Zhi-Jie Zhou

Weapon System Capability Assessment under uncertainty based on the evidential reasoning approach

Abstract Weapon System Capability Assessment (WSCA) is the initial point of quantification of capabilities in the military capability planning (MCP). WSCA is often a multiple criteria decision making (MCDM) problem with both quantitative and qualitative information under uncertain environment. In this paper, the analysis process and algorithm for WSCA problem is proposed on the basis of belief structure (BS) model and evidential reasoning (ER) approach which were developed to deal with various types of uncertainties such as ignorance and subjectiveness. First of all, the WSCA criteria hierarchy is built by analyzing how the capability is measured. Secondly, a weapon system capability model is formulated using BS. Thirdly, both qualitative and quantitative information involved in capability measure are transformed into BSs by the data transformation algorithm based on rules. Then, the analytical ER approach is used to aggregate the capability measurement information from sub-capability criteria to top-capability criterion, and the assessed weapon systems are ranked and analyzed according to utility intervals. Finally, a case study of real Main Battle Tank capability assessment is explored to show the proposed process for WSCA.

A bi-level belief rule based decision support system for diagnosis of lymph node metastasis in gastric cancer

Lymph Node Metastasis (LNM) in gastric cancer is an important prognostic factor regarding long-term survival. As it is difficult for doctors to combine multiple factors for a comprehensive analysis, Clinical Decision Support System (CDSS) is desired to help the analysis. In this paper, a novel Bi-level Belief Rule Based (BBRB) prototype CDSS is proposed. The CDSS consists of a two-layer Belief Rule Base (BRB) system. It can be used to handle uncertainty in both clinical data and specific domain knowledge. Initial BRBs are constructed by domain specific knowledge, which may not be accurate. Traditional methods for optimizing BRB are sensitive to initialization and are limited by their weak local searching abilities. In this paper, a new Clonal Selection Algorithm (CSA) is proposed to train a BRB system. Based on CSA, efficient global search can be achieved by reproducing individuals and selecting their improved maturated progenies after the affinity maturation process. The proposed prototype CDSS is validated using a set of real patient data and performs extremely well. In particular, BBRB is capable of providing more reliable and informative diagnosis than a single-layer BRB system in the case study. Compared with conventional optimization method, the new CSA could improve the diagnostic performance further by trying to avoid immature convergence to local optima.

A cooperative belief rule based decision support system for lymph node metastasis diagnosis in gastric cancer

Lymph Node Metastasis (LNM) has become one of the most important prognostic factors regarding long-term survival in gastric cancer. As it is difficult for doctors to integrate multiple factors for a comprehensive analysis, Clinical Decision Support System (CDSS) is used to help the analysis. In this paper, a new Cooperative Belief Rule Based (CBRB) prototype CDSS is proposed. CBRB consists of two independent Belief Rule Base (BRB) systems and the final output is combined by the Evidential Reasoning (ER) approach. A corresponding new Cooperative CoEvolutionary Algorithm (CCEA) is proposed to train the proposed CBRB model that is nonlinear. A case study demonstrates that the proposed CDSS prototype can obtain the better performance than other CDSS.

Hidden Behavior Prediction of Complex Systems Under Testing Influence Based on Semiquantitative Information and Belief Rule Base

Compared with the observable behavior, it is difficult to predict the hidden behavior of a complex system. In the existing methods for predicting the hidden behavior, a lot of testing data (usually quantitative information) are needed to be sampled. However, some complex engineering systems have the following characteristics: 1) The systems cannot be tested periodically, and the observable information is incomplete; 2) the change process of hidden behavior may be affected by the test; and 3) only part of quantitative information and qualitative knowledge (i.e., semiquantitative information) may be obtained. These characteristics all related to the test are named as testing influence for simplicity. Although a model and a corresponding optimal algorithm for training the model parameters have been proposed to predict the hidden behavior on the basis of semiquantitative information and belief rule base (BRB), the testing influence has not been considered. In order to solve the above problems, a new BRB-based model, which can use the semiquantitative information, is proposed under testing influence in this paper. In the newly proposed forecasting model, there are some parameters of which the initial values are usually assigned by experts and may not be accurate, which can lead to the inaccurate prediction results. As such, an improved optimal algorithm for training the parameters of the forecasting model is further developed on the basis of the expectation-maximization idea and the covariance matrix adaption evolution strategy (CMA-ES). By using the semiquantitative information, the proposed BRB-based model and the improved CMA-ES algorithm can operate together in an integrated manner so as to improve the forecasting precision. A case study is examined to demonstrate the ability and applicability of the newly proposed BRB-based forecasting model and the improved CMA-ES algorithm.

Identification of uncertain nonlinear systems: constructing belief rule-based models

The objective of this paper is to construct reliable belief rule-based (BRB) models for the identification of uncertain nonlinear systems. The BRB methodology is developed from the evidential reasoning (ER) approach and traditional IF–THEN rule based system. It can be used to model complicated nonlinear causal relationships between antecedent attributes and consequents under different types of uncertainty. In a BRB model, various types of information and knowledge with uncertainties can be represented using belief structures, and a belief rule is designed with belief degrees embedded in its possible consequents. In this paper, we first introduce the BRB methodology for modelling uncertain nonlinear systems. Then we present a comparative analysis of three BRB identification models through combining the BRB methodology with nonlinear optimisation techniques. The novel BRB identification models using l8-norm and minimising mean uncertainties in belief rules (MUBR) show remarkable capabilities of capturing the lower and upper bounds of the interval outputs of uncertain nonlinear systems simultaneously. Trade-off analysis between identification accuracy and interval credibility are briefly discussed. Finally, a numerical study of a simplified car dynamics is conducted to demonstrate the capability and effectiveness of the BRB identification models for the modelling and identification of uncertain nonlinear systems.

Hidden Behavior Prediction of Complex Systems Based on Hybrid Information

It is important to predict both observable and hidden behaviors in complex engineering systems. However, compared with observable behavior, it is often difficult to establish a forecasting model for hidden behavior. The existing methods for predicting the hidden behavior cannot effectively and simultaneously use the hybrid information with uncertainties that include qualitative knowledge and quantitative data. Although belief rule base (BRB) has been employed to predict the observable behavior using the hybrid information with uncertainties, it is still not applicable to predict the hidden behavior directly. As such, in this paper, a new BRB-based model is proposed to predict the hidden behavior. In the proposed BRB-based model, the initial values of parameters are usually given by experts, thus some of them may not be accurate, which can lead to inaccurate prediction results. In order to solve the problem, a parameter estimation algorithm for training the parameters of the forecasting model is further proposed on the basis of maximum likelihood algorithm. Using the hybrid information with uncertainties, the proposed model can combine together with the parameter estimation algorithm and improve the forecasting precision in an integrated and effective manner. A case study is conducted to demonstrate the capability and potential applications of the proposed forecasting model with the parameter estimation algorithm.

A model for online failure prognosis subject to two failure modes based on belief rule base and semi-quantitative information

As one of most important aspects in condition-based maintenance (CBM), failure prognosis has attracted an increasing attention with the growing demand for higher operational efficiency and safety in complex engineering systems. Currently there are no effective methods for predicting the failure of a system in real-time by using both expert knowledge and quantitative information (i.e., semi-quantitative information) when degradation failure and shock failure are dependent and competitive. Since belief rule base (BRB) can model the complex system when semi-quantitative information is available, this paper focuses on developing a new BRB based method for online failure prognosis that can deal with this problem. Although it is difficult to obtain accurate and complete quantitative information, some expert knowledge can be collected and represented by a BRB which is an expert system essentially. As such, a new BRB based prognosis model is proposed to predict the system failure in real-time when two failure modes are dependent and competitive. Moreover, a recursive algorithm for online updating the parameters of the failure prognosis model is developed. Equipped with the recursive algorithm, the proposed prognosis model can predict the failure in real-time when two failure modes are dependent and competitive. An experimental case study is examined to demonstrate the implementation and potential applications of the proposed online failure prognosis method.

Condition-based maintenance of dynamic systems using online failure prognosis and belief rule base

Condition-based maintenance has attracted an increasing attention both academically and practically. If the required physical models to describe the dynamic systems are unknown and the monitored information only reflects part of the state of the dynamic systems, expert knowledge is a source of valuable information to be used. However, expert knowledge is usually in a qualitative form, and therefore, needs to be transformed and combined with the measured characteristic information to provide effective prognosis. As such, this paper focuses on developing a novel approach to deal with the problem. In the proposed approach, a belief rule base (BRB) for the failure prognostic model is constructed using the expert knowledge and the analysis of the failure mechanism. An online failure prognostic algorithm is then proposed on the basis of the currently available characteristic variable information. The failure prognostic model is finally used in a condition based decision model to support the replacement decision of the dynamic systems. A case example is examined to demonstrate the implementation and potential applications of the proposed failure prognostic algorithm and the condition-based replacement model.

A new BRB based method to establish hidden failure prognosis model by using life data and monitoring observation

It is important to predict the hidden failure of a complex engineering system. In the current methods for establishing the failure prognosis model, the qualitative knowledge and quantitative information (life data and monitoring observation) cannot be used effectively and simultaneously. In order to predict the hidden failure by using the qualitative knowledge, life data and monitoring observation, a new model for hidden failure prognosis is proposed on the basis of belief rule base (BRB). In the newly proposed model, there are some unknown parameters whose initial values are usually given by experts and may not be accuracy, which may lead to the inaccuracy prediction. In order to tune the parameters of the failure prognosis model according to the life data and monitoring observation, an optimal algorithm for training the parameters is further developed on the basis of maximum likelihood (ML) algorithm. The proposed model and optimal algorithm can operate together in an integrated manner to improve the precision of failure prognosis by using the qualitative knowledge and quantitative information effectively. A case study is examined to demonstrate the ability and potential applications of the newly proposed failure prognosis model.

Construction of a new BRB based model for time series forecasting

It is important to predict the future behavior of complex systems. Currently there are no effective methods to solve time series forecasting problem by using the quantitative and qualitative information. Therefore, based on belief rule base (BRB), this paper focuses on developing a new model that can deal with the problem. Although it is difficult to obtain accurately and completely quantitative information, some qualitative information can be collected and represented by a BRB. As such, a new BRB based forecasting model is proposed when the quantitative and qualitative information exist simultaneously. The performance of the proposed model depends on the structure and belief degrees of BRB simultaneously. Moreover, the structure is determined by the delay step. In order to obtain the appropriate delay step using the available information, a model selection criterion is defined according to Akaikes information criterion (AIC). Based on the proposed model selection criterion and the optimal algorithm for training the belief degrees, an algorithm for constructing the BRB based forecasting model is developed. Experimental results show that the constructed BRB based forecasting model can not only predict the time series accurately, but also has the appropriate structure.