A Case-based Reasoning with Feature Weights Derived by BP Network

Yan Peng 1,2, Like Zhuang2 1 College of Information Engineering, Capital Normal University, Beijing 100037, China

2Ahead Software post-Doctor Scientific Workstation, Beijing 100041, China

pengyanpy@163.com

Abstract

Case-based reasoning (CBR) is a methodology for problem solving and decision-making in complex and changing environments. This study investigates the performance of a hybrid case-based reasoning method that integrates a multi-layer BP neural network with case-based reasoning (CBR) algorithms for derivatives feature weights. This approach is applied to Fault Detection and Diagnosis (FDD) system involves the examination of several criteria. The correct identification of the underlying mechanism of a fault is an important step in the entire fault analysis process. The trained BP neural network provides the basis to obtain attribute weights, whereas CBR serves as a classifier to identify the fault mechanism. Different parameters of the hybrid methods were varied to study their effect. The results indicate that better performance could be achieved by the proposed hybrid method than that using conventional CBR alone. 1. Introduction

As a significant branch of Artificial Intelligence (AI), Case-Based Reasoning (CBR) has received more and more research attention[1]. CBR are both analogous reasoning method and study machine-made, and it combines reasoning and study, let them both become a unit and provide a sort of new methodology for us that is the expert system of close to the human thinking model’s structure. CBR is an analogical reasoning method, which solves problems by relating some previously solved problem or experience to a current unsolved problem to form analogical inferences for problem solving [2]. The key factors affecting the performance of the retrieval mechanism are representation, indexing and similarity metric[3].

However, although CBR is simple in principle, and has been successfully used in engineering problem solving, it still lacks a generally theoretically sound framework[1]. Recently, several methodologies have

been put forward for using the connectionist approach (Artificial Neural Networks (ANN)) in CBR system design [4, 5], and some relating examples in engineering applications have been reported [6–9]. Domains that use the case-based reasoning technique are usually complex. Hybrid CBR and ANNs are a very common architecture for applications to solve complicated problems[10]. Knowledge may first be extracted from the ANNs and represented by symbolic structures for later use by other CBR components.

In majority situations the feature properties of a case are composed of both the feature itself and its weights. So both the choice and confirmation to case feature and the right cluster is the basic of building cases, and they also the two main content of case study. According to the discussion between the feature of network model and the concrete study above mentioned, we can appear clearly that neural network would helpful in adjust the connecting weights among the nerve cells, so, we may use ANN model to help resolve the problem of feature weights. This paper uses BP (back propagation) network generate feature weights of the past cases and improve conventional CBR which spends too much time fining similarities between new case and each past case and comes out with too many similar cases causing inaccuracy of diagnosis results in Fault Detection and Diagnosis(FDD) system, and discuss the case weights building approach during CBR retrieves similar cases.

The remainder of this paper is organized as follows. Section 2 presents the BP Network model. Section 3 depicts hybrid method that integrates BP with CBR and FDD problem description. In Section 4, the conclusion is presented. 2 BP Neural Network Model

BP (back propagation) network is one of the most common network models. It is a sort of forward feedback network of owning layer structure. It includes one input layer, one output layer and a lot of connotative layer. Its capability advantage appears mainly in the aspects of model matching, model classifying model recognition, model analysis and so

Workshop on Intelligent Information Technology Application

0-7695-3063-X/07 $25.00 © 2007 IEEEDOI 10.1109/IITA.2007.98

26

on. BP network learns by example, that is, we must provide a learning set that consists of some input examples and the known-correct output for each case, its basic idea is as follow:

It considers the error’s square of neural network anticipant output value and the network actual output value as the goal function of the study (also called the error function), according to the minimum rule to adjust the network weight, finally this let the goal function reach the minimum or permitted bound. Therefore, we define the objective function as follows:

(1) Where k means dispersing event variable, w means

the vector composed of all weights of the network, Y（k）means anticipated network output value, Y(W，k) means the actual output value of the network, ‖·‖ means the variable’s Euclidean pattern number.

The neural network study method of facing case weights which this article proposes is a process that is to take the neural network technology to use in the process of case structure, which it use to resolve the confirmation question of the case weights, this provides an effect path to case study. 3. The BP Learning for Case Weights According to the discussion between the feature of network model and the concrete study above mentioned, we using BP network model to process the case feature value There are two stages: First is learning stage, which also means to build BP network model, and using this model to educate this swatch may gain the study result; Second is the exchanging weight stage, in this stage it will transfer the nerve cells value in the study result to the case feature value. 3.1 Establishment of BP Network Model

The main content to build BP network model is the model structure, it includes a lot of main factors, such as the number of network layers, the number of the nerve cells every layer, delivering function of the nerve cell and so on.

According to Kolmogorov theorem and consider synthetically many sorts of factors, such as the computing complexity and rapidity, astringency and the generality ability of the model, the number of network layers we choose is three generally. But to the delivering function of the nerve cells, we choose dissymmetrical sigmoid function as follows:

(2) Where a=1.716, b=2/3, Thus, the rest critical

question is the confirmation of the number of the nerve cells every layer, especially the number of the connotative layers’.

In the fault diagnosis system, the case is built to some concrete fault. A fault usually has two basic features, which are fault result and the reason of generate fault. The fault result is the exterior representation form, the influence and means to outside of the fault; the reason of the fault is the interior factor and outside condition of leading the fault. The reason of fault is determinative factor of confirming and knowing the character of the fault, and is also the base of deciding to eliminate fault and the method of dealing with fault so it becomes the main content of record and expressing in the fault case. In the actual fault diagnosis process, so as to be convenient for observation, disposal and expression, we usually need to analyze and subdivide the reason of the fault, and finally analyze it to become the concrete parameters or index which are observed and measured by us, which makes the reason of the fault become the concrete quantity and index. So, we take each parameter or index to call a fault character.

To analyze the reason of the fault may appear that the structure of a fault can be expressed as Fig.2 shown the” feature-reason-result” hiberarchy model. In this model, it will take the expressing object to be analyzed layer upon layer from the common model of high hierarchy to the concrete special model of low hierarchy. When the hierarchy is higher, the model conception is more abstract; when the hierarchy is lower, the model conception is more concrete. The high hierarchy model is further abstract of the low hierarchy.

07-3-3Subtitle Fault Result

Fault Reason

Fault Feature Figure2. Fault Hierarchy “Result-Reason-

Feature” So, this structure model may reflect clearly the

structure character and quality of the fault. Fig.3 shows the fault hierarchy “result-reason-feature” of oil supply.

Oil Supply

Fault

Oil StorageFault

Oil PumpFault

OilRefrigeration

Fault

PowerPressure

PowerCurrent

... OilPressure

Flux Figure 3. Fault Hierarchy Analysis Model of Oil

Supply From this structure we can see that each reason that

leads the occurrence of the fault is the result of a group of the fault feature operating together, it generalizes the group of fault feature, and is the same as the pick-

27

up machine of the fault feature. Thus, we can depict and describe directly the quality of the fault through the fault feature so as to leave out the middle layer (the fault reason) of the structure. So, in the fault testing and diagnosis system, the feature of the case can be looked upon as the configuration record and expression of the fault character (gather) in “feature-reason-result” model (Fig.4 shown), in another word, the feature of the case is the fault character (gather).

…

07-5-5Subtitle

r1 r2

rn

FaultFeature

FaultResult

Figure 4. Feature Map of Fault Case

Using the relation of the “feature-reason-result” structure model and the case feature of the case of the fault and the fault character gather may help to build the model of the PB network model. Concretely speaking, it is to accord to this model to make sure the number of the nerve cells every layer.

During to the structure model of fault, it can be sure that the count of case feature is the number of nerve cell in input layer. Each nerve cell matches a case feature, and the input value of nerve cell is equal to observation value. Towards to the output layer, the count of nerve cells is based on the number of cases which are needed to build. Concretely speaking, on the assumption that the training case expresses a same fault or case, (Each training case is a measure of the case feature) and then, the count of nerve cell is 1, and the expected value of output layer is just the digitized expressive value of fault estate. If the training case expresses some different faults and we need to build a number of cases based on the group of training case, the count of nerve cell must match the number of cases, and the expected value of output layer is just the digitized expressive value of different fault or different estates of a same fault. Towards to the hide layer, we can consult the above-mentioned fault structure model and combine the characters of the fault itself. And then we can compose or pile up case properties in a specifically combination mode which will form directly-observable or definitely-explainable fault reason. Finally, the number of the formative fault reason will be selected as the count of nerve cell in hide layer.

It can be seen in above-mentioned process that we have endued every never cell with a specifically actual-meaning in the process of nerve cell definition and confirmed the count of the nerve cells base on this process. In this way, we have combined the definition and count-selection of nerve cell (especially the nerve cells in hide layer) with practical problems compactly

and finished the definition process with guidance of practical model and definite explanative meanings. Consequently, we have decreased uncertain factors and blindness in operation and enhanced the pertinence of modeling process for actual problems. Contemporary, because each nerve cell has matched an explicable practical meaning, the explainablility of applied results, which produced by the NN-model is greatly advanced, and basis are provided for model training and proof-test. 3.2 Determine of Case-feature Weight The finally purpose of builds BP-model is to evaluate each feature value in the case based on the nerve cell weight value in the model. For that purpose, first, we researched the features in structure of BP-model and case-model and investigated the relationship between them. Sequentially, we confirmed the associated mode between them. Finally, we got the idiographic arithmetic, which realized the transform from nerve cell weight to case-feature weight.

In CBR System, fault feature is depicted in fault character. Towards case, fault feature is depicted in coincidence between fault character gather and fault endings which structurally showed in Fig.4. This graph show us that each fault feature in the case is related with fault ending directly and is one of the factors which affect fault ending directly. The weight was used to show quantification, the degree that fault ending effected by fault feature and the tightness between them. Then, the relation between fault feature and fault ending can be shown in Fig.5:

Figure 5.

To BP network model, according to the “feature-result-reason” structure model of the fault, each fault character (the input nerve cells) is related with the fault result (the output nerve cells) through different connotative nerve cells, and act on the fault result through the relevant connotative nerve cells, the relation among them can be represented as Fig.6:

Figure 6.

Speaking in this way, the fault character can be considered as the indirect influencing factor in BP network model. According to this, we believe that the nerve cells weight in the network model is a sort of analysis to the character value of the case, so the relation among them can be represented as follows:

(3)

28

In the formula above, ri,，j means the weight of the character i in the case j, wk,j means the connection weight between the connotative node k in the network and input node j, tj,k means the connection weight between the connotative node k and output node j.

And then, shall we calculate ri,，j concretely through wk,j and tj,k therefore, we consider the connection relation among the nerve cells in BP network model as an directional graph, in this graph, each nerve cell correspond to one node in the graph, the weight among the nerve cells can be considered as the connection strong value, the connection relation from input nerve cell fi passing the connotative nerve cell pj to output nerve cell ok structures a piece of path (Fig6.), and if it exists a piece of path between any input nerve cell and output nerve cell, this path will be sure uniquely. Thus, according to the above weight’s relation between both of the model, we can take the character value to define as the connection strong value (also called the connection strong value of the path) between fi and ok

in the graph (Fig.5 and Fig6 shown). So according to graph theory, the calculation formula is as follows:

(4) 4. Conclusions

The modeling approach and the case feature arithmetic based on ANN nerve cells weight proposed in this paper, which are the process of taking the neural network technology to apply in case building, so as to resolve the confirmation question of the case feature, which give an efficient way for case study. But with the limited of BP model itself that the approach exists following problems:

The convergence speed of the study arithmetic is very slow, its education usually needs several hundreds times’ or several thousands times’ iteration;

It exists is local minimum point in the objective function. From the view of the math, the process of BP study is a nonlinear optimization process, so it will encounter the most common problem of local minimum unavoidably in the process of optimizing, which dissatisfied us with the results of the study.

First, the artificial neural network technology features are introduced to the case learning process of the feature value in this chapter, which means BP neural network model is applied to the selection of the feature value, and in this process, based on the fault detection and diagnosis, using the general features and the expression of the fault in the case makes a more reasonable explanation to the actual physical meaning which the BP neural network model’s basic factors as

the number of the layers, nerve cells and so on stand for. Based on this, we propose the BP neural network model’s method and basic principle of choosing the number of the nerve cells each layer in the model building process. Finally, we propose the concrete arithmetic of taking nerve cell weight to become the feature value of the case. The ideas and the process of the network model’s model building in this chapter resolve preferably the trouble of confirmation of the number of the nerve cells, especially the number of the connotative nerve cells, -- because the confirmation of the number is due to be lack of the direction of the theory and only depends on mainly the experience of the research, which lead this trouble—they take the confirmation process of the number of the nerve cell to complete in concrete direction of the fault character. Acknowledgments.

This work is supported by Natural Science Foundation of China, under contract N0.60773130. And Foundation for University Key Teacher by the Beijing Education Commission. References [1] Daqing Chen and Phillip Burrell Case-Based Reasoning

System and Artificial Neural Networks: A Review Neural Comput & Applications (2001)10: 264–276.

[2] Kolodner, J. L. (1991). Improving human decision making through case-based decision aiding. AI Magazine, 12(2), 52–68.

[3] Buta, P. (1994). Mining for financial knowledge with CBR. AI Expert, 9(2), 34–41.

[4] Becker L, Jazayeri K. A connectionist approach to case-based reasoning. Proc Case-Based Reasoning Workshop, Morgan Kaufmann, 1989; 213–217

[5] Thrift P. A neural network model for case-based reasoning. Proc Case-Based Reasoning Working, Morgan kaufmann, 1989; 334–337

[6] Main J, Dillon TS. A hybrid case-based reasoner forfootwear design. Case-Based Reasoning Research and Development: Proc 3rd International Conference on Case-Based Reasoning, Springer-Verlag 1999; 497–509.

[7] Myllymaki P, Tirri H. Massively parallel case-based reasoning with probabilistic similarly metrics. Proc 1st European workshop on Case-Based Reasoning, Springer-Verlag, 1993; 144–154.

[8] Micarelli A, Sciarrone F. A case-based systyem for adaptive hypermedia navigation. Proc European Work-shop on Case-Based Reasoning, Springer-Verlag, 1996; 266–279.

[9] Micarelli A, Sciarrone F, Ambrosini L, Cirillo V. A case-based approach to user modeling. Proc European Workshop on Case-Based Reasoning, Springer-Verlag, 1998; 310–321.

29