Sequential time-dependent reliability analysis for the lower extremity exoskeleton under uncertainty

https://doi.org/10.1016/j.ress.2017.10.006Get rights and content

Highlights

  • A kernel density function based uncertainty quantification model is constructed.

  • A series system reliability model is built after decoupling time sequence.

  • Two-dimensional kernel density function is used to quantify failure correlation.

  • With time discretization, time-dependent system reliability analysis is finally performed.

  • Higher accuracy and efficiency of the proposed method have been validated by a case study.

Abstract

This paper proposes a sequential time-dependent reliability analysis method by considering time sequence and correlation of failure processes for the lower extremity exoskeleton under uncertainty, which will provide an approach to improving the comfort and safety for the wearer. A kernel density function based uncertainty quantification method is provided for precisely quantitatively estimating the time-dependent reliability of joints and the position of the end-effector firstly. After decoupling time sequence and failures correlation due to error propagation, the original reliability problem is then transferred to a series time-dependent reliability model. The time-dependent system reliability analysis is finally realized by calculating conditional probability. A case study is implemented to testify the effectiveness of the proposed method.

Introduction

Bionic lower extremity exoskeleton is a wearable robotic device by integrating human brain and mechanical force to increase speed, strength and endurance. Because of its broad application prospects in both medical rehabilitation and military fields, many studies and achievements have been made on the issues of mechanical design, kinematics analysis, control, machine learning and so on for the lower extremity exoskeleton. Furthermore, several representatives such as BLEEX (Berkeley Lower Extremity Exoskeleton) [1], [2], HAL (Hybrid Assistive Leg) [3], [4], ReWalk [5], Rex [6], NTULEE (Nanyang Technology University Lower Extremity Exoskeleton) [7], Lokomat [8], LOPES (Lower-extremity Powered Exoskeleton) [9], EXPOS (Exoskeleton for patients and the old by the Sogang University) [10] have been produced and potentially applied in engineering practices.

Uncertainty is ubiquitous in engineering systems during the systems’ lifecycle [11], [12], [13]. How to keep the consistency between human and the exoskeleton under uncertainty is an important issue to be concerned, which will affect both comfort and safety of the wearer. Basically, the consistency under uncertainty could be generalized in the context of kinematic accuracy reliability. Currently, there are few studies on reliability analysis for the lower extremity exoskeleton. Pan et al. have made many efforts on the kinematic accuracy reliability analysis according to the motion accuracy of the end-effector [14], [15]. However, the lower extremity exoskeleton is a typical system, where the motion accuracy for each joint and the end-effector should be satisfied and furthermore time sequence and correlation of failure processes caused by error propagation from joints to the end-effector should be considered for system reliability estimation.

System reliability depends on its components’ reliability and the system performance configuration [16]. The logic function is to express the relationship between the systems’ state and its components’ states. While the logic function is static, in other words, the performance configuration keeps invariant, static reliability analysis methods, such as Reliability Block Diagram [17], Static Fault Tree [18] and Binary Decision Diagrams [19], are proper for conducting system reliability analysis. In order to capture the time-dependent sate transition during the usage stage, some dynamic reliability analysis methodologies mainly including state transition diagrams [20], [21], Stochastic Petri nets [22], [23], [24], Dynamic fault tree analysis [25], [26], [27], Go-Flow [28], [29], and Dynamic Bayesian network [30], [31] are developed. The current dynamic reliability methods have developed many time-dependent sate transition strategies, namely, transitions based on set points, competing events, simultaneous transition/scenarios, and component influences on transition rates and dependencies [32]. Therefore, the current dynamic reliability methods focus on the trigger rules for state transition, but the correlation of different system states evolution is rarely referred. For the lower extremity exoskeleton, the states of joints and the end-effector are correlated due to the time sequence and error propagation. Hence new dynamic reliability analysis methods are needed for efficiently handle the reliability of the lower extremity exoskeleton.

In this paper, a sequential time-dependent system reliability analysis method is proposed for the lower extremity exoskeleton under uncertainty considering the operating function of the exoskeleton. Contributions of the paper could be summarized as follows: (1) time-dependent uncertainty quantification models are derived for joints and the end-effector; (2) time-dependent reliability analysis for joints and the end-effector is conducted by combining simulation and kernel density function; (3) a series system reliability model is built after decoupling time sequence and correlation of failure processes; (4) time-dependent system reliability analysis is conducted through calculating conditional probability for the decoupled events.

The remainder of the paper is organized as follows. In Section 2, the lower extremity exoskeleton is introduced briefly. Time-dependent reliability analysis for joints and the position of the end-effector based on kernel density function is given in Section 3. Section 4 provides the details for constructing the sequential time-dependent reliability model and conducting reliability analysis. Section 5 illustrates and testifies the proposed methods with a case study. Conclusions are finally summarized in Section 6.

Section snippets

Brief introduction of the lower extremity exoskeleton

As a popular research object of wearable devices currently, the lower extremity exoskeleton provides additional power to the body through the simulation of human lower limb skeletal structure, joint rotation and muscle movement so as to give the wearer to support, protection and assistance effect.

Fig. 1 is the conceptual sketch of a lower extremity exoskeleton, which is made of four components: two powered anthropomorphic legs, a power supply and a backpack-like frame [2]. In order to keep the

Model simplification for the lower extremity exoskeleton

Anthropomorphic is the important issue to be concerned during the design stage of the lower extremity exoskeleton. Therefore the motion of the lower extremity exoskeleton should keep consistent with that of a human. Similar to a human, the lower extremity exoskeleton has 6 distinct degrees of freedom (DOFs) per leg including 3 DOFs at the hip joint, 1 DOF at the knee joint and 2 DOFs at the ankle joint. The DOFs allocation details are summarized in Fig. 4.

As shown in Fig. 4,6 DOFs are

System reliability modeling for the lower extremity exoskeleton

For the lower extremity exoskeleton, the failure mainly stems from the motion accuracy, which will lead to the inconsistency between human and the lower extremity exoskeleton or even the hurt of a human. System reliability for the lower extremity exoskeleton is represented as R=Pr{HKAS}where events H, K, A and S respectively express the safety for the hip, knee, ankle joints and the position of the end-effector.

If the hip joint, knee joint, ankle joint and the position of the end-effector

Case study

In this Section, the simplified configuration of the Berkeley Lower Extremity Exoskeleton is employed to illustrate our proposed method. Table 1 shows the length of the exoskeleton thigh, shank and foot. Three actuators are used to drive the hip, knee and ankle joints and the corresponding actuator dimensions of the example is given in Table 2.

The length of links, the joint tolerance and the hydraulic cylinders are considered to be random variables, which are normally distributed. The variance

Conclusions

This paper presents a system reliability modeling method by considering time-sequence and correlation of failure processes, and an efficient system reliability analysis method by employing KDE for the lower extremity exoskeleton. The proposed method will be effective for improving the comfort and safety while wearing the designed exoskeleton. The time-dependent reliability for joints and the position of the end-effector using kernel function is efficient, which will provide a method to estimate

Acknowledgments

This research was partially supported by the National Natural Science Foundation of China under the Contract No. 11472075, the China Postdoctoral Science Foundation under the Contract No. 2013T60838, and the Fundamental Research Funds for the Central Universities under Contract No. ZYGX2014J071.

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