative frequency
- Distribution of random variables
- Markov inequality, Chebyshev inequality
- Distinct distributions
- Several random variables
- Discrete random variables
- Discrete random vectors: Relations between variates
- Observations on several events
- Independent random variables
- Functions of random variables - expected value
- Properties of expected values
- Determination of mean value and variance
- Approximation of mean value and variance
- Functions of random variables - distribution
- Stochastic simulation
- Appraisal of the approximation methods: Aspects of parameter estimation
- Sample mean and variance
- Maximum likelihood
- Problems Structural analysis by Taylor series expansion Random response
- Introductory remarks
- Finite element representation: Linear elastic systems
- Probabilistic solution
- Computation of derivatives
- Grouping of random input variables: Large displacements
- Iterative solution
- Non-linear analysis
- Small strains: Path-dependence - elastoplasticity
- Incrementation
- Incremental analysis: Performance of the incremental approach: Non-linear dynamics: Problems Design optimization, robustness The optimization task
- Design variables, objective function
- Minimization by the steepest descent method
- Accounting for constraints: Implication of randomness: Robustness: Sensitivity of the objective
- Significance of input variables
- System suitability for robustness: Design sensitivity of the response
- Linear elastic systems
- Large displacements
- Path dependence - incrementation: Structural compliance optimization of a 25-bar space truss: Antenna structure undergoing large displacements: Problem Monte Carlo techniques for system response and design improvement Random sampling and statistical synthesis
- Outline of algorithm
- Application of method: The input sample
- Sampling from univariate distributions
- Sampling multivariate input: Relationships between variables
- Input-output systems
- Simple linear regression
- Multiple regression
- Multivariate multiple regression
- Regarding non-linearity: Modification of design
- Remarks on the objective function
- Design improvement: Exploration of the design space
- Level of design parameters
- Response surface
- Latin square: Problems Reliability Definitions
- Reliability of assemblies
- Elements in series
- Parallel assembly
- Mixed arrangements
- Weibull failure statistics
- Summary: Assessment of system reliability
- Basic variables and performance function
- Linear performance function
- Non-linear performance function
- Transformation to the standard normal space
- Summary: Reliability assessment by simulation
- Integration by Monte Carlo techniques
- Estimation of the failure probability
- Antithetic variables
- Importance sampling: Modelling the performance function: Optimization and reliability
- Problems Time variant phenomena Stochastic processes
- Description
- Autocorrelation
- Stationarity
- Ergodicity
- an example
- Cross-correlation
- Summary
- Discrete representation of process: Random fields: Input-output issues
- Instantaneous response to single action
- Single response to two random processes
- The time rate of a random process: Time to failure - lifetime
- Hazard rate
- Empirical approach
- System time to failure: Problems Material deformation processes Significance of random input
- Extension of viscous rod
- Time discrete representation
- Stochastic simulation
- Taylor series approach: Finite element formalism for inelastic deformation
- Quasistatic deformation of inelastic solids
- Thermal effects: Implication of randomness
- Stochastic process simulation by finite elements
- Process analysis by Taylor series expansion: Process design
- Optimization for robustness
- Die for cold steady-state extrusion
- Preform for net-shape hot upsetting Analysis and comparison of data sets Information on the sample
- Formal treatment of observation data
- Exploration of the covariance matrix
- Distance between observation units: Reduced representation
- Principal component analysis
- Examples on model reduction: Comparison of two data sets
- Parent population
- Hypothesis testing
- Test on the means
- Test on the covariance matrices
- Tests on individual variables, discriminant analysis
- Comparison of group to single observation: Extension to random processes
- Testing sets of realizations
- Test on the mean vector
- One-sample profile analysis on stationarity
- Two-sample profile analysis
- The Kolmogorov-Smirnov test: Distance between random systems
- Preliminaries
- Confidence region when comparing two mean vectors
- A discussion on bivariate systems
- Confidence measures for multivariate samples
- Application to crashworthiness study
- Test case from aerospace engineering
- Summary: multivariate vs. univariate treatment
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