System identification of the upper part of Murray River
Introduction
Water is a precious resource, and in the last few decades large efforts have gone into improving the management of water resources. Due to the rapid development in sensors and information and communication technology, operational data is now widely available. System identification and automatic control can now be used in the operation of large scale open water systems such as irrigation channels and rivers. The models obtained from system identification are simple ordinary differential or difference equations and are suitable for control design, prediction and fault detection purposes. In the last 10–15 years many works have appeared in the area of system identification and control of water systems. E.g. Cantoni et al. (2007), Litrico, Malaterre, Baume, Vion, and R-Bruno (2007), Litrico, Fromion, Baume, Arranja, and Rijo (2005), Malaterre and Baume (1998), Nasir and Muhammad (2011), Negenborn, Van Overloop, Keviczky, and De Schutter (2009), Ooi and Weyer (2008), Schuurmans, Hof, Dijkstra, Bosgra, and Brouwer (1999), Van Overloop, Schuurmans, Brouwer, and Burt (2005), Weyer (2001), and Weyer (2008) have demonstrated that system identification and control can improve the quality of service and water distribution efficiency for irrigation channels. Similarly, several works on modelling and control of rivers are also available, see e.g. Breckpot, Agudelo, Meert, Willems, and De Moor (2013), Foo, Ooi, and Weyer (2012), Foo, Ooi, and Weyer (2014), Glanzmann, von Siebenthal, Geyer, Papafotiou, and Morari (2005), Litrico (2002), Litrico and Pomet (2003), Maxwell and Warnick (2006), Papageorgiou and Messmer (1989), Pianosi, Castelletti, and Lovera (2012), Romanowicz, Young, and Beven (2006), Sahin and Morari (2010), Schoups and Vrugt (2010), Setz, Heinrich, Rostalski, Papafotiou, and Morari (2008), and Sohlberg and Sernfalt (2002).
In this paper we use several system identification techniques to find models of the upper part of Murray River in Australia. The methods we consider are Prediction Error Method (PEM), Maximum Likelihood (ML), continuous time system identification, Refined Instrumental Variable (RIV) method (used within the context of Data-Based Mechanistic (DBM) modelling) and Subspace Identification Method (SIM). Some of the methods have previously been applied to rivers, e.g. PEM was used in Foo et al., 2012, Foo et al., 2014 and Maxwell and Warnick (2006), SIM was used in Pianosi et al. (2012), and DBM was applied in Sohlberg and Sernfalt (2002), Young, 2003, Young, 2013, and Young, Castelletti, and Pianosi (2007).
Important factors in system identification of rivers are the accuracy of the obtained model and its suitability for the intended purpose, the ability to incorporate prior information such as water level-flow relationships (Bos, 1989), the ability to handle multiple inputs and outputs, and the availability of easy to use software.
The above listed methods have their own advantages and drawbacks. It is relatively easy to incorporate prior information in PEM and ML based approaches (Ljung, 1999, Söderström and Stoica, 1988). The Data-Based Mechanistic (DBM) approach has been successfully applied to many catchments and rivers (e.g. Young, 2003, Young, 2013, Young et al., 2007), especially if rainfall-runoff effects need to be taken into account. Subspace identification (Overschee and Moor, 1996, Verhaegen and Verdult, 2007) is well suited for Multi-Input, Multi-Output (MIMO) systems, and rivers are often MIMO with inflows from a number of tributaries, and we are often interested in modelling many flows and water levels along the river. Continuous time system identification (e.g. Garnier, Mensler, & Richard, 2003) is also of interest since continuous time models are often preferred due to easy interpretations and usage. However, each method has drawbacks too, e.g. for optimisation based methods like PEM and ML, it can get computationally difficult to estimate a model with many parameters, and for subspace methods, it becomes challenging to incorporate available prior information if the number of outputs increases.
In this paper we compare the above identification techniques, and in particular we consider (i) simulation performance on validation data, (ii) ability to incorporate available prior information, and (iii) ease in identifying models. The intended use of the models is control under normal operating conditions (i.e. not under flood conditions) and we also put emphasis on the usefulness of the obtained models for control.
This paper is organised as follows. In Section 2 we describe the upper part of Murray River, the operational objectives and the available prior information. We also narrow down the phenomena to be modelled either due to lack of data or due to minor relevance for control. Furthermore we present the dataset used for identification and estimate key time delays in the system. In Section 3 we briefly discuss each identification method and apply them to Multi-Input Single-Output (MISO) models of the upper part of Murray River. Section 4 is dedicated to MIMO models. In Section 5 we compare the identified models before giving some concluding remarks in Section 6.
Section snippets
Upper part of Murray River
In this section we describe the upper part of Murray River, and we discuss the operational objectives and the available prior information. Furthermore, we present the data used for identification.
Identification of a model of the water level in Lake Mulwala (multiple input single output (MISO) case)
In this section we describe different identification methods and use them to identify MISO models of the water level in Lake Mulwala followed by a comparison and a discussion of their simulation performance against validation data. We implemented our own identification routines for all methods except for the continuous time RIV method, where we used the CONTSID toolbox (Garnier & Gilson, 2000) in Matlab.
Identification of a model with water level in Lake Mulwala and flow at doctors point as outputs (multiple input multiple output (MIMO) case)
The water level at Doctors Point is another important variable in the upper part of Murray River. The rate of fall of the water level at Doctors Point has to be kept below 15 cm/Day to avoid river bank slumping. In this section we consider the identification methods described in Section 3 to identify a MIMO model with the water level in Lake Mulwala , and the flow at Doctors Point , as output variables. The water level at Doctors Point is then obtained from the flow using the rating curve
Comparison of results
In this section we continue the discussion from Section 3.6, and we compare the models and simulation results obtained in Section 4.
Conclusions
In this paper we have used the upper part of the Murray River as a case study and compared a number of system identification methods. Based on operational river data, models were identified and validated against other data. In most cases the models performed well, and they are suitable for control and simulation purposes. In particular optimisation based methods in which prior information can easily be incorporated performed very well on the example in this paper.
Acknowledgments
The authors would like to thank Murray Darling Basin Authority (MDBA) Australia for providing the data and for discussions about river operations. The authors would also like to thank their colleagues; Su Ki Ooi, Andrew Western, Dongryeol Ryu and Yuan Li for fruitful discussions. Also, they are thankful to the anonymous reviewers for their constructive and insightful comments which helped to improve the paper.
The authors gratefully acknowledge the financial support from National ICT Australia
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