### Abstract

The first part of the present investigation focuses on the formulation of a novel stochastic model of uncertain properties of media, homogenous in the mean, which are represented as stationary processes. In keeping with standard spatial discretization methods (e.g., finite elements), the process is discrete. It is further required to exhibit a specified mean, standard deviation, and a global measure of correlation, i.e., correlation length. The specification of the random process is completed by imposing that it yields a maximum of the entropy. If no constraint on the sign of the process exists, the maximum entropy is achieved for a Gaussian process the autocovariance of which is constructed. The case of a positive process is considered next and an algorithm is formulated to simulate the non-Gaussian process yielding the maximum entropy. In the second part of the paper, this non-Gaussian model is used to represent the uncertain friction coefficient in a simple, lumped mass model of an elastic structure resting on a frictional support. The dynamic response of this uncertain system to a random excitation at its end is studied, focusing in particular on the occurrence of slip and stick.

Original language | English (US) |
---|---|

Pages (from-to) | 128-137 |

Number of pages | 10 |

Journal | Probabilistic Engineering Mechanics |

Volume | 44 |

DOIs | |

State | Published - 2016 |

### Fingerprint

### Keywords

- Friction
- Maximum entropy
- Microslip
- Simulation
- Stochastic process
- Uncertainty

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mechanical Engineering
- Civil and Structural Engineering
- Aerospace Engineering
- Ocean Engineering
- Nuclear Energy and Engineering

### Cite this

*Probabilistic Engineering Mechanics*,

*44*, 128-137. https://doi.org/10.1016/j.probengmech.2015.10.003

**Maximum entropy modeling of discrete uncertain properties with application to friction.** / Murthy, Raghavendra; Choi, Byeong Keun; Wang, X. Q.; Sipperley, Mark C.; Mignolet, Marc; Soize, Christian.

Research output: Contribution to journal › Article

*Probabilistic Engineering Mechanics*, vol. 44, pp. 128-137. https://doi.org/10.1016/j.probengmech.2015.10.003

}

TY - JOUR

T1 - Maximum entropy modeling of discrete uncertain properties with application to friction

AU - Murthy, Raghavendra

AU - Choi, Byeong Keun

AU - Wang, X. Q.

AU - Sipperley, Mark C.

AU - Mignolet, Marc

AU - Soize, Christian

PY - 2016

Y1 - 2016

N2 - The first part of the present investigation focuses on the formulation of a novel stochastic model of uncertain properties of media, homogenous in the mean, which are represented as stationary processes. In keeping with standard spatial discretization methods (e.g., finite elements), the process is discrete. It is further required to exhibit a specified mean, standard deviation, and a global measure of correlation, i.e., correlation length. The specification of the random process is completed by imposing that it yields a maximum of the entropy. If no constraint on the sign of the process exists, the maximum entropy is achieved for a Gaussian process the autocovariance of which is constructed. The case of a positive process is considered next and an algorithm is formulated to simulate the non-Gaussian process yielding the maximum entropy. In the second part of the paper, this non-Gaussian model is used to represent the uncertain friction coefficient in a simple, lumped mass model of an elastic structure resting on a frictional support. The dynamic response of this uncertain system to a random excitation at its end is studied, focusing in particular on the occurrence of slip and stick.

AB - The first part of the present investigation focuses on the formulation of a novel stochastic model of uncertain properties of media, homogenous in the mean, which are represented as stationary processes. In keeping with standard spatial discretization methods (e.g., finite elements), the process is discrete. It is further required to exhibit a specified mean, standard deviation, and a global measure of correlation, i.e., correlation length. The specification of the random process is completed by imposing that it yields a maximum of the entropy. If no constraint on the sign of the process exists, the maximum entropy is achieved for a Gaussian process the autocovariance of which is constructed. The case of a positive process is considered next and an algorithm is formulated to simulate the non-Gaussian process yielding the maximum entropy. In the second part of the paper, this non-Gaussian model is used to represent the uncertain friction coefficient in a simple, lumped mass model of an elastic structure resting on a frictional support. The dynamic response of this uncertain system to a random excitation at its end is studied, focusing in particular on the occurrence of slip and stick.

KW - Friction

KW - Maximum entropy

KW - Microslip

KW - Simulation

KW - Stochastic process

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=84979523636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979523636&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2015.10.003

DO - 10.1016/j.probengmech.2015.10.003

M3 - Article

AN - SCOPUS:84979523636

VL - 44

SP - 128

EP - 137

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

ER -