Bayesian Belief Network Model of a Xerographic Printing Process
Chunhui Zhong1 and Perry Y. Li2
Department of Mechanical Engineering,
University of Minnesota,
111 Church St. SE.
Minneapolis, MN 55455
EXTENDED ABSTRACT ACC’2000
Invited session on “Controls for Imaging and Printing”
Introduction
Our ultimate research objective is to develop control systems for xerographic printers / copiers
capable of generating high quality color prints despite system faults and component degradation.
Currently, a printer / copier merely shuts down when some components degrade or fail. The
diagnosis and the subsequent repair are done on site by a service personnel. Service calls are
costly to the service providers and machine downtime is a productivity loss for the customers.
Productivity loss can be minimized if the machine can remain available albeit at a degraded
quality. In this case, the machine has to reconfigure its control according to the fault or
degradation so that the system can operate as best as it can in the degraded state. This feature is
especially important for production print jobs with tight schedule or for walk-up users who often
need immediate access. The ability to diagnose faults and to determine the extent of the
degradation of the components is critical to realize this feature. A printer / copier that has the
ability to self diagnose can also decrease the service cost. For example, the duration of each
service call can be minimized, or in the event that customers can carry out the repair themselves
(e.g. by replacing some easily accessible components), the service call will not be needed at all.
In this paper, we describe the development of a Bayesian Belief Network (BBN) model of the
xerographic printing process. It is intended for the diagnosis of system faults and component
degradation and eventually for the reconfiguration of the control system to operate under
degraded conditions.
Bayesian Belief Networks (BBN)
In the xerographic process, the number of sensors are finite so that system faults or component
states cannot usually be directly detected and must be inferred from observations. These
observations may be produced from many sets of fault conditions. The diagnostic problem is to
determine the set of fault states and / or component degradation that best explain the observations.
A Bayesian Belief Network (BBN) is a compact representation of the joint probability
distribution of the various variables that describe the fault conditions and the component states.
Formally, it is a acyclic directed graph with nodes representing the observed or unobserved
system variables, and with the arcs representing the conditional probabilities of the values of the
children nodes given the values of their parent nodes. The network can be used to represent the
1
2
Graduate student. Email: zhongch@me.umn.edu
Assistant Profess and coressponding author. Email: pli@me.umn.edu
generic knowledge of a domain expert, and to function as a computational architecture for storing
factual knowledge and manipulating the flow of knowledge in the network structure. Diagnostic
inference is performed by the application of Bayes rule in probability theory. The graph structure
(hence the assignment of the causal relationship between variables) in the network significantly
reduces the storage required for the joint probability distribution, and the computational burden
associated with the inference process.
In our research, Bayesian network is used to model the xerographic process. This choice is
because BBN is a probabilistic framework with a firm theoretical foundation (probability theory,
and Bayes theorem), and it is computational feasible for use in real time. A probabilistic
description of the system is preferred to deterministic models in which knowledge is represented
in logical form because
1. model uncertainty and sensor noise etc. can be accounted for;
2. it is possible to assign ranking and trust worthiness to the various diagnosis, each individually
can explain the observations;
3. conflicting observations, such as during intermittent faults, can be accommodated;
4. the information content (or worthiness) of various diagnostic tests can be evaluated.
BBN Model of a Printing System
The central component in a xerographic printing process is the photoreceptor which functions as a
staging area where a toner image is first built up before being transferred to the paper. The
density profile of the toner image on the photoreceptor, which is critical to the quality of printing,
is dependent on the behaviors of following subsystems: 1) charging, 2) exposure, 3) development,
and 4) transfer and 5) fusing.
A simple Bayesian network model describing the charging, exposure, development subsystems
and their interactions have been developed based on physical models [1][2]. These three
subsystems sequentially interact with the photoreceptor to determine the toner density profile on
the photoreceptors. There are also sensors and actuators associated with them. In addition these
three systems, the toner charging process, which is critical to the development process is also
included in our model. Because the transfer and fusing systems do not currently have sensing or
actuation capability for the control of the printing process, these two subsystems are excluded in
our current model.
The directed graph structure of the subsequent model is shown in Figure 1. In this model,
ancestral variables (i.e. those variables with no parents) whose values can be deterministically
assigned are the control variables; other ancestral variables whose values cannot be
deterministically assigned are sources of disturbances when they deviate from their nominal
values. The conditional probabilities in the model (i.e. the strengths of the arcs) are obtained via a
combination of physical modeling and the uncertainty modeling.
The above Bayesian network has been implemented on HUGIN, a commercial software for the
simulation of Bayesian networks. Experimentation using this system is currently underway.
Several diagnostic examples will be presented in the full paper.
References
[1] L.B.Schein, Electrophotography and development physics Springer-Verlag, 1988
[2] D. M. Pai and B. Springett, “Physics of Electrophotography,” Review of Modern Physics,
5:163-211, 1993
Charge
Control
variable
I0
C
Vg
Measured
variables

Vi
Vi

P0
Vs
Expose
T
Di
Vp
Toner
dynamics
Q

M
d
Develop
Vb
Do
Transfer and
fuse
Figure .1. Bayesian belief network model for a xerographic printing system