(767c) Optimal Sensor Placement for Agro-Hydrological Systems

The fast increasing global population puts a great demand on agricultural products. To meet the demand for food, the agriculture sector requires large amount of fresh water [1]. Freshwater scarcity became one of the greatest global risks. One critical step to manage the water crisis is to improve the water-use efficiency in agriculture irrigation. In the current practice, irrigation is typically done in an open-loop fashion and no real-time feedback information from the field (e.g., soil moisture) is used in irrigation decision making. It is important to implement closed-loop irrigation in which irrigation decisions are made based on real-time field soil moisture measurements. In the implementation of a closed-loop irrigation system, sensors play a key role. The major obstacle is that we cannot put sensors at each location of the field due to cost and energy constraints. One approach to handle the problem is to estimate the soil moisture (state estimation) using limited number of sensors (measurements). One important question is how to determine the minimum number of sensors and the corresponding best locations for sensor placement so that we can get a reasonable estimate of the field soil moisture condition.

In the literature, there are many existing results on soil moisture estimation. Many researchers have tried to estimate the soil moisture using the extended Kalman filter (EKF) [2], ensemble Kalman filter (ENKF) [3] and particle filter methods [4]. The above studies did not analyse the best position and the minimum number of sensors requirement to obtain a reasonable estimation of soil moisture. Jannatun et al. [5] discussed the procedure to find the best location of a sensor set using the observability analysis but the algorithm is limited to small one–dimensional systems because the rank test of observability matrix suffers numerical issue for large scale systems. The classical approaches to test the observability only confirm the system is observable or not but do not provide any information on how to select the sensor set or the minimum number of sensors for the higher degree of observability.

In this talk, to deal with the above discussed issue, the graphical methods are used to find the minimum number of sensors and the optimal sensor placement for 3D nonlinear agro-hydrological systems. A 3D agro-hydrological system is typically a very large-scale system. First, we apply the concept of modularity to perform model reduction (or node clustering). Note that the classic model reduction approaches like balanced truncation, Krylov subspace method and Hankel norm approximation do not preserve the system architecture and are not appropriate for sensor placement. In this work, we propose a physical structure based clustering approach to reducing the model order while preserving the system structure. Then, based on the reduced-order model, the maximum matching method and Poov-Belevitch-Hautus (PBH) method are implemented to further investigate the symmetries present in the linearized model of the nonlinear system. The minimum number of sensors obtained from the above methods are not unique so the degree of observability analysis is further performed to find the best locations for sensor placement. Specifically, two types of degree of observability analysis are used: modal observability and average observability. Modal observability reflects the ability of sensor node to estimate each mode of the system. One advantage of this method is that it does not require to check all the possibility of sensor sets. However, it may give a sensor set that gives observability but the energy required to estimate the states is practically infeasible. The average observability provides the quantification of energy to estimate the states. A combination of these two methods is used to find the minimum number of sensors and the optimal sensor placement. Extensive simulations have been carried out to verify the effectiveness of the propose approach.

References

[1] “Waste water the untapped resource,” The United Nations World Water Development Report, 2017.

[2] R.H. Reichle, J.P. Walker, R.D. Koster, P.R. Houser “Extended versus ensemble Kalman filtering for land data assimilation” J. Hydrometeoroly., 3 (6) (2002), pp. 728-740.

[3] D. Erdal, M.A. Rahman, I. Neuweiler, “The importance of state transformations when using the ensemble Kalman filter for unsaturated flow modeling: dealing with strong nonlinearities”, Adv. Water Resour., 86 (2015), pp. 354-365.

[4] C. Montzka, H. Moradkhani, L. Weihermuller, H.J.H. Franssen, M. Canty, and H. Vereecken, “Hydraulic parameter estimation by remotely sensed top soil moisture observations with the prticle filter”, J. Hydrol., 399 (2011), pp. 410–421.

[5] J. Nahar, J. Liu, S. L. Shah, “Parameter and state estimation of an agro-hydrological system based on system observability analysis”. Comput. Chem. Eng. 121, (2019) pp. 450−464.