Integrated sensing and modeling on a

sensor node

Yeonjeong Park and Tom HarmonUC Merced Environmental Systems program

Outline• Why do this?• Moisture, specific conductivity, and temperature

sensing in soils• A closed-loop system demonstration pilot scale• Demonstration at full scale

Motivation

• Several reasons for local, automated analysis

– Sensor system design (optimize numbers, locations of sensors while you are installing them)

– Feedback-control algorithms: observe, model, forecast, control, …, observe [emphasis of this presentation]

• Computations locally or remotely?

– If speed is not an issue, than remote computations may be important

Creating higher order virtual sensors

• We notice that data analysis can become routine with arrays of individual sensors

– Energy balances– Water balances– Metabolism– Mixing

• Let the sensor array behave as a more sophisticated “sensor”

“Salinity flux” sensor

Example: Irrigation in the Mojave Desert

Typical sensor array for field testing

• Sensors– Moisture– Temperature– Soil salinity– (also meteorology)

Decagon 5TE

These sensors are robust (much testing in agriculture)

Moi

stu

re (

v/v)

25 cm blue50 cm red100 cm black

Irrigation control “sensor”

Coupling sensors readings with models(compressing the timeframe for analysis)

• Palmdale water reuse experimental site (not in the dairy site, but could be…)

• Microclimate + soil pylons (moisture, temp, short-term nitrate and ammonium)

• sensor feedback, model calibration, model forecast

• After a reasonable amount of time, the model parameters become stable

Pilot demonstration: Sensor-trained simulation model with a management model (feedback-control)

• Receding horizon control• Optimize irrigation rate for

current system state and future states

• Execute the best estimate for the current state and move the management horizon forward, repeating…

Step 1: observe and model

Sample model fits (all at 5 cm depth,

different management steps)

Soi

l moi

stur

e (c

m3 /cm

3 )

Management step 20.225

0.22

0.215

0.21

0.205

0.2

time (min)0 5 10 15 20 25 30

estimated

measured

estimated

measured

time (min)

estimated

measured

estimated

measured

Management step 10.214

0.212

0.21

0.208

0.206

0.204

0.202

0.2

0.198

0.196

0.1940 5 10 15 20 25 30

Soi

l moi

stur

e (c

m3 /cm

3 )

Soi

l moi

stur

e (c

m3 /cm

3 )

Management step 40.245

0.24

0.235

0.23

0.225

0.22

0.215

0.21

time (min)0 5 10 15 20 25 30

estimated

measured

estimated

measured

time (min)

estimated

measured

estimated

measured

Management step 30.225

0.22

0.215

0.21 0 5 10 15 20 25 30

Soi

l moi

stur

e (c

m3 /cm

3 )

Soi

l moi

stur

e (c

m3 /cm

3 )

Management step 60.246

0.244

0.242

0.24

0.238

0.236

0.234

0.232

0.23

0.228

0.226

time (min)

estimated

measured

estimated

measured

time (min)

estimated

measured

estimated

measured

Management step 5

0.245

0.24

0.235

0.23

0.225

0.220 5 10 15 20 25 30

Soi

l moi

stur

e (c

m3 /cm

3 )

0 5 10 15 20 25 30

Note: model is a coupled flow, mass and energy transport model (one-dimensional, 2 soil layers assumed)

Receding Horizon Controlqk | k qk+1| k

• • •

qk+1 | k+1 • • •

qk+2 | k+2 qk+3 | k+2 • • •

k

k

k+2

k+1

k+1 k+2

• • •

qk+2| k+1 k+2 • • •

• • •

k

k

k+2

k+1

k+1 k+2

Optimization Horizon

Next Optimization

Next Optimization

The first Optimal Values

Optimal Sequence

qk | kqk | k qk+1| k qk+1|qk+1| k • • •

qk+1 | k+1qk+1 | k+1 • • •

qk+2 | k+2qk+2 | k+2 qk+3 | k+2 qk+3 | k+2 • • •

k

k

k+2

k+1

k+1 k+2

• • •

qk+2| k+1 k+2qk+2| k+1 k+2 • • •

• • •

k

k

k+2

k+1

k+1 k+2

Optimization Horizon

Next Optimization

Next Optimization

The first Optimal Values

Optimal Sequence

Nonlinear optimization algorithm producing an array of future control actions (here, irrigation rates)

q1

q6

q5q4

q3q2

Optimization Horizon (36hr)

Management Step (6hr)

Op

tim

al A

pplic

atio

n R

ate

(cm

/hr)

10min

q1

q6

q5q4

q3q2

Optimization Horizon (36hr)

Management Step (6hr)

Op

tim

al A

pplic

atio

n R

ate

(cm

/hr)

10min

0 100 200 3000.23

0.235

0.24

0.245

0.25

Depth (cm)

Soi

l moi

stur

e (c

m3 /c

m3 )

0 10 20 30 40 500

0.2

0.4

0.6

0.8

Management step

Opt

imal

val

ue

0 10 20 30 40 504

5

6

7

8

Management step

appl

icat

ion

rate

(cm

/hr)

0 10 20 30 40 500.21

0.22

0.23

0.24

0.25

0.26

Management stepMax

imum

wat

er c

onte

nt (

cm3 /c

m3 )

Upper Bound

Lower Bound: zero

Threshold (0.25)

(a)

(d)

(b)

(c)

Soil Moisture ControlVariable Application Rate of Fixed Frequency and Duration

q is fixed

Applic

atio

n r

ate

(cm

/hr)

Management step is

changing

Optimization horizon

td1

tdi is duration of irrigation, where i=1,…,4

tmg is update time

td2 td3 td4tmg

q is fixed

Applic

atio

n r

ate

(cm

/hr)

Management step is

changing

Optimization horizon

td1

tdi is duration of irrigation, where i=1,…,4

tmg is update time

td2 td3 td4tmg 0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

Management step

time

inte

rval

(hr

)

0 10 20 30 40 500

0.5

1

1.5

Management step

Opt

imal

val

ue

0 100 200 3000.27

0.28

0.29

0.3

0.31

Depth (cm)

Soi

l Moi

stur

e (c

m3/

cm3)

0 10 20 30 40 500.15

0.2

0.25

0.3

0.35

Management step

Soi

l Moi

stur

e at

2ft

(cm

3/cm

3)

(a) (b)

(c) (d)

Upper Bound

Lower Bound

Threshold 0.3

Soil Moisture ControlFixed Application Rate of Variable Frequency and Duration

…and trying feedback-control in the field

• Center pivot irrigation system• Manually control by changing the

rotational speed (not automated)• 3 speeds to simplify the objective space

Park, Shamma, & Harmon (2009) Environ Modell Softw, in press

0 1 2 3 4 5 6 70.195

0.2

0.205

0.21

0.215

0.22

0.225

management step

soil

moi

stur

e at

5 c

m d

epth

(cm

3 /cm

3 )

threshold

4 min

6 min 8 min(4 minapplied)

8 min6 min

6 min 4 min

0 2 4 6 8 10 12 140.19

0.2

0.21

0.22

0.23

0.24

0.25

time (hr)

soil

mois

ture

at

5 c

m d

epth

(cm3 /c

m3 )

estimated

measured

4 min

6 min

8 min(4 minapplied)

8 min 6 min 6 min

4 min