大岡研究室・菊本研究室Ooka Lab., and Kikumoto Lab.

Inverse Parameter Estimation for Design of Ground-Source Heat Pump (GSHP)

Inverse Estimation of Design Parameters for Ground Source Heat Pump ̶Outline of Thermal Response Test (TRT)

Outline of Thermal Response Test (TRT)

1/4

◆１. Problems in TRT ◆２. What is TRT?

CementGrouted BHE

(BF-BHE)

Gravelbackfilled BHE

(BF-BHE)60 m: Fine sand

31 m: Silt

25 m: Fine sand

10–12 m: W ater 10–12 m: level

8 m: Loam, clay

(a) Drill log (b) Setup of two borehole heat exchangers

Ground level

Observationwell

0.75 m 0.75 m

From TRT apparatus

To TRT apparatus

Thermocouples

50

m

Schematic of ground heat exchangers and drill log of experimental site

Schematic of TRT setup

Photo of experimental setup

Heater

FExpansion

tankFlow rate

sensorPump

Temp.sensor

Borehole

heat

exchanger

U-tube

𝑅𝑏

𝜆𝑒𝑓𝑓

◆3. Outline of experimental setup

TRTs are conducted to esti-mate the effective groundthermal conductivity and bo-rehole thermal resistancewhich are needed to decidethe required length of groundheat exchanger

✓ Examine disturbances ✓ Propose solutions✓ Suggest new guideline

大岡研究室・菊本研究室Ooka Lab., and Kikumoto Lab.

Inverse Parameter Estimation for Design of Ground-Source Heat Pump (GSHP)

Inverse Estimation of Design Parameters for Ground Source Heat Pump ̶Disturbance Considered TRT Estimation Method

Disturbance considered TRT estimation method

2/4

◆１. Causes of error in TRT ◆２. Principle idea of developed estimation method

Heat exchange between aboveground TRT setup and outdoor environment (flow sequence 1→２→３→４）

Disturbed thermal response test data

Fluctuating disturbed heat injection rate is known boundary

condition. Thus, the disturbed portion is not a part to be removed:

it is a part of the total heat injection rate.

◆３. Comparison between conventional and developed method

0

1

2

3

4

5

6

7

8

0

5

10

15

20

25

30

35

40

0 24 48 72 96 120 144

Ave. T_GR

DB temp

Heat rate

Tem

per

atur

e [°

C]

Hea

t in

ject

ion

rate

[kW

]

𝑓

Elapsed time [h]

0.13

0.16

0.19

0.22

0.25

0.28

0.31

1.40

1.50

1.60

1.70

1.80

1.90

2.00

20 44 68 92 116 140

Leff(GR4-S) Leff(GR4-P)

Rb(GR4-S) Leff(GR4-P)

𝜆𝑒𝑓𝑓 [W

/(m

·K)]

𝑅𝑏

[(m

·K)/

W]

𝜆𝑒𝑓𝑓(Conven)

𝑅𝑏(Conven)

𝜆𝑒𝑓𝑓(New)

𝑅𝑏(New）

Elapsed time [h]

Comparison between conventionaland new estimation methods

Conventional method

After model correction

Total heat flux to the ground Disturbance

Heat flux from apparatus

Correction of estimation model

to considervariable heat rate

New idea to consider disturbed thermal response test data in parameter estimation

Unstable voltage supplied to heat-

ers in TRT apparatus

Contextual disturbances: heat exchange between TRT setup and outdoor environment

Inconsistency between the TRT and physical model for estimation

大岡研究室・菊本研究室Ooka Lab., and Kikumoto Lab.

Inverse Parameter Estimation for Design of Ground-Source Heat Pump (GSHP)

Inverse Estimation of Design Parameters for Ground Source Heat Pump ̶Development of Bayesian Inference for Thermal Response Test

Development of Bayesian Inference for Thermal Response Test

3/4

◆１. Bayes’ theorem ◆３. Advantages of Bayesian inference

Joint probability distribution of GSHP design parameters

𝑃 𝜃|𝑑𝑃𝑜𝑠𝑡𝑒𝑟𝑖𝑜𝑟

∝ ถ𝑃 𝜃𝑃𝑟𝑖𝑜𝑟

× 𝑃 𝑑|𝜃𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑

Unknown parameter(𝜃) is handled as a

probability distribution. Thus estimated results

is also probability distribution (posterior)

Prior：Expert’s knowledge, experience, hunch,

and available information are used in setting a

prior distribution

Likelihood：It is updated based on the data.

Thus it is objective probability distribution

◆２. Estimated probability

Uncertainty caused by contextual disturbances during TRT (heat

exchange between aboveground TRT setup and outdoor environ-

ment) can be evaluated by extracting statistical indices from

posterior

Credible intervals of unknown parameters and reliability of

estimates can be evaluated

By constructing a joint probability distribution, the correlation

between two parameters can be confirmed

Measured temperature, modeled temperature, and uncertainty range

using 95% credible intervals of estimates

大岡研究室・菊本研究室Ooka Lab., and Kikumoto Lab.

Inverse Parameter Estimation for Design of Ground-Source Heat Pump (GSHP)

Inverse Estimation of Design Parameters for Ground Source Heat Pump ̶Development of Cost-effective Thermal Performance Test Apparatus

Development of Cost-effective Thermal Performance Test Apparatus

4/4

◆１. Background of TRT ◆２. Performance of developed TPT apparatus

Bayesian inference of GSHP design parameters using two TPT datasets

Unlike TRT, thermal performance tests has a constant

inlet temperature as the experimental boundary

condition.

Conventional TPT apparatus requires a massive hot

water tank and complex control logic

Proposed TPT apparatus just requires two additional

control components compared to TRT apparatus:

Solid state relay and PID controller

When inlet setpoint temperature

was 25 ℃, rise time from the initial

ground temperature of 17 ℃ was

approximately 7 min

Overshoot after reaches the

setpoint was just 0.44 ℃

After the elapsed time of 13 min,

the control error was 0.2 ℃ and 1

h, it was less than 0.1 ℃.

Temp.sensor

FExpansion

tankFlow meter

PID

controller

SSRLeakage

breaker

BHE

Pump

Heater

(b) Developed TPT apparatus

Temp.sensor

FExpansion

tankFlow meter

Leakage

breaker

BHE

Pump

Power

Heater

(a) General TRT apparatus

Power cable

Hydraulic circuit

Signal cable

Sensor cable

Power

◆３. Bayesian inference for two TPT datasets (inlet setpoint temperatures of 30 ℃, 40 ℃）