## 3 Fault Diagnosis Method Based on 1 DCNN and INPSO-SVM
### Chaos Based Initialization  
In the standard PSO algorithm, the initial positions of the particles are initialized randomly, which affects the search efficiency of the algorithm and limits the optimization ability of the PSO algorithm. Since the 1990s, with the study of chaos theory, chaotic maps have been widely applied in various fields. Chaos is a typical nonlinear phenomenon in nature, a chaotic system can go through every state in a certain range without repeating according to its own rules. Adding chaos operator into the optimization algorithm can improve the global search ability of the algorithm [30]. Among the chaotic systems, the structure of Tent map is simple, and its ergodic performance produces uniform distribution chaotic sequences, and the iteration process is suitable for computer operation [31]. The mathematical model of Tent chaos map is defined as follows. \[x_{i+1}=\left\{ \begin{array}{c}2x_{i}+rand(0,1)*\frac{1}{N},0\leq x\leq\frac{ 1}{2}\\ 2(1-x_{i})+rand(0,1)*\frac{1}{N},\frac{1}{2}\leq x\leq 1\end{array} \right. \tag{10}\]  
where, \(N\) is the population size, and \(rand\) (0, 1) is a random number within the range of (0, 1). The introduction of random variable not only ensures the randomness, ergodicity and regularity of the Tent chaotic map, but also effectively avoids iterations falling into the points of small period and unstable period. An Enhanced Particle Position Updating Strategy  
Levy flight, proposed by [PERSON], is a non-gaussian random process [32]. The short distance walk of Levy flight mechanism improves the diversity of the population, and the directional variability of the occasional long jump ensures that the population searches the surrounding area in detail. The combination of a short distance walk and a long distance jump can fully search the solution domain and greatly improve the global optimization ability of the algorithm. In the proposed INPSO algorithm, this paper eliminates the influence of the velocity term, and the particle swarm position is updated by the following equation. \[X_{new,i}=\omega X_{g,i}+c_{1}r_{1}\Big{(}P_{g,i}-X_{g,i}\Big{)}+c_{2}r_{2} \Big{(}P_{g}-X_{g,i}\Big{)}+c_{3}r_{3}\Big{(}P_{r}-X_{g,i}\Big{)} \tag{11}\]where, \(P_{r}\) is a random particle in the current set of particles, \(c_{3}\) represents the learning factor of random particle, \(r_{3}\) is drawn from the uniform distribution range in \([0,1]\). The fourth term is a random learning mechanism, which can increase the diversity of the population and overcome premature convergence. In order to make a good balance between local and global search capability, the particle swarm optimization algorithm is combined with an improved Levy flight strategy to obtain a new generation of particle swarm. The updating equation of group position is defined by Equation (12). \[X_{new,i}=\omega X_{g,i}+c_{1}r_{1}\Big{(}P_{g,i}-X_{g,i}\Big{)}+c_{2}r_{2} \Big{(}P_{g}-X_{g,i}\Big{)}+c_{3}r_{3}\Big{(}P_{r}-X_{g,i}\Big{)}\star\alpha \oplus Levy(\lambda) \tag{12}\]  
where, \(\alpha\) is random step size, \(\oplus\) represents the dot product, \(Levy(\lambda)\) is a random search path that conforms to Levy distribution and meets the following constraints [33]. \[Levy(\lambda)\sim\frac{\varphi*u}{|v|^{1/\lambda}} \tag{13}\]  
where, \(u,v\) follow a standard normal distribution, \(\lambda=1.5\), and \(\varphi\) is defined as follows. \[\varphi=\left[\frac{\Gamma(1+\lambda)*\sin(\pi*\lambda/2)}{\Gamma[(1+ \lambda)/2]*\lambda*2^{(\lambda-1)/2}}\right]^{1/\lambda} \tag{14}\]  
Combined with the improved Levy flight, the new algorithm has a better coordination between exploratory and exploitative patterns. At the same time, the greedy selection is added into the algorithm, which helps the PSO to only preserve the better-quality solutions with regard to the fitness values. The implementation of this process is described as follows. \[X_{g+1,i}=\left\{ \begin{array}{c}X_{g+1,i},f(X_{new,i})>f(X_{g+1,i})\\ X_{new,i},\text{ else }\end{array} \right.