Journal of Chemistry

Volume 2018, Article ID 9616841, 14 pages

https://doi.org/10.1155/2018/9616841

## A Fusion Water Quality Soft-Sensing Method Based on WASP Model and Its Application in Water Eutrophication Evaluation

Correspondence should be addressed to Zhiyao Zhao; nc.ude.ubtb@yzoahz

Received 7 November 2017; Revised 24 January 2018; Accepted 6 February 2018; Published 6 March 2018

Academic Editor: Carlos A Martínez-Huitle

Copyright © 2018 Xiaoyi Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Water environment protection is of great significance for both economic development and improvement of people’s livelihood, where modeling of water environment evolution is indispensable in water quality analysis. However, many water quality indexes related to water quality model cannot be measured online, and some model parameters always vary among different water areas. Thus, this paper proposes a water quality soft-sensing method based on the water quality mechanism model to simulate evolution of water quality indexes online, where unscented Kalman filter is utilized to estimate model parameters. Furthermore, a modified fuzzy comprehensive evaluation method is presented to evaluate the level of water eutrophication condition. Finally, the water quality data collected from Taihu Lake and Beihai Lake are used to validate the effectiveness and generality of the proposed method. The results show that the proposed soft-sensing method is able to describe the variation of related water quality indexes, with better accuracy compared to nonlinear least squares based method and traditional trial-and-error based method. On this basis, the water eutrophication condition can be also accurately evaluated.

#### 1. Introduction

With the rapid development of modern society, production of industrial and sanitary sewage is daily increasing, and eutrophication phenomenon of lakes and reservoirs is becoming much more serious [1, 2]. Generally, the occurrence of eutrophication is related to excessive nitrogen, phosphorus, and other inorganic nutrients in water, where nitrogen and phosphorus are the main reasons accounting for the eutrophication of slow flow water, such as lakes, reservoirs, and bays [3–5]. Currently, eutrophication phenomenon exists in 54% of the lakes of Asia-Pacific region [6]. Therefore, how to economically and effectively handle the eutrophication problem has become an urgent priority.

In order to timely evaluate or predict the eutrophication condition, the variation of water quality indexes should be timely measured or learned [7, 8]. However, many water quality indexes, such as biochemical oxygen demand (BOD) and total nitrogen (TN), cannot be measured online [9]. Thus, the manner of soft-sensing is introduced to overcome this limitation in this paper. Soft-sensing is to establish a mathematical relation model between easily measured process variables and difficultly measured process variables based on mechanism analysis and sensor data mining [10]. The existing soft-sensing modeling approach can be classified into three types: mechanism modeling, identification modeling, and artificial intelligence-based modeling [11–13]. The mechanism modeling approach is to obtain a mathematical expression based on the analysis of the system’s internal relations, which adopts the basic physical and chemical laws, such as material, energy, or momentum conservation relation [14]. The identification modeling approach is to establish a mathematical model based on the information of system input and output by certain parameter identification, filtering, or regression analysis methods, without understanding the mechanism of the dynamic process [15]. The artificial intelligence-based modeling approach is to get an underlying model of the real-world system or a portion of system based on artificial intelligent methods [16]. In addition, there also exist fusion methods derived from a combination of the above approaches; that is, the mechanism modeling approach is utilized to describe partial behavior of the studied system with known mechanism, and identification modeling approach or artificial intelligence-based approach is used to handle the remaining part.

Water Quality Analysis Simulation Program (WASP) mechanism model is a comprehensive water quality model that can be used to interpret the process of natural or artificial water quality deterioration [17]. It can simulate migration and transformation of conventional water quality indexes (including dissolved oxygen (DO), BOD, and nutrients) and toxic contaminants (including organic chemicals, metals, and sediment) in water [18]. Currently, WASP model has been widely applied to different water areas, such as Mobile Bay [19], Murderkill River [20], Lake Michigan [21], and Songhua River [22]. However, WASP also has a limitation. That is, some model parameters vary among different water areas, and their values are always determined by trial-and-error method [23]. This is insufficient for accurately modeling the water quality variation of a specific water area.

Therefore, this paper builds a fusion water quality soft-sensing method, where the WASP model is employed as a soft-sensing method and its unknown parameters are estimated by the unscented Kalman filter (UKF) [24]. Then, the variations of DO, BOD, nitrate nitrogen (NO_{3}-N, related to TN), ammonia nitrogen (NH_{3}-N), phytoplankton carbon (Phyt, related to chlorophyll_a (Chl_a)), and so forth can be simulated by the fusion water quality soft-sensing method. On this basis, a modified fuzzy comprehensive evaluation method is presented to evaluate the eutrophication condition of the rivers and lakes, combining both the simulated values of DO, BOD, TN, and Chl_a from the soft-sensing method and the online measured values of transparency (SD) and total phosphorus (TP) [25]. Finally, by taking Taihu Lake and Beihai Lake as examples, the effectiveness and generality of the proposed method are validated and the water eutrophication condition is evaluated. Comparative studies are also presented and discussed.

The remainder of this paper is organized as follows. Section 2 presents the methodology of the WASP based water quality soft-sensing method, where a simplified WASP model is presented and the procedure of unknown parameters estimation by UKF is listed. Section 3 introduces the modified fuzzy comprehensive evaluation method, where the modified methods of selecting water quality indexes and calculation of the corresponding weight are presented. Section 4 presents two case studies of Taihu Lake and Beihai Lake to validate the effectiveness and generality of the proposed fusion soft-sensing method and the water eutrophication evaluation method. Section 5 gives the conclusion and indicates future development.

#### 2. Fusion Water Quality Soft-Sensing Method

##### 2.1. Dynamic Model of Water Quality Based on WASP

Eutrophication module (shorten as EUTRO) is an essential part of the WASP model. This module describes the dynamic behavior of water quality indexes including DO, BOD, Phyt, NO_{3}-N, NH_{3}-N, organic nitrogen (ON), and organic phosphorus (OP). The interacting relations of them can be represented by four reaction systems, namely, phytoplankton kinetics, phosphorus cycle, nitrogen cycle, and DO balance.

In the EUTRO module, a simplified dynamic process of seven water quality indexes are presented as [18]where we let represent concentrations of DO, BOD, Phyt, NO_{3}-N, NH_{3}-N, ON, and OP, respectively. In (1), the chemical meaning of unknown model parameters is shown in Notations [18].

Let . Here, assume that the unknown parameters are piecewise-constant. Then, the process equation can be written as

Further let and the process noise item be added. An augmented process equation is obtained as [26]where is the process noise, satisfying that is the covariance matrix. Then, the observation equation is set as follows:where is the observation matrix, describing the mapping from state indexes to observations; is the measurement noise, satisfying that ; is the covariance matrix. Up to now, we obtain a continuous-time dynamic model of water quality indexes as follows:

To obtain the discrete-time model, the fourth-order Runge-Kutta is utilized, where the step length is . The formula is as follows:

Then, (5) is discretized as

##### 2.2. Unknown Parameter Estimation Based on UKF

In practice, UKF is an effective tool for state estimation [27]. Given the dynamic equation shown in (7) and a series of observations , the state estimation procedure by the UKF is presented as follows [28].

*Step 1 (UT transformation). *In the original state distribution, some sampling points are selected according to certain rules, so that the mean and covariance of these sampling points are equal to the mean and covariance of the previous state distribution. These points are substituted into the nonlinear function, and the corresponding set of the nonlinear function values is obtained. Then, the mean and covariance of the nonlinear transformation are obtained from these sets of points.

First, compute the sigma points, namely, sampling points:where is the number of the state dimension.

Second, calculate the associated weight of the sampling points:where is the estimated covariance, satisfying is the square root of the th column in ; is scaling parameter used to reduce the total prediction error; controls the spread of sampling points; is the selected parameter, and its value is not bounded generally, but it is usually necessary to ensure the semidefinite of matrix. Under normal circumstances, and . is a nonnegative weighting index, and the optimal value is 2 for a Gaussian distribution of .

*Step 2. *Compute predicted state and predicted covariance :

*Step 3. *Compute predicted , measurement covariance , and cross-covariance of the state and measurement :

*Step 4. *Compute gain , updated state , and covariance :From the estimate of the augmented variable , the estimated values of unknown parameters can be obtained as .

#### 3. Eutrophication Condition Evaluation Based on Modified Fuzzy Comprehensive Evaluation Method

On the basis of the output from the proposed fusion water quality soft-sensing method and online measurements of water quality indexes, a modified fuzzy comprehensive evaluation method is used to evaluate the water eutrophication condition.

Fuzzy comprehensive evaluation method adopts fuzzy mathematical theory to obtain a quantitative evaluation result of an object in view of the complexity of object and fuzziness of the evaluation index. The procedure of the proposed fuzzy comprehensive evaluation method is presented as follows.

*Step 1 (water evaluation index selection). *In the traditional fuzzy comprehensive evaluation method, the key evaluation indexes, which have great influence on the water environment, are obtained by empirical measures. Although these methods are relatively convenient, they lack objectivity and theoretical foundation. In order to compensate this limitation, a cumulative frequency method is introduced by calculating the cumulative frequency of excessive multiple of each water quality index [29].

The evaluation set is a collection of criteria for evaluating the object [30]. Suppose the water eutrophication condition can be classified to levels, written asFurther suppose there exist evaluation indexes, written as . On this basis, the cumulative frequency can be calculated as follows:where is the label of the evaluation index; is the label of eutrophication level; is the concentration value of the th index; is the standard value of the th index in level ; is the excessive multiple value of the th index; is the cumulative frequency of the firstindexes*.* According to the statistical analysis requirements in the selection of evaluation indexes, generally take [31]Following (14) and (15), we have the selected key water evaluation indexes as .

*Step 2 (establishment of the fuzzy relation matrix ). *By adopting fuzzy mathematical theory to evaluation study, the most critical issue is to establish the membership functions for the evaluation indexes. Triangular linear membership functions are commonly used in practice, which are also selected for determining the fuzzy relation matrix in this paper [32]. The configuration of the membership function is as follows:

For ,(1)when , the membership function is(2)when , the membership function is(3)when , the membership function iswhere presents the membership degree of index in level ; are the standard values of the th index in level , respectively. When is given, the above membership functions can be applied to determine the membership degree of the evaluation index for each level of water eutrophication.

Then, the fuzzy relation matrix is constructed aswhere .

*Step 3 (weight determination of evaluation index). *The determination of the evaluation index weight is one of the most important factors that directly affect the final evaluation results. In this paper, the clustering weight method is used to determine the weight of each evaluation index, combining the index concentration value with the standard values which more objectively reflect the relative importance of each evaluation index in all the indexes. The method of calculating the index weight is as follows:where is the weight of the th water evaluation index in the th eutrophication level. Therefore, the index weight matrix determined by the clustering method iswhere is the index weight matrix of the th eutrophication level.

*Step 4 (fuzzy synthesis operation). *Combining the index weight with the fuzzy relation matrix , the multiplication and addition method of the weighted average is chosen to obtain fuzzy comprehensive evaluation result based on all indexes. The advantage of this method is that it can balance all indexes according to the weight values to reflect the comprehensive condition of water quality [33]. The specific formula is as follows:where the element is membership of the water object with regard to th water eutrophication level. The water eutrophication level can be obtained by the principle of maximum membership, where the specific formula is as follows:

#### 4. Case Study

In this part, water quality data of Taihu Lake (case 1) and Beihai Lake (case 2) are utilized to verify the effectiveness and generality of the proposed method. First the UKF is used to estimate the unknown parameters in the soft-sensing method, where the estimated result is compared to the results obtained by the nonlinear least squares method and trial-and-error method. Then, simulated values of the water quality indexes are deduced, which are compared to the real measured water quality data. On this basis, the water eutrophication evaluation is carried out by the modified fuzzy comprehensive evaluation method, depending on both simulated values of DO, BOD, TN, Chl_a and real measured values of SD, TP.

##### 4.1. Case 1: Taihu Lake

###### 4.1.1. Model Parameter Estimation Result and Analysis

The UKF is used to estimate the unknown model parameters of Taihu Lake shown in Notations. Besides, due to the limitation of measured data, the TN data are used instead of NO_{3}-N. Since the measured data include DO, BOD, Phyt, TN, and NH_{3}-N, the observation matrix in (7) is set as

Then the real-time estimated values of the ten unknown model parameters can be obtained, which are depicted in Figure 1.