Performance Evaluation Of Nonlinear Automated

Model Generation Approaches For High Level Fault

ModelingM. U. Farooq, L-K. Xia,F. A. Hussin

Pervasive systems research group

Department of Electrical and Electronics Engineering

Universiti Teknologi PETRONAS

Tronoh, Perak, Malaysia

Aamir Saeed Malik

Intelligent signal and imaging research group

Department of Electrical and Electronics Engineering

Universiti Teknologi PETRONAS

Tronoh, Perak, Malaysia

Abstract— It is known that automated model generation (AMG)

techniques are sufficiently mature to handle linear systems.

Other AMG techniques have been working reasonably well for

various levels of nonlinear behavior. However, most of the

modeling are performed under MATLAB environment. To be

more realistic, the models need to be translated into hardware

description language (HDL) models, such as VHDL-AMS or

Verilog-AMS models, to perform high level modeling (HLM) and

high level fault modeling (HLFM), which is a challenging task

due to its nonlinear behavior. In this paper, the capability of

System Identification (SI) based nonlinear AMG techniques is

investigated by converting MATLAB models into VHDL-AMS

models and to perform HLFM. Several faults are modeled

successfully in MATLAB environment using AMG. However,

they failed to perform HLFM when run in HDL simulator

SystemVision.

Keywords-component; HLFM; TLFM; Fault Modeling; Fault

Propagation; VHDL-AMS; Automated Model Generation.

I. INTRODUCTION

Rapid reduction in silicon chips feature size allows designers to encapsulate more complex mixed-signal designs into a single chip. Verification and testing prior to fabrication of integrated circuits (ICs) become more challenging due to their size and complexity. Furthermore, analogue test is very time consuming and expensive, with its cost dominating approximately 90 % of the whole testing cost in modern analogue and mixed-signals ICs [1]. As for digital circuits, mature test and verification methodologies are already available; unfortunately it is still a long way for analogue or mixed-signal circuits and systems. Intuitively, the simplest approach for verification of these circuits is to replace the original complex circuit with much simpler ‘model’ that is able to replicate the exact input-output characteristics of the original circuit. The purpose of focusing on complex systems here is that modern mixed-signal circuits contain may millions of transistors in a single chip, and efficient automated model generation (AMG) techniques are required that can generate a less complex model so that simulation speed at high level modeling (HLM) and high level fault modeling (HLFM) can be increased. The model generated is a mathematical description of the original circuit given in the form of differential algebraic equations (DAE). It offers more flexibility to model weak and strong nonlinear effects than simple nonlinear components, for instance, diodes, transistors

etc., used at circuit level, and also it can be easily converted into hardware description languages (HDL) such as VHDL-AMS or Verilog-AMS, or even in SPICE sub-circuits that can be used at the system level simulations [2]. These HDL models are being increasingly used in high level simulations since from last few years, as they are able to speed up transistor level simulations of complex circuits implemented in SPICE like environments [3].

The selection of AMG primarily depends on the type of systems available, i.e., linear time invariant (LTI), linear time varying (LTV), nonlinear time invariant (NLTI) or nonlinear time varying (NLTV). Several AMG techniques have been developed over the time for these types of systems [4]-[6]. A detailed survey on these techniques can be found in [3].

This paper is to investigate the modeling capability of existing nonlinear AMG techniques, because the techniques developed so far perform modeling of nonlinear systems accurately in MATLAB environment that is less realistic. None of them have been employed to perform HLM or HLFM by translating a MATLAB model into high level HDL model, which is more capable of modeling physical behavior of a circuit or system.

The existing techniques investigated during HLFM are a class of nonlinear AMG techniques, i.e., system identification (SI) based methods: Nonlinear Autoregressive with eXogenous input (NLARX) and Hammerstein-Wiener (H-W) techniques [5]. Several short faults are modeled using these nonlinear AMG techniques and are converted into VHDL-AMS models to perform HLFM. It is seen that SI based nonlinear AMG methods fail to perform HLFM under HDL environment.

The rest of the paper is structured as follows: section II provides an overview of nonlinear AMG techniques, and HLFM in section III; HLFM using SI based nonlinear AMG is introduced in section IV; experimental results and analysis of HLFM using nonlinear AMG techniques are presented in section V; section VI discusses the conclusion and the future work.

II. OVERVIEW OF SI BASED NONLINEAR AMG

TECHNIQUES

From last decade, major thrust of research for generating

AMG techniques is towards the nonlinear systems due to the

continued scaling of integrated micro-systems, the use of new

technologies, and aggressive mixed-signal designs that has

forced the designers to consider nonlinear effects for more

1842978-1-4577-2119-9/12/$26.00 c©2011 IEEE

accurate model representations. Nonlinearity is a fundamental

feature of any electronic block that provides signal gain, or

performs any function more complex than linear filtering [2].

Depending upon the nonlinearity severity level, nonlinear

systems are divided into two categories: weakly nonlinear and

strongly nonlinear systems.

Several techniques have been developed over the time

targeting different classes of nonlinear systems. SI based

nonlinear techniques such as: NLARX, NARMAX and H-W

model generation techniques mainly focus on nonlinear

control systems [5]. Other SI based nonlinear techniques are

also developed for electronic systems such as Situation

Dependent ARX (SDARX) [6], H-W model with feedback [7],

Compact Modelling (CM) approach for model generation [8]

and Multiple Model Generation System using Delta operator

(MMGSD) [9].

However, it is important to notice here that above

mentioned all nonlinear AMG techniques, except for

MMGSD, generate models for electronic system blocks in the

MATLAB environment. These MATLAB models may not be

unable to preserve laws of conservation such as KCL or KVL.

Also, one cannot utilize MATLAB models for system level

simulations, where models are integrated with SPICE level

sub-circuits to evaluate overall electronic systems. The reason

of incapability of MATLAB models is that they do not

incorporate electronics level details such as: input output

impedances, currents, offset voltages and power supply effects

etc. Hence, for mentioned nonlinear AMG techniques to be

effective, one needs to convert these MATLAB models into

HDL models to perform HLM or HLFM.

III. OVERVIEW OF HLFM

Analogue faults can be divided into two main types:

structural faults and parametric faults [10]. Structural faults

are random defects that cause structural deformations like

short and open circuits which change the circuit topology, or

cause large variations in design parameters (e.g., a change in

the W/L ratio of a transistor caused by a dust particle on a

photolithographic mask) [11],[12]. In a transistor such as MOS

transistor short faults include: gate-drain, gate-source, drain-

source shorts (GDS, GSS, DSS), and gate-oxide short (GOS);

open faults include drain/source opens (DOP, SOP) [13].

Parametric faults are caused by statistical fluctuations in the

manufacturing environment [14].

During the last few years, HLFM and High Level Fault

Simulation (HLFS) techniques have been proposed for modern

complex analogue and mixed-signal system design due to their

high speed [20]-[22]. HLFM are obtained by abstracting

faults from transistor level to a behavioural description of their

effects. Generally HLFM are either linear or nonlinear. Linear

models are mainly built with linear elements [18],[19],

whereas nonlinear models are structured with nonlinear

elements such as: diodes, transistors, and nonlinear controlled

sources. Authors in [18], [19] perform HLFM using linear

components to achieve speed up, but accuracy can be doubted

for these models when a nonlinear system is modelled [3].

Similarly authors in [20],[21] perform HLFM, but limitation

of their faults models is that they are developed manually

which is a tedious job. In such situations, nonlinear AMG

techniques can be employed to automatically generate

behavioural fault models from transistor level faulty circuits

and perform HLFM by converting behavioural model into

VHDL-AMS or Verilog-AMS model.

Authors in [9] demonstrate that behavioural models

generated using the AMG approach called Multiple Model

Generation System using Delta Operator (MMGSD) is able to

accurately model nonlinear behaviour, caused by structure

faults, not only in MATLAB environment but also

successfully perform HLFM using VHDL-AMS models. They

replace the faulty operational amplifier (opamp) with the

model generated by the MMGSD in a large system and

observe outputs utilizing transient analysis. Results show that

the models can handle both linear and nonlinear fault

situations with better accuracy than previously published

HLFMs. However, overall speed improvement is not achieved

significantly compared with TLFS, as high level simulator

struggles to implement multiple models and consumes more

CPU time. Furthermore, the HDL simulator [22] used is not

optimized for such logic. Therefore, alternative AMG

approaches are required that can increase HLFS time

compared with TLFS. In this context, two SI based nonlinear AMG techniques

i.e., NLARX and H-W model are used to observe if they are able to perform HLFM. The model structures of NLARX and H-W model are depicted in figure 1.

Fig. 1(a). NLARX model structure.

Fig. 1(b). Hammerstein-Wiener model

Fig 1. SI based Nonlinear AMG model structures [5]

Nonlinearity in both model structures can be estimated

using following functions: sigmoid network, tree partition,

wavelet network and neural network. In this paper, sigmoid

network is employed for NLARX model nonlinearity

estimator. For H-W model, sigmoid network is used for

modeling input nonlinearity and wavelet network is employed

for modeling output nonlinearity.

IV. HLFM USING SI BASED NONLINEAR AMG

To perform HLFM, a CMOS opamp shown in figure 2, is

utilized. The input stage is realized as a CMOS differential

amplifier using p- channel MOSFETs. The differential

amplifier is biased with the current mirror M13&M14. Three

Input

Nonlinearity

(f)

Linear Block

Output

Nonlinearity

(h)

w(t) x(t)u(t) y(t)

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 1843

NMOS diodes (M4, M5 and M6) are used to keep the gate to

source voltage of the current mirror small (VGS = -1.175V).

The output stage (M7 and M10) is a simple CMOS push-pull

inverter [9].

M4

M5

M6

M13 M14

M11 M12

M8 M9

CC

M10

M7

Vdd

Vss

In- In+

Out

2

1

4

4

12

12

11

5

8

3 0

6

9

IEE

Iref

Fig 2. Schematic of the two-stage CMOS opamp [9]

As there are 11 transistors in the opamp, there can be a total

of 33 short faults in the full circuit, with each transistor having

three faults. However, only one fault is analyzed at a time. To

generate training data for AMG, faulty opamp is used in an

open loop configuration and transistor level simulation is run

in high level simulator called SystemVision. Data capturing

processes is implemented through a special virtual bus

interface between Simulink and SystemVision that

communicate data through sockets. Input signal used to

generate the training data for AMG is an 80Hz, ±2.5V

waveform with 500mV PRBS superimposed on it for the

inverting input. PRBS has time interval of 10us. Similar

waveform with low frequency and same voltage levels is used

for noninverting input. Data is captured with sampling time Ts

of 10us.

MATLAB SI tool is then employed to generate NLARX and

H-W models. Nonlinearity estimator block in NLARX model

is based on the expansion shown in (1) [23].

cba QrxfPLrxxF111

)(()()( −−+−=

dQrxf cba nnn+−−+ ))((

(1)

where f (.) is the sigmoidnet function shown in (2).

1

1)(

+

=−

ez

zf (2)

Similarly, nonlinear function in H-W model is based on

sigmoid and wavelet functions expansion whose details can be

found in [5].

The estimated output yest is compared with the original

output y using (2) [24]. To get fit results in percentage, fit

equation is multiplied by 100.

)ˆ

ˆ1(*100

yy

yfit

yest

−

−

−= (3)

To perform HLFM, the MATLAB model is then converted

into a VHDL-AMS model based on the behavioural model

structure seen in figure 3 [9].

- ro

ri

+

gnd

Vin

AMG (Vo=f(Vin))

out

Voffin

Voffout

Vn

Vp

Fig. 3. Structure of the behavioral opamp model [9]

It comprises two linear resistors ri and ro that represent the

input impedance and output impedance, respectively; Voffin and

Voffout model input and output offsets respectively. Model from

AMG act as the voltage controlled voltage source (VCVS),

i.e., Vo = f (Vin).

A MATLAB routine is developed that automatically

converts MATLAB model into VHDL-AMS model called

Automatic Model Converter (AMC). This routine

automatically load model coefficients from MATLAB and

generate HLFM based on the model structure shown in figure

3. The nonlinear functions used in NLARX and H-W models

are implemented using sequential instructions i.e., for loop, in

MATLAB. Implementing this logic in VHDL-AMS can

degrade performance of HLFM in terms of simulation speed.

Therefore, AMC decompose these instructions into tiny

simultaneous multiply and add instruction, that are more

compatible with SystemVision environment. The discrete time

nature of NLARX and H-W are realized in VHDL-AMS with

the help of attributes such as ‘zoh and ‘delay [25].

V. EXPERIMENTAL RESULTS

To evaluate nonlinear AMG for HLFM, TLFS are run for

several faults. Considering the faults M5_gds1 and M9_gss

2

here, the input output data from open loop faulty opamp are

fed to NLARX and H-W AMG. NLARX model output for

fault M5_gds is shown in figure 4. It is seen that the outputs

match well with original fault data and model is 73.85 % fit

with original fault data. However, it should be noticed here

that model order is very high as 120 sigmoid layers are

employed for nonlinearity estimator.

It can be seen from above experimentation that NLARX has

limited capability of modeling strongly nonlinear faulty

behavior. To achieve accuracy more than 90 %, a weak

nonlinear behavior is generated using M9_gss fault. This time

the conditions on input signals used to generate training data

are changed.

1

Short between gate and drain on transistor 52

Short between gate and source on transistor 9

1844 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

Fig. 4. NLARX model output for m5_gds fault

The frequency of input waveform and PRBS is reduced and

input voltage for both the inverting and noninverting faulty

opamp is also reduced. NLARX model output for M9_gss

fault is shown in figure 5. It can be seen that percentage fit is

significantly improved from 75 % to 96.94 %.

Fig. 5. NLARX model output for m9_gss fault

An important conclusion that can be drawn from this

experimentation is that NLARX model is a good estimator for

weakly nonlinear signals, whereas its quality degrades

significantly for strongly nonlinear signals. However, it should

be noticed that in both cases discussed above, model order is

very high as more than 80 sigmoid layers are used in each case

to achieve best results.

Similar to NLARX, H-W model is also deployed to model

m5_gds fault. Model output can be seen in figure 6. Model

output is only 62.78 % fit with original fault data. Then H-W

model is tested with m9_gss fault. Model output, shown in

figure 7, is improved significantly from 62.78 % to 86.6 %.

Fig. 6. H-W model output for m5_gds fault

Hence, it is clear that both NLARX and H-W AMG

techniques are able to model weakly nonlinear faults more

accurately than strongly nonlinear faults.

Fig. 7. H-W model output for m9_gss fault

To perform HLFM, AMC is employed to convert MATLAB

models into VHDL-AMS models. To evaluate VHDL-AMS

models, a simple inverting amplifier circuit is used as shown

in figure 8. The gain of circuit is set to 2. Input waveform is a

1V sine wave with 25Hz frequency.

Fig. 8. Inverting amplifier circuit used for HLFM

Transient analysis in SystemVision is run to obtain HLFM

results. Comparing with TLFM output, unpredictable behavior

is observed at inverting amplifier output when VHDL-AMS

HLFM is employed. The results are shown in figure 9 for last

200ms.

Fig. 9. NLARX HLFM output for m5_gds fault

This unpredictable behavior is observed for both HLFM

generated using NLARX and H-W models. Major reason for

failure is that both AMG models are discrete-time. When these

models are used to perform HLM and HLFM, they may get

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 1845

contaminated with the effects of aliasing and severe phase

shifts for high frequencies [26]. Other reason includes the

failure of Newton-Raphson algorithm to converge to the

solution for nonlinear functions. As a result, high level

simulator ends up with the error of singular values in the

system matrices that become unsolvable [27]. Therefore, it is

realized that discrete time models generated by NLARX and

H-W AMG are not suitable to perform HLM and HLFM.

VI. CONCLUSION AND FUTURE WORK

In this paper the competency of nonlinear AMG techniques

is evaluated by converting the MATLAB models into more

realistic HDL high level fault models. We employed SI base

nonlinear AMG techniques (NLARX and H-W). It is seen that

both the techniques are able to model faults in MATLAB

environment with acceptable accuracy at the expense of highmodel orders. Unfortunately, both techniques fail to perform

HLFM using HDL due to their discrete-time model structure.

In the future work, an AMG will be developed that will

generate continuous time models to accurately handle both

weak and strong nonlinear faulty behaviours not only in

MATLAB environment, but also in HDL. In addition,

important issue of simulation speed up will be addressed and

focused.

ACKNOWLEDGMENT

This work was supported by the Fundamental Research Grand

Scheme (Ref: FRGS 2/2010/TK/UTP/03/8, Ministry Of High

Education (MOHE), Malaysia.

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