Time-dependent system kinematic reliability analysis for robotic manipulators

2020 ◽  
pp. 1-36
Author(s):  
Qiangqiang Zhao ◽  
Junkang Guo ◽  
Dingtang Zhao ◽  
Dewen Yu ◽  
Jun Hong
Keyword(s):  
Reliability Analysis ◽  
Work Performance ◽  
Analytical Formula ◽  
Closed Form Solution ◽  
Robotic Manipulators ◽  
Outcrossing Rate ◽  
Time Dependent ◽  
Order Moment ◽  
Multivariate Gaussian ◽  
Time Dependent System

Abstract Time-dependent system kinematic reliability of robotic manipulators, referring to the probability of the end-effector’s pose error falling into the specified safe boundary over the whole motion input, is of significant importance for its work performance. However, investigations regarding this issue are quite limited. Therefore, this work conducts time-dependent system kinematic reliability analysis defined with respect to the pose error for robotic manipulators based on the first-passage method. Central to the proposed method is to calculate the outcrossing rate. Given that the errors in robotic manipulators are very small, the closed-form solution to the covariance of the joint distribution of the pose error and its derivative is first derived by means of the Lie group theory. Then, by decomposing the outcrossing event of the pose error, calculating the outcrossing rate is transformed into a problem of determining the first-order moment of a truncated multivariate Gaussian. Then, based on the independent assumption that the outcrossing events occur independently, the analytical formula of the outcrossing rate is deduced for the stochastic kinematic process of robotic manipulators via taking advantage of the moment generating function of the multivariate Gaussian, accordingly leading to achievement of the time-dependent system kinematic reliability. Finally, a 6-DOF robotic manipulator is used to demonstrate the effectiveness of the proposed method by comparison with the Monte Carlo simulation and finite-difference based outcrossing rate method.

An Outcrossing Rate Model and Its Efficient Calculation for Time-Dependent System Reliability Analysis

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
C. Jiang ◽  
X. P. Wei ◽  
Z. L. Huang ◽  
J. Liu
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Outcrossing Rate ◽  
Time Dependent ◽  
Engineering Practice ◽  
Rate Model ◽  
Random Loading ◽  
System Reliability Analysis ◽  
Efficient Calculation ◽  
Time Dependent System

Time-dependent reliability problems widely appear in the engineering practice when the material properties of the structure deteriorate in time or random loading modeled as random processes is involved. Among existing methods to the time-dependent reliability problems, the most dominating one is the outcrossing rate method. This paper presents an outcrossing rate model and its efficient calculation approach for system problems, and based on the presented model, a time-dependent system reliability analysis method is proposed. The main idea of the method is to transform the evaluation of the system outcrossing rates into the calculation of a time-invariant system reliability. Three numerical examples are used to demonstrate the effectiveness of the proposed method.

Time-Dependent System Reliability Analysis Using Random Field Discretization

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
System Reliability ◽  
Probability Of Failure ◽  
Two Dimensions ◽  
Time Dependent ◽  
Time Interval ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Time Dependent System

This paper proposes a novel and efficient methodology for time-dependent system reliability analysis of systems with multiple limit-state functions of random variables, stochastic processes, and time. Since there are correlations and variations between components and over time, the overall system is formulated as a random field with two dimensions: component index and time. To overcome the difficulties in modeling the two-dimensional random field, an equivalent Gaussian random field is constructed based on the probability equivalency between the two random fields. The first-order reliability method (FORM) is employed to obtain important features of the equivalent random field. By generating samples from the equivalent random field, the time-dependent system reliability is estimated from Boolean functions defined according to the system topology. Using one system reliability analysis, the proposed method can get not only the entire time-dependent system probability of failure curve up to a time interval of interest but also two other important outputs, namely, the time-dependent probability of failure of individual components and dominant failure sequences. Three examples featuring series, parallel, and combined systems are used to demonstrate the effectiveness of the proposed method.

System Kinematic Reliability Analysis for Robotic Manipulators Under Rectangular and Spherical Tolerant Boundaries

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Qiangqiang Zhao ◽  
Junkang Guo ◽  
Jun Hong
Keyword(s):  
Reliability Analysis ◽  
Degrees Of Freedom ◽  
Work Performance ◽  
Industrial Robot ◽  
Saddlepoint Approximation ◽  
Robotic Manipulators ◽  
Expectation Propagation ◽  
Six Degrees Of Freedom ◽  
Comparison Results ◽  
Input Uncertainties

Abstract Kinematic reliability is an essential index assessing the work performance of robotic manipulators. In general, the kinematic reliability of robotic manipulators is defined as the probability of the pose or position error falling into a specified tolerant region. Therefore, this work proposes an efficient method to conduct kinematic reliability analysis for robotic manipulators under rectangular and spherical allowable safe boundaries in terms of dimension and input uncertainties. First, based on the Baker–Campbell–Hausdorff formula and Lie group theory, the mean and covariance matrix of the distribution of the pose error are analytically determined. Then, the expectation propagation of the multivariate Gaussian and saddlepoint approximation method are employed to calculate the probabilities of kinematic reliability under the rectangular and spherical safe boundaries, respectively. The proposed method takes into account the boundness of the random error variable and is available for arbitrarily distributed errors. Finally, a spatial six degrees-of-freedom industrial robot is used as an example to demonstrate the effectiveness of the proposed method by comparison with other methods. The comparison results indicate that the proposed method has higher accuracy and efficiency.

Time-Dependent System Reliability Analysis With Second-Order Reliability Method

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hao Wu ◽  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

LSTM-Based Ensemble Learning for Time-Dependent Reliability Analysis

2020 ◽  
Author(s):  
Mingyang Li ◽  
Zequn Wang
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Ensemble Learning ◽  
Short Term Memory ◽  
Time Dependent ◽  
Learning Framework ◽  
Lstm Network ◽  
Hidden Layer ◽  
Original Time ◽  
Time Dependent System

Abstract This paper presents a long short-term memory (LSTM)-based ensemble learning framework for time-dependent reliability analysis. To deal with the time-dependent uncertainties, a LSTM network is first adopted to capture the system dynamics. As a result, time-dependent system responses for random realizations of stochastic processes can be accurately predicted by the LSTM. With realizations of the random variables and stochastic processes, multiple LSTMs are trained for generating a set of augmented data. Then a deep feedforward neural network (DFN) is employed to ensemble the knowledge extracted from LSTMs and generate a deep surrogate for the original time-dependent system responses. To improve the performance of DFN in terms of accuracy, the Gaussian process modeling technique is utilized for architecture design, where the number of neurons in the hidden layer is determined by minimizing the validation loss. With the DFN, the time-dependent system reliability can be directly approximated by using the Monte Carlo simulation. Two case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.

Time-Dependent System Reliability Analysis With Second Order Reliability Method

2020 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method that uses the envelop method and second order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the existing second order component reliability method, which produces component reliability indexes. The covariance between components responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint probability of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

scholarly journals Resilience Assessment Based on Time-Dependent System Reliability Analysis

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Assessment Method ◽  
Time Dependent ◽  
Design Stage ◽  
System Failure ◽  
System Reliability Analysis ◽  
System Resilience ◽  
Resilience Assessment ◽  
Time Dependent System

Significant efforts have been recently devoted to the qualitative and quantitative evaluation of resilience in engineering systems. Current resilience evaluation methods, however, have mainly focused on business supply chains and civil infrastructure, and need to be extended for application in engineering design. A new resilience metric is proposed in this paper for the design of mechanical systems to bridge this gap, by investigating the effects of recovery activity and system failure paths on system resilience. The defined resilience metric is connected to design through time-dependent system reliability analysis. This connection enables us to design a system for a specific resilience target in the design stage. Since computationally expensive computer simulations are usually used in design, a surrogate modeling method is developed to efficiently perform time-dependent system reliability analysis. Based on the time-dependent system reliability analysis, dominant system failure paths are enumerated and then the system resilience is estimated. The connection between the proposed resilience assessment method and design is explored through sensitivity analysis and component importance measure (CIM). Two numerical examples are used to illustrate the effectiveness of the proposed resilience assessment method.

Resilience Assessment Based on Time-Dependent System Reliability Analysis

2016 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Assessment Method ◽  
Time Dependent ◽  
Importance Measure ◽  
System Reliability Analysis ◽  
Component Importance ◽  
System Resilience ◽  
Resilience Assessment ◽  
Time Dependent System

Significant efforts have been recently devoted to the qualitative and quantitative evaluation of resilience in engineering systems. Current resilience evaluation methods, however, have mainly focused on business supply chains and civil infrastructure, and need to be extended for application in engineering design. A new resilience metric is proposed in this paper for the design of mechanical systems to bridge this gap, by investigating the effects of recovery activity and failure scenarios on system resilience. The defined resilience metric is connected to design through time-dependent system reliability analysis. This connection enables us to design a system for a specific resilience target in the design stage. Since computationally expensive computer simulations are usually used in design, a surrogate modeling method is developed to efficiently perform time-dependent system reliability analysis for resilience assessment. System resilience assessment is then investigated based on the developed time-dependent system reliability analysis method. The connection between the proposed resilience assessment method and design is discussed through the sensitivity analysis and component importance measure. Two numerical examples are used to illustrate the effectiveness of the proposed resilience assessment method and the associated sensitivity analysis and component importance measure.

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