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Arrays of chemical sensors, usually called electronic noses (ENose), are widely used in industry for classifying and identifying odours. They may also be used to locate the position and detect the direction of an emission source. Usually this task is performed by an ENose cooperating with a mobile vehicle, but when a source is instantaneous, or the surrounding terrain is hard for vehicles to traverse, an alternative approach is needed. Thus a three-step method for a stationary ENose with a novel structure to detect the direction of a dynamic source is presented in this paper. The method uses the ratio of measured concentration from different sensors (_{n}_{1} where n=2, 4) as a discriminator. In addition, this method could easily be adapted to robotics as an optimized algorithm for path tracking to a source location. The paper presents the results of a simulation of the method.

Today quality control with electronic noses is widely used in the food and beverage industry. The classification and identification of chemical emissions or aromas using ENoses is also applied in pollution control and fire detection [

There are few publications about source localization and detection with stationary sensors. In 2005, Jorg Matthes developed a discrete model method to solve this problem with a spatially distributed network of electronic noses, using more than four ENoses in diffusion and advection situations [

In this paper, a method of stationary sensors to detect the direction of both static and dynamic chemical emission sources within natural wind surroundings is presented. The method covers three cases: advection, crosswinds and breaks in the wind. Advection is the case where the wind direction is along the axis of the ENose system (x axis). The crosswind case is considered as advection and y-axis wind effects simultaneously. The case of a break in the wind will be discussed in more detail below.

The whole ENose system is introduced in section II. A new approach for direction detection is presented in section III, which will be divided into the three aspects of: (1) determining the direction of the source in the advection case; (2) resolving the direction in a crosswind and (3) dealing with a break in the wind. A method of tracking dynamic source directions will be presented in section IV. Simulation results are presented in section V; finally some conclusions are drawn in section VI.

The novel electronic nose system is built with four identical sensors (FIGARO TGS 2610) which are separated by a square impermeable separator with four wings. The sensors and separator will be build on a PCB board. The choice of sensor depends on the gas that is to be detected. For the TGS 2610, odor source could be LP gas. The structure of the system is shown in

The left part is the physical structure of this system. Crosswind vector (V_{CrossWind}) could be presented as the sum of x direction vector (V_{x}) and y direction vector (V_{y}). The direction of a crosswind is the included angle of the cross wind vector and the axis of the ENose, which is denoted by

As shown in the right part of _{CrossWind} and _{j}

In this section, the method to determine the static source direction is given for the two different cases, advection and crosswind. The solution for the source direction angle

If

If

If

_{wind}_{1} < _{2}

_{wind}_{1} _{2}

A series of simulations was done to analyse the relation between the source direction angle ^{2} ppm, (3) keeping the distance (

In

Moreover, for most kinds of sensor, the response will monotonically change with concentration. We use the stable response in our analysis. Thus, when the concentration is stable, the response of sensor will be stable too. Therefore,

Now we need to discuss the influence of initial source rate and distance (_{0} is initial source rate, x y and z is spatial variables. To solve _{0} and for all P(x,y), let _{0}(_{0},_{0}) denote for the source location, we can solve for large time _{0}(_{0},_{0}).

Corresponding to _{0} will not affect the ratio
_{i}_{i}_{i}

_{2}/_{1} and _{4}/_{1}. It generated from the simulated data of _{2}/_{1} and _{4}/_{1} are symmetrical about the 180° axis, and a curve can be fitted using the Matlab curvefit toolbox as shown in

Thus, the angle _{2}/_{1}, then if the measured concentration of sensor 4 is smaller than sensor 2 according to ^{°} and 180^{°}, otherwise, ^{°} and 360^{°}.

In this case, a crosswind with V_{x} and V_{y} is applied. We randomly picked a set of wind speeds for V_{x} and V_{y}, of 5m/s and 3m/s respectively. A series of simulations was done to analyse this case.

The diffusion equation in crosswind situation is present as follows:

We use

The diffusion equation for the crosswind situation may then be presented as shown in _{crossWind}_{x}_{y}_{0} and distance

Once again, we did the calculation of the ratio _{2}_{cross}_{1}_{cross}_{4}_{cross}_{1}_{cross}_{2}_{cross}_{1}_{cross}

Corresponding to _{p}_{2}_{cross}_{1}_{cross}_{2}/_{1}. We can then calculate the direction angle corresponding to the peak point in

After we calculated the peak point for several cases (with different wind directions and source directions) based on the simulation results, we found that the peak point occurs when the following conditions are all satisfied:

The source position is on a line with slope of crosswind direction

This line is a tangent of sensor 1.

The equation for this line is easily given by following equation:

_{1} and X_{2} can be replaced by the point sets {T,O}, {O,Q}, and {Q,T}. Thus,

Additionally, the source position _{p}_{p}_{p}

Based on the above analysis, we gathered following information for peak point _{p}_{p}

The second equation in equation set (10) is based on the law of cosines. The peak point angle _{p}

_{2}/_{1} for both advection and crosswind situation; obviously they all accord with Gauss distribution and have similar shape. However, they do not reach a peak at the same angle, therefore we can not simply get a fitting equation for _{2}_{cross}_{1}_{cross}_{2}/_{1} and _{2}_{cross}_{1}_{cross}_{p}_{2}/_{1} and _{2}_{cross}_{1}_{cross}_{p}

We use the Matlab curve fitting toolbox to find an equation relating _{2}_{cross}_{1}_{cross}_{2}/_{1}. Let _{2}/_{1} in advection, then the function _{c}_{2}_{cross}_{1}_{cross}_{p}

Several potential equations were tested; the result shown in _{c}_{2}_{cross}_{1}_{cross}

Matlab repots an SSE of 0.1499, R-square of 0.9981, Adjusted R-square of 0.998 and RMSE of 0.05128, which are acceptable.

We explain SSE, R-square, Adjusted R-square and RMSE below [

SSE -- The sum of squares due to error. This statistic measures the deviation of the responses from the fitted values of the responses. A value closer to 0 indicates a better fit.

R-square -- The coefficient of multiple determination. This statistic measures how successful the fit is in explaining the variation of the data. A value closer to 1 indicates a better fit.

Adjusted R-square -- The degree of freedom adjusted R-square. A value closer to 1 indicates a better fit. It is generally the best indicator of the fit quality when additional coefficients are added to the model.

RMSE -- The root mean squared error. A value closer to 0 indicates a better fit.

From _{c}^{−1}(

To deal with the natural wind situations, we must considerthe situation where wind breaks for a period, then recovers as before. This causes some unexpected noise in the signal from the sensors. While the signal decreases, the noise signal will be influenced by a lot of external factors, such as a gentle breeze caused by a passing animal. Usually, the noise does not have a stable pattern. As a result, the break in the wind interferes with the calculation of the source direction.

In _{2} / _{1} will still track the angle, as it works in previous cases.

Based on the approach stated above, the black box inverse problem was successfully solved for a static aroma source.

Dynamic detection refers to the detection of a source that maybe moving or in some other way varying its output. The basic idea for dynamic source detection is to convert the continuous time into discrete time. We give the marks Φ_{i}^{2} /

As is evident in _{i}_{1} and Φ_{2} will change (increase) faster than concentration changes (decreases) at Φ_{4}. The reason for it is that the diffusion coefficient with a wind blowing is higher than without a wind blowing, and Φ_{4} is behind the separator and shielded from the wind. In addition, the concentration distribution is different from the situation observed previously, with a static source at position 2. Since the spatially distributed concentration at position 2 after a movement from position 1 is different from the concentrations around the sensors analysed in section 3, it would appear that we can no longer solve the diffusion PDE as in section 3. As a result, the unstable ratio _{2}_{unstable}_{1}_{unstable}_{i}

Therefore, we need to quantize time and treat the source movement path as a union of several static points. We assume that the source stays at each position _{i}_{ij}

We then have a set of ratios,
_{i}_{i}_{2}, Ψ_{i}_{4}}. Based on the static solution, we derive the source direction _{i}_{i}

Consequently, given a known wind speed and direction, the method for dynamic source direction detection will have following scheme:

Use the static algorithm to calculate _{1} for source before movement;

Repeat step a) when responses of sensors are stable.

Generate _{i}

After _{i}

Simulation is done in both advection and crosswind cases. We set initial concentration of the source to 1000 ppm (source contains only one kind of odor), advection wind speed V_{x}=5m/s, crosswind wind speed V_{x}=3m/s, V_{y}=1.8m/s. The simulation runs for 20 seconds. The purpose of this method is detection of the direction of the source, thus we do not care about the source composition and the type of sensors chosen, but the physical dimensions of the sensors are set to the same as TGS 2610.

Firstly, we set a series of the real source directions at angles of 0°, 60°, 120°, 180°, 240° and 300° in the Femlab (finite element analysis) simulation package. We then simulate the steady concentration around sensor 1, sensor 2 and sensor 4 on the conditions stated in the previous paragraph.

Then we use the simulated concentrations as input, based on the equations derived in section 3, to calculate the source direction. The simulated concentrations and calculated source directions are listed in _{1}, _{2} and _{4} are ×10^{2}ppm.

As seen in

The calculated relative error is shown in

The result in

In the real world, we need a wind direction detection sensor to detect the wind direction

To simulate the dynamic case we set a source movement path as shown in sketch map,

The measured source direction for time 21 seconds (position 2) and 33 seconds (position 4) is presented in 2 values, as the calculation results for _{2} / _{1} and _{4} / _{1} are not corresponding to a same angle.

From

Therefore, we get a direction movement scheme, which is shown in

In this paper, a novel dynamic direction detection method based on a single electronic nose system is presented in natural wind situations by solving a black box inverse problem. The method is successfully established in the advection and crosswind cases, and also for the case of a break in the wind. The simulation results show the accuracy of this method. Also as the calculation is equation based, it is easy to implement and fast to calculate. The direction movement scheme could also be applied to robotic odour tracks, which will work more efficiently than current robotic tracking systems. The method may be optimized by improving the goodness of fit of the equations for both advection and crosswind cases.

Moreover, the method could be use to locate the odour source, which will make the result more accurate. We could use two of these electronic nose systems to find the cross point of two direction lines, and the cross point will be the source position.

This paper established the theoretical and simulated behaviour of the tracking system. The next step will be to construct and test the hardware. Additionally, locating the source position using a single ENose system is another future research direction for us.

Electronic nose system structure, left part is the physical structure of electronic nose, which contains 4 sensors separated by an impermeable four wings separator; the right part is the black box problem schema for the whole system.

Simulated series of stable sensors responses in advection case for different source directions

Ratio

Simulated series of stable sensors responses in crosswind case according to different source direction

Calculation scheme of peak point angle.

Comparison of _{2}/_{1} for advection and crosswind situation.

Comparison of fitted curve _{c}_{2}_{cross}_{1}_{cross}

Responses of Sensors for both Wind Break Case and Wind Break Free Case

Contour plot of concentration at Φ_{i}

Preset movement sketch map for dynamic source.

Tracking dynamic source direction.

Simulation result and errors for static source.

60° | 120° | 180° | −120° | −60° | 360°(0°) | |||
---|---|---|---|---|---|---|---|---|

_{1}(×10^{2}) |
0.4082 | 0.0054 | 0.0005 | 0.0054 | 0.4082 | 3.355 | ------ | |

_{2}(×10^{2}) |
0.3938 | 0.0132 | 0.0012 | 0.0023 | 0.0995 | 1.291 | ------ | |

_{4}(×10^{2}) |
0.0995 | 0.0023 | 0.0012 | 0.0132 | 0.3938 | 1.297 | ------ | |

_{2}/_{1} |
0.9647 | 2.444 | 2.400 | 0.4259 | 0.2438 | 0.3848 | ------ | |

_{4}/_{1} |
0.2438 | 0.4259 | 2.400 | 2.444 | 0.9647 | 0.3866 | ------ | |

Measured source direction( |
60.71° | 120.54° | 177.41° | −119.46° | −59.29° | 360°(0°) | ------ | |

Relative error | 1.17% | 0.45% | 1.46% | 0.45% | 1.17% | 0.00% | 0.78% | |

_{1}(×10^{2}) |
1.570 | 0.0208 | 0.0003 | 0.0005 | 0.0456 | 2.236 | ------ | |

_{2}(×10^{2}) |
1.765 | 0.0573 | 0.0009 | 0.0002 | 0.0092 | 0.9000 | ------ | |

_{4}(×10^{2}) |
0.3172 | 0.0072 | 0.0007 | 0.0014 | 0.0513 | 0.7801 | ------ | |

_{2}/_{1} |
1.124 | 2.755 | 3.000 | 0.4000 | 0.2018 | 0.4025 | ------ | |

_{4}/_{1} |
0.2020 | 0.3462 | 2.333 | 2.800 | 1.125 | 0.3489 | ------ | |

Measured source direction( |
61.46° | 116.38° | 175.01° | −116.68° | −62.81° | 360.11° | ------ | |

Relative error | 2.38% | 3.11% | 2.85% | 2.85% | 4.47% | 0.03% | 2.62% |

Simulation result and errors for dynamic source tracking.

_{1} (×10^{2}ppm) |
_{2} (×10^{2}ppm) |
_{4} (×10^{2}ppm) |
_{2} / _{1} |
_{4} / _{1} |
|||||
---|---|---|---|---|---|---|---|---|---|

- | 0 | 0 | 0 | 0 | - | - | - | - | - |

1 | 20 | 1.893 | 1.128 | 0.5367 | 0.5959 | 0.2835 | 27.85° | 30° | 7.72% |

2 | 21 | 1.6755 | 1.007 | 0.4514 | 0.6010 | 0.2694 | 28.37° | 45° | 58.62% |

36.14° | 19.69% | ||||||||

3 | 31 | 0.4082 | 0.3938 | 0.0995 | 0.9647 | 0.2438 | 60.71° | 60° | 1.17% |

4 | 33 | 0.8548 | 0.5971 | 0.1210 | 0.6985 | 0.1416 | 38.07° | 0° | 100.00% |

null | -- | ||||||||

5 | 73 | 0.4082 | 0.0995 | 0.3938 | 0.2438 | 0.9647 | −59.29° | −60° | 1.17% |

P represents the position index

T represents the simulation time