Early Detection of Thermoacoustic Combustion Instability Using a Methodology Combining Complex Networks and Machine Learning

We undertake an experimental study on the early detection of combustion-driven thermoacoustic instability using a method combining complex networks and machine learning. The probability distribution of the transition patterns in ordinal partition transition networks significantly captures the subtle changes in the combustion state during a transition from combustion noise with a low amplitude to thermoacoustic combustion instability with a high amplitude. A feature space consisting of the principal component plane estimated from the probability distribution of the transition patterns, which is obtained by a support vector machine, allows us to detect a precursor of thermoacoustic combustion instability.

Figure 1

Schematic of our experimental system.

Figure 2

Variation in the spatial distribution of the synchronization index $S_I$ as a function of equivalence ratio $\varphi$ for different downstream locations $z$.

Figure 3

Variation in the spatial distribution of the Rayleigh index $R_I$ as a function of equivalence ratio $\varphi$ for different downstream locations $z$.

Figure 4

Variation in the probability distribution of the transition patterns in the ordinal partition transition networks $P(W_{ij})$ as a function of equivalence ratio $\varphi$.

Figure 5

Passage on the $S_1\text{−}{S}_2$ plane obtained from PCA of the probability distribution of the transition patterns in ordinal partition transition networks in terms of the equivalence ratio $\varphi$. Here, $S_1$ and $S_2$ are the first and second components, respectively, and the blue lines $W_{ij}$ on the $S_1\text{−}{S}_2$ plane represent the embedded manifold coordinates in 16 dimensions.

Figure 6

(A) The feature space consisting of the first component $S_1$ and second component $S_2$ obtained by SVM. (B) Time variations in pressure fluctuations $p^{\prime }$ and ${\mathrm{OH}}^{\ast }$ chemiluminescence emission intensity fluctuations $I_{{\mathrm{OH}}^{\ast }}^{\prime }$ with increasing equivalence ratio $\varphi$. (a) $t=10.0\mathrm{s}$, (b) $t=13.4\mathrm{s}$, (c) $t=29.6\mathrm{s}$, and (d) $t=42.0\mathrm{s}$.

Figure 7

Time variations in pressure fluctuations $p^{\prime }$ and ${\mathrm{OH}}^{\ast }$ chemiluminescence emission intensity fluctuations $I_{{\mathrm{OH}}^{\ast }}^{\prime }$ with increasing equivalence ratio $\varphi$, together with the feature space. (a) $t=10.0\mathrm{s}$, (b) $t=12.6\mathrm{s}$, and (c) $t=21.3\mathrm{s}$. Note that a secondary air injection is issued from the injector rim shortly after detecting a precursor of thermoacoustic combustion instability.