CN112560261B - A data-driven method for predicting failure rate of key equipment in hydrogen energy systems - Google Patents

Abstract

A failure rate prediction method of key equipment of a hydrogen energy system based on data driving comprises the steps of firstly, calculating initial failure rate of the key equipment of the hydrogen energy system based on a component stress method, then respectively calculating optimized failure rate of the key equipment of the hydrogen energy system based on field data by using a Weibull distribution parameter method and a point estimation method, further calculating weight numbers of 2 failure rates of the key equipment of the hydrogen energy system calculated by the two methods under the field data by using a fuzzy binary comparison sorting method, and calculating optimized failure rate by using a weighted average method; secondly, considering the influence of hydrogen energy flow on the safety performance of the equipment, analyzing and comparing the initial failure rate of the hydrogen energy system key equipment obtained based on the component stress method and the optimized failure rate of the hydrogen energy system key equipment obtained based on field data, and obtaining a correction factor of the hydrogen energy system key equipment; and finally, correcting the optimized failure rate of the key equipment of the hydrogen energy system according to the correction factor, and establishing a failure rate optimization model.

Description

A data-driven method for predicting failure rate of key equipment in hydrogen energy systems

technical field

The invention relates to a failure rate prediction method for key equipment of a hydrogen energy system.

Background technique

With the continuous development of my country's industry, the key equipment of hydrogen energy systems such as electrolyzers, hydrogen storage tanks, hydrogen fuel cells, etc. related to hydrogen energy is also growing. In many links such as use and storage, its own inherent danger has brought great threats to human life and the environment. In recent years, with the increasing supervision and control of the chemical industry in my country and the continuous improvement of safety production standardization, environmental and occupational health and safety systems, the accident rate caused by the failure of key equipment in the hydrogen energy system due to aging and other reasons has continued to decline.

Combining the existing risk research literature at home and abroad, it can be found that the prediction of the failure rate of key equipment in the hydrogen energy system is the basis for scientific and quantitative safety evaluation of the system, and it is also the basis for giving risk control countermeasures. At present, considering the influence of hydrogen energy flow on the safety performance of the equipment in each component of the key equipment of the hydrogen energy system in the factory, the failure rate of the equipment has changed. Such research problems of optimizing the field data and predicting the failure rate of the key equipment of the hydrogen energy system are still urgently needed. solve.

SUMMARY OF THE INVENTION

Aiming at the defect that the failure rate prediction and optimization of key equipment of hydrogen energy in the hydrogen energy system still has the defect of lack, the invention proposes a method for predicting the failure rate of key equipment of the hydrogen energy system. The invention collects the on-site operation data of the key equipment of the system in the factory, in order to obtain a more accurate failure rate of the key equipment of the system, and uses the Weibull distribution parameter method and the point estimation method to establish a failure rate correction model of the key equipment of the hydrogen energy system and Predict the failure rate of key equipment in the hydrogen energy system, and establish an optimization model for the failure rate of key equipment in the hydrogen energy system.

The steps of the present invention are as follows:

1. Analyze the usage time and characteristics of the key equipment of the hydrogen energy system; collect the failure rate data of various key equipment of the system based on the failure database commonly used in the petrochemical process industry, and obtain the failure rate λ _i ′ of each component of the key equipment of each type of hydrogen energy system, where i is the sample capacity of the key equipment of the hydrogen energy system;

2. Calculate the initial failure rate λ ₁ of the key equipment of the hydrogen energy system;

3. Establish the failure rate correction model of key equipment in the hydrogen energy system, and use the Weibull distribution parameter method to obtain the influencing factors λ(t) and the point estimation method to obtain the influencing factors

确定权重比矩阵T_2×2，归一化求出氢能系统关键设备失效率的权重数k₁和氢能系统关键设备失效率的权重数k₂，其中k₁根据威布尔分布参数估计法计算得到，k₂根据点估计法计算得到；4. The influencing factors λ(t) obtained by the Weibull distribution parameter method and the point estimation method and the influencing factors obtained by the point estimation method

Determine the weight ratio matrix T _2×2 , and normalize it to obtain the weight number k ₁ of the failure rate of key equipment in the hydrogen energy system and the weight number k ₂ of the failure rate of key equipment in the hydrogen energy system, where k ₁ is based on the Weibull distribution parameter estimation method Calculated, k ₂ is calculated according to the point estimation method;

5. Obtain the optimized failure rate λ ₂ of the key equipment of the hydrogen energy system through the weight number obtained in step 4;

6. Considering the influence of the hydrogen energy flow in each component of the key equipment of the hydrogen energy system on the safety performance of the equipment, a correction factor is obtained, and the optimized failure rate λ ₂ is corrected.

In the step 1: currently, in the process of predicting and optimizing the failure rate of key equipment of the hydrogen energy system, the key equipment of the hydrogen energy system is generally divided into three types: hydrogen production equipment, hydrogen storage tank and hydrogen fuel cell. These three types of key equipment in the hydrogen energy system have their own characteristics, and the failure rate data is different from the data obtained from on-site testing. The failure rate data and on-site operation data of hydrogen production equipment, hydrogen storage tanks and hydrogen fuel cells can be According to the calculation of the relevant system failure rate and optimization.

Each structure of each type has a corresponding failure rate. The working characteristics and structures of the key equipment of the three types of hydrogen energy systems are as follows.

Hydrogen production equipment is a key equipment in the process of electrolysis of water for hydrogen production. Hydrogen production by electrolysis of water is a process in which the electrolyte dissolved in water is decomposed into new substances by the action of direct current. Hydrogen production equipment includes electrolyzer, hydrogen side system, oxygen side system, make-up water system, and lye system. Electrolyzer is the main equipment in hydrogen production equipment.

A hydrogen storage tank is a special pressure vessel for hydrogen storage. The hydrogen storage tank adopts a three-layer wrapping design, the inner layer is a metal alloy liner, the middle layer is a thermal insulation layer, and warm water flows through it to provide thermal energy for the inner layer, and the outer layer is a protective layer, which is made of materials that resist external corrosion and heat preservation. .

A hydrogen fuel cell is an electrochemical device that continuously and directly converts the chemical energy in the continuously supplied hydrogen energy and oxidant into electrical energy. The general structure of a hydrogen fuel cell system consists of a hydrogen fuel cell, a DC-DC converter and a load. The hydrogen fuel cell is linked to the load through the DC-DC converter, and the power flow can be balanced by controlling the DC-DC converter. High overload power can be provided instantaneously, which accelerates the dynamic response of hydrogen fuel cells.

Based on the initial failure rate of key equipment of the hydrogen energy system obtained by the component stress method, and the failure rate of the key equipment of the hydrogen energy system obtained based on field data, an optimization model of the failure rate of the key equipment of the hydrogen energy system is established, and the key equipment of the hydrogen energy system is constructed. The failure rate framework of equipment predicts the failure rate of key equipment in a certain type of hydrogen energy system.

The invention analyzes the usage time and characteristics of key equipment of the hydrogen energy system, and obtains the data of each component of the three typical system key equipment types of the hydrogen production equipment electrolyzer, hydrogen storage tank and hydrogen fuel cell based on the failure database commonly used in the petrochemical process industry. The failure rate λ _i ', where i is the sample capacity of the key equipment of the hydrogen energy system.

In the step 2, the initial failure rate λ ₁ of the key equipment of the hydrogen energy system is calculated, and the method for establishing the failure rate model of the key equipment of the hydrogen energy system is as follows:

Since the failure rate of each component of the key equipment of the hydrogen energy system basically obeys the exponential distribution, the failure rate is a constant value. If any part of the key equipment of the hydrogen energy system fails, the key equipment of the hydrogen energy system cannot work normally, so each part of the key equipment of the hydrogen energy system is a series system. Assuming that the reliability function of the key equipment and each component of the hydrogen energy system obeys the exponential distribution, the initial failure rate of the key equipment and each component of the hydrogen energy system satisfies the following formula:

In the formula, λ ₁ is the initial failure rate of the key equipment of the hydrogen energy system, λ _i ′ is the initial failure rate of each component of the key equipment of the hydrogen energy system, and i is the sample capacity.

In the step 3, the obtained failure rate data of key equipment of the hydrogen energy system is processed by the Weibull distribution parameter method and the point estimation method, and the influence factor λ(t) obtained by the Weibull distribution parameter method and the point estimation method are obtained. Influencing factors

(1) Using the Weibull distribution method to determine the failure rate influencing factor λ(t) of the key equipment of the hydrogen energy system.

The Weibull distribution is one of the most widely used models in equipment life failure rate analysis, and it is also the most common distribution in equipment failure distribution. At the same time, the average rank is used to improve the accuracy of Weibull distribution parameters, which is an effective method to improve the accuracy of failure rate data analysis.

The approximate median rank formula is:

In the formula, ty is the life data of the _y -th failed equipment; x is the sample capacity of the key equipment of the hydrogen energy system; y is the position after sorting the equipment failure data, which is the average rank A _y of the faulty equipment.

The failure function of the Weibull distribution is:

The failure density function is:

The reliability function is:

Using the Weibull distribution method to determine the failure rate influencing factor function of key equipment in the hydrogen energy system is:

where t is the time, a is the scale parameter, and β is the shape parameter.

(2) Use the point estimation method to determine the factors affecting the failure rate of key equipment in the hydrogen energy system

Analyze the failure data of key equipment of the hydrogen energy system, summarize the same type of failures of the key equipment of the hydrogen energy system, and assign the summarized failure data to each component of the key equipment of the hydrogen energy system according to functional classification. Since the life of the key equipment of the hydrogen energy system basically obeys the exponential distribution, the initial failure rate of the key equipment of the hydrogen energy system is a constant value.

是氢能系统关键设备第j个部件的失效率；r为T时段内氢能系统关键设备发生的故障次数；T为发生故障的时段。In the formula,

is the failure rate of the jth component of the key equipment of the hydrogen energy system; r is the number of failures of the key equipment of the hydrogen energy system in the T period; T is the period of failure.

The failure rate of the key equipment of the hydrogen energy system is the sum of the failure rates of its various components. The mathematical expression for determining the factors affecting the failure rate of the key equipment of the hydrogen energy system using the point estimation method is:

Among them, j is the sequence of key equipment components of the hydrogen energy system, i is the sample capacity, i=1, 2, 3,  …n.

In the step 4, on the basis of the on-site operation data, the initial failure rate of the key equipment of the hydrogen energy system based on the component stress method, and the failure rate based on the on-site data are obtained. In order to make these two failure rates more accurate, the fuzzy binary comparison and ranking method is used to objectively sort and judge the failure rate of key equipment in the hydrogen energy system based on field data, and obtain the weight of the failure rate. The weighted average method optimizes the initial failure rate based on the component stress method, and the failure rate based on field data.

The specific steps to optimize the two failure rates are as follows:

Firstly, determine the influence factor λ(t) of the failure rate of the key equipment of the hydrogen energy system based on the Weibull distribution parameter estimation method and the influence factor of the failure rate of the key equipment of the hydrogen energy system based on the point estimation method.

Next, the weight ratio matrix T _2×2 is determined.

的值，其中U₁为基于威布尔分布参数估计法得到的由氢能系统关键设备各个部件的失效率影响因素集，U₂为基于点估计法得到的氢能系统关键设备各个部件的失效率影响因素集，u_j为失效的设备寿命数据集j＝1,2，

为氢能系统关键设备基于威布尔分布参数估计法的失效率密度函数。According to the factor set U={U ₁ U ₂ }

, where U ₁ is the set of factors affecting the failure rate of each component of the key equipment of the hydrogen energy system obtained based on the Weibull distribution parameter estimation method, and U ₂ is the failure rate of each component of the key equipment of the hydrogen energy system obtained based on the point estimation method Influencing factor set, u _j is the failed equipment life data set j=1, 2,

Failure rate density function based on Weibull distribution parameter estimation method for key equipment of hydrogen energy system.

满足：

其数学表达式为：

Require

Satisfy:

Its mathematical expression is:

The weight ratio matrix is:

为

为氢能系统关键设备基于威布尔分布参数估计法的失效率密度函数，

为氢能系统关键设备基于点估计法的失效率密度函数，t_ij氢能系统关键设备基于威布尔分布参数估计法和基于点估计法的失效率密度函数之比。in

for

is the failure rate density function based on the Weibull distribution parameter estimation method for the key equipment of the hydrogen energy system,

is the failure rate density function based on the point estimation method for the key equipment of the hydrogen energy system, t _ij is the ratio of the failure rate density function based on the Weibull distribution parameter estimation method and the point estimation method for the key equipment of the hydrogen energy system.

The mathematical expression for the weight estimate is:

Among them, W ₁ and W ₂ are the failure rate weights of the key equipment of the hydrogen energy system based on the Weibull distribution parameter estimation method and the point estimation method, respectively, and t _ij is the key equipment of the hydrogen energy system based on the Weibull distribution parameter estimation method and the point estimation method. The ratio of the failure rate density function of the method, i, j = 1, 2.

The weight estimate is then normalized as the estimated weight:

Among them, k ₁ is the weighted number of the failure rate of key equipment of the hydrogen energy system calculated according to the Weibull distribution parameter estimation method, and k ₂ is the weighted number of the failure rate of the key equipment of the hydrogen energy system calculated according to the point estimation method.

In the step 5, after the weights k ₁ and k ₂ are obtained in step 4, the optimized failure rate λ ₂ of the key equipment of the hydrogen energy system based on the field operation data is obtained through the weights k ₁ and k ₂ .

Using the weighted average method, the optimized failure rate of the key equipment of the hydrogen energy system based on the field operation data is obtained as follows:

为利用点估计法确定氢能系统关键设备的失效率影响因素。Among them, k ₁ is the weighted number of the failure rate of key equipment of the hydrogen energy system calculated according to the Weibull distribution parameter estimation method, k ₂ is the weighted number of the failure rate of the key equipment of the hydrogen energy system calculated according to the point estimation method, λ(t ) in order to use the Weibull distribution method to determine the factors affecting the failure rate of key equipment in the hydrogen energy system,

In order to use the point estimation method to determine the factors affecting the failure rate of key equipment in the hydrogen energy system.

In the step 6, the initial failure rate obtained by the component stress method and the working failure rate of the key equipment of the hydrogen energy system obtained by the field operation data are compared and analyzed, and the correction factor is obtained:

τ=λ ₂ /λ ₁ -1

In the formula, τ is the correction factor and also the error coefficient; λ ₁ is the failure rate of the key equipment of the hydrogen energy system calculated based on the component stress method, and λ ₂ is the key equipment of the hydrogen energy system calculated by the weight. Optimized failure rate of equipment.

The failure rate correction model of the key equipment of the hydrogen energy system is:

λ= _λexpected (1+τ)

Among them, λ _{is expected} to be the failure rate of the key equipment of the hydrogen energy system calculated based on the component stress method in the model, and λ is the optimized failure rate of the key equipment of the hydrogen energy system calculated by the weight in the model.

Description of drawings

Fig. 1 is the structure diagram of electrolyzed water hydrogen production unit, in the figure, 1 electrolyzer, 2 hydrogen side system, 3 oxygen side system, 4 make-up water system, 5 lye system;

Figure 2 is a structural diagram of a hydrogen storage tank unit, in the figure, 6 inner layers, 7 intermediate layers, and 8 outer layers;

Figure 3 is a structural diagram of a hydrogen fuel cell power generation system unit, in which the hydrogen fuel cell, DC-DC converter, and load are shown;

Fig. 4 is a flowchart of the present invention based on a data-driven optimization method for predicting failure rate of key equipment in a hydrogen energy system.

Detailed ways

The present invention is further described below with reference to the accompanying drawings and specific embodiments.

As shown in FIG. 4 , the process of the present invention’s optimization method for predicting the failure rate of key equipment in a data-driven hydrogen energy system is as follows:

1. Analyze the usage time and characteristics of key equipment in the hydrogen energy system; based on the commonly used failure database in the petrochemical process industry and the collection of failure rate data of various key equipment in the hydrogen energy system, the analysis of hydrogen production equipment, hydrogen storage tanks, hydrogen fuel cells and other hydrogen energy The system structure of the key equipment of the system is divided. Figure 1 is the structure diagram of the electrolysis water hydrogen production unit. The electrolysis water hydrogen production is the process of decomposing the electrolyte dissolved in water into new substances with the help of direct current. The hydrogen production equipment includes electrolysis cell 1, hydrogen side system 2, oxygen side system 3, make-up water system 4, and lye system 5. Electrolyzer 1 is respectively connected to hydrogen side system 2, oxygen side system 3, make-up water system 4 and lye solution. System 5. The reaction of electrolysis of water to produce hydrogen is carried out in the electrolysis cell 1. The hydrogen side system 2 and the oxygen side system 3 collect the hydrogen and oxygen produced by the electrolysis water. System 5 provides lye to the hydrogen production equipment. The electrolytic cell 1 is the main equipment in the hydrogen production equipment. Figure 2 is a structural diagram of a hydrogen storage tank. The hydrogen storage tank adopts a three-layer wrapping design. As shown in Figure 2, the inner layer 6 is a metal alloy liner, the middle layer 7 is a thermal insulation layer, and warm water flows through it to provide thermal energy for the inner layer, and the outer layer 8 is a protective layer. Made of materials resistant to external corrosion and thermal insulation. Figure 3 is a structural diagram of the hydrogen fuel cell system. As shown in Figure 3, the hydrogen fuel cell power supply system consists of a hydrogen fuel cell, a DC-DC converter and a load. The hydrogen fuel cell system is connected to the load through the DC-DC converter, and can By controlling the DC-DC converter to achieve the balance of power flow, high overload power can be provided in an instant, which accelerates the dynamic response of the hydrogen fuel cell.

2. Calculate the initial failure rate of key equipment in the hydrogen energy system;

3. Establish a failure rate correction model for key equipment in the hydrogen energy system, and use the Weibull distribution parameter method and point estimation method to obtain two influencing factors;

4. Determine the weight ratio matrix by the influencing factors obtained by the Weibull distribution parameter method and the point estimation method, and normalize to obtain the weight of the failure rate of the key equipment of the hydrogen energy system calculated by the Weibull distribution parameter estimation method and the point estimation method number;

5. Obtain the optimized failure rate of key equipment of the hydrogen energy system through the weight number;

6. Considering the influence of the hydrogen energy flow in each component of the key equipment of the hydrogen energy system on the safety performance of the equipment, a correction factor is obtained to correct the optimized failure rate.

The invention analyzes the structural characteristics of key equipment of hydrogen energy system such as hydrogen production equipment, hydrogen storage tank, hydrogen fuel cell, etc., and calculates the failure rate of key equipment of hydrogen energy system based on the component stress method and data driving, considering hydrogen energy The influence of the flow on the safety performance of each component of the key equipment of the hydrogen energy system will change the failure rate, optimize the field data, and predict the failure rate of the key equipment of the hydrogen energy system, and further improve the safety system of the hydrogen energy for the key equipment of the hydrogen energy system. .

Claims (5)

1. a data-driven method for predicting failure rate of key equipment in a hydrogen energy system, wherein the method for predicting comprises the following steps: (1) Analyze the usage time and characteristics of key equipment in the hydrogen energy system; based on the failure rate database commonly used in the petrochemical process industry and the collection of failure rate data of various key equipment in the hydrogen energy system, the electrolyzers, hydrogen storage tanks, and hydrogen fuel cells of hydrogen production equipment are obtained. The failure rate λ _i ' of each component of the key equipment of the three typical hydrogen energy systems, where i is the sample capacity of the key equipment of the hydrogen energy system; (2) Calculate the initial failure rate λ ₁ of the key equipment of the hydrogen energy system; (3) Establish the failure rate correction model of key equipment in the hydrogen energy system, and use the Weibull distribution parameter method to obtain the influencing factors λ(t) and the point estimation method to obtain the influencing factors

(4) The influencing factors λ(t) obtained by the Weibull distribution parameter method and the point estimation method and the influencing factors obtained by the point estimation method

Determine the weight ratio matrix T _2×2 , and normalize to obtain the weight number k ₁ of the failure rate of the key equipment of the hydrogen energy system and the weight number k ₂ of the failure rate of the key equipment of the hydrogen energy system; (5) Obtain the optimized failure rate λ ₂ of the key equipment of the hydrogen energy system through the weight number obtained in step 4; (6) Considering the influence of the hydrogen energy flow in each component of the key equipment of the hydrogen energy system on the safety performance of the equipment, the correction factor is obtained, and the optimized failure rate λ ₂ is corrected. 2. The data-driven method for predicting the failure rate of key equipment in a hydrogen energy system according to claim 1, wherein the step (3) utilizes the Weibull distribution parameter method and the point estimation method to establish a method for predicting the failure rate of the key equipment in the hydrogen energy system. The factors affecting the failure rate are as follows: (1) The influencing factor λ(t) of the failure rate of key equipment in the hydrogen energy system determined by the Weibull distribution method:

Among them, t is the time, a is the scale parameter, and β is the shape parameter; (2) Factors affecting the failure rate of key equipment in the hydrogen energy system determined by the point estimation method

Among them, j is the sequence of key equipment components of the hydrogen energy system, i is the sample capacity, i=1, 2, 3,  …n. 3. The data-driven method for predicting failure rate of key equipment in a hydrogen energy system according to claim 1, wherein in the step 4, the initial failure rate obtained based on the component stress method is optimized using a weighted average method, and The specific steps to obtain the failure rate based on field data are as follows: (1) First, determine the working failure rate influencing factors λ(t) of key equipment of hydrogen energy system based on Weibull distribution parameter estimation method and the working failure rate influencing factors of key equipment of hydrogen energy system obtained based on point estimation method

(2) Next, determine the weight ratio matrix T _2×2 According to the factor set U={U ₁ U ₂ }

, where U ₁ is the set of factors affecting the failure rate of each component of the key equipment of the hydrogen energy system obtained based on the Weibull distribution parameter estimation method, and U ₂ is the failure rate of each component of the key equipment of the hydrogen energy system obtained based on the point estimation method Influencing factor set, u _j , j=1, 2 is the failure data set of equipment life,

The failure rate density function based on the Weibull distribution parameter estimation method for the key equipment of the hydrogen energy system; Require

Satisfy:

The weight ratio matrix is:

in

is the failure rate density function based on the Weibull distribution parameter estimation method for the key equipment of the hydrogen energy system,

is the failure rate density function of the key equipment of the hydrogen energy system based on the point estimation method, t _ij is the ratio of the failure rate density function based on the Weibull distribution parameter estimation method and the point estimation method for the key equipment of the hydrogen energy system; The mathematical expression for the weight estimate is:

Among them, W ₁ and W ₂ are the failure rate weights of the key equipment of the hydrogen energy system based on the Weibull distribution parameter estimation method and the point estimation method, respectively, and t _ij is the key equipment of the hydrogen energy system based on the Weibull distribution parameter estimation method and the point estimation method. The ratio of the failure rate density function of the method, i,j=1,2; The weight estimate is then normalized as the estimated weight:

Among them, k ₁ is the weight of the failure rate calculated according to the Weibull distribution parameter estimation method, and k ₂ is the weight of the failure rate of the key equipment of the hydrogen energy system calculated according to the point estimation method. 4. The data-driven method for predicting the failure rate of key equipment in a hydrogen energy system according to claim 1, wherein in the step 5, after the weights k ₁ and k ₂ are obtained in the step 4, the weight k ₁ , k ₂ to find the optimized failure rate λ ₂ of the key equipment of the hydrogen energy system based on the field operation data; Using the weighted average method, the optimized failure rate of the key equipment of the hydrogen energy system based on the field operation data is obtained as follows:

Among them, k ₁ is the weighted number of the failure rate of the key equipment of the hydrogen energy system calculated according to the Weibull distribution parameter estimation method, k ₂ is the weighted number of the failure rate of the key equipment of the hydrogen energy system calculated according to the point estimation method, λ( t) In order to use the Weibull distribution method to determine the factors affecting the failure rate of key equipment in the hydrogen energy system,

In order to use the point estimation method to determine the factors affecting the failure rate of key equipment in the hydrogen energy system. 5. The data-driven method for predicting failure rate of key equipment in a hydrogen energy system according to claim 1, wherein in the step 6, the initial failure rate obtained by the component stress method and the on-site operation data are compared and analyzed. The obtained failure rate of key equipment of the hydrogen energy system is obtained, and the correction factor is obtained: τ=λ ₂ /λ ₁ -1 In the formula, τ is the correction factor and also the error coefficient; λ ₁ is the failure rate of the key equipment of the hydrogen energy system calculated based on the component stress method, and λ ₂ is the key equipment of the hydrogen energy system calculated by the weight. Optimized failure rate of equipment; The failure rate correction model of the key equipment of the hydrogen energy system is: λ= _λexpected (1+τ) Among them, λ _{is expected} to be the failure rate of the key equipment of the hydrogen energy system calculated based on the component stress method in the model, and λ is the optimized failure rate of the key equipment of the hydrogen energy system calculated by the weight in the model.

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