Fujitsu’s Digital Annealer Calculations Improve Efficiency of Vibration Harvesting 16%

July 21, 2019 by Scott McMahan

Fujitsu Laboratories, Ltd. has demonstrated the capability of the Digital Annealer, Fujitsu's computational architecture that is inspired by quantum phenomena. According to Fujitsu Laboratories, the Digital Annealer computational architecture can rapidly solve combinatorial optimization problems to maximize the performance of magnetic devices that are critical for renewable energy harvesting and other uses.

The company says that the application of its next-generation architecture allows for the almost instantaneous calculation of the optimal arrangement of multiple planar (2D) magnets to maximize the strength of the magnetic field in a device. (See the image above in which optimum arrangement of the 100 magnets maximizes the flux density toward the coil).

Many magnetic devices used for environmental power generation produce magnetic flux via the arrangement of a large number of small magnets.

Finding the optimal planar arrangement for maximizing power generation efficiency remains difficult to calculate because of the enormous number of possible combinations of magnet arrangements, however, the company noted.

To overcome this issue, Fujitsu has developed a technology that utilizes its Digital Annealer to calculate in a matter of seconds how to arrange each magnet to achieve maximum magnetic flux density. Fujitsu says that optimization calculations deliver an efficiency gain of 16%.

This breakthrough enables quickly calculation of the optimal design for magnetic devices with significantly higher power generation efficiency.

Fujitsu asserts that the advance will ultimately contribute to the spread of power generation devices that use renewable energy such as energy harvesting.

This calculating technology was developed in collaboration with Professor Hajime Igarashi of Hokkaido University's Institute of Information Science. An abstract outlining the technology was presented at the COMPUMAG 2019 (The 22nd International Conference on the Computation of Electromagnetic Fields) conference held in Paris, France beginning, July 15th.


Energy harvesting devices that convert vibrations from motors, engines, bridges, and buildings into electricity, are increasingly attracting attention. Energy harvesting technology eliminates the need for power transmission cables, battery replacement, and charging for IoT devices installed both indoors and outdoors. The technology also can offer on-board power supplies for wearable devices and automotive components.

While adopting this technology presents an attractive and practical solution for powering IoT devices, further improvements in the efficiency of energy harvesting devices will prove critical to solving the more significant environmental and energy problems facing humanity.


In energy harvesting devices that are powered by vibration, electromagnetic induction produced by permanent magnets and coils converts the vibrations into electrical power

Maximizing the power generation efficiency of a vibration-induced energy harvesting device requires that the magnitude of the magnetic flux density from the numerous magnets located within the device must also be maximized relative to the coil's location.

At present, the layout of a number of magnets arranged in a row (One Dimension) with a concentration of magnetic flux on one side is well-known.

However, the company said that arranging the magnets in a planar shape (2D) will prove effective in boosting the amount of power generated, leading to devices with even greater efficiency in the future.

Since the arrangement of the magnets in a 2D planar shape is complicated, designers face a formidable challenge when looking for the optimal magnet placement that maximizes flux density near the coil.

In fact, for example, the company points out that the number of possible combinations of magnet orientations of 10 × 10 magnets that are arranged in a square shape along a 3D coordinate axis is more than 10 to the power of 77.

The Digital Annealer

For the Digital Annealer as the name implies, problems must be defined over binary (0 and 1) variables. In this study, the direction of a magnet that can be oriented along the 3 axes of X, Y, and Z is expressed by 3 bit variables.

The magnetic flux density produced is formulated using the variable and Bio-Savart's law, one of the laws of electromagnetism. Then, it solves an objective function (function whose value should be maximized) as a combinatorial optimization problem to maximize the magnetic flux density for a specific part.

Furthermore, with the addition of a new variable to the objective function in the QUBO(1) format, the Digital Annealer can calculate the optimum design structure for planar magnet arrays.

An image in which the optimum arrangement of magnets maximizes the flux density toward the coil


Using Fujitsu's Digital Annealer, Fujitsu was able to calculate the optimum design of a planar (2D) magnet array from a vast number of potential combinations. The simulation proved that the design optimization problem of 10 × 10 2D magnet arrays can be solved in a few seconds.

The resulting array improved the magnetic flux density by 17% and the power generation efficiency of the energy harvesting device by 16% compared with the conventionally-designed 2-dimensional array.

The company expects to apply the technology to optimize the placement of the magnet arrays for linear motors, where magnetic flux density must be controlled as intended for higher performance.

Future Plans

Fujitsu Laboratories intends to contribute to the further develop magnetic devices used in energy harvesting and other applications by implementing the company's Digital Annealer technology as one of the professional services in fiscal 2020.