模糊+卡尔曼滤波.zip_卡尔曼滤波_寿命预测_寿命预测_寿命预测matlab_预测matlab

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卡尔曼滤波

寿命预测

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模糊+卡尔曼滤波.zip （27个子文件）

模糊+卡尔曼滤波

entrophy.asv 793B

可靠性曲线.asv 1KB

juece.m 4KB

position.m 700B

降半矩形.m 4KB

降半正态.asv 4KB

zuotu.asv 2KB

决策曲线2.fig 5KB

隶属函数.fig 18KB

决策曲线2.asv 3KB

决策曲线1.fig 9KB

降半梯形.m 4KB

降半矩形.asv 4KB

可靠性曲线.m 1KB

entrophy.m 398B

决策曲线1.m 2KB

降半正态.m 4KB

tool.mat 103KB

决策曲线2.m 3KB

可靠性曲线.fig 9KB

隶属度.m 869B

Fuzzy Reliability Estimation for Cutting Tools Based on State Space Model.docx 903KB

30步预测.fig 8KB

zuotu.m 2KB

隶属度.asv 869B

juece.asv 4KB

决策曲线1.asv 2KB

Fuzzy Reliability Estimation for Cutting

Tools Based on State Space Model

Shujie Liu, Chao Li, Hongchao Zhang

Sustainable Manufacturing Research Institute

Mechanical Engineering Academy, Dalian University of Technology

Dalian, China

liushujie@dlut.edu.cn

Abstract

A cutting tool is an important part of machine tools and its reliability influences the total manufacturing

effectiveness and stability of machine tools. The paper presents the application of state space model in

the cutting tools reliability assessment. As the single evaluation threshold is not easy to determine, the

paper puts forward the concept of fuzzy sets to solve this problem. The performance variable acquired

through feature extraction is used to fuzzify the states of the cutting tools and the degeneration state is

treated as a fuzzy event which is uniquely characterized by membership function. The deterioration of

the tool is seen as a stochastic dynamic process with continuous degrading and the deterioration

tendency is predicted by the Kalman filter algorithm. Fuzzy reliability is defined and the

condition-based replacement strategy is introduced. In the case study, the acoustic emission signal is

measured, and wavelet packet (WP) energy extracted from the acoustic emission signals is used to

estimate the tool state. The corresponding fuzzy reliability is calculated based on the distribution of the

forecasted state and a pre-set fuzzy membership function. The best time of when the tool should be

replaced is obtained from a cost model. The positive results show the plausibility and effectiveness of the

proposed approach, which can facilitate machine performance and reliability estimation.

Key words: Cutting tool, state space model, Kalman filter, fuzzy reliability, condition-based

replacement.

1Introduction

As an important part of CNC machine, cutting tools will be aging in the long-term operation. The

reliability of cutting tools influences the whole manufacturing effectiveness and stability of equipment.

The malfunction of machine tools may result in the halt of the whole production and bring about

tremendous financial losses. For example, in the case of complex installations such as automobile

assembly lines, it can be as high as $20,000 per minute. With an accurate estimate of tool lifetime,

worn tools can be changed in time to reduce waste product and tools costs noticeably. It is even

possible to guarantee a certain surface quality(Chen et al. 2011). Requirements for increased plant

productivity, safety, and reduced maintenance costs, have led to a growth in popularity of methods for

condition monitoring to aid the planning of plant preventive maintenance and operational policies.

Effective and reliable condition monitoring methods and procedures are seen as a means to achieve

high availability and reduce unscheduled production shutdowns(Gebraeel et al. 2009) .

Traditional approaches to reliability analysis of physical and other electro-mechanical products are

predominantly based on lifetime of large sample size. The degradations are significantly different from

one another even for the same type of equipment, and it is necessary to establish the forecasting model

for the deterioration process individually. Tool failure and lifetime is judged by its wear measurement

described in several standards (ISO3685, ISO8688 and ANSI/ASME B94.55M) [1]. Due to the

constraints of high cost, discontinuity and susceptibility to operational environment, the direct methods

are restricted to a very narrow range of applications and need to be improved. In indirect methods, the

wear state can be estimated by the cutting force, torque, temperature, acoustic emission and vibration

[2–4]. For individual condition, tool wear is a gradual process, and the working condition as well as the

future trend of the tool can be estimated and predicted through this kind of signals, which are known as

the data-driven approaches. These approaches attempt to derive models directly from collected history

data or performance data instead of building models based on failure mechanisms. Data-driven

approaches either use statistical methods, such as autoregressive models and stochastic process

techniques, or artificial intelligence tools, such as neural networks, support vector machines, and fuzzy

theory(Si et al. 2011).（可尝试补充文献）

In recent years, the state-space model is widely used to predict the reliability of mechanical

products. The establishment of the two equations provides a consistent modeling framework for

adequately describing the motion characteristics of the dynamic system.

Diego J. Pedregal developed a system for Condition Monitoring to carry out the maintenance of a

critical turbine. Estimation of the states of the system and extrapolation of failure probabilities are

carried out by the recursive algorithms associated to the State Space system (namely the Kalman

Filter and Fixed Interval Smoothing) [5]. Fausto Pedro applied unobserved component models to the

assessment of wear in railway points, set up in a State Space framework [6]. Anthony Stathopoulos

developed flexible and explicitly multivariate time-series state space models using core urban area

loop detector data for urban traffic flow modeling and prediction[7].

By establishing appropriate state space equations, the state in different time can be predicted, and

according to a predetermined state threshold, the reliability is regarded as the probability that the state

meets or exceeds the critical threshold. The traditional reliability theory emphasizes that the system

performance is either satisfactory or unsatisfactory randomly. However the system state transition

process is continuous, which means there is neither totally success state nor failure state, but a state

between success and failure. The fuzziness which is another respect of the uncertainty can’t be

ignored and the fuzziness implies the development and changes of things. The binary state model for

the reliability of components or the system is too simplistic and does not capture the reality for most

systems which can have many levels of performance. As the single evaluation threshold is not easy to

determine, and the paper puts forward the concept of fuzzy sets to solve this problem. Theory of state

space model with Kalman filter and fuzzy sets is proposed to model the behavior of the cutting tools.

Fuzzy reliability modeling is a generalization of the traditional binary state reliability modeling, which

can capture more realistic performance information of the system for its evaluation and decision

making processes.

The rest of the paper is organized as follows: The reliability assessment method based on state

space model is described in Section 2, including WP transform, state space model, kalman filter, fuzzy

reliability evaluation and a cost model. Section 3 reports the experimental setup and the results of the

application of the proposed approach to a case study of literature. Finally, some concluding remarks are

given in Section 4.

2 Fuzzy reliability estimation method based on state space model

2.1Wavelet packet decomposition

Given a finite energy signal whose scaling is assumed as

, wavelet packet(WP) transform can

decompose

into small subspaces

in dichotomous way. The dichotomous way is realized by the

following recursive scheme:

2 2 1

m n n

j j j

U U U j Z n Z

+ +

= Å Î Î

Where

( 0)j j £

is the resolution level and

denotes orthogonal decomposition.

denotes the

domain of integers.

denotes the domain of positive integers.

and

2 1n

are the three

close spaces corresponding to

( )

and

2 1

( )

satisfies the following equation:

2 2 1

( ) 2 ( ) (2 ) ( ) 2 ( ) (2 )

n n n n

k Z k Z

t h k t k t g k t k

y y y y

Î Î

= - = -

å å

Note that the first wavelet is the so-called mother wavelet function

0 1

( ) ( ) ( ) ( )t t t t

y j y y

= =，

The discrete filters

( )h k

and

( )g k

are quadrature mirror filter (QMF) associated with the scaling

function

( )t

and the mother wavelet function

( )t

. The sub-signal at

, the

th subspace on the

th level can be reconstructed by a linear combination of WP function

,j n

as follows:

, ,

( ) ( )

n j n j n

j k k

k Z

s t D t k Z

= Î

The WP coefficients

,j n

can be obtained from

, ,

( ) ( )

j n j n

k k

D f t t dt

+¥

-¥

Since the wavelet

( )

j k

is an orthogonal basis at

( )L Â

, the energy of the sub-signal

( )

s t

calculated by

, 2

| |

j n

n k

E D=

The normalized energy of

( )

s t

/ ( )

n n n

P E E=

2.2The state space model

The state space method is a time domain method and it adopts the concept of state variable. A state

space model is composed of an observation equation and a transition equation. The observation

equation describes the change rule of dynamic system state from a previous moment to the current and

the transition equation describes the relationship between the observed value and the state of the

system(Kalman 1960). The discrete state space model in general can be written as follows:

1 1 1 1

( , , , )

k k k k k

x f x u w

y h x u

q n

- - - -

(1)

Where

x Î ¡

is a vector of the state variables,

Î ¡

is a vector of the input variables,

Î ¡

is an unknown parameter vector,

y Î ¡

is a vector of the measured variables,

Î ¡

and

Î ¡

are process and measurement noise vectors. The process and measurement noise vectors have

the following properties:

[ ]E

[ ]

k k k

w w

[ ] 0

[ ]

k k k

E R

n n

A number of facts show that a non-stationary time series can be decomposed into trend

component, stochastic perturbation component, seasonal component, and irregular component (Harvey

and Peters 1990), that is:

( ) ( ) ( ) ( ) ( )Y t T t C t S t I t= + + +

(2)

The system’s deterioration, represented by the trend of the deterioration measure, is the component

featured by low frequency. In this research, an integrated random walk (IRW) model is adopted to

model the low frequency trend, which is represented by the following state-space model(Ng et al.

1988):

厂叔小陈

2024-03-13

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