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Journal ArticleDOI

A methodology for identification of narmax models applied to diesel engines

TL;DR: In this article, a nonlinear system identification methodology based on a polynomial NARMAX model representation is considered and algorithms for structure selection and parameter estimation are presented and evaluated.
About: This article is published in IFAC Proceedings Volumes.The article was published on 2005-01-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: System identification & Nonlinear system identification.

Summary (3 min read)

1. INTRODUCTION

  • Industrial applications present challenging problems to face when dynamic models are required for the control of nonlinear systems.
  • In model based control input-output nonlinear models can be either developed from physics principles or obtained from a system identification procedure.
  • A first classification can be done with respect to prior knowledge : “black-box models”are commonly defined as those models whose structure is chosen with no physical insight about the system.
  • The polynomial NARMAX model representation is a black-box nonlinear model set that can be applied to a wide class of nonlinear systems and that can be easily integrated in a simple parameter estimation and structure selection procedure.

2.1 NARMAX representation

  • The NARMAX representation is a well-known tool for nonlinear modeling which includes several other nonlinear representations such as blockstructured models and Volterra series.
  • The choice of a polynomial expression for the regressor is based on the possibility to derive nonlinear control algorithms for a nonlinear polynomial model as a direct extension of classic linear poleplacement control problem.

2.2 Input signal design

  • Input signal design is a very important step for nonlinear system identification.
  • As for the linear case, the input signal should be persistently exciting.
  • All the frequencies of interest for the system should be excited, and the input signal should cover the whole range of operation.
  • Small amplitude perturbing signals may be superposed to the different operating levels, exciting all dynamic modes of the system.
  • Different classes of signals can be employed for the identification process as multi-sine signals, maximum length binary sequences (MLBS) and classic pseudo-random signals.

2.3 Structure selection

  • If the values of ny, nu, ne and L are increased to obtain a good accuracy, an excessively complex model will result together with a numerical ill-conditioning.
  • Several techniques have been proposed in the literature for selecting the best model structure, some of these are enhancements of the ERR algorithm or are used in conjunction with it as in (Aguirre and BIllings, 1995; Piroddi and Spinelli, 2003).

2.5 Model validation

  • A statistical validation of the identified NARMAX model is performed with high order correlation functions defined in (Billings and Voon, 1986; Billings and Zhu, 1994) to detect the presence of unmodelled terms in the residuals of the nonlinear model.
  • It is necessary, in order to check the ability of the model to represent system dynamics, to validate the estimated model on a new set of data (validation data) different from the set used for the identification (learning data).
  • Model prediction ability has to be assessed, together with statistical tests, with signals that may catch system nonlinearities.
  • Triangular or step signals of different amplitude levels are ideal input signals used for time-domain model validation.

3. THE VGT TURBOCHARGED DIESEL ENGINE

  • Variable geometry turbochargers (VGT) are employed to achieve good boost at all speed conditions, with no lose in terms of efficiency and transient performances.
  • A pressure surge in exhaust manifold, in fact, has a detrimental effect for the engine acceleration performances.
  • A VGT is composed with adjustable vanes that can vary the effective flow area of the turbine, thereby affecting the compressor mass airflow in the exhaust manifold.
  • Examples of diesel engine models were presented in (Guzzella and Amstutz, 1998; Jankovic et al., 2000; Kao and Moskwa, 1995) to be used in the control design phase.
  • A polynomial NARMAX model is used in the identification algorithm, together with techniques for structure selection which preserve from overparametrization.

4.1 Simulation setup

  • The identification algorithm presented in the previous sections is applied to a high pressure direct injection (HDI) engine model simulated with The MathWorks Simulink environment.
  • For identification purposes the system could be seen as a SISO nonlinear black-box, as shown in Fig.2.
  • The input (V GT ) to the system is the command of the actuator that adjusts the angle of guide vanes placed to vary the incoming exhaust gas flow at the entrance of the turbine.
  • The identification algorithm is feeded with inputoutput data sets generated from several simulations in order to find a polynomial NARMAX model of the V GT–boost pressure nonlinear relation for different pairs (N,W ), that specify the operative conditions of interest for the engine.
  • Tables 1 and 2 resume all the different operating points for a full and 50% driver acceleration.

4.2 Excitation signal design

  • The signal used for the identification is, for all the operating points, a concatenated data set of small signals.
  • A sequence of increasing and decreasing steps describes the different regions of the VGT command, and small amplitude signals are superposed as excitation signals.

4.3 VGT–boost pressure Model identification

  • The first choice for the parameters ny, nu and L is based on step responses analysis to estimate dynamics and nonlinearity orders.
  • Tests for nonlinearity detection are presented in (Haber, 1985).
  • This means that the global nonlinear discrete time model, after a linearization, should provide a second order discrete time system.
  • On the basis of this model efficient but still robust nonlinear control algorithms can be directly applied.

4.4 VGT–boost pressure Model validation

  • Statistical and time-domain validations are employed to assess the model quality.
  • Fig.3 and Fig.4 show respectively model long-term prediction with validation data and step model validation with small and high amplitude data.
  • In these last two cases a step-sequence is applied to the identified model to verify that, for small and large variations in the input signal, the system output is matched from the nonlinear NARMAX model output.
  • The first step sequence is the same used to sweep input amplitude range in the identification data acquisition (△ = 5%), in the second one a larger amplitude variation is applied (△ = 15%).
  • This typical engine test confirm that the model is suitable to represent system dynamics in both input direction.

5. CONCLUSIONS

  • The availability of simple and control-oriented models is a key element in the phase of engine development and tuning.
  • An efficient solution to the modeling problem is represented by a black-box nonlinear identification via polynomial NARMAX models.
  • In this paper a practical identification procedure based on polynomial NARMAX modeling has been developed and applied to a HDI diesel engine.
  • Parsimonious nonlinear models have been derived in view of an efficient nonlinear control algorithms implementation.

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Citations
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Proceedings ArticleDOI
09 Nov 2015
TL;DR: A novel input design framework in terms of multi-sweep chirP signals is developed and airpath input channels are excited by designed chirp signals, and linear and nonlinear system identification methods are utilized to model NOx emissions with air path input channels.
Abstract: Stringent international regulations in terms of emissions necessitate more efficient transient calibration procedures for diesel engines which in turn implies utilization of dynamic models of the combustion process. In this paper, a novel input design framework in terms of multi-sweep chirp signals is developed and airpath input channels are excited by designed chirp signals. Linear and nonlinear system identification methods are utilized to model NOx emissions with airpath input channels. Experimental results show that while linear identification techniques provide poor performance in terms of training and validation fits, nonlinear models achieve remarkable performance in training and validation fits.

9 citations


Cites methods from "A methodology for identification of..."

  • ...A polynomial NARMAX representation is used for relation between the variable geometry turbine command and the intake manifold air pressure [12]....

    [...]

Book ChapterDOI
05 Sep 2018
TL;DR: The results show that the generated NARMAX model is good at describing the input-output relationship of energy prices, and works best with a low-order input regression parameter and linear polynomial degree.
Abstract: Energy prices are not easy to forecast due to nonlinearity from seasonal trends. In this paper a Nonlinear AutoRegressive Moving Average model with eXogenous input (NARMAX model) is created using nonlinear energy price data. To investigate if a short-term forecasting model is capable of predicting energy prices a model was developed using daily data from 2017 over a period of five weeks: observing 1 input lag prediction up to 12 input lag prediction for low-order polynomials (linear, quadratic, and cubic). Various input factors were explored (energy demand and previous price) with different combinations to observe which factors, if any, had an impact on the current price prediction. The results show that the generated NARMAX model is good at describing the input-output relationship of energy prices. The model works best with a low-order input regression parameter and linear polynomial degree. It was also noted that including energy demand as an input factor slightly improves the model validation results suggesting that there is a relationship between demand and energy prices.

4 citations

Journal ArticleDOI
TL;DR: In this paper , a nonlinear auto-regressive moving average model with eXogenous inputs (NARMAX) was used to identify key energy-related factors that influence hourly electricity price through prediction modelling.
Abstract: Electricity price prediction through statistical and machine learning techniques captures market trends and would be a useful tool for energy traders to observe price fluctuations and increase their profits over time. A Nonlinear AutoRegressive Moving Average model with eXogenous inputs (NARMAX) identifies key energy-related factors that influence hourly electricity price through prediction modelling. We propose to use a transparent NARMAX model and analyse Irish Integrated Single Electricity Market (ISEM) data from May 2019 until April 2020 to determine which external factors have a significant impact on the electricity pricing. The experimental results indicate that historical electricity price, demand, and system generation are the most significant factors with historical electricity price being the most weighted factor and the largest Error Reduction Ratio (ERR). A NARMAX model generated using correlated lags was also considered to identify key energy-related lag factors that influence the electricity price. For justification, the significant lag factors are included as inputs in a Seasonal AutoRegressive Integrated Moving Average model with eXogenous input (SARIMAX) to determine if model performance improves with refinement. To conclude, using the NARMAX methodology with energy-related input factors helps to determine the significant factors and results in accurate predictions of electricity price. • Hourly electricity price forecasting with a hybrid approach of statistical and regression models. • Key factors (electricity price, demand, and system generation) identified from regression model. • Peak correlated lags determined from autocorrelation testing. • Refinement with statistical model enhanced prediction accuracy and improved market performance.

4 citations

Proceedings ArticleDOI
01 Sep 2018
TL;DR: A NARMAX model with an input regression lag of one and previous price included generates the best day-ahead forecast of electricity prices, indicating that previous price, demand, gas, coal, and nuclear are the most significant factors that influence electricity prices.
Abstract: Forecasting algorithms are a valuable mechanism to aid in the prediction of future prices. Although various black-box modelling techniques have been applied to variations of this problem, we focus on the use of transparent models to enable understanding and interpretation of the developed model. We utilize a Nonlinear AutoRegressive Moving Average model with eXogenous input(NARMAX) for electricity price forecasting using multiple input factors. Energy data from a 14-week period in 2017 were analyzed to determine whether a NARMAX model could accurately predict day-ahead electricity prices and to check which input factors in the model were most significant. The model considered the closely correlated lags and included 13 input factors. There were two models developed in order to determine which variables played an important role in predicting future prices. Experimental results indicate that previous price, demand, gas, coal, and nuclear are the most significant factors that influence electricity prices. Gas was the highest weighted factor for both developed models. Previous price yielded the biggest Error Reduction Ratio(ERR), but when not included in the model, demand generated the biggest ERR value. To summarize a NARMAX model with an input regression lag of one and previous price included generates the best day-ahead forecast of electricity prices.

2 citations


Cites background or methods from "A methodology for identification of..."

  • ...In particular polynomial NARMAX models are a popular technique due to their simplicity in controlling input and output variables to estimate parameters [9]....

    [...]

  • ...NARMAX models have been widely used within industry: for instance to examine China’s housing prices and investigate the main determinants [10] to relate air pressure and turbines in diesel engines [9], and to develop a model that can predict Automatic Teller Machines (ATMs) cash demands [11]....

    [...]

  • ...A transparent modelling approach, known as a Nonlinear AutoRegressive Moving Average model with eXogenous input (NARMAX) model is a simple method that can be easily applied to nonlinear data for estimation of parameters [9]....

    [...]

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, a fault detection and localization method based on the parametric estimation is presented and applied to the air path system of a diesel engine, which is nonlinear and whose state variables and parameters are strongly coupled.
Abstract: In this paper, a fault detection and localization method based on the parametric estimation is presented and applied to the air path system of a diesel engine. This method uses directly the results of a parametric estimation of the system which is nonlinear and whose state variables and parameters are strongly coupled. Our goal is to detect clearly a fault occurred on a nonlinear model of Turbocharged Diesel Engine (TDE) published in the literature and to decide if this fault represents a fault of sensor, actuator or system. After that, we would like to build a control strategy called Fault Tolerant Control (FTC) with which all detected dysfunctions and parametric variations will be taken into account.

2 citations

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TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
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TL;DR: In this correspondence, a formula for the phase angles is derived that yields generally low peak factors, often comparable to that of a sinusoidal signal of equal power.
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Q1. What are the contributions in "A methodology for identification of narmax models applied to diesel engines" ?

In this paper a nonlinear system identification methodology based on a polynomial NARMAX model representation is considered. The goal of the procedure is to provide a nonlinear model characterized by a low complexity and that can be efficiently used in industrial applications.