Damage model of turbine rotor based on DPLS

The working environment of the steam turbine rotor is very bad, the thermal stress changes greatly, plus its own moment of inertia is large, there are many stress concentra tion parts, its material performance, geometry and operation conditions have a great impact on the normal operation of the steam turbine [1]. Rotor is the most dangerous part in the whole unit, its life determines the life of the whole turbine unit. Because when the rotor is rotating at high speed, with the change of unit load, the rotor itself will produce large al ternating thermal stress. Therefore, the life of the whole unit can be controlled by controlling the thermal stress change of the rotor.


Research background and research status
The working environment of the steam turbine rotor is very bad, the thermal stress changes greatly, plus its own moment of inertia is large, there are many stress concentra tion parts, its material performance, geometry and operation conditions have a great impact on the normal operation of the steam turbine [1]. Rotor is the most dangerous part in the whole unit, its life determines the life of the whole turbine unit. Because when the rotor is rotating at high speed, with the change of unit load, the rotor itself will produce large al ternating thermal stress. Therefore, the life of the whole unit can be controlled by controlling the thermal stress change of the rotor.
At present, the research focus in the field of steam turbine life assessment and management mainly focuses on the calculation method of life loss and the research of various nonlinear damage accumulation methods in the process of start-up and shut-down [2].
During the start-up and operation of steam turbine, the thermal stress and mechanical stress on the rotor gradually change, involving many process variables, including steam pressure, steam temperature, steam temperature change rate, rotor speed, etc., which belongs to the transient condition of steam turbine [3]. The variation of these variable parameters has a direct impact on the service life of turbine rotor metal materials. For example, the large change of steam temperature will cause great thermal stress and metal fatigue dam age, while the continuous high temperature and high pres sure will cause the creep damage of rotor metal materials [4].
During the transient condition, the heat transfer process inside the steam turbine components is unstable, which leads to the uneven temperature distribution inside the metal, thus causing the thermal stress inside the metal. In order to con-Citation: Dong  process is simple and practical, and it can be used for online monitoring of turbine rotor damage. However, the method simplifies the rotor as a cylinder, which not only ignores the influence of the geometry on the stress concentration, but also directly treats the heat transfer conditions on the rotor surface and the physical characteristics of the metal as constants, which affects the calculation accuracy. With the rapid development of computer technology, the numerical analysis technology represented by the finite element analysis has been highly valued and widely used in the subject of Turbine Damage Assessment and life prediction [9].
For steam turbine in thermal power plant, the ultimate goal of optimization is to reduce the stress value and startup time of rotor. In the unit, the rotor of steam turbine is an important part, which carries the energy and torque [10].
The safety of steam turbine unit is mainly determined by the quality of turbine rotor. Reducing the start-up time of the equipment is a decisive factor while ensuring that the stress value of the turbine rotor is less than the yield limit value of the rotor material. From a few years ago to now, the quality of life has improved signifi cantly, the grid capacity has increased signifi cantly, so the peak value of the grid has been increasing [11]. Frequent peak shaving operation means frequent startup and shutdown of the steam turbine unit. The change of working condition of steam turbine unit will cause the damage of rotor material, thus shortening the life of the unit [12]. The parameters of steam turbine will change greatly during startup. Among them, the change of temperature parameter is the most important [13]. It will make the rotor produce a force, which is called thermal stress. At the same time, it will make the metal material deform, mainly in the form of expansion deformation [14]. Once the thermal stress exceeds the yield limit of the rotor material, the high-temperature components, mainly the turbine rotor, will produce certain damage, which will eventually bring some security risks [15].
The needs of today's society should be met, so it is necessary and very important to study the rapid start-up process. The start and stop of steam turbine depends on how long it can be used, which means that it directly affects the life of the unit. After a detailed study of the start and stop of the steam turbine unit, a curve of start-up is given and used to guide the unit, which can improves security and economy at the same time. In brief, the start-up optimization of steam turbine is to optimize a function. At the same time, this function has constraint conditions. Generally speaking, the start-up time is the shortest and the stress is within a reasonable range\ cite{C04}.
Before that, there were many ways to optimize start-up of unit. It is impractical to measure and test the input data in the actual power plant, so using complex simulation software is the most commonly used method to evaluate the solution.
For an axisymmetric body, such as a steam turbine rotor, whose geometry is irregular and boundary conditions vary greatly, it is necessary to apply numerical method to obtain accurate calculation results [16]. The rotor is considered as an ax isymmetric two-dimensional computational model, and the complex geometric continuum is discretized. The heat release coefficient and material properties of the medium on the surface of the rotor are treated as variables with starting time.
The Finite Element Method (FEM) is the most com monly used numerical method for thermal stress calculation. It is developed on the basis of energy method and differ ence method, and has both advantages. The essence of the finite element method is to use the variational calculation in the element and the overall synthesis to replace the differ ential equation solution [17].
As long as the partition element is small enough, the result can be obtained with enough accura cy by using simple linear interpolation function. Moreover, the mesh division is flexible and the adaptability to irregular boundary is good.

Research objective
The pre d iction process of dynamic partial least squares is dynamic, which can change with the input data, and directly refl ect the stress and damage data of turbine rotor in the whole start-up process. In the past, only three-dimensional modeling of turbine rotor was carried out in the research of steam turbine, which was imported into the fi nite element analysis software

Structure of turbine starting system
At present, in order to analyze the actual working condition more effectively and economically, the system structure model which is basically consistent with the actual working condition has been established in most industrial occasions. Through the analysis and experiment of the structure model, the working state and effi ciency of the system can be judged. However, the accuracy and effi ciency of different structural models are different. In this paper, a high precision stress damage model of steam turbine starting system is established. Figure 1 shows It should be noted that the controller does not need to be changed. The stress feedback control is introduced into the structural model to judge the load level of the unit according to the monitoring of the corresponding stress value, so as to extend the service life of the unit. The damage model is used to evaluate the damage value in the process of unit startup. This structural model is suitable for online implementation, and its features include: 1. Stress model and damage model belong to the level of accurate life assessment, which can give more accurate assessment of stress value and damage value.
2. The evaluation is faster and more effi cient.
3. The system can adjust the input and output according to the feedback of stress value and damage value, so as to prolong the life of the unit.

Establishment of online damage assessment model based on DPLS
The work ing environment of the steam turbine rotor is very bad, the thermal stress changes greatly, plus its own moment of inertia is large, there are many stress concentra tion parts, its material performance, geometry and operation conditions have a great impact on the normal operation of the steam turbine. Rotor is the most dangerous part in the whole unit, its life determines the life of the whole turbine unit. Because when the rotor is rotating at high speed, with the change of unit load, the rotor itself will produce large al ternating thermal stress. Therefore, the life of the whole unit can be controlled by controlling the thermal stress change of the rotor.

Establishment and analysis of DPLS prediction model
The partial least squares method was fi rst proposed by wold.
It is a regression modeling method that multiple independent variables correspond to multiple dependent variables. Partial least square method decomposes independent variable x and dependent variable y of life loss, and extracts useful data from them.
In the start-up process of steam turbine, the high temperature and high pressure steam drives the turbine rotor to rotate, steam and temperature are continuously changing, and there is a high correlation between parameters. In order to maximize the use of fi nite element analysis data and more truly refl ect the impact of process variables on the life of turbine rotor, this paper adopts DPLS regression modeling method, that is, in the input and output The data of dependent and independent variables are included in the matrix, and the expanded matrix is regressed by partial least squares.
Defi ne input variables, output variables and matrices t u ,  In this way, the input matrix X can be constructed as: At the same time, the output matrix Y can also be obtained: In this paper, the design idea of partial least squares is to extract t i , i = 1,2..., from the independent variable X of turbine rotor. The i u is extracted from the dependent variable Y and the regression equation is established.
Firstly, the process variable matrix X and Y of the steam turbine rotor are processed. In this paper, the mean value and proportion are taken. The X matrix can be decomposed into the product of the score vector H and the load vector I, plus the form of the residual matrix F, the Y matrix can be decomposed into the product of the score vector K and the load vector R, plus the form of the residual matrix E: where H i u By regression analysis of the score vectors  u j and P of Y and X matrices, including: is the dynamic regression coeffi cient, j=1,2,...,a. The form of matrix can be expressed as: If  j U is introduced into  u j , the residual matrix will be changed, as follows: Where E  is the prediction error matrix, The criterion for selecting matrix 1 ( ) j L q  is to minimize the two norm of matrix E  . The form of score vector matrix of input-output matrix is defi ned as The input and output measurements are: t is the loading matrix after adding the new test input value.
Bring in the formula to get: Determine the following conditions: get: The low cycle fatigue damage of steam turbine can be decomposed into a dynamic linear model and a static nonlinear model. The key point is to identify the dynamic characteristics of temperature and stress. In the real-time monitoring of damage, these information are the basis of making decisions and controlling actions. Because of the complex physical mechanism of metal low cycle fatigue damage, it is very diffi cult to write its mathematical model directly. In this section, the rotor metal damage model of 300MW steam turbine during impulse running is established by nonlinear decomposition and model identifi cation based on fi nite element simulation data.
In order to establish the on-line monitoring model of rotor metal, it is necessary to identify the transfer function of main steam temperature to rotor surface temperature G 1 and the transfer function of heat fl ow density to thermal stress G 2 . These two transfer functions can be inferred from the temperature data of the fi nite element analysis software: The temperature data used in this paper is the data optimized by genetic algorithm according to the results under the starting curve of the original working condition. First, calculate the temperature and temperature output curve under the original working condition curve, and calculate G 11 and G 22 .
The following is the fi tting process of the transfer function. Through the system identifi cation toolbox of MATLAB, the transfer function shown in formula 19 and formula 20 can be obtained. The accuracy of the transfer function is 98.23% Figure 3.
The starting curve of the original working condition is shown in the Figure 4 below: After fi tting the data, G 11 and G 22 are as follows: 11 In this paper, the optimized results are used. The optimized temperature curve and temperature output curve are shown in the Figure 5 below: The resulting transfer function is: The optimized results greatly shorten the start-up time of the steam turbine unit. However, through comparison, the parameters of the transfer function have some changes, but the data changes little.
In this paper, according to the consideration of different working conditions, the temperature rise rate of the cold startup curve under the real working condition is changed by using

Model simulation results
In the process of starting, stopping and changing working conditions of steam turbine, the rotor of steam turbine must bear huge temperature changes, which will cause uneven heating of rotor metal and generate thermal stress. During the start-up process of steam turbine, the stress of rotor is the superposition of various forces, including thermal stress caused by temperature, centrifugal force caused by rotation of rotor itself, pressure of working medium on rotor metal, bending moment caused by weight of rotor itself and torque caused by power transmission of steam turbine. Among them, the thermal stress value is the largest, which can reach the order of 100MPa, followed by centrifugal force, which can reach the order of 10MPa, and other force orders are very small.
In order to ensure the calculation is simple, it can be ignored.
Therefore As can be seen in the fi gure, after the start of the impulse process, a large number of high temperature and high pressure steam enters the cylinder, and the heat is continuously released on the rotor surface, resulting in the increasing thermal stress of the rotor, so the real-time data of low cycle fatigue damage is maintained in a high level data fl uctuation.

Analysis of model results
The results obtained from the model can be shown as follows: the results of the model are very close to the operation results of the actual plant, and the accuracy is a high level, through the analysis of the input and output data of the model, a relationship between the cold start-up curve and the thermal stress of the turbine rotor can be obtained. In the process of cold start-up, the thermal stress has a very direct relationship with the turbine rotor speed, steam temperature and steam pressure.

Conclusion
In view of the high spatial-temporal correlation of steam turbine system operation process data, a DPLS method is proposed in this chapter, which maximizes the covariance of steam parameter matrix and low cycle fatigue life loss, retains useful information, eliminates the correlation between variables, selects the same variables in different time series, reduces the dimension of simulation data from high-dimensional space, establishes an accurate model, and establishes a mathematical model Low cycle fatigue life loss model of steam turbine rotor. Finally, by comparing the experimental data with the simulation results, the online damage assessment model based on fi nite element technology is verifi ed, and the effectiveness of DPLS algorithm in low cycle fatigue damage prediction of turbine rotor is verifi ed. The inaccuracy of one-dimensional analysis method in the fi eld is solved, while the inaccuracy of numerical analysis method in the fi eld of life assessment is solved, which provides reference for the life prediction of turbine rotor It provides a new way of thinking in practice.