Dynamic soft sensor based parameters and demand curve estimation for Water Distribution System: Theoretical and Experimental cross validation
Graphical abstract
Introduction
The significant parameters of process industries are mostly either inaccessible or measurable only with expensive measuring techniques. The intricacies in measuring obviously make the parameters and other unobservable states of the process to be estimated using available measurements, which are prone to noises and uncertainties under real time conditions. The quality and the complexity of estimating the parameters and the unobservable states depend upon the key factors such as (i) number of measurements available (ii) dynamical complexity of the process and (iii) the noise magnitude in the available measurements (Torre, Hong, & Deng, 2010). In general, WDS is considered as a significant component in the modern civic society. The complete entity governed through various hydraulic components such as reservoir tanks, pipes, pumps, valves and so on. The WDS branches out as interconnected widespread networks. The nominal operation of the WDS is essential for uninterrupted water supply, which relies on the continuous monitoring and regulating the hydraulic pressure and flows through valves and pumps (Sankar et al., 2015, Wang et al., 2017). However, an efficient regulation of WDS requires the appropriate operating conditions of the valves and the other hydraulic entities such as dimensional characteristics of the WDS. The high capital investment of placing the sensors in wide spread WDS and recurrent maintenance of the placed sensor limits the measurement of significant parameters and the other required states (Langowski, Brdys, & Qi, 2012). In such scenario, the analytical techniques are required to assessment the factors along with a mathematical model of representing the WDS and the available measurements, which are termed as soft sensor. Conventional estimation techniques such as Least Square (LS) Estimation, (Arsene & Gabrys, 2014) model-based approaches such as Kalman Filters (KF) (Nahar, Liu, & Shah, 2019) and the other techniques (Housh & Ohar, 2018) used to estimate the demand and other unobservable states of WDS under the condition that the governing parameters of the process are available. However, in many circumstances the governing parameters are not available for constructing a mathematical model. Moreover, for an under-defined system WDS (where the amount of unidentified factors is above the amount of standard computations), the factor approximation employing the well-known approximation procedures offers unbounded results (Sankaranarayanan, Sivakumaran, Radhakrishnan, & Swaminathan, 2018), which are undesirable from the water management perspective. The ideal solution for the under defined system can be known by means of random probable idealization methods. It infers the aforementioned approximation method is modelled as ideal method by describing a suitable method that correlates the course restraints and related randomly probable ideal method (Sankaranarayanan et al., 2018).
This implies, the alternative soft sensing method is required for finding the factors and unobservable states of an under-defined WDS (Li, Li, Huang, Liu, & Zhang, 2016), where a stochastic based optimization technique can be an appropriate solution to unravel the parameter estimation method for an under-defined system. Thus, the estimation problem is converted to the corresponding optimization problem through a suitable objective function, which relates the dynamics of the process and the optimization technique. The Nature Inspired (NI) algorithms are one of the most successful stochastic optimization techniques in literature. The NI based algorithm represents the characteristics derived through the laws defined by nature. The familiar phases of NI algorithms classified into three main categories. (i) Evolution based procedures like Genetic Algorithm (GA) (Holland, 1992), the enhanced versions of GA (Do et al., 2017, Jukka and Kauko, 2013, Zhang and Wang, 2012), similar algorithm Bio-Geography Based Optimization (BBO) (Niu et al., 2012, Ren et al., 2015) also used in the parameter estimation and it is also applied in the problem of study in this work, WDS, where the GA is used to estimate the leakage position for an under-defined WDS (Abo-Hammour, Alsmadi, Momani, & Abu Arqub, 2012). (ii) The second category of the NI algorithms developed with the laws of physics and some of the well-known algorithms such as Simulated Annealing (SA) (Bonilla-Petriciolet et al., 2007, Eftaxias et al., 2002, Lombardi, 2015) and the improved versions of the Gravity Search Algorithm (GSA) termed to be a Modified Gravity Search Algorithm (MGSA) are also implemented in estimating the parameters for the hydraulic turbine regulating systems. (iii) Finally swarm centred algorithms are the third and widely accepted category among the entire NI algorithm. The swarm based algorithm mimics any specific characteristics of a particular species and some of the techniques like Particle Swarm Optimization (PSO) (Han et al., 2018, Jakubcova et al., 2015, Shan, et al., 2016, Zheng and Liao, 2016), Ant Colony Optimization (ACO) (Fernández-Vargas et al., 2013, Sitarz and PowalKa, 2016), Bat and the upgraded Chaotic Bat Algorithms are also applied for the parameter estimation in diversified applications (Kirubakaran et al., 2014, Roeva and Fidanova, 2013).
The computational capacity of digital era plays a major role to solve the parameter estimation problem of WDS. A diversified problem requires different key factors to solve it. For e.g., fast convergence is required for certain problems and more exploring properties are required for different applications. In case of WDS, an algorithm should offer both the properties with a reasonable trade-off between the two. This is achieved by combining the merit characteristics of the two algorithms, which is commonly termed as hybridization. In general, the hybridization of an existing algorithm usually done to solve a specific problem. Some of the hybridization algorithms is carved out by combining PSO with GA as the base algorithm to improve the cross-over and the mutation rate (Nika, Nejadb, & Zakeric, 2016) for civil applications. A hybrid Cuckoo Search Algorithm (Wood, 2016) for fast scheduling in petroleum industries and Kalman based hybridization for process industries (Naha and Deb, 2014, Sankaranarayanan, Sivakumaran, Swaminathan, and Radhakrishnan, 2017) and so on. The swarm-based algorithms are considered to be highly reliable and convergent (Mirjalili, Mirjalili, & Lewis, 2014). One among the recently developed pack centred method is Grey Wolf Optimization (GWO) (Mirjalili et al., 2014), which outcomes on inspiration after the hunting technique of Grey Wolves.
Many recent literatures have reported the utilization of GWO algorithm for diversified applications such as biomedical (Bian et al., 2017, Jayabarathi et al., 2016, Song et al., 2015) and power system (Nuaekaew, Artrit, Pholdee, & Bureerat, 2017) domains; thus can be projected as a desirable algorithm for WDS application. Even though GWO exhibits an improved performance related to the other conventional procedures (Mirjalili et al., 2014), it has limitations of trapping in the local optimum under noisy and complex structural conditions, which is significantly prevailing in the measurements of WDS. This motivates for combining the existing GWO with other techniques, which can handle the above-mentioned limitations and improve the performance of the algorithm. But, the algorithm used to improve the existing GWO must not cause limitations in aspects of computational complexity, leading to local optimum. These constraints must also be accounted for a better estimation algorithm.
This further motivates to improve the existing GWO algorithm must be hybridized with the steady state Kalman Bucy (KB) (Kalman & Bucy, 1961) algorithm to surpass the effect of uncertainties, which helps to explore the global optimum and the algorithm, is termed as Hybrid Grey Wolf Optimization (HGWO) algorithm (Sankaranarayanan et al., 2018) for WDS application, which is a major technical contribution of this work towards the parameter estimation specially for WDS application. The proposed HGWO method to assessment states and factors of WDS even in presence of uncertainties and training the algorithm to identify the fault location in edict to re-estimate the factors of the process is lacking in the existing scenario. The HGWO algorithm is configured to address the optimal estimation of parameters and states of WDS proposed by KWA for the residential WDS section of Peroorkada town, Trivandrum city, Kerala.
The efficiency of the algorithm is experimented with the following two case studies (i) firstly, a three node synthetic WDS is considered and purposeful fault conditions injected into the process to exam the ability of HGWO algorithm in estimating the parameters. The faulty condition represents the state and input dependent uncertainties through Water Hammer (WH) phenomenon and it propagates through the entire WDS. (ii) The second case study is the Peroorkada WDS, where the size of unknown parameter vector spans to 110 and six other demand profiles for the 24 h profile needs to be predicted. To evaluate the fidelity of the projected algorithm for field applications, the entire model-based estimation strategy and fault identification techniques are implemented in HIL platform, which is an another significant contribution to improve the reliability of the proposed algorithm. The dimension of the unknown parameters and the noisy conditions prevailing in the available measurements creates a challenging environment for the HGWO algorithm in the HIL platform. In order to ascertain and highlight the significance of the hybridization, a quantitative and novel qualitative analysis is carried out by comparing the HGWO with the conventional PSO and GWO algorithms, similar to HGWO, the PSO and GWO algorithms are also implemented in HIL platform. The motivation behind the implementation of HIL platform is to provide a vivid picture that the proposed technique can be scaled up for real world WDS automation applications.
Further sections of the work ordered as mentioned, subdivision 2 delivers a concise discussion on Grey Wolf Optimization in addition to detailed enumeration over the hybridization algorithm. In Section 3, the above-mentioned case studies are discussed in detail and the performance of HGWO studied in estimating the parameters and compared along with the other conventional algorithms. The acquired results also validated statistically. Finally, the contributions and the concluding remarks are mentioned in Section 5.
Section snippets
Summary of Grey Wolf Optimization
The Grey Wolf Optimization GWO (Mirjalili et al., 2014) is the parent optimization algorithm, which is further considered for hybridization purpose. The GWO algorithm built over by using the hunting strategy and social hierarchy of the Grey Wolves for identifying the optimal solution. The mathematical execution of finding the optimal solution is carried over in four stages (i) Social Hierarchy, (ii) Encircling Prey, (iii) Hunting and (iv) Hunting Target, which are described in the supplementary
GWO algorithm hybridization
In edict to increase the hunt efficacy across the distinct hunt size, the Grey Wolf Optimization hybridized by means of KB (Kalman Bucy) method (Kalman & Bucy, 1961). The numerical view of the anticipated process (Sankaranarayanan et al., 2018) given below. The empirical function for parameter estimation is mentioned by Eq. (1). where, is the frame size of state window consumed in addition is the sum of factors. The varying features categorized by means of
Results and discussion
To demonstrate the efficacy of the suggested HGWO algorithm, it is implemented using the conventional GWO and PSO algorithms. The simulation platform used to execute the parameter estimation is MATLAB R2018a and the computer configuration is 3.4 GHz, 8 GB RAM Intel core i7 processor. The case studies are considered, in such a way to explore the capabilities of the algorithms in estimating the model parameters and the unmeasured states of WDS. The first case study consist of a synthesized WDS
Conclusion
In this study, the HGWO algorithm is proposed to estimate the vital parameters of the WDS and the unobservable states of WDS through the estimated model. This is mainly to address the problem given by KWA, Trivandrum, Kerala. The parameters estimated under state input dependent and independent uncertainties, which is a challenge to the optimization algorithms. The hybridization of GWO with the steady state KB mechanism improves the exploration performance of the existing algorithm. The
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The first author was supported by ‘Ministry of Electronics & Information Technology , Government of India’ under Visvesvaraya PhD scheme for Electronics and IT. The authors extend their thanks to Mr. Ashok Kumar Singh, Director, Kerala Water Authority (KWA), Thiruvananthapuram, Kerala for granting immediate permission to acquire the data. The authors also thank Dr. Rominus Valsalam, former head of Control and Instrumentation Group (CIG) and Associate Director of Centre for Development of
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