Results for “Design Information Verification” — Page 13

DOE OSTI2024

The Design and Evaluation of Zero Trust Architecture for Electric Vehicle Charging Infrastructure: EVs @ Scale Series on EV Charging Station Cybersecurity

Implementing a zero trust architecture can significantly bolster the security of electric vehicle (EV) charging infrastructure. EV charging infrastructure includes numerous networked interfaces, each of which can present potential vulnerabilities. When these vulnerabilities are exploited, they can compromise the entire system, leading to severe operational and security risks. Zero trust is a security model that operates on the principle of "never trust, always verify," which helps manage the attack surface and limit the scope of any potential compromises. Fundamentally, this model ensures that no entity, whether inside or outside the network, is trusted by default. The design principles of zero trust include continuous verification, strict deny-by-default access controls, and micro-segmentation. Continuous verification ensures that every request is thoroughly checked, regardless of its origin. Strict access controls enforce the principle of least privilege, allowing users and devices only the minimum necessary access to perform their functions. Micro-segmentation involves dividing the network into smaller, isolated segments to prevent lateral movement in case of a breach. In the context of EV charging infrastructure, zero trust can be implemented through various strategies. For example, multi-factor authentication (MFA) can be required for engineers to access the management interfaces and control systems of charging stations. Real-time monitoring and analysis of network traffic can help detect and respond to anomalies. Systems that do not need to communicate with each other can be micro-segmented to enhance security. All communications should adhere to predefined policies to be permitted. Additionally, encrypting communications can protect sensitive information exchanged between chargers and management systems. This paper presents a zero trust architecture specifically designed for EV charging infrastructure. Implementing zero trust not only mitigates risks but also builds a resilient infrastructure capable of withstanding and quickly recovering from cyber threats. The architecture addresses six defined security objectives. A comprehensive test plan is developed to assess the architecture against these objectives, and the results of the evaluation are reported. This approach is essential for maintaining the reliability and integrity of EV charging services in an increasingly interconnected and vulnerable digital landscape. This is the first in a planned series of papers exploring the implementation of zero trust in EV charging infrastructure. Each paper will delve into different aspects and applications of zero trust, highlighting how various work processes and requirements can lead to distinct architectural designs. These architectures will be tailored to address specific security challenges and operational needs within the EV charging ecosystem, ensuring a robust and adaptable security framework.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1973

User's guide to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

The MAESTRO system is a mission analysis tool designed to present to the user information necessary to make the various decisions required in the design and execution of a spaceflight mission. The system was designed so that it can be used in both the pre-launch mission planning phase of a mission and during the flight as an in-flight decision making tool. A description of each of the following modes is presented: (1) trajectory propagation mode; (2) retro-fire determination mode; (3) midcourse analysis determination mode; (4) Monte Carlo mode; (5) verification mode; (6) orbit stability mode; and (7) post injection trim mode. A description of the inputs necessary to run the program mode is given along with a sample case.

Lutzky, D.↗

NASA NTRS1987

Liquid Engine Jet Atomization Workshop report

The workshop was oriented to disclose information and unsettled problems to understand the fundamental physical mechanism of the droplet formation process. Based on presentation and discussion of results, recommendations were made which should lead to associated future activities. To accomplish this task, existing observations and experiments, contributing to the basic knowledge, providing data for analytical concept verification, and forming a basis for empirical correlations were solicited. Advanced analytical modeling methods or results from specific studies were requested as well as the experience and advice from injector designers. All effort is directed to advance current analytical techniques, simulating the flow behavior downstream of the injection elements in a liquid rocket combustion chamber. Such a tool can be used to optimize injector designs with respect to short length weight savings, wall material protection, or large heat energy transport to a regenerative cooling fluid, while simultaneously achieving the maximum specific impulse in performance. The liquid atomization process also forms a sound basis for combustion instability analysis.

Gross, Klaus W.↗

NASA NTRS1998

Forced Flow Flame Spreading Test: Preliminary Findings From the USMP-3 Shuttle Mission

The Forced Flow Flame spreading Test (FFFT) is a study of flame spreading over solid fuels in very low-speed air flows. The FFFT experiment is part of research entitled Solid Inflammability Boundary at Low Speeds, (SIBAL) intended for operations on the Space Station. In the FFFT experiment, a series of 15 experiments conducted aboard the space shuttle during the United States Microgravity Payload (USMP-3) mission provided information about the structure and spreading characteristics of flames in low-speed, concurrent flows. The test samples included flat sheets of cellulose and cast cylinders of cellulose, burned in air at velocities of approximately 1 to 8 cm/sec. The test results have been successfully compared to theoretical predictions of the SIBAL program, a fundamentally based numerical simulation of concurrent flow flame spread. Additionally, some guidance for the design characteristics of the SIBAL flight experiment have been obtained including some verification of the theoretical predictions of flame size versus the required size of the SIBAL flow duct, and the effect of the presence of thermocouples in the vicinity of near-limit flames in microgravity.

Sacksteder, Kurt R.↗

NASA NTRS2001

Preliminary Results Obtained in Integrated Safety Analysis of NASA Aviation Safety Program Technologies

This is a listing of recent unclassified RTO technical publications processed by the NASA Center for AeroSpace Information from January 1, 2001 through March 31, 2001 available on the NASA Aeronautics and Space Database. Contents include 1) Cognitive Task Analysis; 2) RTO Educational Notes; 3) The Capability of Virtual Reality to Meet Military Requirements; 4) Aging Engines, Avionics, Subsystems and Helicopters; 5) RTO Meeting Proceedings; 6) RTO Technical Reports; 7) Low Grazing Angle Clutter...; 8) Verification and Validation Data for Computational Unsteady Aerodynamics; 9) Space Observation Technology; 10) The Human Factor in System Reliability...; 11) Flight Control Design...; 12) Commercial Off-the-Shelf Products in Defense Applications.

Source record↗

DOE OSTI2020

Predicting Biological Cleanliness: An Empirical Bayes Approach for Spacecraft Bioburden Accounting

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Bayesian Framework for Bioburden Density Estimation in Planetary Protection

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗

DOE OSTI2020

Cyber‐physical system testbed for power system monitoring and wide‐area control verification

The electric power system is intrinsically a cyber‐physical system (CPS) with power flowing inthe physical system and information flowing in the cyber‐network. Testbeds arecrucial for understanding the cyber‐physical interactions and provideenvironments for prototyping novel applications. This study proposes afour‐layer architecture for CPS testbeds with emphases on communication networkemulation and networked physical components. A configurable software‐definednetwork is employed to bridge physical components with wide‐area applicationsfor closed‐loop control. In order to distribute physically coupled devices intomultiple software simulations, this study proposes a data broker setup based ona distributed messaging environment to achieve low‐latency data streaming. Thedecoupled design with data streaming allows for building testbed components asmodules and running them in a distributed manner. Case studies verify the databroker setup for low‐latency sensing and actuation, as well as the communicationemulation setup for the desired network latency. Also illustrated is a replayattack scenario using synchrophasors in the Western Electricity CoordinatingCouncil (WECC) 181‐bus system for demonstrating the closed‐loop cyber‐physicalsimulation capability of the testbed.

Cui, Hantao↗

NASA NTRS2016

Assurance of Fault Management: Risk-Significant Adverse Condition Awareness

Fault Management (FM) systems are ranked high in risk-based assessment of criticality within flight software, emphasizing the importance of establishing highly competent domain expertise to provide assurance for NASA projects, especially as spaceflight systems continue to increase in complexity. Insight into specific characteristics of FM architectures seen embedded within safety- and mission-critical software systems analyzed by the NASA Independent Verification Validation (IVV) Program has been enhanced with an FM Technical Reference (TR) suite. Benefits are aimed beyond the IVV community to those that seek ways to efficiently and effectively provide software assurance to reduce the FM risk posture of NASA and other space missions. The identification of particular FM architectures, visibility, and associated IVV techniques provides a TR suite that enables greater assurance that critical software systems will adequately protect against faults and respond to adverse conditions. The role FM has with regard to overall asset protection of flight software systems is being addressed with the development of an adverse condition (AC) database encompassing flight software vulnerabilities.Identification of potential off-nominal conditions and analysis to determine how a system responds to these conditions are important aspects of hazard analysis and fault management. Understanding what ACs the mission may face, and ensuring they are prevented or addressed is the responsibility of the assurance team, which necessarily should have insight into ACs beyond those defined by the project itself. Research efforts sponsored by NASAs Office of Safety and Mission Assurance defined terminology, categorized data fields, and designed a baseline repository that centralizes and compiles a comprehensive listing of ACs and correlated data relevant across many NASA missions. This prototype tool helps projects improve analysis by tracking ACs, and allowing queries based on project, mission type, domain component, causal fault, and other key characteristics. The repository has a firm structure, initial collection of data, and an interface established for informational queries, with plans for integration within the Enterprise Architecture at NASA IVV, enabling support and accessibility across the Agency. The development of an improved workflow process for adaptive, risk-informed FM assurance is currently underway.

Software Verification & Validation↗

NASA NTRS1991

Progress in the measurement of SSME turbine heat flux with plug-type sensors

Data reduction was completed for tests of plug-type heat flux sensors (gauges) in a turbine blade thermal cycling tester (TBT) that is located at NASA/Marshall Space Flight Center, and a typical gauge is illustrated. This is the first time that heat flux has been measured in a Space Shuttle Main Engine (SSME) Turbopump Turbine environment. The development of the concept for the gauge was performed in a heat flux measurement facility at Lewis. In this facility, transient and steady state absorbed surface heat flux information was obtained from transient temperature measurements taken at points within the gauge. A schematic of the TBT is presented, and plots of the absorbed surface heat flux measured on the three blades tested in the TBT are presented. High quality heat flux values were measured on all three blades. The experiments demonstrated that reliable and durable gauges can be repeatedly fabricated into the airfoils. The experiment heat flux data are being used for verification of SSME analytical stress, boundary layer, and heat transfer design models. Other experimental results and future plans are also presented.

Liebert, Curt H.↗

NASA NTRS2021

Perspectives on flood forecast-based early action and opportunities for Earth observations

This paper seeks to identify opportunities to integrate Earth observations (EO) into flood forecast-based early action and propose future directions for research and collaboration between EO and humanitarian communities. Forecast-based early action (FbA) is an approach to shift disaster response toward anticipation to mitigate impacts to at-risk communities; however, timely and accurate information is needed in the development of data-based triggers and thresholds for action. Therefore, this paper considers the readiness of a wide range of EO for flood monitoring and forecasting in the design, operations, and evaluation phases of FbA. The most significant opportunities for EO to inform FbA efforts lie in the design and evaluation phases, as EO can aid in the development of impact-based triggers. The EO products most readily applicable include precipitation, streamflow estimates, and exposure mapping, and those requiring the greatest amount of further research include vulnerability and impact assessments. This paper identifies collaboration opportunities for the EO and humanitarian communities to create tailored products, such as overlays combining flood extents with exposure maps. Such collaboration opportunities can be fostered by open data sharing, data verification efforts, and incentives for supporting boundary organizations capable of enabling the use of EO for FbA.

disasters↗

NASA NTRS1982

Structural assembly demonstration experiment

The experiment is of an operational variety, designed to assess crew capability in Large Space System (LSS) assembly. The six Structural Assembly Demonstration Experiment objectives include: (1) the establishment of a quantitative correlation between LSS neutral buoyancy simulation and on-orbit assembly operations in order to enhance the validity of those assembly simulations; (2) the quantitative study of the capabilities and mechanics of human assembly in an Extravehicular Activity environment; (3) the further corroboration of the LSS Assembly Analysis cost algorithm through the obtainment of hard data base information; (4) the verification of LSS assembly techniques and timeless, as well as the identification of crew imposed loads and assembly aid requirements and concepts; (5) verification of a Launch/Assembly Platform structure concept for other LSS missions; and (6) lastly, to advance thermal control concepts through a flexible heat pipe.

Stokes, J. W.↗

NASA NTRS1939

Full-Scale Wind-Tunnel Investigation of Wing-Cooling Ducts Effects of Propeller Slipstream, Special Report

The safety of remotely operated vehicles depends on the correctness of the distributed protocol that facilitates the communication between the vehicle and the operator. A failure in this communication can result in catastrophic loss of the vehicle. To complicate matters, the communication system may be required to satisfy several, possibly conflicting, requirements. The design of protocols is typically an informal process based on successive iterations of a prototype implementation. Yet distributed protocols are notoriously difficult to get correct using such informal techniques. We present a formal specification of the design of a distributed protocol intended for use in a remotely operated vehicle, which is built from the composition of several simpler protocols. We demonstrate proof strategies that allow us to prove properties of each component protocol individually while ensuring that the property is preserved in the composition forming the entire system. Given that designs are likely to evolve as additional requirements emerge, we show how we have automated most of the repetitive proof steps to enable verification of rapidly changing designs.

Nickle, F. R.↗

DOE OSTI2025

Status Report on Design of In-situ Thermomechanical Testing at LANSCE

Nuclear fuel encounters severe thermomechanical environments in which its mechanical response is determined by its microstructure, temperature and stress level histories. Simulating the response of such microstructures is crucial for predicting both performance and transient fuel mechanical responses and experimental verification of such predictions is therefore of great interest. While most of the deformation in a nuclear fuel rod occurs in the cladding, deformation of the fuel itself is still of interest with deformation mechanisms at operating temperature and above including creep, swelling, cracking as well as pellet-clad interaction. Characterization of these properties and understanding of the underlying deformation phenomena at operating or excursion temperatures is therefore of great importance for development and ultimately licensing of improved and novel nuclear fuel forms. Diffraction techniques offer unique insight on the atomistic (e.g. crystal structure) and microstructure (e.g. phase transformations, texture, defects) length scales and have a long history of providing unique data to inform relevant deformation models that enable the required predictive capabilities. For example, dislocations lead to diffraction peak broadening that can be characterized to estimate the dislocation density and study the role of dislocations on the deformation while measuring lattice strains allows to studie load sharing in two phase materials. In this report the requirements for a sample environment for high temperature deformation of nuclear fuels are defined. The HIPPO neutron time-of-flight diffractometer at LANSCE will host this sample environment and is also described. This instrument covers diffraction angles from 140° to 40° and is also equipped with an event-mode neutron imaging detector system, enabling energy-resolved neutron imaging in parallel with the diffraction that could measure sample temperature from Doppler broadening of neutron absorption resonances or measure pore densities from changes in the attenuation. Designs of devices to characterize thermomechanical properties of nuclear fuel without diffraction are also considered to guide the design. While this report is focused on applications for nuclear fuels, the device can also characterize cladding, moderator or structural materials and therefore contribute to other fields of research and development for advanced reactors. The temperatures planned to be reached are above 2000℃, thus enabling characterization of LWR reactor fuels under accident scenarios but also reaching temperatures of fuels developed for nuclear thermal propulsion and providing opportunities to characterize those. In conjunction with the energy-resolved neutron imaging detector, this setup would allow to measure neutron cross-sections at high temperatures, filling a gap towards development of reactors operating at high temperatures.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Development and validation of a next-generation sequencing-based multigene assay to predict the prognosis of estrogen receptor-positive, HER2-negative breast cancer

Purpose: Multigene assays provide useful prognostic information regarding hormone receptor (HR)-positive breast cancer. Next-generation sequencing (NGS)-based platforms have numerous advantages including reproducibility and adaptability in local laboratories. Here we aimed to develop and validate an NGS-based multigene assay to predict the distant recurrence risk. Experimental Design: In total, 179 genes including 30 reference genes highly correlated with the 21-gene recurrence score (RS) algorithm were selected from public databases. Targeted RNA-sequencing was performed using 250 and 93 archived breast cancer samples with a known RS in the training and verification sets, respectively, to develop the algorithm and NGS–Prognostic Score (NGS-PS). The assay was validated in 413 independent samples with long-term follow-up data on distant metastasis. Results: In the verification set, the NGS-PS and 21-gene RS displayed 91.4% concurrence (85/93 samples). In the validation cohort of 413 samples, area under the receiver operating characteristic curve plotted using NGS-PS values classified for distant recurrence was 0.76. The best NGS-PS cut-off value predicting distant metastasis was 20. Furthermore, 269 and 144 patients were classified as low- and high-risk patients in accordance with the cut-off. Five- and 10-year estimates of distant metastasis–free survival (DMFS) for low- versus high-risk groups were 97.0% versus 77.8% and 93.2% versus 64.4%, respectively. The age-related HR for distant recurrence without chemotherapy was 9.73 (95% CI, 3.59–26.40) and 3.19 (95% CI, 1.40–7.29) for patients aged ≤50 and >50 years, respectively. Conclusions: The newly developed and validated NGS-based multigene assay can predict the distant recurrence risk in ER-positive, HER2-negative breast cancer.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1985

Space station data system analysis/architecture study. Task 3: Trade studies, DR-5, volume 2

Results of a Space Station Data System Analysis/Architecture Study for the Goddard Space Flight Center are presented. This study, which emphasized a system engineering design for a complete, end-to-end data system, was divided into six tasks: (1); Functional requirements definition; (2) Options development; (3) Trade studies; (4) System definitions; (5) Program plan; and (6) Study maintenance. The Task inter-relationship and documentation flow are described. Information in volume 2 is devoted to Task 3: trade Studies. Trade Studies have been carried out in the following areas: (1) software development test and integration capability; (2) fault tolerant computing; (3) space qualified computers; (4) distributed data base management system; (5) system integration test and verification; (6) crew workstations; (7) mass storage; (8) command and resource management; and (9) space communications. Results are presented for each task.

Source record↗

DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗