Processing data to characterize the thermal behavior of a battery

1. A method for monitoring performance characteristics of a battery, the method comprising:

obtaining by a data processing system temperature data of one or more locations within or on the surface of a battery, the temperature data comprising time-varying heat flow inputs applied to the battery and temperature signals, with the temperature signals varying with time and being generated by the battery;

processing the temperature data through a reduced order thermal basis model that comprises a set of positive and linearly independent basis functions that have one or more time-delay elements and one or more parameters, with parameter values of the one or more parameters fitted to the set of basis functions using the obtained temperature data, and with the reduced order thermal basis model including a finite set of first order lag filters with different time constants to fit the time-delay elements of the set of basis functions;

wherein the reduced order thermal basis model is of the form

S={σ 1 ,σ 2 , . . . ,σ K }

where σ K is a set of k basis models and is given by

σ

k

=

{

f

k

⁢

:

⁢

x

.

=

-

λ

k

·

x

+

u

g

k

⁢

:

⁢

y

=

x

}

that is a first order lag filter parameterized by λk: where ƒ k is the dynamics equation, {dot over (x)} is a time derivative, g k : is an output equation, y is a time varying output and u is a time varying input; and

diagnosing by the data processing system based on processing of the temperature data through the reduced order thermal basis model at least one of electrical usage and thermal performance of the battery.

2. The method of claim 1 , wherein the thermal model is configured to produce a prediction of battery thermal behavior for a plurality of heat flows.

3. The method of claim 2 , wherein the plurality of heat flows are each applied to boundary conditions or volumetric regions in the battery.

4. The method of claim 1 , wherein the temperature signals are obtained from an experimental environment or from a simulation.

5. The method of claim 1 , wherein the reduced order thermal basis model is linearized at equilibrium.

6. The method of claim 1 , wherein the temperature signals comprise data indicative of temperature and heat boundary conditions of the battery in a set of steady state conditions.

7. The method of claim 6 , wherein generating the thermal model comprises minimizing differences between the temperature signals and modelled temperatures of the battery under the set of steady state conditions.

8. The method of claim 1 , wherein the temperature signals comprise data indicative of temperature and heat boundary conditions of the battery in a set of transient conditions at the equilibrium condition.

9. The method of claim 8 , wherein the temperature signals comprise a plurality of sets of transient measurements starting from the same battery equilibrium condition.

10. The method of claim 1 , wherein the time delay is implemented using a Pade approximation with a different order for the numerator and denominator.

11. The method of claim 1 , wherein the temperature signals are obtained from a simulation.

12. The method of claim 11 , wherein the simulation includes heat transfer at the boundary of the battery.

13. The method of claim 11 , where the simulation isolates the battery from all external heat sources and sinks.

14. The method of claim 1 , wherein the temperature signals are obtained from the battery in a vehicle.

15. The method of claim 1 , wherein the temperature signals are generated using a physical test stand.

16. The method of claim 1 , further comprising determining if a battery thermal protection system is consistent with the reduced order thermal basis model.

17. A system for monitoring performance characteristics of a battery, the system comprising:

a processor and a memory being configured to:

obtain temperature data for one or more locations within or on the surface of a battery, the temperature data comprising time-varying heat flow inputs applied to the battery and temperature signals, with the temperature signals varying with time and being generated by the battery;

process the temperature data through a reduced order thermal basis model that comprises a set of positive and linearly independent plural basis functions that have one or more time-delay elements and one or more parameters, with parameter values fitted to the set of basis functions using the obtained temperature data, and with the reduced order thermal basis model including a finite set of first order lag filters with different time constants to fit the time-delay elements of the set of basis functions;

wherein the reduced order thermal basis model is of the form

s={σ 1 ,σ 2 , . . . ,σ K }

where σ K is a set of k basis models and is given by

σ

k

=

{

f

k

⁢

:

⁢

x

.

=

-

λ

k

·

x

+

u

g

k

⁢

:

⁢

y

=

x

}

that is a first order lag filter parameterized by λk: where ƒ k is the dynamics equation, {dot over (x)} is a time derivative, g k : is an output equation, y is a time varying output and u is a time varying input; and

diagnose by the data processing system based on processing of the temperature data through the thermal model at least one of electrical usage and thermal performance of the battery.

18. A non-transitory computer-readable data storage medium for monitoring performance characteristics of a battery, the medium storing computer-executable instructions that, when executed, cause a computer to:

obtain temperature data for one or more locations within or on the surface of a battery, the temperature data comprising time-varying heat flow inputs applied to the battery and temperature signals, with the temperature signals varying with time and being generated by the battery;

process the temperature data through a reduced order thermal basis model that comprises a set of positive and linearly independent plural basis functions that have one or more time-delay elements and one or more parameters, with parameter values fitted to the set of basis functions using the obtained temperature data, and with the reduced order thermal basis model including a finite set of first order lag filters with different time constants to fit the time-delay elements of the set of basis functions;

wherein the reduced order thermal basis model is of the form

s={σ 1 ,σ 2 , . . . ,σ K }

where σ K is a set of k basis models and is given by

σ

k

=

{

f

k

⁢

:

⁢

x

.

=

-

λ

k

·

x

+

u

g

k

⁢

:

⁢

y

=

x

}

that is a first order lag filter parameterized by λk: where ƒ k is the dynamics equation, {dot over (x)} is a time derivative, g k : is an output equation, y is a time varying output and u is a time varying input; and

diagnose by the data processing system based on processing of the temperature data through the thermal model at least one of electrical usage and thermal performance of the battery.