Intelligent Monitoring of Thermodynamic Parameters in Compressor Operations and Development of a Fault Prediction Model Using Deep Learning

In the operation of compressors, multiple parameters such as pressure, temperature, and flow are involved, and these parameters exhibit complex dynamic patterns over time due to influences from the mechanical structure and process conditions. Traditional fault prediction methods often struggle to fully uncover deeper patterns within high-dimensional, nonlinear data. Therefore, this paper adopts the SSA-LSTM model for compressor fault prediction. The SSA has a global search capability that allows it to find optimal solutions within a large hyperparameter space. Meanwhile, the LSTM network effectively retains long-term dependencies when handling time-series data. Combining these two methods enables the SSA-LSTM model to adaptively extract essential features from multi-dimensional time-series data for compressors, while the LSTM's memory mechanism captures long-term temporal trends within the data, providing higher accuracy in fault prediction. Additionally, compressor fault prediction requires a model that can maintain high predictive accuracy in variable operating environments and with incomplete sensor data. SSA not only efficiently adjusts LSTM's hyperparameters but also adapts to various changes and interference factors that may occur during compressor operation. LSTM handles data irregularities and missing data, ensuring the model's stability in practical applications. The integration of SSA and LSTM enables the SSA-LSTM model to adapt to various dynamic changes in the compressor's operating process and to perform real-time fault diagnosis and prediction, providing a scientific basis for preventive maintenance and fault management of equipment.

Specifically, the SSA is employed to optimize the parameters of the LSTM model, enhancing the accuracy and reliability of compressor fault prediction. SSA is a swarm intelligence optimization algorithm that simulates the foraging behavior of sparrows. By modeling the collaborative and competitive behavior mechanisms among sparrows during foraging, the algorithm seeks the optimal solution within the search space. In this model, the "leader sparrow" guides the group toward optimal food sources in an unknown environment, while the "follower sparrows" adjust their positions according to the leader's position. This strategy balances global and local search, enabling SSA to effectively avoid local optima and enhancing the global search capability of the optimization process.

Let s denote the current iteration count, IT_MAX represents the maximum number of iterations, and A_u,k be the position of the u-th sparrow in the k-th dimension. Β ∈ (0, 1] is a random number, with alert and safety values represented by E₂ and TS, respectively. Let W be a random number following a normal distribution, M be a matrix with one row and f columns of all ones, and f denotes the dimensionality of the compressor fault prediction problem. The position update formula for the discoverers is as follows:

$A_{u, k}^{s+1}=\left\{\begin{array}{c}A_{u, k}^s \cdot \exp \left(\frac{-u}{\beta \cdot I T_{M A X}}\right)\left(E_2<T S\right) \\ A_{u, k}^s+W \cdot M\left(E_2 \geq T S\right)\end{array}\right.$          (13)

Assume that the current optimal position occupied by the discoverers is A_O and the current global worst position is A_WO. Let X⁺ be a constant controlling the magnitude of individual position updates. Then the position update formula for the joiners is as follows:

$A_{u, k}^{s+1}=\left\{\begin{array}{c}W \cdot \exp \left(\frac{A_{W O}^s-A_{u, k}^s}{u^2}\right)\left(u>\frac{v}{2}\right) \\ A_O^{s+1}+\left|A_{u, k}^s-A_O^{s+1}\right| X^{+} M \quad( {otherwise})\end{array}\right.$           (14)

When aware of danger, the sparrow population exhibits anti-predation behavior. Suppose the step control parameter is α, the current global optimal position is A_BE, and J ∈ [-1, 1] is a random number. Let d_u be the fitness value of the current sparrow individual, with d_h and d_q representing the current global best and worst fitness values, respectively. A very small constant is denoted by γ, and the corresponding mathematical expression is as follows:

$A_{u, k}^{s+1}=\left\{\begin{array}{l}A_{B E}^s+\alpha \cdot\left|A_{u, k}^s-A_{B E}^{s+1}\right|\left(d_u>d_h\right) \\ A_{u, k}^s+J \cdot\left(\frac{\left|A_{u, k}^s-A_{W O}^s\right|}{\left(d_u-d_q\right)+\gamma}\right) \quad\left(d_u=d_h\right)\end{array}\right.$              (15)

In the compressor fault prediction model, the LSTM neural network is the core component, used for processing complex time-series data from the compressor operation process, extracting the long-term dependency features from the data to achieve accurate fault prediction. The basic structure of LSTM includes the forget gate, input gate, and output gate. These three gating mechanisms are responsible for determining the “memory” and “forgetting” processes within the neural network. Through these gating mechanisms, the LSTM network can selectively “remember” important historical information related to faults while “forgetting” redundant information unrelated to fault prediction, thereby significantly improving prediction accuracy. In the specific task of compressor fault prediction, the time-memory capability of LSTM is particularly important. The operating state of the compressor often includes parameters with complex dependencies, such as temperature, pressure, and vibration, and the dynamic changes of these parameters over a long period are crucial for fault prediction.

Assume the previous cell state is z_s-1, and the connection between the previous hidden state g_s-1 and the current input a_s is represented by |g_s-1, a_s|. The weight matrix and bias term of the forget gate are represented by q_d and y_d, respectively. Sigmoid is the activation function, and the forget gate expression is as follows:

$d_s={sigmoid}\left(q_d \cdot\left|g_{s-1}, a_s\right|+y_d\right)$            (16)

Assuming the current cell state is z_s, the input gate expression is:

$u_s={sigmoid}\left(q_u \cdot\left|g_{s-1}, a_s\right|+y_u\right)$             (17)

The candidate cell state z'_s is calculated using the tanh function, with the calculation formula as:

$z_s^{\prime}=\tanh \left(Q_{z g} g_{s-1}+Q_{z a} a_s+y_z\right)$             (18)

The forget gate d_s and the input gate u_s control the size of the updated cell state z_s, with the calculation formula:

$z_s=d_s * z_{s-1}+u_s * z_s^{\prime}$             (19)

Assuming the current hidden state is g_s, the output gate expression is:

$p_s={sigmoid}\left(Q_{p g} g_{s-1}+Q_{p a} a_u+y_p\right)$              (20)

The calculation of the hidden state g_s is determined by p_s and z_s:

$g_s=p_s * \tanh \left(z_s\right)$              (21)

Through its detailed internal structure, the LSTM neural network can capture the deep-level associations of these parameters over time, thus learning the latent patterns in the data. In the compressor operation data, the occurrence of certain faults may require prediction based on historical data spanning hours or even days, and the LSTM, with its “long short-term memory” capability, can maintain stable learning performance over such extended time spans.

In the compressor fault prediction model, the basic principle of the SSA-LSTM model is to optimize the hyperparameters of the LSTM model using the SSA to improve the accuracy and stability of compressor fault prediction. The LSTM itself, as a powerful time-series data processing model, can effectively capture the long-term dependency relationships in the compressor operation process. However, the performance of LSTM largely depends on the selection of its hyperparameters, such as learning rate, hidden layer size, and the number of iterations, and the reasonable setting of these hyperparameters directly affects the model’s training results and prediction accuracy. SSA, as a swarm intelligence-based optimization algorithm, simulates the foraging behavior of sparrows to perform a global search in the hyperparameter space and automatically finds the optimal combination of hyperparameters. By using SSA to optimize the LSTM model, it can be ensured that the model maintains high training efficiency and prediction accuracy when processing compressor operation data. Especially when dealing with complex time-series data and multiple variables, the optimized LSTM can better capture potential fault patterns and trends. Figure 4 shows the compressor fault prediction process based on the SSA-LSTM model.

Specifically, in this paper, the Sparrow Search Algorithm sets the maximum number of iterations to 100 and the population size to 50, with 20% of the individuals designated as “discoverers,” responsible for exploring a broader hyperparameter space. This setup allows SSA to effectively search for the optimal solution across multiple hyperparameter dimensions, including learning rate, number of iterations, and the number of neurons in the two hidden layers. After 80 iterations, SSA quickly converges, finding the optimal combination of hyperparameters, with a learning rate of 0.0016 and the best number of iterations as 83. This hyperparameter combination provides the LSTM network with an efficient training framework, enabling the model to accurately identify and predict compressor faults.