Kai-Yuan Cai

A critical review on software reliability modeling

Abstract Almost all the existing software reliability models are developed in the context of probability, and thus called probabilistic software reliability models (PSRMs). Unfortunately PSRMs have serious shortcomings such that we have to face the unpleasant fact that more and more PSRMs are proposed and none of them is shown to be tractable and universal. In this paper we show that the probability assumption for PSRMs is not reasonable as a result of the uniqueness of software. Fuzzy software reliability models (FSRMs) should be developed in place of PSRMs because the software reliability behavior is fuzzy in nature. Finally we demonstrate how to develop a simple fuzzy model to characterize software reliability behavior.

Fuzzy states as a basis for a theory of fuzzy reliability

Abstract Various engineering backgrounds have shown that the binary state assumption in probist (i.e., conventional) reliability theory, i.e. defining a system as fully failed or functioning, is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. As a result, the concept of profust reliability is introduced and a conceptual framework of profust reliability theory is developed on the basis of the fuzzy state assumption and the probability assumption. Profust reliability function, profust lifetime function and profust failure rate function and the mathematically rigorous relationships among them, lay a solid foundation for profust reliability theory. On the other hand, the concept of the virtual random lifetime builds a bridge linking profust reliability theory with probist reliability theory. In addition, in this paper, typical systems including the series system, parallel system, Markov model, mixture model and coherent system are briefly discussed within the conceptual framework of profust reliability theory.

Brief paper: Tracking control for a velocity-sensorless VTOL aircraft with delayed outputs

This paper presents a nonlinear output-feedback control method to force an underactuated vertical take-off and landing (VTOL) aircraft with delayed measurement outputs to asymptotically track a given reference trajectory. The control development is based on a delayed-output observer. The proposed observer consists of two-step observation algorithms reconstructing the system state with multi-delayed time instants. Conditions are given ensuring global exponential convergence to zero of the observation error for the given the delays in the measurements. Moreover, two low-dimensional controllers are designed separately to stabilize the two decomposed flight dynamics, and make the overall closed-loop system stable. The merits of method include its simple implementation and interesting application. Numerical simulations illustrate the effectiveness of the proposed control method.

A novel approach to software reliability modeling

Abstract A fuzzy software reliability model (FSRM) has been developed in place of probabilistic software reliability models (PSRMs). In this paper a comparison has been made with Singpurwalla-Soyer models in order to validate the proposed FSRM.

Quadrotor aircraft control without velocity measurements

In this paper a quadrotor aircraft is developed with the signals of attitude angle and angular rate being filtered by using frequency analysis. A PD sliding mode controller is designed to stabilize the attitude and position while a tracking-differentiator is employed to obtain the estimate of the required velocity. Experiments are conducted to demonstrate the developed quadrotor can be appropriately controlled in terms of attitude as well as position.

A Profust Reliability Based Approach to Prognostics and Health Management

Prognostics and health management (PHM) technology has been widely accepted, and employed to evaluate system performance. In practice, system performance often varies continually rather than just being functional or failed, especially for a complex system. Profust reliability theory extends the traditional binary state space {0, 1} into a fuzzy state space [0, 1], which is therefore suitable to characterize a gradual physical degradation. Moreover, in profust reliability theory, fuzzy state transitions can also help to describe the health evolution of a component or a system. Accordingly, this paper proposes a profust reliability based PHM approach, where the profust reliability is employed as a health indicator to evaluate the real-time system performance. On the basis of the health estimation, the system remaining useful life (RUL) is further defined, and the mean RUL estimate is predicted by using a degraded Markov model. Finally, an experimental case study of Li-ion batteries is presented to demonstrate the effectiveness of the proposed approach.

Controllability Analysis and Degraded Control for a Class of Hexacopters Subject to Rotor Failures

This paper considers the controllability analysis and fault tolerant control problem for a class of hexacopters. It is shown that the considered hexacopter is uncontrollable when one rotor fails, even though the hexacopter is over-actuated and its controllability matrix is row full rank. According to this, a fault tolerant control strategy is proposed to control a degraded system, where the yaw states of the considered hexacopter are ignored. Theoretical analysis indicates that the degraded system is controllable if and only if the maximum lift of each rotor is greater than a certain value. The simulation and experiment results on a prototype hexacopter show the feasibility of our controllability analysis and degraded control strategy.

A feedback based CRI approach to fuzzy reasoning

Fuzzy reasoning methods are extensively used in intelligent systems and fuzzy control. In our previous work, an explicit feedback mechanism is embedded into optimal fuzzy reasoning methods, and the resulting fuzzy reasoning methods are more robust than the optimal fuzzy reasoning methods. An interesting question is that, without the introduction of optimization goals, can the robustness of fuzzy reasoning methods be improved by embedding feedback mechanisms? This paper is intended to answer the question. By embedding feedback mechanisms into CRI approach, a new feedback based CRI (FBCRI) approach is proposed and three implementation methods with different strategies are obtained. Simulation results show that the feedback mechanisms are really useful for the improvement of the robustness of CRI methods. At last, to test the applicability of the proposed approach, it is applied to the solution of a real-time path planning problem for UAVs. The effectiveness and efficiency of an FBCRI based real-time path planning algorithm are verified by representative test examples, which show that embedding feedback information into the fuzzy reasoning process actually improve the quality of flight paths.

Time-domain analysis of the Savitzky-Golay filters

This paper proposes a time-domain method to analyze the estimation performance of Savitzky-Golay (SG) filters, which includes estimation performance of SG smoothing filters and SG differentiation filters. An estimation error bound is given and its qualitative properties are analyzed. Statistical properties of the estimation error in the presence of random noise are analyzed as well.

Coherent Systems in Profust Reliability Theory

Profust reliability theory is based on the probability assumption and the fuzzy-state assumption. In an attempt to provide a uniform foundation for profust reliability theory, in this paper we introduce the concept of coherent systems and distinguish two classes of systems: closely coherent systems and loosely coherent systems. To formulate the relationships between system reliabilities and component reliabilities, we present a number of general results, results concerning convexity, and results concerning unimodality. It is argued that for a coherent system, component reliability improvements don’t certainly enhance the system reliability.