A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system
Introduction
The configuration of an error detection and diagnosis mechanism (EDDM) for a fault-tolerant computer-controlled system has been described in the previous researches (Ting et al., 2002; Ting et al., 2004). The detection mechanism employs the hook process to capture the message in and between the various application programs (APs) and the operating system (OS), and detects whether the monitored AP is failed. Establishment of error classification and standardization was developed in the previous research (Lu et al., 2003). The diagnosis mechanism identifies the failure type and the location of error message, and makes predictable estimation on the executing APs. As been known, while the AP is failed, the OS of computer sends an error message with illustration of the failure event. However, most displayed error messages are difficult for the user to understand, letting alone for them to know the damage level, so that one can hardly deal with the failure appropriately. Also, when different APs are executed in the PC, there may be similar error message but with different error definition and illustration in different programming language (Inprise Corporation, 2002; Richter, 1999). Therefore, it is demanding to investigate how to unify the illustration of error message and examine the closeness degree of the same failure event but with different error description, so that a unified error knowledge database could be established, and then the error symptoms could be better inferred via the reasoning algorithm to acquire a final decision-making. The proposed EDDM, which is a fault-tolerant computer-controlled system, is designed and aimed to satisfy the above needs. Petri nets (PNs) is an ideal candidate for investigating and modeling of systems, and it can represent the inference process as a discrete-event dynamic system. The advantages of using PNs in rule-based systems include: (1) the graphical formalism, which can visualize the inference states step by step; (2) the transparent modeling, which has well-established formal mechanisms for modeling and structure inconsistency checking; (3) the analyzing capability, which can express dynamic and structural behaviors of a rule-based system via algebraic forms (Scarpelli et al., 1996; Tsang et al., 1999; Yang et al., 2003). The fuzzy PNs combines the graphical technique of PNs, the fuzzy sets theory, and the fuzzy production rule, so it has the advantage of the graphical power of PNs and the capability of fuzzy to model rule-based decision system effectively (Fay, 2001). Thus, fuzzy PNs would outperform the PNs and improve the efficiency of fuzzy reasoning (Yang et al., 1997). In general, fuzzy rule-based system consists of knowledge base, database of event facts, rule base, and inference engine. In order to deal with the input information from the non-fuzzy system, the fuzzy inference mechanism will carry on fuzzification, rule matching, and defuzzification in advance to allow the likely incomplete and imprecise information to match the antecedent proposition of the fuzzy rule and then obtain an inference result. Quite a few researches use PNs to construct the fuzzy rule-based system (Chen et al., 1990; Koriem, 2000; Chen, 2002). The input and output places of each transition in a PNs can be used to represent the knowledge of the antecedent and consequent propositions by the fuzzy production rule. Many researches have investigated on the extension of PNs to fuzzy PNs, and the modeling as well as the reasoning of fuzzy rule-based system. For instance, Gao et al. used the fuzzy reasoning PNs model to describe the production rule-based system and verify its performance as a diagnostic expert system on the turbine (Gao et al., 2003). Chen used fuzzy PNs to construct knowledge description and fuzzy reasoning, and developed a weighted fuzzy PNs method (Chen et al., 1990; Chen, 2002). Looney developed an algorithm of rule-based decision-making by using fuzzy PNs (Looney, 1998).
In this study, it is attempted to use the PNs, the fuzzy sets theory, and the fuzzy production rule to establish the fuzzy reasoning and verification Petri nets (FRVPNs) model for the diagnosis mechanism. The FRVPNs is designed based on the fuzzy rule decision tree (FRDT) with the merit of hierarchical structure. It provides different level of abstraction, which can be used to represent the sub-model construction and the rule decision for independent level of the FRVPNs. Regarding the efficiency of hierarchical design, it has been discussed in several research articles. For example, Delgado et al. proposed a multi-objective decision making scheme, allowing the evolutionary parameters based on a hierarchical genetic fuzzy system adjustable, so it not only improves the models performance (accuracy), but also guarantees the interpretability of the resulting fuzzy models (Delgado et al., 2002); Joo et al. also demonstrated a scheme of hierarchical fuzzy system with constraints on the fuzzy rules approximating with high accuracy and fewer fuzzy rules (Joo and Lee, 2005); Wang proposed a hierarchical structure in a fuzzy system achieving good approximation accuracy (Wang, 1999). According to these works, it is therefore believed that improvement of inference accuracy can be achieved by use of the hierarchical design.
Since different types of AP may have different definition of the failure event, it is likely to describe the error symptoms in terms of linguistic variables via the fuzzy set theory, and construct the inference contexts by use of the fuzzy production rule. The fuzzy production rule makes use of the “IF…THEN…” rule to describe the conditions of the antecedent and consequent propositions. The membership degrees (MDs) of the propositions on the fuzzy rule are calculated via the membership function (MF). Then, the damage level decision-making is determined by using the fuzzy reasoning method. In addition, the rule-checking process and the verification and modification module are included in the FRVPNs. The former one is used to confirm the correctness of the winning rule. The latter one is used to deal with the problem of redundancy, conflict, circularity, and incompleteness while new fuzzy rules are added. The rule verification and modification module will address in another article. Simulations are carried out with several sets of examples by using the developed FRVPNs and the fuzzy logic toolbox of MATLAB. As compared with the inferred results, both methods draw the same conclusions.
Section snippets
Fuzzy diagnosis reasoning structure of EDDM
The EDDM is proposed for a fault-tolerant computer-controlled system and is a middleware structured in and between the user applications of the user mode and the kernel mode for error detection and diagnosis of the AP. The EDDM consists of the retrieve process, the detection mechanism, the diagnosis mechanism, the information record database, and the knowledge base (Ting et al., 2004). Several important parameters such as the total central processing unit (CPU) usage (TCPUU), process CPU usage
Definition of fuzzy sets and linguistic variables
The input variables of the antecedent proposition considered for the fuzzy rule include the TCPUU, the PCPUU, the TMU, the HT, and the EHL. The output variables of the fuzzy reasoning include the response time (RT) and the damage level decision-making (DLDM). In reference to Negnevitsky (2002), linguistic value, notation and normalized numerical range of the linguistic variable are included in the fuzzy rule and illustrated in Table 1. The values of linguistic variables are fuzzified to obtain
Structure and modeling of FRVPNs
In Fig. 2, Fig. 3, an example of a two-level FRVPNs including the rule-checking process as well as the verification and modification module is presented. The proposed FRVPNs is constructed based on the FRDT with the merits of hierarchical design and PNs technique. It uses the rule-checking transitions and places to confirm the correctness of the firing rule so as to protect the accuracy of inference result of the winning rule. The verification and modification module is another important
FRVPNs reasoning strategy
As illustrated in Fig. 6, the examples of FR1 and FR2 are used to describe the FRVPNs modeling and the dynamic reasoning behavior. Fig. 6(a) shows the contents of the fuzzy rule in the Level_I and Level_II. Fig. 6(b) shows part of the FRVPNs model by means of the PNs technique. Fig. 6(c) shows the dynamic reasoning behavior of the rules FR1 and FR2. The properties of the proposition set of places and the firing transitions are described as follows:
- (1)
and : represents the
Simulations
As shown in Fig. 2, Fig. 3, the fuzzy rule base of the reasoning processor in the EDDM is constructed of two levels in this study. The measurement values [TCPUU, PCPU, TMU, HT, EML]=[73%, 33%, 65%, 10.5 s, 72%], are assumed to be the inputs variables to the antecedent propositions of FRVPNs model, which is the example_1 with the inference results in the Level_I and Level_II listed in Table 2. With this example, the reasoning process is described in detail through the following steps.
Step 1.
Conclusions
In this article, the fuzzy set theory and the fuzzy production rule method are used to establish the fuzzy rules for the failure events of the AP. The proposed FRVPNs is designed based on the FRDT in association with the PN technique, and constructed with the rule-checking process as well as the verification and modification module. The computational complexity (Chen et al., 1990; Gao et al., 2003; Kungas, 2005) is defined by O(ptl) and determined by the number of p, t and l, where p and t are
Acknowledgment
This research is supported by NSC89-TPC-7-033-009 & NSC88-2212-E-033-018.
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