Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 130790, 14 pages

http://dx.doi.org/10.1155/2015/130790

## Diagnosis of Intermittent Faults in IGBTs Using the Latent Nestling Method with Hybrid Coloured Petri Nets

^{1}Facultad de Ingeniería, Universidad EAN, Bogotá, Colombia^{2}Departamento de Ingeniería de Sistemas y Automática, Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain

Received 14 October 2014; Revised 26 December 2014; Accepted 6 January 2015

Academic Editor: GuanJun Liu

Copyright © 2015 Leonardo Rodriguez-Urrego et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a fault diagnosis application of the Latent Nestling Method to IGBTs. The paper extends the Latent Nestling Method based in Coloured Petri Nets (CPNs) to hybrid systems in such a manner that IGBTs performance can be modeled. CPNs allow for an enhanced capability for synthesis and modeling in contrast to the classical phenomena of combinational state explosion when Finite State Machine methods are applied. We present an IGBT model with different fault modes including those of intermittent nature that can be used advantageously as predictive symptoms within a predictive maintenance strategy. Ageing stress tests have been experimentally applied to the IGBTs modules and intermittent faults are diagnosed as precursors of permanent failures. In addition, ageing is validated with morphological analysis (Scanning Electron Microscopy) and semiqualitative analysis (Energy Dispersive Spectrometry).

#### 1. Introduction

Nowadays digital electronic applications [1], power electronics [2], and even PCB [3] introduce IF diagnosis techniques for the analysis of faults by corrosion, contamination, overtemperature, overloads, electrochemical migration, and defects in manufacturing. IF diagnosis allows the utilization of preventive maintenance routines instead of corrective maintenance, so system reliability is increased.

PSD and particularly IGBT are fundamental in many industrial systems. Some of the most important IGBT applications include lighting controls, power supplies, computer systems, industrial control devices, voltage converters [4], motors, or electric generators [5–7]. Recent studies about IGBT diagnosis focus on optimizing their properties as power inverter [8], as a switch [9], aging [10], thermal fatigue [11], or manufacturing defects [12].

IF diagnosis in PSDs can be applied to predict the onset of permanent failures. Moreover it can be used to detect persistent IF episodes that degrade the operation of the system and can be considered as a failure. IF diagnosis applied to PSDs under stress tests predict the wearing-out of the component and can be contrasted with the aging related damage or morphological changes on the physical structure of the component allowing for the validation of the proposed diagnosis model. Then IF diagnosis allows for the estimation of the wear out phase in the hazard rate curve of electronic devices and can be applied in preventive maintenance procedures [13].

Low power equipment is subjected to lower levels of energy during operation and gets discontinued before reaching the wearing-out stage. On the other hand, high power electronics equipment (IGBTs) is subjected to higher energy levels and faces wearing-out due to aging. The main objective of the paper is to show the relevance of the LNM to detect IF in IGBTs.

Different methods have been proposed to diagnose semiconductor faults [14]. In [15] a study to characterize the IGBT behavior under stress conditions using a SPICE model was introduced. The authors develop an IGBT test circuit and they tested it in two conditions: normal operation and under stress. It is important to note that this diagnosis does not allow predictive maintenance tasks.

In [16] it is discussed as a new method for IGBT fault detection based on gate voltage monitoring. This study takes into account only the degradation due to overcurrent or overtemperature. This analysis is very interesting and is taken into account for our prototype test development.

Another interesting work [17] shows different methods for the aging analysis, such as thermal cycling (TC), hot carrier injection on electrical stress, and dielectric breakdown of time-dependent stimulus. Two of these techniques are applied in our work as accelerated test methods.

The LNM was introduced by García et al. (2008) for the fault diagnosis in complex, large scale systems. LNM relies on CPNs as design platform and a method for nesting faulty marks in every place of the net. The formalization and methodology as well as some examples of the LNM can be seen in [18–21].

The LNM was developed to handle complex discrete event systems, but many systems can be better modeled with hybrid models. This paper will extend the LNM to hybrid systems so it could be applied to diagnose them.

Numerous studies have been carried out to explain hybrid process fault diagnosis using different methodologies [22–24]. New techniques need to be developed for diagnosis of Ifs, like the residual analysis proposed in our method.

Furthermore, some researchers [25] analyzed fault models in hybrid PNs. Other authors propose an approximation of differential places to represent continuous places with negative markings (differential PNs [26]) in each place of latent nesting faults in order to avoid unobservable transitions and allow faulty tokens of discrete type to be nested in places of continuous nature. The above provide advantages in solving hybrid systems of increasing complexity and finding failure times of each faulty token in the using the stay time.

IF diagnosis is carried out based on the work by [27] where the authors present a prognosis method to diagnose IF and predict the lifetime of electromechanical devices.

The paper is structured as follows. Section 2 introduces LNM for hybrid systems. It also includes a simple example to show its performance. Section 3 shows the IF diagnosis modeling based on LNM applied to IGBTs. Section 4 explains the test bench, the analysis, and experimental results. Finally, Section 5 draws some relevant conclusions.

#### 2. Latent Nestling Method in Hybrid Systems

##### 2.1. LNM Definition in Hybrid Systems

LNM is a methodology for fault diagnosis of discrete event complex systems (see [18, 20, 21]). Because this paper introduces a hybrid model for the IGBTs (presented in Section 3.2) we present an update of LNM to handle hybrid systems.

The diagnoser will be a hybrid model of the system including normal and faulty behavior of each device in the system. In order to avoid the combinational explosion, [19] the model is built using hybrid colored PNs.

A hybrid CPN for fault diagnosis (HCPNFD) is defined aswhere is a finite set of places, is a finite set of transitions and Pre and Post are the input and output arc functions, with an additional argument which is the color of the transition firing . Thus and correspond in the general case to a linear combination of token colours related to place .

These functions can be divided into two subsets, depending on the transition-type behavior, namely, normal transition or faulty transition where and are the fault and recovery transitions, respectively. is the initial marking. is the subset of fault latent nestling places, where . If includes a faulty token in . This is now called . is the subset of fault verification places.

The places set and transitions set can be divided into two subsets

is the set of discrete places and is the set of continuous places. is the discrete transitions set and is the continuous transitions set.

will represent discrete states of a device such that the device is on and off and is starting and stopping, and so forth.

will represent the continuous states of a device so it computes a differential equation model.

will represent a discrete state change.

will represent step execution of the model contained in a .

In addition, the normal behavior marks can have discrete or continuous nature:

will represent a normal behavior token of a device and its evolution through the diagnoser will show the device state.

is the colour set assigned to different identifiers. , where is the subset of coloured tokens representing the fault set.

Initial marking for a place in (called ) will be , and the initial marking for a place in (called ) will be . or , or . stands for the rational numbers (positives or zero). Then, for ,

Let be the input arc function corresponding to subset . Consider

Let be the output arc function corresponding to subset . In and case, the number of arc functions corresponding to subset of each depends on the continuous places mutually influenced, such that is the initial continuous place influenced and is the last continuous place influenced.

This represents a continuously variable behavior and also allows the nesting of discrete type faults.

: is a composite function that is defined for every place of the net.

: it is the hybrid states set in the analyzed system. This set is composed of the operating states OS, fault signatures , and recovery signatures .

: it is a delay function that associates a rational number to each timed transition, where if for a function , is a delay associated with the transition , expressed in time units, if for a function , , such that represents the maximum firing speed associated with the transition and is the firing frequency that represents the sampling time. The method for delay fixing or fixing the frequency firing depends on the system behaviour.

*Definition 1. *A normal discrete transition in a HCPNFD is enabled at a marking if each place in meets the condition:

*Definition 2. *A normal continuous transition in a HCPNFD is enabled at a marking if each place in meets the condition:where is the set of the input places of discrete and is the set of the input places of continuous . Likewise, it is necessary to meet the condition and , . .

##### 2.2. Initial Model and Fault Selection

The initial model is similar to that presented in the LNM. However, it includes continuous places where we could model the continuous behavior of the system variables. This step applies the techniques of modeling hybrid PNs [25].

According to [19], the sensors map is defined as sm: , where SR is the sensor readings, such that for marking the expression is given by , . In the discrete case is the set of sensor read output values for each discrete marking, such thatwhere , are subsets of expected and unexpected values accordingly.

##### 2.3. Latent Nestling Places and Trajectories of Fault Verification and Fault Recovery

Latent nestling places are defined by the LNM. However, in a hybrid system, there is a continuous place which represents an operating state during a certain time according to the states of the discrete places. Faults are assigned to this continuous place, such that . This implies that the faults have been generated by the anomalous behavior of the continuous variable, where the faults are nesting in the same continuous place now called owing to this hybrid character.

The trajectories of the faulty tokens are defined only by the fault and recovery transitions. The normal discrete and continuous transitions are defined by a classical method for modeling Hybrid PNs [25], as well as the firing rules for these transitions. Furthermore, fault and recovery transitions must be added to make restrictions that allow including both the place status as tokens of normal behavior.

*Definition 3. *A fault or recovery transition in a CPNFD or HCPNFD is enabled at a marking for discrete places if each place or in meets the condition: for fault transitions for recovery transitions Let be the fault marking obtained after firing of transition with respect to the fault signature . This fault marking is deducted from the marking by the following relation.

For fault trajectory,For recovery trajectory, is the last , is the initial continuous place influenced, and is the last continuous place influenced.

In the example case of Figure 3 we have for fault verificationAnd for fault recovery,To find the residues, it is necessary to obtain the operation dynamic model of the continuous variables. Depending on the complexity, the models could be represented in state variables, as in the hybrid PN analysis [26]. In this case, the approach presented in our example introduces a series of residues of the form in every continuous place. The residue is computed in the continuous place, while the residual evaluation is checked in each fault and recovery transition.

The definitions on states of hybrid operation, fault signatures, and diagnosability can be seen in [21].

#### 3. IFs Diagnosis Using the LNM Based on HCPNFD

##### 3.1. Temporal Modeling of IFs

The main purpose of diagnosing IFs is the generation of tools to perform preventive maintenance of devices in industrial systems. It becomes necessary to apply data obtained online to determine the best time to replace or repair a component. The basic idea is to employ prediction methods based on process fault information. This information is indicative of the deterioration that is suffering the component.

From this method we get two measures based on [27]: temporal failure density and pseudo period. Temporal failure density ( or density in the rest of the paper) is defined as the average time a particular fault is active within a sliding time window of duration . computed at time for failure is defined aswhere CNT is the number of faults inside the window, stands for the index of the first fault detected inside the window , and if it exists; otherwise and takes into account the duration of a failure occurred before which continues active inside the window. Therefore,

Equation (17) is valid only if is positive; otherwise , as this fact would indicate that the th failure time is completely outside of the window. In a real system, DF tends to increase with time, thus confirming the hypothesis that IFs progressively damage the faulty device. In our case we only apply this measure DF with the LNM.

##### 3.2. Initial Hybrid Model

For this case we will focus on a nonlinear model that represents the turn-on and turn-off switching waveforms and will get the and value that must have the IGBT. Some references that model different aspects of IGBTs and MOSFETs and the turn-on and turn-off waveforms can be seen in [28]. For each state (turn-on, turn-off) there are equations that define its operation.

For the turn-on these equations are as follows.

The increasing time constant from to is limited by

The decreasing time constant from to is limited bywhere is the voltage when it reaches the maximum collector current and is the voltage across the gate to the emitter of the transistor during conduction. The increasing time constant from to is limited by

The reverse transfer capacitance or is approximately equal to because the emitter is connected to ground. Then we will use in our final model.

Based on the equivalent circuit of the IGBT gate, the gate current is deduced by

Note that is directly affected by which causes a large change in gate voltage.

For the turn-off the equations are as follows.

falls from injected to with a time constant given by (21). At this time, there is no change in the values of or .

Then increases in this region, and the rate can be controlled with as shown in the equation below:

Then the value of is maintained at , while decreases at a rate defined by the following equation. The rate of increase can also be controlled with where is the input capacitance measured between the gate and emitter terminals with the collector shorted to the emitter for AC signals, . The value of these fixed capacitances can be found in the data sheet of the manufacturer.

###### 3.2.1. Hybrid Model Using Hybrid PNs

The hybrid model is implemented following the scheme of Figure 1. Continuous places and represent the ideal behavior of voltages and , respectively. The continuous place represents the load voltage as a function of the collector current. Transition represents the activation of the IGBT (turn-on) and transition shows the switch off the IGBT (turn-off).