# A Comprehensive Evaluation Model for Optimizing the Sensor Array of Electronic Nose
## 1 Introduction  
As an emerging gas-sensing technology, electronic nose (E-nose) has been widely used in many fields, such as disease diagnosis [1], environmental detection [2], the agriculture and food industry [3], and public security [4]. The sensor array is the acquisition unit of odor information, so it is the key component of the E-nose and directly determines its overall performance. Due to the inherent cross-sensitivity of the gas sensor, it is difficult to intuitively know the contribution of a certain sensor to the E-nose performance. Therefore, when an E-nose is designed, the usual method is to include as many sensors with different sensitivities in the initial array as possible so as to obtain richer response information. However, increasing the number of sensors may result in the following problems: (1) The amount of collected data will increase dramatically, which will inevitably increase the complexity of the pattern recognition model [5]. (2) The collected data may contain a lot of redundant information, which may affect the recognition accuracy of the E-nose [6]. (3) The cost of the hardware will increase at the same time, which cannot meet the current requirements of miniaturization, portability, and low power consumption for E-nose [7]. Therefore, it is of great significance to study effective sensor array optimization methods to improve the performance of E-nose. The conventional method of sensor array optimization can be obtained by testing different sub-arrays (i.e., full factorial design) [8, 9]. This method is practicable if the amount of sensors is small, but the possible amount of sub-arrays and the computational complexity will increase significantly when there are more sensors employed in the initial sensor array. Over the past decade, statistical analysis is the common method used inresearch to optimize the sensor array [9; 10], which evaluates the sensors according to a certain indicator, and then eliminates the underperforming sensors from the initial array to achieve the optimization. For example, [PERSON] et al. [11] used the Wilks' lambda statistical method to determine the redundant sensors and remove them from the sensor array. [PERSON] et al. [12] optimized the sensor array according to the correlation indicator and recommend removing those sensors whose responses to different gases are highly correlated. [PERSON] et al. [13] optimized the sensing array based on the odor classification accuracy of the E-nose. However, it is difficult for those methods to obtain a comprehensive evaluation of the sensor array from only a single indicator. [PERSON] et al. [14] evaluated the sensors via the response sensitivity and selectivity. Although the number of evaluation indicators in this study was expanded to two, it ignored the weight relationship between these two indicators, because if the sensitivity of a sensor is low, it is not necessarily poor in terms of gas selectivity. If a sensor with low response sensitivity is excluded from the array, the contribution of that sensor's selectivity to E-nose may be overlooked. Therefore, in order to explore the effect of different evaluation indicators on sensor array optimization, the weight relationship between each indicator should be considered. For the weight measurement of multi-dimensional evaluation indicators, there are two main methods: subjective weighting method and objective weighting method. The subjective weighting method is to assign a weight value to each indicator based on expert experience, such as the analytic hierarchy process (AHP) [15]. However, this method is greatly affected by subjective factors and is, therefore, more suitable for the occasions where quantitative analysis cannot be performed. The objective weighting method is to calculate the weight based on experimental data, such as the entropy weight method (EWM) [16]. For the E-nose system, it is obvious that the objective weighting method is more suitable.