# Performance Prediction using Neural Network and Confidence Intervals: a Gas Turbine application

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## Summary (3 min read)

### INTRODUCTION

- In the current market, the ability to react quickly to production problems and minimize downtime and costs has become a fundamental feature for the survival of companies.
- The maintenance function has increasingly covered a key role in maximizing production performance and minimizing the costs incurred by the companies.
- The authors analyses and selection of the attributes emphasize the importance of data understanding and pre-processing and show that they may simplify the analysis of the data through dimensionality reduction for example.
- Motivated by the large number of attributes in the Naval propulsion system and the complexity and high correlation of the hidden patterns that represent fault and healthy conditions of the system, the authors then implement a Radial Basis Function Neural Network model (RBF) to predict the performance of the system.
- In addition, RBF models can be trained much faster than other neural networks architectures, such as Multilayer Perceptron Neural Networks for example, and they are very stable, as discussed and demonstrated in [9] .

### II. RADIAL BASIS FUNCTIONS

- Radial Basis Function Neural Network (RBF) are a class of neural networks made of an input layer, a hidden layer, and an output layer.
- The activation function of the hidden layer neurons is specified by the distance between the input vector and the prototype or target vector [8] .
- The first layer of weights is dedicated to the parameters of the basis functions while the second layer represents the linear combinations of the basis function activation functions.
- For further details please refer to [8] .

### III. DATA

- The analyzed dataset in this paper is an open access synthetic dataset generated from a Simulink® model of a Naval Gas Turbine [10] and it can be found at: (https://archive.ics.uci.edu/ml/machine-learningdatabases/00 316/).
- The Gas Turbine model is made of 16 input features, listed in Table 1 and two outputs, the Compressor Decay coefficient and the Turbine Decay coefficient.
- The first output variable is related to the decay of the performance of the gas turbine compressor and it varies in the range [0.95; 1], where 0.95 means that a 5% decay in the compressor performances is recorded.
- The optimal number of hidden neurons in the RBF model is decided in the validation phase where the optimal number of hidden neurons is selected by calculating the error between the network prediction of the validation data set and their actual values.
- In the final stage of the RBF model creation, the performance of the specified optimal structure is tested on the test dataset which is a sub-set of the original dataset that has normally never been seen before by the network.

### IV. DATA PREPROCESSING

- Before going on to the actual analysis, the dataset was preprocessed in order to remove the non-relevant features for the prediction of the system performance decay.
- This is an important data analysis stage that is very often overlooked.
- This will subsequently introduce unneeded noise, time delays in the results calculations, and more in general, reduction in the algorithm predictions performances.
- The preprocessing of the dataset mainly includes the calculation of the correlation coefficients between the 16 input features and the 2 output variables.
- Then, features 6 and 7, starboard propeller torque and port propeller torque, show identical correlation coefficients and indeed they have identical values, so one of them, feature 7, has been removed.

### V. REGULARISATION WITH NOISE INTRODUCTION

- As discussed before, the gas turbine data has been generated through simulation, therefore it is purely deterministic.
- In order to mimic the real-world situation where sensors' noise and uncertainty are unavoidable, the authors added some noise to the outputs (turbine decay coefficient and compressor decay coefficient).
- Some noise has also been introduced to the training data set and added to the 11-correlation based selected inputfeatures as a regularization mechanism for the neural network learning.
- Given a random vector noise n and its probability p(n), the error used to determine the weights using the error equation 4 for the limit of an infinite number of data points can be rewritten as [8] : EQUATION.
- Given that the noise amplitude is small enough to neglect the Taylor expansion high order terms, the minimization of the error with the noise added in the input is equivalent to the minimization of the error without the noise terms added to the input plus the regularization term in equation 12 .

### VI. PREDICTION OF CONFIDENCE INTERVAL

- An aspect that is often overlooked is the development of metrics that are suitable for measuring the accuracy of a specific prediction of neural networks.
- When the accuracy of the forecast is not sufficiently precise, alternative decisions can be made in order to avoid worsening the situation if the machine learning algorithm is unable to provide reliable predictions within a certain range of precision.
- The Confidence Interval (CI) of the network prediction has been used as a metric of the RBF prediction performance.
- In order to be able to predict the confidence interval of the neural network estimates of the system decay, a second RBF network is used to estimate the calculated residual error values between the actual decays and estimated ones after the completion of the training of the RBF that estimates the decays.
- This is the level that the authors aim to achieve in this work, therefore they expect to define a results accuracy level that allows for outliers only for 5% of the cases.

### VII. NUMERICAL SIMULATION: EXPERIMENTS SETUP AND RESULTS

- The RBF has been used to predict the system decay and the confidence interval of the prediction.
- The complexity of the neural network then decreases with the increase in the noise level.
- This residual error is then used as the target value for a second RBF network in order to determine the level of accuracy of the system decay prediction on the test dataset.
- The incorrect interpretation of these false can lead to poor and potential harmful decisions as well as unneeded stoppages, thus increasing the costs of maintenance operations.
- With the introduction of the CI, more careful attention can be given to the predictions that present a wider CI and therefore a lower reliability of the prediction.

### VIII. CONCLUSIONS

- In the context of Industrial Analytics, the performance prediction of a system represents a highly nonlinear and uncertain problem where the status of several attributes of the system and its components might or might not concur simultaneously to the overall performance decay.
- This combined with the estimation of the result reliability through the CI implementation aims to provide a support for the maintenance strategic decision-making process with a reduction in the probability of false alarms.
- The importance of understanding and preprocessing the data to select the relevant features only are emphasized.
- It is shown that the noise in the input can in fact help in reducing the number of parameters of the trained RBF neural network.
- This is mostly because the studied gas turbine problem is a standard regression problem for which the authors used and implemented dimensionality reduction techniques and universal function approximators.

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##### Citations

19 citations

### Cites background or methods from "Performance Prediction using Neural..."

...4 BSOA, GN, NII aHardware Connection (HC), Information Discovery (ID), Intelligent Production (IP), Predictive Maintenance (PdM). bAcoustic (Ac), Car Manufacturing (CM), Car Specification (CS), Chemical (Ch), Chemical Laboratory (ChL), Gas Turbine (GT), Gesture Images (GI), Image (I), Machine (Mc), Machine Centre (McC), Material (Ma), Network (N), Pellets Images (PI), Production (Pr), Reference Metadata (RM), Robotic (Rb), Sensor (S), Sheet Material (SM), Simulated Sensor (SimS), Solar Panel (SolP), Steel (St), Text (T), Time Series (TS), Welding Images (WI). cAerospacial (Ae), Automotive (A), Coil (C), Electronic (El), Energy (En), Food (Fo), Footwear (F), Furniture (Fu), Healthcare (Hc), Naval (Na), Not Disclosed (ND), Oil (O) Petrochemical (Pc), Polymer (Pl), Robotic (Rb), Semiconductor (SC), Spring (Sp), Steel Plate (SP), Transportation (Tr). dAdaptive Neuro-Fuzzy Inference Systems (ANFIS), Analysis of Variances (ANOVA), Artificial Neural Networks (ANN), Association Rules (AsR), Backtracking Search Optimization Algorithm (BSOA) Bagged Decision Trees (BDT), Bagged Trees (BagT), Bagging (Bag), Bayesian Filter (BF) Boosting Trees (BosT), Complex Fuzzy (CF), Conference Trees (CT), Convolutional Neural Networks (CNN), Decision Forest (DF), Decision Jungle (DJ), Decision Trees (DT), Deep Learning (DL), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Discriminant Analysis (DA), Extreme Gradient Boosting (EGB), Extreme Learning Machine Boundary (ELMB), Extremely Randomized Trees (ERT), Fast Nearest Neighbours (FaNN), Feed Forward Neural Network (FeNN), Fog Computing (FC), Fuzzy-Logic (FL), Gaussian Model (GM), Gaussian Noise (GN), Genetic Algorithm (GA), Genetic Programming Based Symbolic Regression (GPBSR), Global Local Outliers in Sub Spaces (GLOSS), Gradient Boosted Regression Trees (GBRT), Gradient Boosted Tree Classifier (GBTC), Gradient Boosting (GB), Gradient Boosting Decision Trees (GBDT), Gradient Boosting Machine (GBM), H20 Deep Learning (h2oDL), Hidden Gama Process-Particle Filter (HGP-PF), Hidden Markov (HM), In Situ Classification System (ISCS), Isolation Forest (IF), Kalman Filter (KF), Kurtosis (K), K-Means (KM), K-Nearest Neighbor (KNN), Linear and Polynomial Fit (LPF), Linear Regression (LinR), Local Outlier Factor (LOF), Logistic Regression (LogR), Map Reduce (MR), Matlab Model Predictive Toolbox (MMPT), Mean and Standard Deviation (MSD), Mean Shift (MS), Microsoft Azure Machine Learning (MAML), Micro-Cluster Continuous Outlier Detection (MCCOD), Model Predictive Controller (MPC), Multiple Regression (MR), Multivariate Adaptive Regression Splines (MARS), Multi-Entity Bayesian Networks Regression (MEBNR), Multi-Layer Regression (MLR), Naive Bayes (NB), Neural Networks (NN), Neuro-Fuzzy Networks (NFN), Noise Impulse Integration (NII), Novelty Classifier (NOVCLASS), Out-of-Bag Error (OBE), Partial Least Squares (PLS), Particle Swarm Optimization (PSO), Principal Component Analysis (PCA), Pure Quadratic Regression (PQR), Quadratic Discriminant Analysis (QDA), Random Forest (RF), Random Support Vector Machine (RSVM) Recursive Partitioning (RP), Regression Trees (RT), Ridge Regression (RR), Rule-Based (RB), Skewness (Sk), Spectral and Agglomerative Clustering (SAC), SRT Model (SRTM), Stochastic Model Predictive Controller (SMPC), Support Vector Machines (SVM) Survival Analysis (SA), Time Series Forecasting (TSF), ZeroR (ZR)....

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...Simple neural networks are used in several research works such as (Cisotto & Herzallah, 2018; Kabugo et al., 2020; Miškuf & Zolotov a, 2016; Soto et al., 2019; Spendla et al., 2017)....

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...2 SRTM Cisotto and Herzallah (2018) PdM GT Na Used NNs in a system that support the maintenance function in the decision-making process....

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##### References

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19,056 citations

13,033 citations

### "Performance Prediction using Neural..." refers background or methods in this paper

...The output of the RBF network is calculated as [8]:...

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...For further details please refer to [8]....

[...]

...Further details on the definition of regularization functions can be found in [8]....

[...]

...Given a random vector noise n and its probability p(n), the error used to determine the weights using the error equation 4 for the limit of an infinite number of data points can be rewritten as [8]: = 12 [ ( ) − ] ∙ ( | ) ∙ ( ) (9)...

[...]

...Indeed, as extensively discussed in [8], introducing noise during the training phase in the input vector can help in controlling the network mapping complexity as well as reducing the probability of data over-fitting....

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481 citations

168 citations

### "Performance Prediction using Neural..." refers methods in this paper

...0" where already known and developed tools, such as CBM, are empowered by the analysis and processing of data collected using IoT and cloud-based solutions and processed using ML applications [4-7]....

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135 citations

### "Performance Prediction using Neural..." refers background or methods in this paper

...DATA The analyzed dataset in this paper is an open access synthetic dataset generated from a Simulink® model of a Naval Gas Turbine [10] and it can be found at: (https://archive.ics.uci.edu/ml/machine-learningdatabases/00 316/)....

[...]

...An important point to make is that although the developed approach in this paper has been tested only on the Gas Turbine dataset application, the method we developed is definitely transferable to other applications....

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...The Gas Turbine model is made of 16 input features, listed in Table 1 and two outputs, the Compressor Decay coefficient and the Turbine Decay coefficient....

[...]

...Thus, the dimensionality of the input variables has been consequently reduced, an aspect that has been overlooked by the authors in [10]....

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...Based on the value of the correlation coefficients, feature 1 and 2 (lever position and sheep speed) have been removed due to their low correlation with the outputs and the fact that they are both included in the constitutive model of the Gas Turbine [10]....

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