An Online Data-Driven LPV Modeling Method for Turbo-Shaft Engines

Ziyu Gu,Qiuhong Li,Wenxiang Zhou,Yuchen Li,Shuwei Pang

doi:10.3390/en15041255

Abstract

The linear parameter-varying (LPV) model is widely used in aero engine control system design. The conventional local modeling method is inaccurate and inefficient in the full flying envelope. Hence, a novel online data-driven LPV modeling method based on the online sequential extreme learning machine (OS-ELM) with an additional multiplying layer (MLOS-ELM) was proposed. An extra multiplying layer was inserted between the hidden layer and the output layer, where the hidden layer outputs were multiplied by the input variables and state variables of the LPV model. Additionally, the input layer was set to the LPV model’s scheduling parameter. With the multiplying layer added, the state space equation matrices of the LPV model could be easily calculated using online gathered data. Simulation results showed that the outputs of the MLOS-ELM matched that of the component level model of a turbo-shaft engine precisely. The maximum approximation error was less than 0.18%. The predictive outputs of the proposed online data-driven LPV model after five samples also matched that of the component level model well, and the maximum predictive error within a large flight envelope was less than 1.1% with measurement noise considered. Thus, the efficiency and accuracy of the proposed method were validated.

Highlights

The behavior of an aero engine can be described by a linear parameter-varying (LPV)model, which can approximate a nonlinear system or a time-varying linear system with a combination of linear time-invariant (LTI) models [1–3]
The simulation results showed that the special online sequential extreme learning machine (OS-ELM), with an additional multiplying layer, achieved a high degree of approximation accuracy, which implied the effectiveness of the online data-driven LPV (DD-LPV) model derived by MLOS-ELM
Iefrtrhoersmaetatsimureemk +en5tonfoDisDe -wLaPsVnmotocdoenlsridoteorerdsp, seiemdilar parameter variations resulted, as Figure 6 illustrates. This meant that the changes were aroused by the measurement noise added to the online training data of the MLOS-ELM, which in turn affected the parameters of the DD-LPV model

Summary

Introduction

The behavior of an aero engine can be described by a linear parameter-varying (LPV). model, which can approximate a nonlinear system or a time-varying linear system with a combination of linear time-invariant (LTI) models [1–3]. A novel online data-driven LPV (DD-LPV) modeling method for turbo-shaft engines based on a special neural network was proposed in this paper. It derived the DDLPV model from an online sequential extreme learning machine (OS-ELM), with an extra multiplying layer (MLOS-ELM). TThhee sskkeettcchh ooff tthhee bbii--rroottoorr ttuurrbboo--sshhaafftt eennggiinnee rreesseeaarrcchheedd iinn tthhiiss ppaappeerr iiss sshhoowwnn iinn FFiigguurree11[4[422].].DuDruinrgintghethoepeorpaetiroanti,otnh,e tchoemcpormespsreedssaeirdisaidrraiswdnrfarwomn ftrhoemintlehteainndleftloawnds tflhorowusgthhrthoeugchomthperecsosmorptroestshoerctoomtbhuesctomr wbuhsetroerfuwehleirseinfutreoldius ciendtr,omdiuxceedd,,amndixiegdn,itaendd. Owing to there being 3 independent state and input variables x1, x2, u in turbo-shaft engine’s LPV model, the nodes in the multiplying layer must be divided into 3 groups, evenly or not. Taking more parameters as the inputs of MLOS-ELM could have affected the accuracy of the DD-LPV

Online Updating Algorithm of MLOS-ELM

Simulation and Discussions

Prediction Ability Validation of the Online DD-LPV Model in Flight Envelope

Findings

Conclusions