Public-Private Partnership Transportation Projects: An Exploratory Study

When public transportation projects were delivered through design-bid-build and later design-build, governments found a serious issue: inadequate funding. With population growth, governments began to develop new arrangements in which the private sectors were involved to cut the financial burden. This arrangement, Public-Private Partnership (PPP), has its own risks; however, performance outputs can motivate or discourage its use. On top of such output are time and budget, which can be affected by the type of project delivery methods. Project completion within or ahead of schedule as well as within or under budget is among any owner’s objectives. With a higher application of PPP in the highway industry in the US and insufficient research, the current study addresses the schedule and cost performance of PPP highway projects and determines which one outperforms the other. To meet this objective, after collecting performance data of all PPP projects, schedule growth and cost growth are calculated, and finally, statistical analysis is conducted to evaluate the PPP performance. The results show that PPP highway projects on average have saved time and cost; however, the main benefit is a faster delivery rather than an under-budget completion. This study can provide better insights to understand PPP highways’ performance and assist practitioners in applying PPP for transportation projects with the opportunity to save time and cost.

Matrix Completion with Heterogeneous Observation Cost Using Sparsity-Number of Column-Space

The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

A Generic Middleware to Instantly Sync Intensive Writes of Heterogeneous Massive Data via Internet

Industry data centers often need to sync data changes reliably and instantly from a large-scale of heterogeneous autonomous relational databases accessed via the not-so-reliable Internet, for which a practical generic sync middleware of low maintenance and operation costs is most wanted. To this demand, this paper presented a generic sync middleware system (GSMS), which has been developed, applied and optimized since 2006, holding the principles or advantages that it must be SyncML-compliant and transparent to data application layer logic without referring to implementation details of databases synced, does not rely on host computer operating systems deployed, and its construction is light weighted and hence of low cost. Regarding these hard commitments of developing GSMS, in this paper we stressed the significant optimization breakthrough of GSMS sync delay being well below a fraction of millisecond per record sync. A series of ultimate tests with GSMS sync performance were conducted for a persuasive example, in which the source relational database underwent a broad range of write loads (from one thousand to one million intensive writes within a few minutes). All these tests showed that the performance of GSMS is competent and smooth even under ultimate write loads.

A Real-Time Monitoring System of the Supply Chain Conditions, Products and Means of Transport

Real-time monitoring of the supply chain conditions and procedures is a critical element for the optimal coordination and safety of the deliveries, as well as for the minimization of the delivery time and cost. Real time monitoring requires IoT data streams, which are related to the conditions of the products and the means of transport (e.g., location, temperature/humidity conditions, kinematic state, ambient light conditions, etc.). These streams are generated by battery-based IoT tracking devices, equipped with appropriate sensors, and are transmitted to a cloud-based back-end system. Proper handling and processing of the IoT data streams, using predictive and artificial intelligence algorithms, can provide significant and useful results, which can be exploited by the supply chain stakeholders in order to enhance their financial benefits, as well as the efficiency, security, transparency, coordination and sustainability of the supply chain procedures. The technology, the features and the characteristics of a complete, proprietary system, including hardware, firmware and software tools - developed in the context of a co-funded R&D program - are addressed and presented in this paper. 

Heavy Deformation and High-Temperature Annealing Microstructure and Texture Studies of TaHfNbZrTi Equiatomic Refractory High Entropy Alloy

The refractory alloys are crucial for high-temperature applications to improve performance and reduce cost. They are used in several applications such as aerospace, outer space, military and defense, nuclear powerplants, automobiles, and industry. The conventional refractory alloys show greater stability at high temperatures and in contrast they have operational limitations due to their low melting temperatures. However, there is a huge requirement to improve the refractory alloys’ operational temperatures and replace the conventional alloys. The newly emerging refractory high entropy alloys (RHEAs) could be alternative materials for conventional refractory alloys and fulfill the demands and requirements of various practical applications in the future. The RHEA TaHfNbZrTi was prepared through an arc melting process. The annealing behavior of severely deformed equiatomic RHEATaHfNbZrTi has been investigated. To obtain deformed condition, the alloy is cold-rolled to 90% thickness reduction and then subjected to an annealing process to observe recrystallization and microstructural evolution in the range of 800 °C to 1400 °C temperatures. The cold-rolled – 90% condition shows the presence of microstructural heterogeneity. The annealing microstructure of 800 °C temperature reveals that partial recrystallization and further annealing treatment carried out annealing treatment in the range of 850 °C to 1400 °C temperatures exhibits completely recrystallized microstructures, followed by coarsening with a degree of annealing temperature. The deformed and annealed conditions featured the development of body-centered cubic (BCC) fiber textures. The experimental investigation of heavy deformation and followed by high-temperature annealing up to 1400 °C temperature will contribute to the understanding of microstructure and texture evolution of emerging RHEAs.

Catalytic Pyrolysis of Sewage Sludge for Upgrading Bio-Oil Quality Using Sludge-Based Activated Char as an Alternative to HZSM5

Due to the concerns about the depletion of fossil fuel sources and the deteriorating environment, the attempt to investigate the production of renewable energy will play a crucial role as a potential to alleviate the dependency on mineral fuels. One particular area of interest is generation of bio-oil through sewage sludge (SS) pyrolysis. SS can be a potential candidate in contrast to other types of biomasses due to its availability and low cost. However, the presence of high molecular weight hydrocarbons and oxygenated compounds in the SS bio-oil hinders some of its fuel applications. In this context, catalytic pyrolysis is another attainable route to upgrade bio-oil quality. Among different catalysts (i.e., zeolites) studied for SS pyrolysis, activated chars (AC) are eco-friendly alternatives. The beneficial features of AC derived from SS comprise the comparatively large surface area, porosity, enriched surface functional groups and presence of a high amount of metal species that can improve the catalytic activity. Hence, a sludge-based AC catalyst was fabricated in a single-step pyrolysis reaction with NaOH as the activation agent and was compared with HZSM5 zeolite in this study. The thermal decomposition and kinetics were invested via thermogravimetric analysis (TGA) for guidance and control of pyrolysis and catalytic pyrolysis and the design of the pyrolysis setup. The results indicated that the pyrolysis and catalytic pyrolysis contain four obvious stages and the main decomposition reaction occurred in the range of 200-600 °C. Coats-Redfern method was applied in the 2nd and 3rd devolatilization stages to estimate the reaction order and activation energy (E) from the mass loss data. The average activation energy (Em) values for the reaction orders n = 1, 2 and 3 were in the range of 6.67-20.37 kJ/mol for SS; 1.51-6.87 kJ/mol for HZSM5; and 2.29-9.17 kJ/mol for AC, respectively. According to the results, AC and HZSM5 both were able to improve the reaction rate of SS pyrolysis by abridging the Em value. Moreover, to generate and examine the effect of the catalysts on the quality of bio-oil, a fixed-bed pyrolysis system was designed and implemented. The composition analysis of the produced bio-oil was carried out via gas chromatography/mass spectrometry (GC/MS). The selected SS to catalyst ratios were 1:1, 2:1 and 4:1. The optimum ratio in terms of cracking the long-chain hydrocarbons and removing oxygen-containing compounds was 1:1 for both catalysts. The upgraded bio-oils with HZSM5 and AC were in the total range of C4-C17 with around 72% in the range of C4-C9. The bio-oil from pyrolysis of SS contained 49.27% oxygenated compounds while the presence of HZSM5 and AC dropped to 7.3% and 13.02%, respectively. Meanwhile, generation of value-added chemicals such as light aromatic compounds were significantly improved in the catalytic process. Furthermore, the fabricated AC catalyst was characterized by BET, SEM-EDX, FT-IR and TGA techniques. Overall, this research demonstrated that AC is an efficient catalyst in the pyrolysis of SS and can be used as a cost-competitive catalyst in contrast to HZSM5.

Pension Plan Member’s Investment Strategies with Transaction Cost and Couple Risky Assets Modelled by the O-U Process

This paper studies the optimal investment strategies for a plan member (PM) in a defined contribution (DC) pension scheme with transaction cost, taxes on invested funds and couple risky assets (stocks) under the Ornstein-Uhlenbeck (O-U) process. The PM’s portfolio is assumed to consist of a risk-free asset and two risky assets where the two risky assets are driven by the O-U process. The Legendre transformation and dual theory is use to transform the resultant optimal control problem which is a nonlinear partial differential equation (PDE) into linear PDE and the resultant linear PDE is then solved for the explicit solutions of the optimal investment strategies for PM exhibiting constant absolute risk aversion (CARA) using change of variable technique. Furthermore, theoretical analysis is used to study the influences of some sensitive parameters on the optimal investment strategies with observations that the optimal investment strategies for the two risky assets increase with increase in the dividend and decreases with increase in tax on the invested funds, risk averse coefficient, initial fund size and the transaction cost.

An Evaluation on the Effectiveness of a 3D Printed Composite Compression Mold

The applications of composite materials within the aviation industry has been increasing at a rapid pace.  However, the growing applications of composite materials have also led to growing demand for more tooling to support its manufacturing processes. Tooling and tooling maintenance represents a large portion of the composite manufacturing process and cost. Therefore, the industry’s adaptability to new techniques for fabricating high quality tools quickly and inexpensively will play a crucial role in composite material’s growing popularity in the aviation industry. One popular tool fabrication technique currently being developed involves additive manufacturing such as 3D printing. Although additive manufacturing and 3D printing are not entirely new concepts, the technique has been gaining popularity due to its ability to quickly fabricate components, maintain low material waste, and low cost. In this study, a team of Purdue University School of Aviation and Transportation Technology (SATT) faculty and students investigated the effectiveness of a 3D printed composite compression mold. A 3D printed composite compression mold was fabricated by 3D scanning a steel valve cover of an aircraft reciprocating engine. The 3D printed composite compression mold was used to fabricate carbon fiber versions of the aircraft reciprocating engine valve cover. The 3D printed composite compression mold was evaluated for its performance, durability, and dimensional stability while the fabricated carbon fiber valve covers were evaluated for its accuracy and quality. The results and data gathered from this study will determine the effectiveness of the 3D printed composite compression mold in a mass production environment and provide valuable information for future understanding, improvements, and design considerations of 3D printed composite molds.

Comparison of Two Maintenance Policies for a Two-Unit Series System Considering General Repair

In recent years, maintenance optimization has attracted special attention due to the growth of industrial systems complexity. Maintenance costs are high for many systems, and preventive maintenance is effective when it increases operations' reliability and safety at a reduced cost. The novelty of this research is to consider general repair in the modeling of multi-unit series systems and solve the maintenance problem for such systems using the semi-Markov decision process (SMDP) framework. We propose an opportunistic maintenance policy for a series system composed of two main units. Unit 1, which is more expensive than unit 2, is subjected to condition monitoring, and its deterioration is modeled using a gamma process. Unit 1 hazard rate is estimated by the proportional hazards model (PHM), and two hazard rate control limits are considered as the thresholds of maintenance interventions for unit 1. Maintenance is performed on unit 2, considering an age control limit. The objective is to find the optimal control limits and minimize the long-run expected average cost per unit time. The proposed algorithm is applied to a numerical example to compare the effectiveness of the proposed policy (policy Ⅰ) with policy Ⅱ, which is similar to policy Ⅰ, but instead of general repair, replacement is performed. Results show that policy Ⅰ leads to lower average cost compared with policy Ⅱ. 

Research on Morning Commuting Behavior under Autonomous Vehicle Environment Based on Activity Method

Based on activity method, this paper focuses on morning commuting behavior when commuters travel with autonomous vehicles (AVs). Firstly, a net utility function of commuters is constructed by the activity utility of commuters at home, in car and at workplace, and the disutility of travel time cost and that of schedule delay cost. Then, this net utility function is applied to build an equilibrium model. Finally, under the assumption of constant marginal activity utility, the properties of equilibrium are analyzed. The results show that, in autonomous driving, the starting and ending time of morning peak and the number of commuters who arrive early and late at workplace are the same as those in manual driving. In automatic driving, however, the departure rate of arriving early at workplace is higher than that of manual driving, while the departure rate of arriving late is just the opposite. In addition, compared with manual driving, the departure time of arriving at workplace on time is earlier and the number of people queuing at the bottleneck is larger in automatic driving. However, the net utility of commuters and the total net utility of system in automatic driving are greater than those in manual driving.

Fast Approximate Bayesian Contextual Cold Start Learning (FAB-COST)

Cold-start is a notoriously difficult problem which can occur in recommendation systems, and arises when there is insufficient information to draw inferences for users or items. To address this challenge, a contextual bandit algorithm – the Fast Approximate Bayesian Contextual Cold Start Learning algorithm (FAB-COST) – is proposed, which is designed to provide improved accuracy compared to the traditionally used Laplace approximation in the logistic contextual bandit, while controlling both algorithmic complexity and computational cost. To this end, FAB-COST uses a combination of two moment projection variational methods: Expectation Propagation (EP), which performs well at the cold start, but becomes slow as the amount of data increases; and Assumed Density Filtering (ADF), which has slower growth of computational cost with data size but requires more data to obtain an acceptable level of accuracy. By switching from EP to ADF when the dataset becomes large, it is able to exploit their complementary strengths. The empirical justification for FAB-COST is presented, and systematically compared to other approaches on simulated data. In a benchmark against the Laplace approximation on real data consisting of over 670, 000 impressions from autotrader.co.uk, FAB-COST demonstrates at one point increase of over 16% in user clicks. On the basis of these results, it is argued that FAB-COST is likely to be an attractive approach to cold-start recommendation systems in a variety of contexts.

Comparison between Conventional Bacterial and Algal-Bacterial Aerobic Granular Sludge Systems in the Treatment of Saline Wastewater

The increasing generation of saline wastewater through various industrial activities is becoming a global concern for activated sludge (AS) based biological treatment which is widely applied in wastewater treatment plants (WWTPs). As for the AS process, an increase in wastewater salinity has negative impact on its overall performance. The advent of conventional aerobic granular sludge (AGS) or bacterial AGS biotechnology has gained much attention because of its superior performance. The development of algal-bacterial AGS could enhance better nutrients removal, potentially reduce aeration cost through symbiotic algae-bacterial activity, and thus, can also reduce overall treatment cost. Nonetheless, the potential of salt stress to decrease biomass growth, microbial activity and nutrient removal exist. Up to the present, little information is available on saline wastewater treatment by algal-bacterial AGS. To the authors’ best knowledge, a comparison of the two AGS systems has not been done to evaluate nutrients removal capacity in the context of salinity increase. This study sought to figure out the impact of salinity on the algal-bacterial AGS system in comparison to bacterial AGS one, contributing to the application of AGS technology in the real world of saline wastewater treatment. In this study, the salt concentrations tested were 0 g/L, 1 g/L, 5 g/L, 10 g/L and 15 g/L of NaCl with 24-hr artificial illuminance of approximately 97.2 µmol m¯²s¯¹, and mature bacterial and algal-bacterial AGS were used for the operation of two identical sequencing batch reactors (SBRs) with a working volume of 0.9 L each, respectively. The results showed that salinity increase caused no apparent change in the color of bacterial AGS; while for algal-bacterial AGS, its color was progressively changed from green to dark green. A consequent increase in granule diameter and fluffiness was observed in the bacterial AGS reactor with the increase of salinity in comparison to a decrease in algal-bacterial AGS diameter. However, nitrite accumulation peaked from 1.0 mg/L and 0.4 mg/L at 1 g/L NaCl in the bacterial and algal-bacterial AGS systems, respectively to 9.8 mg/L in both systems when NaCl concentration varied from 5 g/L to 15 g/L. Almost no ammonia nitrogen was detected in the effluent except at 10 g/L NaCl concentration, where it averaged 4.2 mg/L and 2.4 mg/L, respectively, in the bacterial and algal-bacterial AGS systems. Nutrients removal in the algal-bacterial system was relatively higher than the bacterial AGS in terms of nitrogen and phosphorus removals. Nonetheless, the nutrient removal rate was almost 50% or lower. Results show that algal-bacterial AGS is more adaptable to salinity increase and could be more suitable for saline wastewater treatment. Optimization of operation conditions for algal-bacterial AGS system would be important to ensure its stably high efficiency in practice.

Review of Strategies for Hybrid Energy Storage Management System in Electric Vehicle Application

Electric Vehicles (EV) appear to be gaining increasing patronage as a feasible alternative to Internal Combustion Engine Vehicles (ICEVs) for having low emission and high operation efficiency. The EV energy storage systems are required to handle high energy and power density capacity constrained by limited space, operating temperature, weight and cost. The choice of strategies for energy storage evaluation, monitoring and control remains a challenging task. This paper presents review of various energy storage technologies and recent researches in battery evaluation techniques used in EV applications. It also underscores strategies for the hybrid energy storage management and control schemes for the improvement of EV stability and reliability. The study reveals that despite the advances recorded in battery technologies there is still no cell which possess both the optimum power and energy densities among other requirements, for EV application. However combination of two or more energy storages as hybrid and allowing the advantageous attributes from each device to be utilized is a promising solution. The review also reveals that State-of-Charge (SoC) is the most crucial method for battery estimation. The conventional method of SoC measurement is however questioned in the literature and adaptive algorithms that include all model of disturbances are being proposed. The review further suggests that heuristic-based approach is commonly adopted in the development of strategies for hybrid energy storage system management. The alternative approach which is optimization-based is found to be more accurate but is memory and computational intensive and as such not recommended in most real-time applications.

Low Cost Microcontroller Based ECG Machine

Electrocardiographic (ECG) machine is an important equipment to diagnose heart problems. Besides, the ECG signals are used to detect many other features of human body and behavior. But it is not so cheap and simple in operation to be used in the countries like Bangladesh, where most of the people are very low income earners. Therefore, in this paper, we have tried to implement a simple and portable ECG machine. Since Arduino Uno microcontroller is very cheap, we have used it in our system to minimize the cost. Our designed system is powered by a 2-voltage level DC power supply. It provides wireless connectivity to have ECG data either in smartphone having android operating system or a PC/laptop having Windows operating system. To get the data, a graphic user interface has been designed. Android application has also been made using IDE for Android 2.3 and API 10. Since it requires no USB host API, almost 98% Android smartphones, available in the country, will be able to use it. We have calculated the heart rate from the measured ECG by our designed machine and by an ECG machine of a reputed diagnostic center in Dhaka city for the same people at the same time on same day. Then we calculated the percentage of errors between the readings of two machines and computed its average. From this computation, we have found out that the average percentage of error is within an acceptable limit.

An Optimal Control Method for Reconstruction of Topography in Dam-Break Flows

Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Design of Reconfigurable Supernumerary Robotic Limb Based on Differential Actuated Joints

This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Evaluations of 3D Concrete Printing Produced in the Environment of United Arab Emirates

3D concrete printing is one of the most innovative and modern techniques in the field of construction that achieved several milestones in that field for the following advantages: saving project’s time, ability to execute complicated shapes, reduce waste and low cost. However, the concept of 3D printing in UAE is relatively new where construction teams, including clients, consultants, and contractors, do not have the required knowledge and experience in the field. This is the most significant obstacle for the construction parties, which make them refrained from using 3D concrete printing compared to conventional concreting methods. This study shows the historical development of the 3D concrete printing, its advantages, and the challenges facing this innovation. Concrete mixes and materials have been proposed and evaluated to select the best combination for successful 3D concrete printing. The main characteristics of the 3D concrete printing in the fresh and hardened states are considered, such as slump test, flow table, compressive strength, tensile, and flexural strengths. There is need to assess the structural stability of the 3D concrete by testing the bond between interlayers of the concrete.  

Investigating the Effectiveness of a 3D Printed Composite Mold

In composite manufacturing, the fabrication of tooling and tooling maintenance contributes to a large portion of the total cost. However, as the applications of composite materials continue to increase, there is also a growing demand for more tooling. The demand for more tooling places heavy emphasis on the industry’s ability to fabricate high quality tools while maintaining the tool’s cost effectiveness. One of the popular techniques of tool fabrication currently being developed utilizes additive manufacturing technology known as 3D printing. The popularity of 3D printing is due to 3D printing’s ability to maintain low material waste, low cost, and quick fabrication time. In this study, a team of Purdue University School of Aviation and Transportation Technology (SATT) faculty and students investigated the effectiveness of a 3D printed composite mold. A steel valve cover from an aircraft reciprocating engine was modeled utilizing 3D scanning and computer-aided design (CAD) to create a 3D printed composite mold. The mold was used to fabricate carbon fiber versions of the aircraft reciprocating engine valve cover. The carbon fiber valve covers were evaluated for dimensional accuracy and quality while the 3D printed composite mold was evaluated for durability and dimensional stability. The data collected from this study provided valuable information in the understanding of 3D printed composite molds, potential improvements for the molds, and considerations for future tooling design.

Non-parametric Linear Technique for Measuring the Efficiency of Winter Road Maintenance in the Arctic Area

Improving the performance of Winter Road Maintenance (WRM) can increase the traffic safety and reduce the cost as well as environmental impacts. This study evaluates the efficiency of WRM technique, named salting, in the Arctic area by using Data Envelopment Analysis (DEA), which is a non-parametric linear method to measure the efficiencies of decision-making units (DMUs) based on handling multiple inputs and multiple outputs at the same time that their associated weights are not known. Here, roads are considered as DMUs for which the efficiency must be determined. The three input variables considered are traffic flow, road area and WRM cost. In addition, the two output variables included are level of safety in the roads and environment impacts resulted from WRM, which is also considered as an uncontrollable factor in the second scenario. The results show the performance of DMUs from the most efficient WRM to the inefficient/least efficient one and this information provides decision makers with technical support and the required suggested improvements for inefficient WRM, in order to achieve a cost-effective WRM and a safe road transportation during wintertime in the Arctic areas.

Development of a Real Time Axial Force Measurement System and IoT-Based Monitoring for Smart Bearing

The purpose of this research is to develop a real time axial force measurement system for a smart bearing through the use of strain-gauges, whereby the data acquisition is performed by an Arduino microcontroller due to its easy manipulation and low-cost. The measured signal is acquired and then discretized using a Wheatstone Bridge and an Analog-Digital Converter (ADC) respectively. For bearing monitoring, a real time monitoring system based on Internet of things (IoT) and Bluetooth were developed. Experimental tests were performed on a bearing within a force range up to 600 kN. The experimental results show that there is a proportional linear relationship between the applied force and the output voltage, and the error R squared is within 0.9878 based on the regression analysis.