Research on fault detection method for heat pump air conditioning system under cold weather☆

Liangliang Sun *,Jianghua Wu ,Haiqi Jia ,Xuebin Liu

1 Information and Control Engineering,Shenyang Jianzhu University,Shenyang 110168,China

2 Electrical Engineering,University of Connecticut,Storrs 06269,USA

1.Introduction

Owing to globalenergy shortage and increasingly severe pollution,environment protection has garnered considerable attention in the pursuit of a green and healthy living place.Compared to the damage to the ozone layer caused by refrigerants,the high energy consumption of HVAC systems is a significantly more eminent danger to the environment.Energy exploitation has been a great burden to our environment,and HVAC systems are responsible for a large proportion of it in domestic and industrial areas—comparable to even the proportion of traffic energy consumption.However,this fact escaped notice because of the traffic energy consumption.In this case,once the HVAC system fails,the energy consumption of HVAC system will be doubled,although this is completely avoidable.A fast and effective fault detection method can significantly reduce the energy consumption caused by the system failure.Therefore,developing a fast and effective HVAC system fault detection method is an important issue.

Traditional HVAC system is mainly composed of a cold machine system,a cooling tower system,and an indoor air processor system.The heat pump system is a type of HVAC system composed of many devices that communicate with each other using an interconnected pipe.As shown in Fig.1,the entire system is very complex and in the process of system operation,there would certainly be equipment failure.For a heat pump system,if there is a fault in any place in the system,it may affect the other devices,and consequently,the stability and controlling performance of the heat pump system.The heat pump air conditioning system,a type of HVAC system,is more energy-efficient than the traditional air conditioning system and is being more widely used to save more energy.In the northern cold area,heat pump system in a building usually works under variant circumstances,and there are too many natural factors,especially the fierce temperature changes between morning and evening,which can affect the devices.Additionally,each system parameter in the heat pump system migrates as the temperature changes.Moreover,when the heat pump system operates normally,the migration of system parameters caused by natural factors will influence our judgment on whether the system is working well.

Fig.1.The description of HVAC system.

Normally,the fault types can be divided in the following ways.First,classified by cause of faults,the types can be divided into natural faults and man-made faults.Second,by fault extent,it can be divided into the softfaultand the sudden fault which means that the equip mentor component is completely disabled with destructive.Usually,the sudden faults are more obvious and more serious which may be caused by external force,but the gradual faults are generally more difficult to detect which is mainly caused by fatigue,abrasion and wear in the process of the use.Because of the difficulty in its fault detection,the in fluence of the gradual faults must not be overlooked.Third,classified by faulty devices,there are component fault and sensor fault.The component fault refers to the air conditioning equipment fault,such as the faults of fan coil.And the sensorfaultrefers to the temperature sensor,pressure sensor,such as deviation or drift of the measurement parameters.The cold systemis responsible for the heat exchange with the outside;ifthere is a problem with the chiller in the air conditioning system,like the scale accumulation in the chiller's water pipe,or the slightly leaking in it,the cooling power of the air conditioning system would be obviously reduced and the energy consumption of the system will be increased.Therefore,this paper mainly focuses on the chiller fault detection.

Generally,the fault detection of a heat pump system is conducted by testing whether the system parameters float beyond its set limit.However,for a system that is located in the north cold area,the violent migration of the natural factors may let the detection get a wrong answer.If the error cannot be removed on time,severe migration of the system parameters will occur.In addition,it will affect the indoor environment and comfort of the people.Moreover,the energy consumption of the heat pump system and the load of system equipment increased,and the service life of equipment is curtailed.In addition,the facility maintenance of the heat pump system needs a considerable amount of money and time.If the detection goes wrong,not only will the previous efforts be in vain,but the waste of resources will also increase and influence the daily use of users.Therefore,it is very important to carry out a rapid and accurate fault detection method[1].

The fault detection methods studied in this paper are mainly concerned with the failure of cooling system in northern China.In the winter of northern China,the temperature difference between morning and evening is too large,so the outdoor environment parameters change violently,which leads to a non-linear change in the cooling system parameters.In this paper,the modeling platform is based on Sino-German Energy Conservation Demonstration Center which is the intelligent building.In the intelligent building,the various parameters will be directly fed back to the console.In order to simplify the collection and calculation of parameters,it needs to linearize the various parameters.In view of the above problems,the nonlinear model of the corresponding cooling system is established and linearized,which makes the cooling model suitable for the cold winter environment in northern China.

However,there are still many challenges in the fault detection of HVAC.First,heat pump systems vary with the weather and load,and the parameters of the device change over time,e.g.,construction cooling load changes with the diurnal and seasonal change.Although the control of chillers'open units is determined by the cooling load of constructions,refrigeration load of chillers still inevitably varies with diurnal and seasonal change,and causes fluctuations in the refrigerator's operating point and refrigeration efficiency.These bring about the change of devices'performance,and this change is difficult to separate from the performance change that is caused by the fault.Therefore,it is difficult to eliminate the effect of system performance that is caused by system parameter drift or the change of environment while judging whether the system is faulty.Second,the basic idea of the fault detection of heat pump system is based on the real-time data,and then using the value of output parameters that is predicted by computers and compared with the predicted values with the next measured values.If the two values differ more than a certain amount,then we consider that as an equipment or system failure.This method usually uses “control limit”to detect faults.There are some hypothetical model's parameters fluctuating around the target,and the normal fluctuation range is fixed.If the parameters of the model exceed the fixed control limit,it will issue an alarm.The major drawback is that the heat pump system operates under the time-varying weather,and even if no fault occurs,the change of weather and load will lead the equipment performance to be offset.As a result,the model parameters may exceed the control limit and a false alarm will be issued.Therefore,another difficulty for taking a failure detection of heat pump system is how to select a suitable control limit in a very small range;the false alarm rate of system is likely to be very high in the morning and the evening.

The mentioned problems are the main difficulties in the currentheat pump air conditioning system fault detection.A reliable fault detection method needs to overcome these problems,effectively improve the heat pump air conditioning system fault detection rate,and reduce the energy loss caused by system failure.

2.Literature Review

Fault detection is an important and effective way to assure the safety of the HVAC system and it has already raised many concerns in the scientific community.There are many types of fault detection methods.Generally speaking,fault detection methods can be classified into three groups,the analytical-based methods,the artificial intelligent-based methods,and the data-driven methods.

The analytical-based methods use the difference between measured data of a plant and a modeling process(mathematical model)in terms of residuals to detect any fault.In the field of analytical based methods[2-8],many researchers proposed the parameter estimation methods and the output residual methods based on the different modes of the HVAC system.In the artificial intelligent-based methods,artificial intelligence technology provides the condition and platform for the intelligent fault detection,and it also makes fault detection coming into a new stage of development.Intelligent fault detection has become the forefront of the fault detection methods.However,the development time of the intelligent fault detection is too short to have a complete theoretical system and it leaves many problems for us to solve.In general,the intelligent fault detection for equipment has not reached the point of completeness and it is still in the early stage of development.In the previous works,some researchers took the thermal transmission parameters of the heat exchanger as signals to calculate and monitor the operation condition of the heat pumps[9].At the same time,other researchers took heat transfer coefficient,K,as the monitoring parameters and when K diminished,they could realize that the heat exchanger may be dirty or scaling.When both of the evaporator and condenser are considered as a common heat exchanger,the operation condition of heat pump can be monitored[10].Moreover,some researchers adopted two artificial intelligence methods,i.e.,neural network and genetic programming,to solve the identification problem of the ground source heat pump system.The errors of the average model obtained by the above two methods are within 7%.This shows that it is feasible to identify the ground source heat pump system simply using the artificial intelligence method[11].In addition,some researchers applied the artificial neural network technology and clarified its application in load forecasting,energy management,fault diagnosis,system identification and control,etc.[12].The last method is the data-driven methods[13-15]which use relation between data patterns and fault classes in terms of modeling process.There are two types of methods in this class.The multi-variable statistics approach and the signal based approach.Some researchers introduced the basic flow,fault classification,research status,common methods,and application of automated fault detection and diagnosis in the HVAC System.In the building energy management and control system,developing models using principal component analysis based on the fault types of the heat exchanger,can detect and diagnose four types of heat exchangers in the aircondition detection diagnosis system[16-19].

This paper is organized as follows.Section 3 describes the graymodels of the heat pump systems.Section 4 presents the Kalman filter and SPC fault detection method for the HVAC systems.In Section 5,a case for SINO-German building is studied.Section 6 concludes our study and states our future work.

3.Gray-models of the Heat Pump System

This paperintroduces the modelofheatpump units and the physical modelofthe buried pipe selected fromthe literature.The research background of this paper is the grand heat source pump system of Sino-German Energy Conservation Demonstration Center in Northeastern of China.Compared with the traditional HVAC,it is characterized by the access of cold and heat source and the cooling of cooling water through the buried pipes,not through the traditional cooling tower Water,but in the cold machine,its working principle is no different from the one of the traditional central air conditioning.So this article's chiller model uses the cold model which is suitable for a variety of air conditioning,while for the buried pipe part,the underground temperature is a significant difference if the depth is different,resulting in the heat transfer in the buried pipe that is non-linear,for this point,using a special way to describe the non-linear operation of the mathematical model.In order to apply the above method to the models,we make great efforts on the model selection and adjustment.The purpose is to make a simplified model,and make sure the model parameters can re flect the performance of the equipment and have physical meanings.In our models,if there is no fault,the model parameters usually remain within the normalrange,and ifany failure occurs,they willdeviate from the normal range.

3.1.Chiller model

The model of heat pump units we selected is developed by J.M.Gordon and K.C.Ng.This model is described as follows[8]:

Here,COPchrepresents the unit refrigeration coefficient which is the amountofcold that produced by one unit of electricity.COPchis equalto the ratio of refrigeration power of the cooler Lchand the electric power of the cooler P.a1is the entropy generation rate inside the cooler,a2is the heat loss rate of the cooler,a3is associated with the cold machine of evaporator and condenser heat exchange of the heat resistance,Tchris the frozen return water temperature from the air handler to the cooler,Tciis the water temperature of the cooling water from the buried pipe to the cooler,Lchis the refrigeration power of the cooler and can be expressed as follows:

Here,Cwis the heat capacity of the water,gwchis chilled water flow,Tchsis the frozen water temperature.For the mathematical model,in addition to the parameters a1,a2and a3,the remaining value can be obtained directly or indirectly measure,approach the related parameters a1,a2and a3as state variables to the state of the unit.

3.2.Heat pump system heat exchanger model

Heat pump system has various types,and different buildings need different heat pump systems.Nowadays,it is used more widely in the ground source heat pump system,water source heat pump system,air source heat pump system,as well as the composite heat source heat pump system.Additionally,heat pump systems with different heat sources also have different components,connections,and terminal forms.For example,the buried pipe of GSHP system has direct buried pipe,U pipe,spiral pipe,and so on.The case study of this article is a ground source heat pump system,which uses a U-shaped buried tube.Its structure is mainly composed of U pipe,refrigerator,and terminal equipment.The terminal equipment is directly responsible for the indoor air conditioning,which includes fan coil,fresh air and so on.Each part of the system is connected through the air pipe and the water pipe.Each subsystem also may include multiple devices.Such as the cold machine subsystem,it is composed of many cold machines in parallel.Its refrigeration working principle will be introduced as follows.Terminal equipment releases excess air heat to the frozen water through the heat exchanger.Chilled water is pumped into the cooler.After cooler takes away a large quantity of heat using the frozen water and passed it through the compressor,refrigeration loop cools down the water,and makes the chilled water cooling.After cooling is completed,the chilled water will be pumped back again to the end of the equipment for recycling.Then,cooling water will be pumped to the buried pipe.In the buried pipe,cooling water releases its heat to the soil heat exchanger and be cooled,eventually transmits excess heat to the outside.Cooling water that has been cooled down will be pumped back to the cold machine,used for cooling machine cycle[9].Buried pipe model uses a cylindrical ground heat exchanger heat transfer model.The model is described as follows[10]:

Here,Tfis the average temperature for the borehole fluid in the heat exchanger,T0is the initial soil temperature,q is the heat of the line source,λsis the thermal conductivity of the soil,C is the nonuniform heat flow correction factor,N1is the number of boreholes pins(when N1=2C=0.85,when N1=4,C=0.6-0.7),r0is the outer diameter of the pipe,heqis the overall thermal conductivity reference to the tube diameter,G(z,p)is a function of time τ and distance r,and it can be described as follows:

Here,β is the integration variable and asis the thermal diffusivity of soil.The value of T f-T0 we can hardly get.However,according to the principle of conservation of energy,we can find the total energy of the fluid in the inner tube and the soil exchange is equal to the total energy of the fluid obtained.Therefore,we can use Tout-Tinto compute,while Toutis the outlet fluid temperature and Tinis the inlet fluid temperature.Model after the transformation is described below:

Outlet fluid temperature Toutand inlet fluid temperature Tincan be measured using a sensor.Under normal circumstances,the number of ground heat pipe is often more than one.If we have a presence sensor in each borehole,it only needs a simple superposition of its value.However,with only one sensor,the value can be calculated using the energy balance equation and the water flow balance equation.

4.Kalman Filter and SPC Fault Detection Method

It is difficult to eliminate the effect of system performance that is caused by system parameter drift or the change in external environment when deciding whether the system is really in trouble.Because of that,we have some solutions as follows.First,the heat pump system is divided into three parts,heat pump units,U-ground heat,and air handler.We establish the gray-box models,and then through the priori estimate and the posteriori estimate,we can get the dynamic time varying model parameters.These system parameters can be a valid data when a fault is detected,and it can be the basis to judge whether the system failed.Then,it can effectively avoid false alarms caused by the performance of the system changes which environment caused[11-12].

This method usually uses “control limit”to detect faults.They are hypothetical model's parameters that fluctuate around the target,and the normal fluctuation range is fixed.If the parameters of the modelexceed the fixed control limit,it will issue an alarm.The disadvantage of this method is that the heat pump system operates in a time-varying weather and load,and even if no fault occurs,the change of weather and load will lead the equipment performance to be faulty.Because of this problem,our solution is to establish a dynamic control limit based on the parameters estimation and standard deviations,and then,set the dynamic control limit as a dynamic target plus or minus standard sliding deviations.Dynamic control limits will dynamically adjust with the change of device performance due to the external environment.To achieve this,we combine Kalman filter with SPC rules,and establish the control limit dynamically adjusted with the weather load,which will dynamically adjust with the change in device performance due to the external environment,and finally,reduce the rate of false alarms.

4.1.Kalman filter estimation of the model parameters

This section will introduce how to use the Kalman filter to estimate the model parameters of the heat pump units and the buried pipe.Kalman filter is a type of recursive filter used for varying linear system.It follows the model of the system:

Here,X(k)is the system state at time k,U(k)is the control volume of the system attime k.A,B and H are the parameters,and formulti-model system,they are matrices.Z(k)is the measurement at time k,W(k)and V(k)represent process and measure mentnoise,and Q,R represent their covariance.

Performing prediction calculation process,using an iterative method as follows:

Here,X(k|k-1)is the value which is predicted by a last time state,X(k-1|k-1)is the optimal results of the last state.P(k|k-1)is covariance correspond to X(k|k-1),P(k|k)is covariance correspond to X(k|k).Kg(k)is the Kalman Gain.

Due to the impact of the weather and cooling loads,there will be some deviation that varies with time.To solve this problem,we introduce the process noise w to reflect these changes.And then,in order to reduce the influence of model parameters caused by historical data,we eliminate 24-h cycle fluctuations by the ground heat equation of state as follows:

where xk+1and xkare the cold state at k time and k+1 time,andare the state estimation value at23 h or 24 h ago,wkis the process noise at time k.

H=I;I is a matrix,which estimates the state by Kalman filter including the time update and measurement update.Time update:Not yet know the measured value of the output variable,but only in accordance with the equation of state,estimate state variables the next time.Measure mentupdate:Known output measurement variables,correct the state variables in time update.Firstly,we do the time update:

Among themis the state variable estimates in the next moment,is the state variable estimates at the present time,is the covariance matrix correspond to,Pkis the covariance matrix correspond to,Qkis the process noise covariance matrix.Then,update based on real-time data,

Therein,Kk+1is the Kalman Gain attime k+1.Rk+1is the measurement noise covariance matrix at time k+1

4.2.Chiller model parameter estimation

When considering the heat pump model,the heat pump state variable x is composed of three vector parameters a1,a2and a3.Because it is a linear heat pump model,we can directly use the Kalman filter to estimate the model parameters.At this point,we can get the output equation of heat pump units by having the method with the same model parameter estimation of the ground pipe.

4.3.Buried pipe model parameter estimation

When we use the Kalman filter to deal with the buried pipe model,firstly,we regard G(z,p),q and heqas a state variable x.However,because the underground pipe model is nonlinear,we have to deal with our models.Our method is making the model take a log operation on both ends of the equation at the same time,and then we can get the linear model about lg(Tout-Tin)and lg q,lg G(z,p),lg heq.

Output equation can be obtained according to the physical model(Eq.(24)),just regard the left side as the output variable z,and its right side as the state variable x,equation coefficients can be calculated from the measured data.Accordingly,the output equation at time k is:

4.4.Construct dynamic SPC control limit

In order to obtain dynamic control limits,we set target parameters of the model as the sliding average value of the parameter estimation in the last K h,and obtain a dynamic model parameter target.And then,we compute the standard deviation of parameter estimates to obtain covariance matrix P of parameter estimates by the Kalman filter.Finally,the dynamic control of the upper limit was set as the target value plus the several fold standard deviation of sliding average value,and the lower limit of dynamic control was set as the dynamic target value minus the several fold standard deviation of the sliding average value.Among them,we choose twice over the standard deviation of the normal range as a parameter.Suppose we select twice standard deviation range as the normal range of parameters,an alarm requires a parameter estimation jump out of the normal range for 5 h.If we choose a double standard deviation of the normal range as a parameter,an alarm can be issued only by the parameterestimation jump outofthe normal range for 10 h,so that the time it will take will be much greater than twice the standard deviation detection time.If we choose triple standard deviations,the parameter variation will not exceed triple times of the standard deviation detection when some minor faults appear,the failure time is very short,it needs to detect a fault very quickly,so the fault is difficult to be detected,and the result is failure detection rate decline[13].

So,in order to meet the reduction of fault detection time and improve the fault detection rate,we choose twice standard deviation range as the normal range of parameters.So,we can get

μ1，kis the moving average ofin the last K h,is the moving average of the standard deviation of the State variable x in the last K h.Additionally,this paper uses the EWMA control chart,the observations in the EWMA control chart include not only the currents ample observations but also the past sample values.By this,the SPC method in this paper estimates the current state by using the past time state estimate and the current state parameter,so that the control limit can be adjusted in time to avoid the false alarm when the outdoor environment parameters fluctuate too much.And EWMA control chart also has the advantage in the continuous fluctuation detection of small fluctuation.

5.Numerical Results

This section describes the simulation testing result of Kalan filter and SPC fault detection method on ground source heat pump system of Sino-German building by design builder platform in Shenyang Jinzhou University.First part introduces the Sino-German building ground source heat pump system,and the second part describes the fault detection result to the pipe section.

5.1.SINO-German Building and Its HVAC System

Sino-German building in Shenyang Jianzhu University is a cold assembled passive buildings,it makes“passive technology priority,active technical assistance”for the design principles,a comprehensive display of passive low-energy building design and green building integration technology systems,achieve a cold area of green building ultra-low power design goals.

Sino-German Building is located in Shenyang City,Liaoning Province,China,located in northern China.The city is located in east longitude 122.25°to 123.48°,north latitude 41.11°to 43.2°,east-west span 115 km and north-south span 205 km,the climate belongs to the North Temperate Zone,and it is affected by the Asian monsoon climate.The main climate in Shenyang performance for the long winter period,plain windy,summer is hot,and the annual average rainfall is 715 mm.In general,the summer of Shenyang lasts from June to August,and it is the hottest in July.At extreme temperatures,the temperature can reach 33.7°C.And the winter from November to March,which lasted five months,at extreme weather temperature can reach-28°C.

Fig.2.The description of HVAC system of SINO—German Building.Nomenclature:c01—frequency of cooling tower fan;c02—frequency of cooling pump;c03—frequency of curtain wallfan;c1—frequency of second pump;c211—opening of chilled water valve 1;c212—frequency of fan 1;c213—opening of FAUvalve 1;c221—opening of chilled water valve 2;c222—frequency of fan 2;c223—opening of FAU valve 2;c311—opening of end valve 1;c312—opening of end valve 2;c313—opening of end valve 3;c314—opening of end valve 4;c321—opening of end valve 5;c322—opening of end valve 6;u01—cooling supply water flow;u02—supply water temperature;u03—supply air velocity;u04—supply air temperature;u11—chilled water flow;u12—return chilled water temperature;u211—return air temperature 1;u212—return CO2 concentrations 1;u213—pressure difference between chilled supply water and return water;u214,y12—supply chilled water temperature;u221—return air temperature 2;u222—Return CO2 concentration 2;u223 y11—pressure difference between chilled supply water and return water;u224—supply chilled water temperature;y01—return cooling water flow;y02—return water temperature;y03—return air velocity;y04—return air temperature;y211—supply air temperature 1;y213—supply CO2 concentration 1;y214—return chilled water temperature 1;y215—chilled water flow 1;y221—supply air temperature 2;y223—supply CO2 concentration 2;y224—return chilled water temperature 2;y225—chilled water flow 2.

Sino-German Building has four floors,with three floors on the ground and a layer of building underground.The total area is 1647.02 m2,the ground area is 1050.41 m2,and underground area 596.1 m2.This building has 16 rooms,including a 1600 m2aircond itioned area,and a 447.2 m2non-air-conditioned area.The dualsource heat pump system which is composed by the ground source heat pump and air source heat pump is used for chilled water system services.The selection of the heat pump unit is two 17.9 kWairsource—soil source dual source heat pumps,and the single power is 4.5 kW,voltage is 380 V,and current is 8.8 A.Two chillers and phase change tank systems provide cooling and heat to the air handler via a water pump.One of the air handlers leads to the basement and the other to the first and second floor,as shown in Fig.2.The main lowtemperature heat source of heating mode for the winter is the waste heat of the curtain wall.The intermittent operation mode adopted by the heat pump unit is that the air source heat pump operates while the solar radiation is in the daytime and store heats while heating the building.

When the solar radiation stops,the heat pump stops running,and heating relies on the phase change tank storage of heat;when tank heat is low,the heat pump unit turns on the ground source model,continues to heat the building.In the case of cloudy days,the heating completely relies on heat pump source mode

The radiating end of building is floor radiant heating.In summer,it mainly relies on the ground source heat pump model cooling to regulate the building's air,and the end of the summer cooling is fan coil.

5.2.A case study for Sino-German building

This simulation is mainly for the heat pump system to the buried pipe.First of all,we use the ordinary sensor to the parameters of the buried pipe to observe the situation without using the Kalman filter and SPC fault detection method,the test result is shown in Fig.3.In the figure,the blue line is the measurement and the green line is the target value,from it,we can easily find that there has a great deviation between the target value and the measurement,and the measurement drifts seriously.

And then,we use the Kalman filter and SPC fault detection method to detect the fault,and the results show that the method can deal with the difficulties caused by the extreme environment and the non-linear in fluence of the parameters when we detect the fault.In the paper,we detect two kinds of fault,and the result is as follows.

Fig.3.The lg q detected by ordinary sensor.

Case 1.The sudden fault

The sudden fault simulated here is the buried pipe water which is frozen,and the ice plugs the pipe,which results in inadequate cooling capacity.The simulation method here is that,reduce pipe radius by 40%in Design Builder,and the fault time is from 120th h(September 5)to 130th h(September 5).Using the fault detection method based on SPC and Kalman filter,the fault detection result is shown in Figs.4,5,the ifrst time when the fault is detected by lg q is the 3rd hour after the start of the sudden fault.This sudden fault is only related to the buried pipe,with the inputvariables that Kalman filterrequires(including groundwater flow g and water temperature Toutand Tin),the repeated verification of fault detection is easy to implement.

Fig.4.The sudden fault was detected by lg q.

Fig.5.The sudden fault was detected by lg q after 3 h

Case 2.The gradual fault

The gradual fault simulated here is the buried pipe water that leaks gradually from 150th h(September 6th),and it is not processed all the time.The simulation method here is that,from September 6th,water flow decreases by 2%of its normal value every day.Using the fault detection method based on SPC and Kalman filter,the fault detection result is shown in Fig.6,the time when the fault is detected is the fourth day after the start of the gradual fault,and after the fifth day,it remains in the state of a fault alarm which can be seen in Fig.7.When the fault is detected by parameter lg q,water flow decreases by only 8%.

Fig.6.The gradual fault was detected by lg q after 4 days.

Fig.7.The gradual fault was detected by lg q after 4 days

6.Conclusions

In the modern cities,global energy shortages and pollution make people focus on finding a way to save energy.One effective solution is reducing the fault of heat pump air conditioning system which can help us save an enormous amount of energy.In this paper,we developed a fault detection method for the heat pump system of Sino-German building based on SPC and Kalman filter.First,by estimating the model parameters using Kalman filter,and then by setting the dynamic control limits using SPC rule,this method has a great detection rate and a few false alarms.The advantage of this method is not only using the gray-box model,which simplifies the traditional physical model,but also reflecting accurately the performance of the device.At the same time,the combination of SPC rule and Kalman filter could effectively reduce the false alarm rate of fault detection.The simulation results of Sino-German building show that using faultdetection method based on Kalman filter and SPC,the equipment failure can be effectively detected and be identified with the parameter fluctuations caused by natural factors,and it can deal with the difficulties caused by the extreme environment and the non-linear in fluence of the parameters.The major drawback of this method is that we need to test every part of the heat pump air conditioning system separately to find the fault,and this may need considerable amountoftime and effort.In the future,we will find a better way to test the heat pump air conditioning system directly to reduce the system workload and simplify the operations.

Nomenclature

A parameter

a1cooler inside the entropy generation rate

a2heat loss rate of the cooler

a3heat resistance associated with the heat exchange of cold machine of evaporator and condenser

asthermal diffusivity of soil

B parameter

C non-uniform heat flow correction factor

COPchrepresentative of a unit refrigeration coefficient

Cwheat capacity of the water

G(z,p) a function about time τ and the distance r

gwchchilled water flow

H parameter

heqoverall thermal conductivity reference to the tube diameter

Kg Kalman Gain

Kk+1Kalman Gain at time k+1

Lchrefrigeration power of the cooler

N1the number of boreholes pins

P(k|k-1)covariance of X(k|k-1)

Pkcovariance matrix of

covariance matrix of

Q covariance of represent process noise

Qkprocess noise covariance matrix

q heat of the line source

R covariance of measurement noise

Rkmeasurement noise covariance matrix at time k+1

r0outer diameter of the pipe

Tchrfrozen water return water temperature from the air handler to the cooler

Tchsfrozen water temperature

Tciwater temperature of cooling water from the buried pipe to the cooler

Tfaverage temperature for the borehole fluid in the heat exchanger

Tininlet fluid temperature

Toinitial soil temperature

Toutoutlet fluid temperature

Ukcontrol volume of the system at time k

Vkmeasurement noise

Wkrepresent process noise

X(k|k-1)the value predicted by a last time state

Xkcold state at k time

^xkstate variable estimates at the present time

state estimation value at 23 h ago

^x

k+1state variable priori estimates in the next moment

Zkmeasurement at time k

β integration variable

λsthermal conductivity of soil

moving average ofin the last K hours

σ1，kmoving average of the standard deviation ofthe state variable x in the last K hours

Acknowledgments

The author gratefully acknowledge the contributions of Prof.Tianyou Chai of Northeastern University and Prof.Peter B.Luh,Ph.D Bing Yan,Xuesong Lu,Xiaorong Sun,Ying Yan and Danxu Zhang of University of Connecticut,Professor Hong Wang of United Kingdom of Manchester for their valuable suggestions,which have been used to improve the readability of the paper.

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