در قابلیت اطمینان تجزیه و تحلیل حساسیت شبکه عصبی به کار رفته برای بهینه سازی آرایه حسگر

Sensor arrays are nowadays first choice solution for low-cost and portable gas mixtures analysis systems. The key issue in construction of such systems is selection of sensors. The authors try to apply neural network sensitivity analysis for this task. The algorithm starts from huge set of sensors, which provides satisfying operation of the system, and then detects the most redundant elements, which may be removed without significant decrease of system accuracy. Eventually the small but efficient array of sensors is obtained. Authors present the method, propose some modifications and discuss problems with its application. Results of sensitivity analysis approach are compared with exhaustive search for the best set of sensors. The case study is quantitative analysis of volatile organic compounds mixtures by means of commercial, tin dioxide, TGS 800 series sensors characterized in in-house developed gas chamber.

Gas mixtures analysis, both qualitative and quantitative, performed with electronic sensors, became the significant research domain which nowadays involves quite interdisciplinary knowledge, with chemistry, solid state electronics, metrology, data processing and system theory included. Two main fields of research could be distinguished here – the first one concerning the technology of sensors fabrication, and the second one concerning sensor systems construction. In the latter case, matrices of sensors applied together with neural processing became the dominating solution elaborated during the last two decades by several research teams. The series of quite successful constructions described in the literature [1], [2], [3], [4], [5], [6], [7], [8] and [9] disregard, however, optimal selection of sensors. It was caused by the character of research (which was rather preliminary at that stage), and the lack of reasonable and efficient methods of sensors selection. The second stage of electronic noses development may be recognized by common understanding that each redundant sensor applied in the matrix increases the cost of both fabrication and operation of prospective system. Several methods of sensors selection or reduction were proposed. Perhaps the most simple one could be the analysis of correlation ratio of sensors responses and eliminating sensors giving the same information. There are problems however with correlation ratio, which will be discussed in further sections. In [10] and [11] the reverse approach is proposed – the search for sensors reacting in different way for various compounds. The method seems quite effective but it relies on sensors selectivity, the feature which is not common among popular semiconductor gas sensors. Another classic approach is PCA (Principal Component Analysis) [12] and [13]. It may be used for both sensors responses preprocessing and for evaluation of sensors array feasibility for specific task. The PCA however is strongly related with classification and hence cannot say much about sensors capability for quantitative analysis. Another troublesome feature is that PCA estimates the performance of a whole set of inputs/sensors, rather than individual elements of array. Perhaps for these reasons some authors apply the PCA for rough evaluation only and relay more on exhaustive search eventually [14], others try to apply clusterization technique to sensors rather then responses [15] or to use Genetic Algorithms [16] and [17]. In [18] it is shown that two tasks – sensor fabrication and selection, may be integrated into a single process of development of optimal set of gas sensors. This paper starts from the assumption that preliminary version of a sensor system providing acceptable accuracy of measurements is available (thanks to huge enough sensor array). Thus the task consists in the elimination of redundant sensors. For this purpose the authors apply the neural networks sensitivity analysis [19], [20] and [21]. It derives from both classic neural processing theory and general sensitivity analysis approach [22]. The utilisation of neural networks is somewhat unusual there. Instead of permanent placement in the system, they are temporarily used at preliminary stages of system configuration to provide the information about particular sensors influence on the system response. This way the most redundant sensors are found and removed one after another. After selection of the optimal set of sensors the appropriate algorithm (which may be neural network again) providing sensor matrix responses processing is constructed. When using the neural network sensitivity approach for reduction of sensor matrix [23] and [24], authors noticed that sometimes the results of its application are confusing. These observations encouraged to perform series of experiments, targeting in finding weak points of the method and a way to improve it. The results are presented in this paper, organized in the following way: Section 2 outlines the method. Section 3 provides an example of its application for sensor array reduction. Section 4 contains the key considerations on the reliability of sensitivity analysis and its comparison with experimental exhaustive search for the best set of sensors. Final conclusions are presented in Section 5.

Neural network sensitivity analysis method was adopted for efficient reduction of sensor array applied for gas mixtures analysis system. Neural network sensitivity formula, known from the literature, was extended to cover feedforward neural networks containing unlimited number of layers. It was observed that neural networks of the higher performance may give more reliable results of the sensitivity analysis. Some problems with application of the method were revealed, including the requirement on the similar range of the numbers appearing in all the inputs. The other problem is confusing result of the analysis, appearing when the inputs are dependent (e.g. the array contains sensors reacting in a similar way). However, in most cases, the suggested strategy of removing only 1 sensor in each stage, leads to removal of only one of the highly dependent sensors, whilst the other one is preserved. The efficiency of the method was investigated in the exhaustive experiment, involving development and testing of all possible variants of reduced sensor arrays, coupled with dedicated neural networks. It was revealed that sensor array obtained by neural network sensitivity analysis driven reduction is not strictly an optimal one, but it is very close to optimum, providing quite similar performance, better than most of the other solutions. Presented method starts from the redundant and good enough array of sensors and consists in its reduction. The reverse strategy, consisting in iterative extension of the sensor array, could be perceived as more convenient. Taking into account however that both strategies consist in gaining the same kind of knowledge about sensors responses and then working with various software tools, the superiority of extension over reduction approach seems questionable. Sensitivity analysis of neural model, when applied with mentioned carefulness, may be an attractive tool for all kinds of non-selective sensing elements selection as well as their working conditions optimization. Varying temperature or dynamic response approach seem very promising fields of prospective application.