Tech Briefs Magazine - October 2021 - 44

Software
New Variables for Iterative Transform Phase Retrieval
This approach provides a more general framework for performing Discrete Fourier Transform
(DFT) calculations.
Goddard Space Flight Center, Greenbelt, Maryland
he Discrete Fourier Transform (DFT)
is the primary tool of digital signal processing.
By defining new variables for iterative
transform phase retrieval using a
diagonal form of the DFT matrix, the
phase retrieval problem appears to decouple
in special cases that can increase the
computational efficiency of phase re -
trieval. The current state of the art in
increasing the DFT computational efficiency
is the Fast Fourier Transform
(FFT). In prior art, no acknowledgment of
special-purpose computational architectures
is given, which is common to some
digital signal processing applications.
T
NASA Goddard developed alternative
computational strategies for the DFT
that use analysis on geometric manifolds
to provide a more general framework for
DFT calculations. This technique also
delivers a more efficient implementation
of the DFT for applications using iterative
transform methods, particularly
phase retrieval. Diagonalizing the conventional
DFT array introduces new variables
that facilitate a decoupling of the
conventional variables used in iterative
transform phase retrieval.
The new DFT method exploits a special
computational approach based on
analysis of the DFT as a transformation
in a complex vector space. Traditional
iterative transform techniques can be
slow to converge but in this new basis
set, the algorithm can decouple to allow
a closed form expression in special
cases.
NASA is actively seeking licensees to commercialize
this technology. Please contact
NASA's Licensing Concierge at Agency-PatentLicensing@mail.nasa.gov
or call us at 202358-7432
to initiate licensing discussions.
Follow this link for more information:
https://technology.nasa.gov/patent/GSCTOPS-122.
Analytical
Model Evaluates Battery Capability
The model helps researchers fine-tune battery performance.
Rice University, Houston, Texas
attery optimization generally in volves a
tradeoff between energy (the amount it
can store) and power density (the rate of its
release), all of which depends on the materials,
their configurations, and such internal
structures as porosity. There are ad -
justable parameters associated with the
structure that need to be optimized.
Typically, tens of thousands of calculations
need to be made to search the pa -
rameter space and find the best combination.
This is a time-consuming process.
Researchers have developed a faster
and simpler method that does not re -
quire complex numerical simulation to
guide the selection and design of battery
components and how they interact. The
simplified model has an accuracy within
10% of more computationally intensive
algorithms and will allow researchers to
quickly evaluate the rate capability of
batteries.
B
Specific capacity (mAh/g)
0.4
0.35
0.3
0.25
0.2
0.15
50
100
Optimum from
Analytical model
P2D simulations
80
70
60
50
40
30
20
150
200
250
Cathode thickness (μm)
A graph that maps the capacity of batteries to cathode thickness and porosity shows a laborious
search based on numerical simulations (black square) and the new algorithm (red dot) return nearly
the same result. (Credit: Fan Wang/Rice University)
Almost all battery cell designers and
optimizers use pseudo-two dimensional
(P2D) simulations, which are expensive to
run. This especially becomes a problem
when optimizing battery cells because
they have many variables and parameters
that need to be carefully tuned to maximize
the performance.
The new tool provides a faster, more
transparent way to accelerate the design
44
Cov
process and offers simple, clear insights
that are not always easy to obtain from
numerical simulations. The model could
be easily implemented in such common
software as MATLAB and Excel, and even
on calculators.
To test the model, the researchers let
it search for the optimal porosity and
thickness of an electrode in common
full- and half-cell batteries. In the pro -
cess, they discovered that electrodes with
" uniform reaction " behavior such as
www.techbriefs.com
ToC
nickel-manganese-cobalt and nickelcobalt-aluminum
oxide are best for ap -
plications that require thick electrodes
to increase the energy density. They also
found that battery half-cells (with only
one electrode) have inherently better
rate capability, meaning their performance
is not a reliable indicator of how
electrodes will perform in the full cells
used in commercial batteries.
For more information, contact Jeff Falk at
jfalk@rice.edu; 713-348-6775.
Tech Briefs, October 2021
300
Cathode porosity

https://technology.nasa.gov/patent/GSC-TOPS-122 http://www.techbriefs.com http://info.hotims.com/79418-936

Tech Briefs Magazine - October 2021

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